{"id":965,"date":"2026-10-06T19:41:39","date_gmt":"2026-10-06T19:41:39","guid":{"rendered":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/?p=965"},"modified":"2026-10-17T01:44:37","modified_gmt":"2026-10-17T01:44:37","slug":"6-plane-measurement-perimeter-and-area","status":"publish","type":"post","link":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/2026\/10\/06\/6-plane-measurement-perimeter-and-area\/","title":{"rendered":"*6* | \u0938\u092e\u0924\u0932 \u092e\u093e\u092a\u0928 &#8211; \u092a\u0930\u093f\u092e\u093e\u092a \u0914\u0930 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 | Plane Measurement &#8211; Perimeter and Area"},"content":{"rendered":"<div id=\"pl-965\"  class=\"panel-layout\" ><div id=\"pg-965-0\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-965-0-0\"  class=\"panel-grid-cell\" ><div id=\"panel-965-0-0-0\" class=\"widget_text so-panel widget widget_custom_html panel-first-child panel-last-child\" data-index=\"0\" ><div class=\"textwidget custom-html-widget\"><div id=\"FILE1-CH6-GANIT\" style=\"max-width:860px;margin:12px auto;border:3.5px solid #0f5e4b;border-radius:14px;background:#e6f4f1;font-family:'Noto Sans Devanagari',Arial,sans-serif;overflow:hidden;\">\n<div style=\"background:#0a5c4b;padding:8px 10px;text-align:center;\"><span style=\"background:#fff;color:#0a3d33;padding:6px 18px;border-radius:20px;font-weight:bold;font-size:11px;\">Ch6 - \u0938\u092e\u0924\u0932 \u092e\u093e\u092a\u0928 - \u092d\u093e\u0917 1\/4 - \u092a\u0930\u093f\u091a\u092f<\/span><\/div>\n\n<div style=\"padding:10px 12px;\">\n<div id=\"ch6g-1\" style=\"display:block;\"><div style=\"background:#d32f2f;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udd34 \u092d\u093e\u0917 1\/4 - \u092a\u0930\u093f\u092e\u093e\u092a \u0915\u094d\u092f\u093e? \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u094d\u092f\u093e?<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:13.5px;line-height:1.9;height:380px;overflow-y:auto;\"><div style=\"background:#ffebee;border-left:4px solid #d32f2f;padding:6px 10px;font-weight:bold;\">\u092a\u0930\u093f\u092e\u093e\u092a \u0914\u0930 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u092a\u0930\u093f\u092e\u093e\u092a = \u091a\u093e\u0930\u094b\u0902 \u0924\u0930\u092b \u0915\u0940 \u092c\u093e\u0921\u093c\u0964 \u0915\u093f\u0924\u0928\u093e \u0924\u093e\u0930 \u0932\u0917\u0947\u0917\u093e? \u091a\u093e\u0930\u094b\u0902 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u093e \u091c\u094b\u0921\u093c\u0964<br>\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = \u0905\u0902\u0926\u0930 \u0915\u093f\u0924\u0928\u0940 \u091c\u0917\u0939? \u092b\u0930\u094d\u0936 \u092a\u0930 \u0915\u093f\u0924\u0928\u0940 \u091f\u093e\u0907\u0932 \u0932\u0917\u0947\u0917\u0940? \u0932\u0902\u092c\u093e\u0908\u00d7\u091a\u094c\u0921\u093c\u093e\u0908\u0964<div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:10px;border-radius:10px;text-align:center;margin:6px 0;\"><div style=\"font-size:18px;font-weight:bold;\">\u092a\u0930\u093f\u092e\u093e\u092a = \u091a\u093e\u0930\u094b\u0902 \u0924\u0930\u092b \u091c\u094b\u0921\u093c = \u092c\u093e\u0921\u093c<\/div><div style=\"font-size:18px;font-weight:bold;\">\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = \u0905\u0902\u0926\u0930 = \u092b\u0930\u094d\u0936 L\u00d7B<\/div><div>4\u00d73 \u0916\u0947\u0924 \u092a\u0930\u093f\u092e\u093e\u092a 14 \u0924\u093e\u0930 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 12 \u091f\u093e\u0907\u0932<\/div><div>\u092a\u0930\u093f\u092e\u093e\u092a \u0907\u0915\u093e\u0908 cm \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 cm\u00b2<\/div><\/div>\u0909\u0926\u093e: 5\u00d74 \u0906\u092f\u0924 \u092a\u0930\u093f\u092e\u093e\u092a 18, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 20\u0964<br>5 \u0915\u093e \u0935\u0930\u094d\u0917 \u092a\u0930\u093f\u092e\u093e\u092a 20, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 25\u0964<br><div style=\"background:#e3f2fd;border-left:4px solid #1565c0;padding:6px 10px;font-weight:bold;margin-top:8px;\">\u0907\u0915\u093e\u0908 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u092a\u0930\u093f\u092e\u093e\u092a \u090f\u0915 \u0930\u0947\u0916\u093e \u0907\u0915\u093e\u0908 cm m km\u0964<br>\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0926\u094b \u0930\u0947\u0916\u093e \u0935\u0930\u094d\u0917 \u0907\u0915\u093e\u0908 cm\u00b2 m\u00b2\u0964<\/div><\/div>\n\n<div id=\"ch6g-2\" style=\"display:none;\"><div style=\"background:#1565c0;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udd35 \u092d\u093e\u0917 2\/4 - \u0906\u092f\u0924 \u0935\u0930\u094d\u0917<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:13.5px;line-height:1.9;height:380px;overflow-y:auto;\"><div style=\"background:#e3f2fd;border-left:4px solid #1565c0;padding:6px 10px;font-weight:bold;\">\u0906\u092f\u0924 \u0935\u0930\u094d\u0917 \u0938\u0942\u0924\u094d\u0930 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:10px;border-radius:10px;text-align:center;margin:6px 0;\"><div style=\"font-size:18px;font-weight:bold;\">\u0906\u092f\u0924: L \u0932\u0902\u092c\u093e\u0908 B \u091a\u094c\u0921\u093c\u093e\u0908<\/div><div>\u092a\u0930\u093f\u092e\u093e\u092a = 2(L+B)<\/div><div>\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = L\u00d7B<\/div><div>\u0935\u0930\u094d\u0917: \u092d\u0941\u091c\u093e a<\/div><div>\u092a\u0930\u093f\u092e\u093e\u092a = 4a, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = a\u00b2<\/div><div>\u0906\u092f\u0924 6\u00d74 \u092a\u0930\u093f 20 \u0915\u094d\u0937\u0947 24<\/div><div>\u0935\u0930\u094d\u0917 5 \u092a\u0930\u093f 20 \u0915\u094d\u0937\u0947 25<\/div><\/div>\u0906\u092f\u0924 \u092e\u0947\u0902 \u0906\u092e\u0928\u0947-\u0938\u093e\u092e\u0928\u0947 \u092c\u0930\u093e\u092c\u0930 \u0907\u0938\u0932\u093f\u090f 2(L+B)\u0964<br>\u0935\u0930\u094d\u0917 \u092e\u0947\u0902 \u091a\u093e\u0930\u094b\u0902 \u092c\u0930\u093e\u092c\u0930 4a\u0964<br>\u092f\u0926\u093f L=8 B=5 \u092a\u0930\u093f\u092e\u093e\u092a 26 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 40\u0964<div style=\"background:#e8f5e9;border-left:4px solid #2e7d32;padding:6px 10px;font-weight:bold;margin-top:8px;\">Trick - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u092a\u0930\u093f\u092e\u093e\u092a \u0938\u0947 \u092d\u0941\u091c\u093e: \u0906\u092f\u0924 L+B=\u092a\u0930\u093f\u092e\u093e\u092a\/2, \u0935\u0930\u094d\u0917 a=\u092a\u0930\u093f\u092e\u093e\u092a\/4\u0964<br>\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0938\u0947 \u092d\u0941\u091c\u093e: \u0935\u0930\u094d\u0917 a=\u221a\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932\u0964<\/div><\/div>\n\n<div id=\"ch6g-3\" style=\"display:none;\"><div style=\"background:#2e7d32;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe2 \u092d\u093e\u0917 3\/4 - \u0924\u094d\u0930\u093f\u092d\u0941\u091c<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:13.5px;line-height:1.9;height:380px;overflow-y:auto;\"><div style=\"background:#e8f5e9;border-left:4px solid #2e7d32;padding:6px 10px;font-weight:bold;\">\u0924\u094d\u0930\u093f\u092d\u0941\u091c \u092a\u0930\u093f\u092e\u093e\u092a \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0924\u0940\u0928 \u092d\u0941\u091c\u093e\u090f\u0901 a,b,c\u0964<div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:10px;border-radius:10px;text-align:center;margin:6px 0;\"><div style=\"font-size:18px;font-weight:bold;\">\u0924\u094d\u0930\u093f\u092d\u0941\u091c \u092a\u0930\u093f\u092e\u093e\u092a = a+b+c<\/div><div>\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = \u00bd\u00d7\u0906\u0927\u093e\u0930\u00d7\u090a\u0901\u091a\u093e\u0908<\/div><div>\u0938\u092e\u092c\u093e\u0939\u0941 a: \u092a\u0930\u093f 3a \u0915\u094d\u0937\u0947 (\u221a3\/4)a\u00b2<\/div><div>\u0938\u092e\u0915\u094b\u0923: \u0915\u094d\u0937\u0947 \u00bd\u00d7\u0926\u094b \u092d\u0941\u091c\u093e\u090f\u0901 \u091c\u094b \u0938\u092e\u0915\u094b\u0923 \u092a\u0930<\/div><div>3-4-5 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u092a\u0930\u093f 12 \u0915\u094d\u0937\u0947 6<\/div><\/div>\u0906\u0927\u093e\u0930 \u0915\u094b\u0908 \u092d\u0940, \u090a\u0901\u091a\u093e\u0908 \u0906\u0927\u093e\u0930 \u092a\u0930 \u0932\u0902\u092c\u0930\u0964<br>\u0938\u092e\u092c\u093e\u0939\u0941 \u092e\u0947\u0902 \u0938\u092d\u0940 60\u00b0 \u0938\u092d\u0940 \u092d\u0941\u091c\u093e \u092c\u0930\u093e\u092c\u0930\u0964<br>\u0938\u092e\u0915\u094b\u0923 \u092e\u0947\u0902 \u090f\u0915 \u0915\u094b\u0923 90\u00b0 \u0926\u094b \u092d\u0941\u091c\u093e\u090f\u0901 \u0932\u0902\u092c\u0935\u0924\u0964<div style=\"background:#e3f2fd;border-left:4px solid #1565c0;padding:6px 10px;font-weight:bold;margin-top:8px;\">\u0939\u0940\u0930\u094b\u0928 \u0938\u0942\u0924\u094d\u0930 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u092f\u0926\u093f \u0924\u0940\u0928 \u092d\u0941\u091c\u093e \u092a\u0924\u093e \u0939\u094b a,b,c, s=(a+b+c)\/2 \u0905\u0930\u094d\u0927\u092a\u0930\u093f\u092e\u093e\u092a, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=\u221a[s(s-a)(s-b)(s-c)]\u0964<br>\u0909\u0926\u093e: 5,5,6 s=8 \u0915\u094d\u0937\u0947=\u221a[8\u00d73\u00d73\u00d72]=\u221a144=12\u0964<\/div><\/div>\n\n<div id=\"ch6g-4\" style=\"display:none;\"><div style=\"background:#6a1b9a;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe3 \u092d\u093e\u0917 4\/4 - \u0935\u0943\u0924\u094d\u0924 \u0914\u0930 \u0905\u0928\u094d\u092f<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:13.5px;line-height:1.9;height:380px;overflow-y:auto;\"><div style=\"background:#f3e5f5;border-left:4px solid #6a1b9a;padding:6px 10px;font-weight:bold;\">\u0935\u0943\u0924\u094d\u0924 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:10px;border-radius:10px;text-align:center;margin:6px 0;\"><div style=\"font-size:18px;font-weight:bold;\">\u0935\u0943\u0924\u094d\u0924 r \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e<\/div><div>\u092a\u0930\u093f\u0927\u093f = 2\u03c0r \u092c\u093e\u0921\u093c<\/div><div>\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = \u03c0r\u00b2 \u092b\u0930\u094d\u0936<\/div><div>\u0905\u0930\u094d\u0927\u0935\u0943\u0924\u094d\u0924 \u092a\u0930\u093f \u03c0r+2r \u0915\u094d\u0937\u0947 (\u03c0r\u00b2)\/2<\/div><div>r=7 \u092a\u0930\u093f\u0927\u093f 44 \u0915\u094d\u0937\u0947 154 \u03c0=22\/7<\/div><\/div><div style=\"background:#e3f2fd;border:2px solid #2196f3;padding:6px;border-radius:8px;text-align:center;margin:6px 0;\"><span style=\"font-weight:bold;\">\u0938\u092e\u093e\u0928\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c: \u092a\u0930\u093f 2(a+b) \u0915\u094d\u0937\u0947 \u0906\u0927\u093e\u0930\u00d7\u090a\u0901\u091a\u093e\u0908<\/span><br><span style=\"font-weight:bold;\">\u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c: \u092a\u0930\u093f 4a \u0915\u094d\u0937\u0947 \u00bd\u00d7d1\u00d7d2 \u0935\u093f\u0915\u0930\u094d\u0923<\/span><br><span style=\"font-weight:bold;\">\u0938\u092e\u0932\u0902\u092c: \u092a\u0930\u093f \u091a\u093e\u0930\u094b\u0902 \u091c\u094b\u0921\u093c \u0915\u094d\u0937\u0947 \u00bd\u00d7(a+b)\u00d7h<\/span><\/div>\u0935\u0943\u0924\u094d\u0924 \u092e\u0947\u0902 r \u0906\u0927\u0940 \u0935\u094d\u092f\u093e\u0938\u0964<br>\u03c0=22\/7 \u092f\u093e 3.14\u0964<br>\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u092e\u0947\u0902 \u0935\u093f\u0915\u0930\u094d\u0923 \u0938\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0928\u093f\u0915\u093e\u0932\u0924\u0947\u0964<\/div><\/div>\n<\/div>\n\n<div style=\"background:#0a5c4b;padding:12px;display:flex;justify-content:space-between;align-items:center;\">\n<button type=\"button\" id=\"ch6gp\" style=\"background:#ffcc00;color:#000;border:3px solid #fff;border-radius:30px;padding:10px 22px;font-weight:bold;font-size:15px;cursor:pointer;min-width:100px;\">&larr; \u092a\u0940\u091b\u0947<\/button>\n<span id=\"ch6gi\" style=\"background:#fff;color:#0a5c4b;padding:8px 20px;border-radius:20px;font-size:15px;font-weight:bold;\">1 \/ 4<\/span>\n<button type=\"button\" id=\"ch6gn\" style=\"background:#00e676;color:#000;border:3px solid #fff;border-radius:30px;padding:10px 22px;font-weight:bold;font-size:15px;cursor:pointer;min-width:100px;\">\u0906\u0917\u0947 &rarr;<\/button>\n<\/div>\n<\/div>\n\n<script>\n(function(){\nvar c=1,t=4;\nfunction s(n){\nfor(var i=1;i<=t;i++){\nvar el=document.getElementById('ch6g-'+i);\nif(el)el.style.display=(i===n?'block':'none');\n}\ndocument.getElementById('ch6gi').textContent=n+' \/ '+t;\nc=n;\n}\ndocument.getElementById('ch6gn').onclick=function(){var n=c+1;if(n>t)n=1;s(n);};\ndocument.getElementById('ch6gp').onclick=function(){var n=c-1;if(n<1)n=t;s(n);};\n})();\n<\/script><\/div><\/div><\/div><\/div><div id=\"pg-965-1\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-965-1-0\"  class=\"panel-grid-cell\" ><div id=\"panel-965-1-0-0\" class=\"widget_text so-panel widget widget_custom_html panel-first-child panel-last-child\" data-index=\"1\" ><div class=\"textwidget custom-html-widget\"><div id=\"FILE2-CH6-GANIT\" style=\"max-width:860px;margin:12px auto;border:3.5px solid #0f5e4b;border-radius:14px;background:#e6f4f1;font-family:'Noto Sans Devanagari',Arial,sans-serif;overflow:hidden;\">\n<div style=\"background:#0a5c4b;padding:8px 10px;text-align:center;\"><span style=\"background:#fff;color:#0a3d33;padding:6px 18px;border-radius:20px;font-weight:bold;font-size:11px;\">Ch6 - \u092d\u093e\u0917 2\/4 - 6.1 \u0938\u0947 6.5 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u092a\u0930\u093f\u092d\u093e\u0937\u093e<\/span><\/div>\n\n<div style=\"padding:10px 12px;\">\n<div id=\"ch6f2-1\" style=\"display:block;\"><div style=\"background:#d32f2f;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udd34 \u092d\u093e\u0917 1\/4 - 6.1 \u0906\u092f\u0924 \u0935\u0930\u094d\u0917 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:13.5px;line-height:1.9;height:380px;overflow-y:auto;\"><div style=\"background:#ffebee;border-left:4px solid #d32f2f;padding:6px 10px;font-weight:bold;\">6.1 \u0906\u092f\u0924 \u0935\u0930\u094d\u0917 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u0906\u092f\u0924 \u091a\u093e\u0930 \u0915\u094b\u0923 90\u00b0 \u0906\u092e\u0928\u0947 \u0938\u093e\u092e\u0928\u0947 \u092c\u0930\u093e\u092c\u0930\u0964 L \u0932\u0902\u092c\u0940 B \u091b\u094b\u091f\u0940\u0964<br>\u0935\u0930\u094d\u0917 \u0935\u093f\u0936\u0947\u0937 \u0906\u092f\u0924 \u091a\u093e\u0930\u094b\u0902 \u092c\u0930\u093e\u092c\u0930 \u091a\u093e\u0930\u094b\u0902 90\u00b0\u0964<div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:10px;border-radius:10px;text-align:center;margin:6px 0;\"><div style=\"font-size:18px;font-weight:bold;\">6.1 \u0906\u092f\u0924<\/div><div>\u092a\u0930\u093f\u092e\u093e\u092a = 2(L+B) = 2\u00d7(\u0932\u0902\u092c\u093e\u0908+\u091a\u094c\u0921\u093c\u093e\u0908)<\/div><div>\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = L\u00d7B<\/div><div>\u0935\u093f\u0915\u0930\u094d\u0923 = \u221a(L\u00b2+B\u00b2) \u092a\u093e\u0907\u0925\u093e\u0917\u094b\u0930\u0938<\/div><div>\u0909\u0926\u093e: L8 B6 \u092a\u0930\u093f28 \u0915\u094d\u0937\u094748 \u0935\u093f\u0915\u0930\u094d\u092310<\/div><div style=\"font-size:15px;margin-top:6px;font-weight:bold;\">\u0935\u0930\u094d\u0917 a<\/div><div>\u092a\u0930\u093f 4a \u0915\u094d\u0937\u0947 a\u00b2 \u0935\u093f\u0915\u0930\u094d\u0923 a\u221a2<\/div><div>5 \u0915\u093e \u0935\u0930\u094d\u0917 \u092a\u0930\u093f20 \u0915\u094d\u0937\u094725 \u0935\u093f\u0915\u0930\u094d\u0923 5\u221a2<\/div><\/div>\u0906\u092f\u0924 \u092e\u0947\u0902 \u0935\u093f\u0915\u0930\u094d\u0923 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0924\u0947\u0964<br>\u0935\u0930\u094d\u0917 \u092e\u0947\u0902 \u0935\u093f\u0915\u0930\u094d\u0923 \u092c\u0930\u093e\u092c\u0930 90\u00b0 \u092a\u0930 \u0928\u0939\u0940\u0902 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0906\u092f\u0924 \u092e\u0947\u0902 \u092c\u0930\u093e\u092c\u0930 \u092a\u0930 90\u00b0 \u0928\u0939\u0940\u0902\u0964<br>\u092f\u0926\u093f \u092a\u0930\u093f\u092e\u093e\u092a \u0926\u093f\u092f\u093e \u0939\u094b \u0924\u094b L+B=\u092a\u0930\u093f\/2\u0964<br>\u092f\u0926\u093f \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0914\u0930 \u090f\u0915 \u092d\u0941\u091c\u093e \u0926\u0940 \u0924\u094b \u0926\u0942\u0938\u0930\u0940=\u0915\u094d\u0937\u0947\/\u092d\u0941\u091c\u093e\u0964<div style=\"background:#e3f2fd;border-left:4px solid #1565c0;padding:6px 10px;font-weight:bold;margin-top:8px;\">\u092a\u0930\u093f\u092d\u093e\u0937\u093e - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u0906\u092f\u0924 \u0935\u0939 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u091c\u093f\u0938\u0915\u0947 \u091a\u093e\u0930\u094b\u0902 \u0915\u094b\u0923 \u0938\u092e\u0915\u094b\u0923 \u0914\u0930 \u0938\u093e\u092e\u0928\u0947 \u0915\u0940 \u092d\u0941\u091c\u093e \u092c\u0930\u093e\u092c\u0930\u0964<br>\u0935\u0930\u094d\u0917 \u0935\u0939 \u0906\u092f\u0924 \u091c\u093f\u0938\u0915\u0940 \u091a\u093e\u0930\u094b\u0902 \u092d\u0941\u091c\u093e \u092c\u0930\u093e\u092c\u0930\u0964<\/div><\/div>\n\n<div id=\"ch6f2-2\" style=\"display:none;\"><div style=\"background:#1565c0;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udd35 \u092d\u093e\u0917 2\/4 - 6.2 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:13.5px;line-height:1.9;height:380px;overflow-y:auto;\"><div style=\"background:#e3f2fd;border-left:4px solid #1565c0;padding:6px 10px;font-weight:bold;\">6.2 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u0924\u0940\u0928 \u092d\u0941\u091c\u093e\u0913\u0902 \u0938\u0947 \u0918\u093f\u0930\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u0964 a,b,c\u0964<div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:10px;border-radius:10px;text-align:center;margin:6px 0;\"><div style=\"font-size:18px;font-weight:bold;\">\u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0924\u094d\u0930\u093f\u092d\u0941\u091c<\/div><div>\u092a\u0930\u093f\u092e\u093e\u092a = a+b+c<\/div><div>\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = \u00bd\u00d7\u0906\u0927\u093e\u0930\u00d7\u090a\u0901\u091a\u093e\u0908<\/div><div>\u090a\u0901\u091a\u093e\u0908 \u0906\u0927\u093e\u0930 \u092a\u0930 \u0932\u0902\u092c\u0930<\/div><div>\u0938\u092e\u092c\u093e\u0939\u0941 a: \u092a\u0930\u093f3a \u0915\u094d\u0937\u0947 (\u221a3\/4)a\u00b2 \u090a\u0901\u091a\u093e\u0908 (\u221a3\/2)a<\/div><div>\u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 a,a,b: \u0915\u094d\u0937\u0947 (b\/4)\u221a(4a\u00b2-b\u00b2)<\/div><div>\u0938\u092e\u0915\u094b\u0923: \u0915\u094d\u0937\u0947 \u00bd\u00d7\u0932\u0902\u092c\u00d7\u0906\u0927\u093e\u0930<\/div><div>3-4-5 \u092a\u0930\u093f12 \u0915\u094d\u0937\u09476 5-12-13 \u092a\u0930\u093f30 \u0915\u094d\u0937\u094730<\/div><\/div>\u0906\u0927\u093e\u0930 \u0915\u093f\u0938\u0940 \u092d\u0940 \u092d\u0941\u091c\u093e \u0915\u094b \u0932\u0947 \u0938\u0915\u0924\u0947 \u090a\u0901\u091a\u093e\u0908 \u0909\u0938\u0940 \u092a\u0930 \u0932\u0902\u092c\u0930\u0964<br>\u0938\u092e\u092c\u093e\u0939\u0941 \u092e\u0947\u0902 \u090a\u0901\u091a\u093e\u0908 \u092e\u0927\u094d\u092f \u092e\u0947\u0902 \u0917\u093f\u0930\u0924\u0940\u0964<div style=\"background:#e8f5e9;border-left:4px solid #2e7d32;padding:6px 10px;font-weight:bold;margin-top:8px;\">\u0939\u0940\u0930\u094b\u0928 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u092f\u0926\u093f \u0924\u0940\u0928 \u092d\u0941\u091c\u093e \u092a\u0924\u093e \u092a\u0930 \u090a\u0901\u091a\u093e\u0908 \u0928\u0939\u0940\u0902 \u0924\u094b \u0939\u0940\u0930\u094b\u0928\u0964<br>s=(a+b+c)\/2 \u0905\u0930\u094d\u0927 \u092a\u0930\u093f\u092e\u093e\u092a\u0964<br>\u0915\u094d\u0937\u0947=\u221a[s(s-a)(s-b)(s-c)]\u0964<br>\u0909\u0926\u093e 13,14,15 s=21 \u0915\u094d\u0937\u0947=\u221a[21\u00d78\u00d77\u00d76]=\u221a7056=84\u0964<br>\u092f\u0939 \u0938\u0942\u0924\u094d\u0930 \u0939\u0930 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0932\u093f\u090f\u0964<\/div><\/div>\n\n<div id=\"ch6f2-3\" style=\"display:none;\"><div style=\"background:#2e7d32;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe2 \u092d\u093e\u0917 3\/4 - 6.3 6.4 \u0938\u092e\u093e\u0928\u093e\u0902\u0924\u0930 \u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0938\u092e\u0932\u0902\u092c<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:13.5px;line-height:1.9;height:380px;overflow-y:auto;\"><div style=\"background:#e8f5e9;border-left:4px solid #2e7d32;padding:6px 10px;font-weight:bold;\">6.3 6.4 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u0938\u092e\u093e\u0928\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0938\u093e\u092e\u0928\u0947 \u092c\u0930\u093e\u092c\u0930 \u0938\u093e\u092e\u0928\u0947 \u0938\u092e\u093e\u0928\u093e\u0902\u0924\u0930\u0964<br>\u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u091a\u093e\u0930\u094b\u0902 \u092c\u0930\u093e\u092c\u0930 \u0938\u093e\u092e\u0928\u0947 \u0938\u092e\u093e\u0928\u093e\u0902\u0924\u0930 \u0935\u093f\u0915\u0930\u094d\u0923 \u0932\u0902\u092c\u0930\u0964<br>\u0938\u092e\u0932\u0902\u092c \u090f\u0915 \u091c\u094b\u0921\u093c\u0940 \u0938\u092e\u093e\u0928\u093e\u0902\u0924\u0930\u0964<div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:10px;border-radius:10px;text-align:center;margin:6px 0;\"><div style=\"font-size:18px;font-weight:bold;\">6.3 \u0938\u092e\u093e\u0928\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c a,b \u092d\u0941\u091c\u093e h \u090a\u0901\u091a\u093e\u0908<\/div><div>\u092a\u0930\u093f\u092e\u093e\u092a = 2(a+b)<\/div><div>\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = \u0906\u0927\u093e\u0930\u00d7\u090a\u0901\u091a\u093e\u0908 = a\u00d7h<\/div><div>6\u00d74 h3 \u0915\u094d\u0937\u0947 18 \u092a\u0930\u093f20<\/div><div style=\"font-size:15px;margin-top:6px;font-weight:bold;\">6.4 \u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c a \u092d\u0941\u091c\u093e d1,d2 \u0935\u093f\u0915\u0930\u094d\u0923<\/div><div>\u092a\u0930\u093f 4a<\/div><div>\u0915\u094d\u0937\u0947 \u00bd\u00d7d1\u00d7d2<\/div><div>\u092d\u0941\u091c\u093e = \u00bd\u221a(d1\u00b2+d2\u00b2)<\/div><div>d1=6 d2=8 \u0915\u094d\u0937\u094724 \u092d\u0941\u091c\u093e5 \u092a\u0930\u093f20<\/div><\/div><div style=\"background:#e3f2fd;border-left:4px solid #1565c0;padding:6px 10px;font-weight:bold;margin-top:8px;\">6.4 \u0938\u092e\u0932\u0902\u092c - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><div style=\"background:#fff9c4;border:2px solid #fbc02d;padding:6px;border-radius:8px;text-align:center;margin:6px 0;\"><span style=\"font-weight:bold;\">\u0938\u092e\u0932\u0902\u092c a,b \u0938\u092e\u093e\u0928\u093e\u0902\u0924\u0930 \u092d\u0941\u091c\u093e h \u0926\u0942\u0930\u0940<\/span><br>\u092a\u0930\u093f\u092e\u093e\u092a = \u091a\u093e\u0930\u094b\u0902 \u091c\u094b\u0921\u093c a+b+c+d<br>\u0915\u094d\u0937\u0947 = \u00bd\u00d7(a+b)\u00d7h = \u0914\u0938\u0924\u00d7\u090a\u0901\u091a\u093e\u0908<br>a=8 b=5 h=4 \u0915\u094d\u0937\u094726<\/div>\u0938\u092e\u0932\u0902\u092c \u092e\u0947\u0902 \u0926\u094b \u092d\u0941\u091c\u093e \u0938\u092e\u093e\u0928\u093e\u0902\u0924\u0930 \u092c\u093e\u0915\u0940 \u0924\u093f\u0930\u091b\u0940\u0964<br>\u0914\u0938\u0924 (a+b)\/2 \u00d7 h \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932\u0964<\/div><\/div>\n\n<div id=\"ch6f2-4\" style=\"display:none;\"><div style=\"background:#6a1b9a;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe3 \u092d\u093e\u0917 4\/4 - 6.5 \u0935\u0943\u0924\u094d\u0924 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:13.5px;line-height:1.9;height:380px;overflow-y:auto;\"><div style=\"background:#f3e5f5;border-left:4px solid #6a1b9a;padding:6px 10px;font-weight:bold;\">6.5 \u0935\u0943\u0924\u094d\u0924 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u0935\u0943\u0924\u094d\u0924 \u092c\u093f\u0902\u0926\u0941 \u091c\u093f\u0938\u0915\u093e \u0915\u0947\u0902\u0926\u094d\u0930 \u0938\u0947 \u0926\u0942\u0930\u0940 r \u092c\u0930\u093e\u092c\u0930\u0964 \u0935\u094d\u092f\u093e\u0938 2r\u0964<br>\u03c0=22\/7=3.14 \u092a\u0930\u093f\u0927\u093f \u0914\u0930 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u092e\u0947\u0902\u0964<div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:10px;border-radius:10px;text-align:center;margin:6px 0;\"><div style=\"font-size:18px;font-weight:bold;\">\u0935\u0943\u0924\u094d\u0924 r<\/div><div>\u092a\u0930\u093f\u0927\u093f = 2\u03c0r = \u03c0d<\/div><div>\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = \u03c0r\u00b2<\/div><div>\u0905\u0930\u094d\u0927\u0935\u0943\u0924\u094d\u0924: \u092a\u0930\u093f \u03c0r+2r = r(\u03c0+2) \u0915\u094d\u0937\u0947 \u03c0r\u00b2\/2<\/div><div>\u091a\u094c\u0925\u093e\u0908: \u092a\u0930\u093f (\u03c0r\/2)+2r \u0915\u094d\u0937\u0947 \u03c0r\u00b2\/4<\/div><div>\u091b\u0932\u094d\u0932\u093e R,r: \u0915\u094d\u0937\u0947 \u03c0(R\u00b2-r\u00b2) \u092a\u0930\u093f 2\u03c0(R+r) \u092c\u093e\u0939\u0930+\u0905\u0902\u0926\u0930<\/div><div>r=7 \u092a\u0930\u093f\u0927\u093f44 \u0915\u094d\u0937\u0947154<\/div><div>r=14 \u092a\u0930\u093f\u0927\u093f88 \u0915\u094d\u0937\u0947616<\/div><\/div>\u0905\u0930\u094d\u0927\u0935\u0943\u0924\u094d\u0924 \u092a\u0930\u093f\u092e\u093e\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u093e\u0938 \u091c\u094b\u0921\u093c\u0928\u093e \u092e\u0924 \u092d\u0942\u0932\u094b \u092c\u093e\u0921\u093c \u092e\u0947\u0902 \u0935\u094d\u092f\u093e\u0938 \u092d\u0940\u0964<br>\u0915\u0947\u0935\u0932 \u091a\u093e\u092a \u091a\u093e\u0939\u093f\u090f \u0924\u094b \u03c0r, \u092a\u0942\u0930\u0940 \u092c\u093e\u0921\u093c \u0924\u094b +2r\u0964<div style=\"background:#e3f2fd;border-left:4px solid #1565c0;padding:6px 10px;font-weight:bold;margin-top:8px;\">\u092a\u0930\u093f\u092d\u093e\u0937\u093e - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u092a\u0930\u093f\u0927\u093f \u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u092c\u093e\u0921\u093c, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0905\u0902\u0926\u0930 \u091c\u0917\u0939\u0964<br>\u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e \u0915\u0947\u0902\u0926\u094d\u0930 \u0938\u0947 \u0915\u093f\u0928\u093e\u0930\u093e, \u0935\u094d\u092f\u093e\u0938 \u0926\u094b \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e \u0915\u0947\u0902\u0926\u094d\u0930 \u0938\u0947 \u0939\u094b\u0915\u0930\u0964<br>\u091b\u0932\u094d\u0932\u093e \u0926\u094b \u0935\u0943\u0924\u094d\u0924 \u092c\u0940\u091a \u0915\u0940 \u091c\u0917\u0939 \u091f\u093e\u092f\u0930 \u091c\u0948\u0938\u093e\u0964<\/div><\/div>\n<\/div>\n\n<div style=\"background:#0a5c4b;padding:12px;display:flex;justify-content:space-between;align-items:center;\">\n<button type=\"button\" id=\"ch6f2p\" style=\"background:#ffcc00;color:#000;border:3px solid #fff;border-radius:30px;padding:10px 22px;font-weight:bold;font-size:15px;cursor:pointer;min-width:100px;\">&larr; \u092a\u0940\u091b\u0947<\/button>\n<span id=\"ch6f2i\" style=\"background:#fff;color:#0a5c4b;padding:8px 20px;border-radius:20px;font-size:15px;font-weight:bold;\">1 \/ 4<\/span>\n<button type=\"button\" id=\"ch6f2n\" style=\"background:#00e676;color:#000;border:3px solid #fff;border-radius:30px;padding:10px 22px;font-weight:bold;font-size:15px;cursor:pointer;min-width:100px;\">\u0906\u0917\u0947 &rarr;<\/button>\n<\/div>\n<\/div>\n\n<script>\n(function(){\nvar c=1,t=4;\nfunction s(n){\nfor(var i=1;i<=t;i++){\nvar el=document.getElementById('ch6f2-'+i);\nif(el)el.style.display=(i===n?'block':'none');\n}\ndocument.getElementById('ch6f2i').textContent=n+' \/ '+t;\nc=n;\n}\ndocument.getElementById('ch6f2n').onclick=function(){var n=c+1;if(n>t)n=1;s(n);};\ndocument.getElementById('ch6f2p').onclick=function(){var n=c-1;if(n<1)n=t;s(n);};\n})();\n<\/script><\/div><\/div><\/div><\/div><div id=\"pg-965-2\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-965-2-0\"  class=\"panel-grid-cell\" ><div id=\"panel-965-2-0-0\" class=\"widget_text so-panel widget widget_custom_html panel-first-child panel-last-child\" data-index=\"2\" ><div class=\"textwidget custom-html-widget\"><div id=\"Q61-Q1TOQ8-SUPERFINAL\" style=\"max-width:860px;margin:12px auto;border:4px solid #0f5e4b;border-radius:14px;background:#e6f4f1;font-family:'Noto Sans Devanagari',Arial,sans-serif;overflow:hidden;\">\n<div style=\"background:#0a5c4b;padding:10px;text-align:center;\"><span style=\"background:#fff;color:#0a3d33;padding:7px 20px;border-radius:20px;font-weight:bold;font-size:13px;\">\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 6.1 - Q1 \u0938\u0947 Q8 - SUPER FINAL<\/span><\/div>\n\n<div style=\"padding:10px 12px;\">\n<div id=\"sf-1\" style=\"display:block;\"><div style=\"background:#d32f2f;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udd34 \u092d\u093e\u0917 1\/6 - Q1-Q3<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:2;height:520px;overflow-y:auto;\">\n<div style=\"background:#fff9c4;border:2px solid #fbc02d;padding:6px;border-radius:8px;text-align:center;font-weight:bold;\">\u03c0=22\/7<\/div>\n\n<b>Q1. \u090f\u0915 \u0935\u0943\u0924\u094d\u0924 \u0915\u093e \u092a\u0930\u093f\u092e\u093e\u092a 44 \u0938\u0947\u092e\u0940 \u0939\u0948\u0964 \u0907\u0938\u0915\u0940 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e \u0915\u094d\u092f\u093e \u0939\u094b\u0917\u0940?<\/b><br>\n2\u03c0r=44 =>2\u00d722\/7\u00d7r=44 =>r=7 \u0938\u0947\u092e\u0940<br>\n<b>\u0909\u0924\u094d\u0924\u0930 7 \u0938\u0947\u092e\u0940<\/b><br><br>\n\n<b>Q2. \u0928\u093f\u092e\u094d\u0928 \u0935\u0943\u0924\u094d\u0924\u094b\u0902 \u0915\u0940 \u092a\u0930\u093f\u0927\u093f 3 \u0926\u0936\u092e\u0932\u0935 \u0924\u0915\u2014 (i) r7 (ii) r10 (iii) r12<\/b><br>\n(i)2\u00d722\/7\u00d77=44.000 \u0938\u0947\u092e\u0940<br>\n(ii)2\u00d722\/7\u00d710=62.857 \u0938\u0947\u092e\u0940<br>\n(iii)2\u00d722\/7\u00d712=75.428 \u0938\u0947\u092e\u0940<br><br>\n\n<b>Q3. \u091a\u093e\u092a \u0915\u0940 \u0932\u0902\u092c\u093e\u0908\u2014 (i) r3.5 \u03b860\u00b0 (ii) r6.3 \u03b8120\u00b0<\/b><br>\nl=\u03b8\/360\u00d72\u03c0r<br>\n(i)60\/360\u00d72\u00d722\/7\u00d73.5=11\/3=3.667 \u0938\u0947\u092e\u0940<br>\n(ii)120\/360\u00d72\u00d722\/7\u00d76.3=13.2 \u092e\u0940\u091f\u0930<br>\n<b>\u0909\u0924\u094d\u0924\u0930 3.667 \u0938\u0947\u092e\u0940, 13.2 \u092e\u0940<\/b><br>\n<\/div><\/div>\n\n<div id=\"sf-2\" style=\"display:none;\"><div style=\"background:#1565c0;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udd35 \u092d\u093e\u0917 2\/6 - Q4-Q5(i)(ii)<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:1.9;height:520px;overflow-y:auto;\">\n<b>Q4. r14 \u03b875\u00b0 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921 \u0915\u093e \u092a\u0930\u093f\u092e\u093e\u092a (\u0935\u0915\u094d\u0930+2 \u0938\u0940\u0927\u0940)<\/b><br>\n\u091a\u093e\u092a=75\/360\u00d788=55\/3=18.333 \u0938\u0947\u092e\u0940<br>\n\u092a\u0930\u093f\u092e\u093e\u092a=18.333+28=46.333=139\/3 \u0938\u0947\u092e\u0940<br><br>\n\n<b>Q5(i). 60 \u092e\u0940 \u0935\u094d\u092f\u093e\u0938 80 \u092e\u0940 \u0932\u0902\u092c\u093e \u0938\u094d\u091f\u0947\u0921\u093f\u092f\u092e - \u091a\u093f\u0924\u094d\u0930 6.14(i)<\/b><br>\n2 \u0938\u0940\u0927\u0940 80+80=160<br>\n2 \u0905\u0930\u094d\u0927\u0935\u0943\u0924\u094d\u0924=\u092a\u0942\u0930\u093e \u0935\u0943\u0924\u094d\u0924 \u0935\u094d\u092f\u093e\u093860 =>\u03c0\u00d760=188.571<br>\n\u0915\u0941\u0932=348.571 \u092e\u0940<br><br>\n\n<b>Q5(ii). 12 \u0938\u0947\u092e\u0940 \u092c\u093e\u0939\u0930 8 \u0938\u0947\u092e\u0940 \u0905\u0902\u0926\u0930 \u0905\u0930\u094d\u0927 \u091b\u0932\u094d\u0932\u093e - \u091a\u093f\u0924\u094d\u0930(ii)<\/b><br>\n\u092c\u093e\u0939\u0930 \u0905\u0930\u094d\u0927 r6 \u0906\u0930\u094d\u0915 \u03c0\u00d76=18.857<br>\n\u0905\u0902\u0926\u0930 \u0905\u0930\u094d\u0927 r4 \u0906\u0930\u094d\u0915 \u03c0\u00d74=12.571<br>\n\u0938\u0940\u0927\u0940 2+2=4<br>\n\u0915\u0941\u0932=10\u03c0+4=35.428 \u0938\u0947\u092e\u0940<br>\n<\/div><\/div>\n\n<div id=\"sf-3\" style=\"display:none;\"><div style=\"background:#2e7d32;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe2 \u092d\u093e\u0917 3\/6 - Q5(iii)(iv)(v)(vi)<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:1.9;height:520px;overflow-y:auto;\">\n<b>(iii) 10 \u0938\u0947\u092e\u0940 \u0935\u0930\u094d\u0917 \u092a\u0930 \u091a\u093e\u0930 \u0905\u0930\u094d\u0927\u0935\u0943\u0924\u094d\u0924 - \u091a\u093f\u0924\u094d\u0930(iii)<\/b><br>\n4 \u0905\u0930\u094d\u0927 r5 =>20\u03c0=62.857 \u0938\u0947\u092e\u0940<br><br>\n\n<b>(iv) 12 \u0938\u0947\u092e\u0940 \u0924\u0940\u0928 \u0905\u0930\u094d\u0927\u0935\u0943\u0924\u094d\u0924 \u0924\u093f\u0915\u094b\u0928\u093e - \u091a\u093f\u0924\u094d\u0930(iv)<\/b><br>\n3 \u0905\u0930\u094d\u0927 r6 =>18\u03c0=56.571 \u0938\u0947\u092e\u0940<br><br>\n\n<b>(v) 14 \u0938\u0947\u092e\u0940 4 \u0905\u0930\u094d\u0927 +4 \u091a\u094c\u0925\u093e\u0908 - \u091a\u093f\u0924\u094d\u0930(v)<\/b><br>\n4 \u0905\u0930\u094d\u0927 r7=28\u03c0 +2\u03c0r=28\u03c0 =>56\u03c0=176 \u0938\u0947\u092e\u0940<br><br>\n\n<b>(vi) 28 \u0938\u0947\u092e\u0940 \u092c\u0921\u093c\u093e \u0905\u0930\u094d\u0927 +4 \u091b\u094b\u091f\u0947 7 \u0935\u094d\u092f\u093e\u0938 - \u091a\u093f\u0924\u094d\u0930(vi)<\/b><br>\n\u092c\u0921\u093c\u093e r14 \u0906\u0930\u094d\u0915 44 +4 \u091b\u094b\u091f\u0947 r3.5 \u0906\u0930\u094d\u0915 44 =>88 \u0938\u0947\u092e\u0940<br>\n<\/div><\/div>\n\n<div id=\"sf-4\" style=\"display:none;\"><div style=\"background:#6a1b9a;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe3 \u092d\u093e\u0917 4\/6 - Q5(vii)(viii)(ix)<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:1.9;height:520px;overflow-y:auto;\">\n<b>(vii) 6 \u0938\u0947\u092e\u0940 8 \u0938\u0947\u092e\u0940 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u092a\u0930 \u0905\u0930\u094d\u0927\u0935\u0943\u0924\u094d\u0924 - \u091a\u093f\u0924\u094d\u0930(vii)<\/b><br>\n\u0915\u0930\u094d\u0923=10, 6 \u0935\u093e\u0932\u093e \u0905\u0930\u094d\u0927 \u03c0\u00d73=9.428, 8 \u0935\u093e\u0932\u093e \u03c0\u00d74=12.571, 10 \u0935\u093e\u0932\u093e \u03c0\u00d75=15.714<br>\n\u0915\u0941\u0932 \u092c\u093e\u0939\u0930\u0940=37.714=12\u03c0 \u0938\u0947\u092e\u0940<br><br>\n\n<b>(viii) 4-4-4 \u0924\u0940\u0928 \u091b\u094b\u091f\u0947 + \u092c\u0921\u093c\u093e 12 \u0905\u0930\u094d\u0927 - \u091a\u093f\u0924\u094d\u0930(viii)<\/b><br>\n\u092c\u0921\u093c\u093e r6 \u0906\u0930\u094d\u0915 18.857 +3 \u091b\u094b\u091f\u0947 r2 \u0906\u0930\u094d\u0915 3\u00d76.285=18.857 =>37.714 \u0938\u0947\u092e\u0940<br><br>\n\n<b>(ix) 10+10=20 \u0906\u0927\u093e\u0930 \u0926\u094b \u0905\u0930\u094d\u0927 - \u091a\u093f\u0924\u094d\u0930(ix)<\/b><br>\n\u092c\u0921\u093c\u093e r10 \u0906\u0930\u094d\u0915 31.428 + \u091b\u094b\u091f\u093e r5 \u0906\u0930\u094d\u0915 15.714 + \u0938\u0940\u0927\u0940 10 =57.142<br>\n\u0915\u0947\u0935\u0932 \u091a\u093e\u092a=47.142 \u0938\u0947\u092e\u0940<br>\n\n<div style=\"background:#fff9c4;border:2px solid #fbc02d;padding:6px;border-radius:8px;text-align:center;font-weight:bold;margin-top:6px;\">Q5(i)- (ix) \u0916\u0924\u094d\u092e: 348.57m, 35.43cm, 62.86cm, 56.57cm, 176cm, 88cm, 37.71cm, 37.71cm, 47.14cm<\/div>\n<\/div><\/div>\n\n<div id=\"sf-5\" style=\"display:none;\"><div style=\"background:#ff6f00;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe0 \u092d\u093e\u0917 5\/6 - Q6 \u0915\u093e\u0930 \u092a\u0939\u093f\u092f\u093e<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14.5px;line-height:2;height:520px;overflow-y:auto;\">\n<b>Q6. \u0915\u093e\u0930 \u092a\u0939\u093f\u092f\u093e \u0935\u094d\u092f\u093e\u093856 \u0938\u0947\u092e\u0940\u2014 (i)1 \u091a\u0915\u094d\u0915\u0930 \u0926\u0942\u0930\u0940 (ii)10 \u0915\u093f\u092e\u0940 \u092e\u0947\u0902 \u091a\u0915\u094d\u0915\u0930?<\/b><br><br>\nd=56 r=28<br>\n(i) \u092a\u0930\u093f\u0927\u093f=\u03c0d=22\/7\u00d756=176 \u0938\u0947\u092e\u0940=1.76 \u092e\u0940<br>\n<b>\u0909\u0924\u094d\u0924\u0930 176 \u0938\u0947\u092e\u0940<\/b><br><br>\n(ii) 10 \u0915\u093f\u092e\u0940=10,00,000 \u0938\u0947\u092e\u0940<br>\n\u091a\u0915\u094d\u0915\u0930=10,00,000\/176=5681.81\u22485682 \u091a\u0915\u094d\u0915\u0930<br>\n<b>\u0909\u0924\u094d\u0924\u0930 5682 \u091a\u0915\u094d\u0915\u0930 \u0932\u0917\u092d\u0917<\/b><br>\n<\/div><\/div>\n\n<div id=\"sf-6\" style=\"display:none;\"><div style=\"background:#0d47a1;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udd35 \u092d\u093e\u0917 6\/6 - Q7 Q8 \u092b\u0942\u0932<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14.5px;line-height:1.9;height:520px;overflow-y:auto;\">\n<b>Q7(i). \u0935\u0930\u094d\u0917 14 \u0938\u0947\u092e\u0940 \u092b\u0942\u0932 - \u091a\u093e\u092a \u0915\u0947\u0902\u0926\u094d\u0930 \u092d\u0941\u091c\u093e \u092e\u0927\u094d\u092f\u092c\u093f\u0902\u0926\u0941 - \u091a\u093f\u0924\u094d\u0930 6.15(\u0915)<\/b><br>\nr=7, 90\u00b0 \u091a\u093e\u092a=\u03c0r\/2=11 \u0938\u0947\u092e\u0940<br>\n4 \u092a\u0902\u0916\u0941\u0921\u093c\u0940 \u092c\u093e\u0939\u0930\u0940=44 \u0938\u0947\u092e\u0940, \u0915\u0941\u0932 \u0926\u094b\u0928\u094b\u0902 \u0924\u0930\u092b=88 \u0938\u0947\u092e\u0940<br>\n<b>\u0909\u0924\u094d\u0924\u0930 88 \u0938\u0947\u092e\u0940 \u0915\u0941\u0932<\/b><br><br>\n\n<b>Q7(ii). \u0937\u091f\u094d\u092d\u0941\u091c 42 \u0938\u0947\u092e\u0940 \u092b\u0942\u0932 - \u0915\u0947\u0902\u0926\u094d\u0930 \u0936\u0940\u0930\u094d\u0937 - \u091a\u093f\u0924\u094d\u0930 6.15(\u0916)<\/b><br>\nr=42, 60\u00b0 \u091a\u093e\u092a=\u03c0r\/3=44 \u0938\u0947\u092e\u0940<br>\n6 \u091a\u093e\u092a \u092c\u093e\u0939\u0930\u0940=264 \u0938\u0947\u092e\u0940, \u0915\u0941\u0932 12 \u091a\u093e\u092a=528 \u0938\u0947\u092e\u0940<br>\n<b>\u0909\u0924\u094d\u0924\u0930 528 \u0938\u0947\u092e\u0940 \u0915\u0941\u0932, 264 \u092c\u093e\u0939\u0930\u0940<\/b><br><br>\n\n<b>Q8. \u0926\u094b \u0935\u0943\u0924\u094d\u0924 \u092a\u0930\u093f\u092e\u093e\u092a \u0905\u0928\u0941\u092a\u093e\u0924 5:4 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e \u0905\u0928\u0941\u092a\u093e\u0924?<\/b><br>\n2\u03c0r1\/2\u03c0r2=5\/4 =>r1\/r2=5\/4<br>\n<b>\u0909\u0924\u094d\u0924\u0930 5:4<\/b><br>\n\n<div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:10px;border-radius:10px;text-align:center;margin-top:10px;font-weight:bold;\">\n6.1 Q1-Q8 \u092a\u0942\u0930\u093e \u0916\u0924\u094d\u092e \u2705<br>\n\u092a\u0930\u093f\u0927\u093f 2\u03c0r, \u091a\u093e\u092a \u03b8\/360\u00d72\u03c0r<br>\n\u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921 \u092a\u0930\u093f \u091a\u093e\u092a+2r<br>\n\u092b\u0942\u0932 r=\u092d\u0941\u091c\u093e\/2 \u092f\u093e \u092d\u0941\u091c\u093e\n<\/div>\n<\/div><\/div>\n<\/div>\n\n<div style=\"background:#0a5c4b;padding:12px;display:flex;justify-content:space-between;align-items:center;\">\n<button type=\"button\" id=\"sfp\" style=\"background:#ffcc00;color:#000;border:3px solid #fff;border-radius:30px;padding:10px 22px;font-weight:bold;font-size:15px;cursor:pointer;min-width:100px;\">&larr; \u092a\u0940\u091b\u0947<\/button>\n<span id=\"sfi\" style=\"background:#fff;color:#0a5c4b;padding:8px 20px;border-radius:20px;font-size:15px;font-weight:bold;\">1 \/ 6<\/span>\n<button type=\"button\" id=\"sfn\" style=\"background:#00e676;color:#000;border:3px solid #fff;border-radius:30px;padding:10px 22px;font-weight:bold;font-size:15px;cursor:pointer;min-width:100px;\">\u0906\u0917\u0947 &rarr;<\/button>\n<\/div>\n<\/div>\n\n<script>\n(function(){\nvar c=1,t=6;\nfunction s(n){\nfor(var i=1;i<=t;i++){\nvar el=document.getElementById('sf-'+i);\nif(el)el.style.display=(i===n?'block':'none');\n}\ndocument.getElementById('sfi').textContent=n+' \/ '+t;\nc=n;\n}\ndocument.getElementById('sfn').onclick=function(){var n=c+1;if(n>t)n=1;s(n);};\ndocument.getElementById('sfp').onclick=function(){var n=c-1;if(n<1)n=t;s(n);};\n})();\n<\/script><\/div><\/div><\/div><\/div><div id=\"pg-965-3\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-965-3-0\"  class=\"panel-grid-cell\" ><div id=\"panel-965-3-0-0\" class=\"widget_text so-panel widget widget_custom_html panel-first-child panel-last-child\" data-index=\"3\" ><div class=\"textwidget custom-html-widget\"><div id=\"CH6-134-142-CORRECT\" style=\"max-width:860px;margin:12px auto;border:4px solid #0f5e4b;border-radius:14px;background:#e6f4f1;font-family:'Noto Sans Devanagari',Arial,sans-serif;overflow:hidden;\">\n<div style=\"background:#0a5c4b;padding:10px;text-align:center;\"><span style=\"background:#fff;color:#0a3d33;padding:7px 20px;border-radius:20px;font-weight:bold;font-size:13px;\">\u092a\u0947\u091c 134-142 - \u0936\u0941\u0926\u094d\u0927 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 - \u0938\u0942\u0924\u094d\u0930 \u0938\u0939\u0940<\/span><\/div>\n\n<div style=\"padding:10px 12px;\">\n<div id=\"c142-1\" style=\"display:block;\"><div style=\"background:#d32f2f;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udd34 \u092d\u093e\u0917 1\/5 - \u0938\u094b\u091a\u093f\u090f \u0914\u0930 \u0935\u093f\u091a\u093e\u0930 \u0915\u0940\u091c\u093f\u090f + 6.8.1 \u0939\u0940\u0930\u094b\u0928<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:2;height:540px;overflow-y:auto;\">\n\n<div style=\"background:#ffebee;border-left:4px solid #d32f2f;padding:8px 10px;font-weight:bold;\">\u0938\u094b\u091a\u093f\u090f \u0914\u0930 \u0935\u093f\u091a\u093e\u0930 \u0915\u0940\u091c\u093f\u090f - \u092a\u0947\u091c 134<\/div>\n<b>\u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0926\u094b \u0938\u092e\u093e\u0928 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0935\u093e\u0932\u0947 \u092c\u0939\u0941\u092d\u0941\u091c P \u0914\u0930 Q \u0926\u093f\u090f \u0917\u090f \u0939\u0948\u0902\u0964 \u0915\u094d\u092f\u093e \u0909\u0928\u092e\u0947\u0902 \u0938\u0947 \u090f\u0915 \u0915\u094b \u0938\u0940\u0927\u0940 \u0930\u0947\u0916\u093e \u0938\u0947 \u0926\u094b \u092f\u093e \u0905\u0927\u093f\u0915 \u092d\u093e\u0917\u094b\u0902 \u092e\u0947\u0902 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u092c\u093e\u0901\u091f\u0928\u093e \u0938\u0902\u092d\u0935 \u0939\u0948 \u0914\u0930 \u092b\u093f\u0930 \u0909\u0928 \u0915\u091f\u0947 \u0939\u0941\u090f \u092d\u093e\u0917\u094b\u0902 \u0915\u094b \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u0947 \u0935\u094d\u092f\u0935\u0938\u094d\u0925\u093f\u0924 \u0915\u0930\u0928\u093e \u0938\u0902\u092d\u0935 \u0939\u0948 \u0915\u093f \u0935\u0947 \u0938\u092d\u0940 \u092d\u093e\u0917 \u092e\u093f\u0932\u0915\u0930 \u0926\u0942\u0938\u0930\u0947 \u092c\u0939\u0941\u092d\u0941\u091c \u0915\u094b \u092d\u0940 \u092a\u0942\u0930\u093e \u0922\u0915 \u0932\u0947\u0902?<\/b><br><br>\n\n\u0905\u092a\u0928\u0947 \u091a\u093e\u0930\u094b\u0902 \u0913\u0930 \u0915\u0940 \u0906\u0915\u0943\u0924\u093f\u092f\u094b\u0902 \u0915\u0947 \u0909\u0926\u093e\u0939\u0930\u0923 \u0938\u094b\u091a\u093f\u090f\u2014<br>\n1. \u0938\u092e\u093e\u0928 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0935\u093e\u0932\u0947 \u0935\u0930\u094d\u0917 \u0914\u0930 \u0917\u0948\u0930-\u0935\u0930\u094d\u0917\u093e\u0915\u093e\u0930 \u0906\u092f\u0924,<br>\n2. \u092d\u093f\u0928\u094d\u0928-\u092d\u093f\u0928\u094d\u0928 \u0906\u0915\u0943\u0924\u093f \u0935\u093e\u0932\u0947 \u0926\u094b \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u091c\u093f\u0928\u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0938\u092e\u093e\u0928 \u0939\u0948\u0964<br>\n3. \u0938\u092e\u093e\u0928 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0935\u093e\u0932\u093e \u090f\u0915 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0914\u0930 \u090f\u0915 \u0935\u0930\u094d\u0917 - \u0907\u0938\u0947 \u0906\u092a \u0905\u092a\u0928\u0940 \u0915\u0932\u094d\u092a\u0928\u093e \u0938\u0947 \u0924\u0948\u092f\u093e\u0930 \u0915\u0940\u091c\u093f\u090f\u0964<br><br>\n\n<b>40 \u0907\u0915\u093e\u0908 \u092a\u0930\u093f\u092e\u093e\u092a \u0935\u093e\u0932\u0947 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0906\u092f\u0924\u094b\u0902 \u0915\u0947 \u0935\u093f\u0937\u092f \u092e\u0947\u0902 \u0935\u093f\u091a\u093e\u0930 \u0915\u0940\u091c\u093f\u090f (\u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u093e \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 \u0939\u094b\u0928\u093e \u0906\u0935\u0936\u094d\u092f\u0915 \u0928\u0939\u0940\u0902 \u0939\u0948)\u0964<\/b><br>\n1. \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0947 \u0915\u093f\u0924\u0928\u0947 \u0906\u092f\u0924 \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902?<br>\n2. \u0907\u0928\u092e\u0947\u0902 \u0938\u0947 \u0915\u094b\u0908 \u0910\u0938\u093e \u0939\u0948 \u091c\u093f\u0938\u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0938\u092c\u0938\u0947 \u0905\u0927\u093f\u0915 \u0939\u094b? \u0907\u0938\u0915\u0940 \u0935\u093f\u092e\u093e\u090f\u0901 \u0915\u094d\u092f\u093e \u0939\u094b\u0902\u0917\u0940?<br>\n3. \u0915\u094d\u092f\u093e \u0907\u0928 \u0938\u092d\u0940 \u0906\u092f\u0924\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u0910\u0938\u093e \u0915\u094b\u0908 \u090f\u0915 \u0906\u092f\u0924 \u0939\u0948 \u091c\u093f\u0938\u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0938\u092c\u0938\u0947 \u0915\u092e \u0939\u0948? \u0909\u0938\u0915\u0940 \u0935\u093f\u092e\u093e\u090f\u0901 \u0915\u094d\u092f\u093e \u0939\u094b\u0902\u0917\u0940? \u0915\u094d\u092f\u093e \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u093e \u0915\u094b\u0908 \u092d\u0940 \u0909\u0924\u094d\u0924\u0930 \u0906\u092a\u0915\u094b \u0906\u0936\u094d\u091a\u0930\u094d\u092f\u091a\u0915\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948?<br>\n\n<div style=\"background:#e3f2fd;border-left:4px solid #1565c0;padding:8px 10px;font-weight:bold;margin-top:10px;\">6.8.1 \u0939\u0940\u0930\u094b\u0928 \u0915\u093e \u0938\u0942\u0924\u094d\u0930<\/div>\n\u0906\u092a \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u0947 \u0938\u0942\u0924\u094d\u0930 1\/2 \u00d7 \u0906\u0927\u093e\u0930 \u00d7 \u090a\u0901\u091a\u093e\u0908 \u0938\u0947 \u092d\u0932\u0940-\u092d\u093e\u0901\u0924\u093f \u092a\u0930\u093f\u091a\u093f\u0924 \u0939\u0948\u0902\u0964 \u0915\u094d\u092f\u093e \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0928\u093f\u0915\u093e\u0932\u0928\u0947 \u0915\u093e \u0915\u094b\u0908 \u0914\u0930 \u092d\u0940 \u0938\u0942\u0924\u094d\u0930 \u0939\u0948? \u0939\u093e\u0901, \u0905\u0928\u094d\u092f \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u0947 \u092d\u0940 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<br><br>\n\n\u0905\u092c \u0939\u092e \u0939\u0940\u0930\u094b\u0928 \u0915\u0947 \u0938\u0942\u0924\u094d\u0930 \u092a\u0930 \u091a\u0930\u094d\u091a\u093e \u0915\u0930\u0947\u0902\u0917\u0947, \u091c\u093f\u0938\u0915\u094b \u092f\u0942\u0928\u093e\u0928 \u0926\u0947\u0936 \u0915\u0947 \u0917\u0923\u093f\u0924\u091c\u094d\u091e \u0914\u0930 \u0906\u0935\u093f\u0937\u094d\u0915\u093e\u0930\u0915 \u0939\u0940\u0930\u094b\u0928 \u0928\u0947 \u091c\u094d\u091e\u093e\u0924 \u0915\u093f\u092f\u093e \u0925\u093e\u0964 \u0909\u0928\u094d\u0939\u094b\u0902\u0928\u0947 \u0907\u0938\u0947 \u092a\u094d\u0930\u093e\u091a\u0940\u0928 \u092e\u0947\u0902 \u092e\u093f\u0938\u094d\u0930 \u0926\u0947\u0936 \u0915\u0947 \u0928\u0940\u0932 \u0928\u0926\u0940 \u0915\u0947 \u0915\u093f\u0928\u093e\u0930\u0947 \u0938\u094d\u0925\u093f\u0924 \u0936\u0939\u0930 \u0905\u0932\u0947\u0915\u094d\u091c\u0947\u0902\u0921\u094d\u0930\u093f\u092f\u093e \u0915\u0947 \u0938\u0902\u0917\u094d\u0930\u0939\u093e\u0932\u092f \u092e\u0947\u0902 \u092a\u0922\u093c\u093e \u0925\u093e\u0964<br><br>\n\n<b>\u0938\u0942\u0924\u094d\u0930:<\/b> \u092f\u0926\u093f \u0394ABC \u0915\u0940 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 BC=a, CA=b \u0914\u0930 AB=c \u0939\u0948 \u0924\u094b \u0907\u0938\u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u0947 \u091c\u094d\u091e\u093e\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0938\u0930\u094d\u0935\u092a\u094d\u0930\u0925\u092e \u0939\u092e \u0907\u0938\u0915\u093e \u0905\u0930\u094d\u0926\u094d\u0927-\u092a\u0930\u093f\u092e\u093e\u092a \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0947\u0902\u0917\u0947, \u091c\u094b \u0915\u093f \u0907\u0938\u0915\u0947 \u092a\u0930\u093f\u092e\u093e\u092a \u0915\u093e \u0906\u0927\u093e \u0939\u094b\u0917\u093e \u0905\u0930\u094d\u0925\u093e\u0924\u094d<br>\n<div style=\"background:#fff9c4;border:2px solid #fbc02d;padding:8px;border-radius:8px;text-align:center;font-weight:bold;margin:6px 0;\">\ns = (a+b+c)\/2<br>\n\u0924\u094d\u0930\u093f\u092d\u0941\u091c (\u0394ABC) \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = \u221a[s(s-a)(s-b)(s-c)]\n<\/div>\n<\/div><\/div>\n\n<div id=\"c142-2\" style=\"display:none;\"><div style=\"background:#1565c0;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udd35 \u092d\u093e\u0917 2\/5 - \u0909\u0926\u093e\u0939\u0930\u0923 3,4,5 - \u092a\u0947\u091c 135-136<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:1.9;height:540px;overflow-y:auto;\">\n\n<div style=\"background:#e8f5e9;border-left:4px solid #2e7d32;padding:8px 10px;font-weight:bold;\">\u0909\u0926\u093e\u0939\u0930\u0923 3 \u2014 \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c<\/div>\n<b>\u090f\u0915 \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u092d\u0941\u091c\u093e a \u0907\u0915\u093e\u0908 \u0939\u0948\u0964<\/b><br>\n\u0938\u092d\u0940 \u0924\u0940\u0928\u094b\u0902 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 a \u0907\u0915\u093e\u0908 \u0939\u0948 \u0924\u094b \u0907\u0938\u0915\u093e \u0905\u0930\u094d\u0926\u094d\u0927-\u092a\u0930\u093f\u092e\u093e\u092a s=(a+a+a)\/2=3a\/2 \u0907\u0915\u093e\u0908 \u0939\u0948\u0964<br>\n\u0905\u092c \u0939\u0940\u0930\u094b\u0928 \u0915\u0947 \u0938\u0942\u0924\u094d\u0930 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = \u221a[3a\/2 \u00d7 (3a\/2-a)\u00d7(3a\/2-a)\u00d7(3a\/2-a)] = \u221a[3a\/2 \u00d7 a\/2 \u00d7 a\/2 \u00d7 a\/2] = \u221a3\/4 a\u00b2 \u0935\u0930\u094d\u0917 \u0907\u0915\u093e\u0908 \u0939\u094b\u0917\u093e\u0964<br>\n\u092c\u094c\u0927\u093e\u092f\u0928-\u092a\u093e\u0907\u0925\u093e\u0917\u094b\u0930\u0938 \u0938\u0947 h\u00b2 = a\u00b2-(a\/2)\u00b2 =3a\u00b2\/4 =>h=\u221a3a\/2<br>\n\u0907\u0938\u0932\u093f\u090f \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 1\/2\u00d7a\u00d7\u221a3a\/2=\u221a3\/4 a\u00b2 \u0938\u092e\u093e\u0928 \u0938\u0942\u0924\u094d\u0930 \u0939\u0948\u0964<br>\n<b>\u2234 \u092a\u094d\u0930\u0924\u0940\u0915 \u0915\u093e \u0924\u093e\u0924\u094d\u092a\u0930\u094d\u092f \u2018\u0907\u0938\u0932\u093f\u090f\u2019 \u0939\u0948\u0964<\/b><br><br>\n\n<div style=\"background:#e3f2fd;border-left:4px solid #1565c0;padding:8px 10px;font-weight:bold;\">\u0909\u0926\u093e\u0939\u0930\u0923 4 \u2014 \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c<\/div>\n<b>\u090f\u0915 \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0938\u092e\u093e\u0928 \u092d\u0941\u091c\u093e a \u0907\u0915\u093e\u0908 \u0914\u0930 \u0906\u0927\u093e\u0930 2b \u0907\u0915\u093e\u0908 \u0939\u0948\u0964<\/b><br>\n\u0905\u0930\u094d\u0926\u094d\u0927-\u092a\u0930\u093f\u092e\u093e\u092a s=1\/2(2a+2b)=a+b \u0907\u0915\u093e\u0908 \u0939\u0948\u0964 \u0939\u0940\u0930\u094b\u0928 \u0938\u0942\u0924\u094d\u0930 \u0905\u0928\u0941\u0938\u093e\u0930 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = \u221a[(a+b)(a+b-a)(a+b-a)(a+b-2b)]? \u0928\u0939\u0940\u0902 \u0938\u0939\u0940:<br>\n\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = \u221a[(a+b)(a+b-a)(a+b-a)(a+b-2b)] = \u221a[(a+b)\u00d7b\u00d7b\u00d7(a-b)] = b\u221a(a\u00b2-b\u00b2) \u0935\u0930\u094d\u0917 \u0907\u0915\u093e\u0908 \u0939\u0948\u0964<br>\n\u092c\u094c\u0927\u093e\u092f\u0928-\u092a\u093e\u0907\u0925\u093e\u0917\u094b\u0930\u0938 \u0938\u0947 h\u00b2=a\u00b2-b\u00b2 =>h=\u221a(a\u00b2-b\u00b2)<br>\n\u0907\u0938\u0932\u093f\u090f \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 1\/2\u00d72b\u00d7\u221a(a\u00b2-b\u00b2)=b\u221a(a\u00b2-b\u00b2) \u092a\u0942\u0930\u094d\u0935 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u0948\u0964<br><br>\n\n<div style=\"background:#fff3e0;border-left:4px solid #ff6f00;padding:8px 10px;font-weight:bold;\">\u0909\u0926\u093e\u0939\u0930\u0923 5 \u2014 3,4,5 \u0924\u094d\u0930\u093f\u092d\u0941\u091c<\/div>\n<b>\u090f\u0915 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u092d\u0941\u091c\u093e\u090f\u0901 3 \u0907\u0915\u093e\u0908, 4 \u0907\u0915\u093e\u0908 \u0914\u0930 5 \u0907\u0915\u093e\u0908 \u0939\u0948\u0902\u0964<\/b><br>\n\u0905\u0930\u094d\u0926\u094d\u0927-\u092a\u0930\u093f\u092e\u093e\u092a s=(3+4+5)\/2=6 \u0907\u0915\u093e\u0908 \u0939\u0948\u0964 \u0939\u0940\u0930\u094b\u0928 \u0938\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = \u221a[6(6-3)(6-4)(6-5)] = \u221a[6\u00d73\u00d72\u00d71]=\u221a36=6 \u0935\u0930\u094d\u0917 \u0907\u0915\u093e\u0908<br>\n\u091a\u093f\u0924\u094d\u0930 6.25 \u0926\u0947\u0916\u093f\u090f \u0924\u094b 3\u00b2+4\u00b2=5\u00b2 \u0939\u0948\u0964 \u0905\u0924\u0903 \u092c\u094c\u0927\u093e\u092f\u0928-\u092a\u093e\u0907\u0925\u093e\u0917\u094b\u0930\u0938 \u0915\u0947 \u0935\u093f\u0932\u094b\u092e \u0905\u0928\u0941\u0938\u093e\u0930 \u0394ABC, B \u092a\u0930 \u0938\u092e\u0915\u094b\u0923 \u0939\u0948\u0964<br>\n\u0906\u0927\u093e\u0930=3 \u090a\u0901\u091a\u093e\u0908=4 \u0905\u0924\u0903 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=1\/2\u00d73\u00d74=6 \u0935\u0930\u094d\u0917 \u0907\u0915\u093e\u0908\u0964 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0924\u0925\u094d\u092f \u092e\u0947\u0902 \u0939\u092e \u090f\u0915 \u0938\u092e\u093e\u0928 \u0938\u0939\u0940 \u092a\u0930\u093f\u0923\u093e\u092e \u092a\u093e\u0924\u0947 \u0939\u0948\u0902\u0964<br>\n<\/div><\/div>\n\n<div id=\"c142-3\" style=\"display:none;\"><div style=\"background:#2e7d32;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe2 \u092d\u093e\u0917 3\/5 - \u092a\u0930\u093f\u092c\u0943\u0924\u094d\u0924 \u0905\u0902\u0924\u0935\u0943\u0924\u094d\u0924 + \u091a\u0915\u094d\u0930\u0940\u092f \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c - \u092a\u0947\u091c 137-138<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:1.9;height:540px;overflow-y:auto;\">\n\n\u0939\u0940\u0930\u094b\u0928 \u0915\u093e \u0938\u0942\u0924\u094d\u0930 \u0915\u0948\u0938\u0947 \u0938\u093f\u0926\u094d\u0927 \u0939\u094b\u0917\u093e\u0964 \u0907\u0938\u0915\u0947 \u0915\u0908 \u092a\u094d\u0930\u092e\u093e\u0923 \u091c\u094d\u091e\u093e\u0924 \u0939\u0941\u090f \u0939\u0948\u0902\u0964 \u0909\u0928\u092e\u0947\u0902 \u0938\u0947 \u090f\u0915 \u092c\u094c\u0927\u093e\u092f\u0928-\u092a\u093e\u0907\u0925\u093e\u0917\u094b\u0930\u0938 \u092a\u094d\u0930\u092e\u0947\u092f \u0914\u0930 \u2018\u0926\u094b \u0935\u0930\u094d\u0917\u094b\u0902 \u0915\u0947 \u0905\u0902\u0924\u0930\u2019 \u0915\u093e \u0938\u0942\u0924\u094d\u0930 a\u00b2-b\u00b2=(a-b)(a+b) \u092c\u093e\u0930\u0902\u092c\u093e\u0930 \u0909\u092a\u092f\u094b\u0917 \u0939\u0941\u0906 \u0939\u0948\u0964 \u0939\u092e \u0915\u0915\u094d\u0937\u093e 10 \u092e\u0947\u0902 \u092d\u0940 \u0907\u0928\u092e\u0947\u0902 \u0938\u0947 \u0915\u0941\u091b \u092a\u094d\u0930\u092e\u093e\u0923\u094b\u0902 \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0947\u0902\u0917\u0947\u0964 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0910\u0938\u0947 \u0905\u0928\u094d\u092f \u0926\u094b \u0914\u0930 \u0938\u0942\u0924\u094d\u0930 \u092d\u0940 \u0939\u0948\u0902\u0964 \u0926\u094b\u0928\u094b\u0902 \u0915\u093e \u0938\u0902\u092c\u0902\u0927 \u0935\u0943\u0924\u094d\u0924\u094b\u0902 \u0938\u0947 \u0939\u0948\u0964<br><br>\n\n<b>\u092a\u0930\u093f\u0935\u0943\u0924\u094d\u0924 \u0914\u0930 \u0905\u0902\u0924\u0935\u0943\u0924\u094d\u0924:<\/b> \u0915\u093f\u0938\u0940 \u092d\u0940 \u0924\u094d\u0930\u093f\u092d\u0941\u091c ABC \u0915\u0947 \u0924\u0940\u0928\u094b\u0902 \u0936\u0940\u0930\u094d\u0937\u094b\u0902 \u0938\u0947 \u0939\u094b\u0915\u0930 \u0917\u0941\u091c\u0930\u0928\u0947 \u0935\u093e\u0932\u093e \u0915\u0947\u0935\u0932 \u090f\u0915 \u0939\u0940 \u0935\u0943\u0924\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0947 \u0394ABC \u0915\u093e \u092a\u0930\u093f\u0935\u0943\u0924\u094d\u0924 \u0915\u0939\u0924\u0947 \u0939\u0948\u0902\u0964 \u0907\u0938\u0940 \u092a\u094d\u0930\u0915\u093e\u0930 \u0394ABC \u092e\u0947\u0902 \u090f\u0915 \u0935\u0943\u0924\u094d\u0924 \u0910\u0938\u093e \u092d\u0940 \u0939\u0948 \u091c\u094b \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0920\u0940\u0915 \u092e\u0927\u094d\u092f \u092e\u0947\u0902 \u0938\u094d\u0925\u093f\u0924 \u0939\u0948 \u0914\u0930 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u0924\u0940\u0928\u094b\u0902 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u094b \u0938\u094d\u092a\u0930\u094d\u0936 \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0947 \u0394ABC \u0915\u093e \u0905\u0902\u0924\u0935\u0943\u0924\u094d\u0924 \u0915\u0939\u0924\u0947 \u0939\u0948\u0902\u0964<br>\n\n<div style=\"background:#fff9c4;border:2px solid #fbc02d;padding:8px;border-radius:8px;text-align:center;font-weight:bold;margin:6px 0;\">\n\u092e\u093e\u0928\u093e \u0394ABC \u0915\u0940 \u092d\u0941\u091c\u093e\u090f\u0901 a,b,c \u0939\u0948\u0902\u0964 \u092a\u0930\u093f\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e R \u0939\u0948 \u0914\u0930 \u0905\u0902\u0924\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e r \u0939\u0948 \u0924\u092c<br>\n\u0394ABC \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = abc \/4R<br>\n\u0394ABC \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = r\u00d7(a+b+c)\/2 = r\u00d7s\n<\/div>\n\n<div style=\"background:#ffebee;border-left:4px solid #d32f2f;padding:8px 10px;font-weight:bold;margin-top:10px;\">\u091a\u0915\u094d\u0930\u0940\u092f \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u0947 \u0932\u093f\u090f \u092c\u094d\u0930\u0939\u094d\u092e\u0917\u0941\u092a\u094d\u0924 \u0915\u093e \u0938\u0942\u0924\u094d\u0930<\/div>\n\u0939\u092e\u0928\u0947 \u0926\u0947\u0916\u093e \u0915\u093f \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u0924\u0940\u0928\u094b\u0902 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 \u0926\u0940 \u0917\u0908 \u0939\u0948 \u0924\u094b \u0909\u0938\u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u0948\u0938\u0947 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0947\u0902\u0917\u0947\u0964 \u0905\u092c \u0938\u094d\u0935\u093e\u092d\u093e\u0935\u093f\u0915 \u092a\u094d\u0930\u0936\u094d\u0928 \u092f\u0939 \u0909\u0920\u0924\u093e \u0939\u0948 \u0915\u093f \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u091a\u093e\u0930 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 \u0926\u093f\u090f \u091c\u093e\u0928\u0947 \u092a\u0930 \u0909\u0938\u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u0948\u0938\u0947 \u0928\u093f\u0915\u093e\u0932\u0947\u0902\u0917\u0947?<br><br>\n\n\u092a\u0942\u0930\u094d\u0935 \u092e\u0947\u0902 \u0939\u092e\u0928\u0947 \u092a\u0942\u091b\u093e \u0925\u093e \u0915\u093f \u0915\u094d\u092f\u093e \u0939\u092e \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u091c\u092c \u0915\u0947\u0935\u0932 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 \u091c\u094d\u091e\u093e\u0924 \u0939\u094b? \u0909\u0924\u094d\u0924\u0930 \u0939\u0948\u2014 \u0928\u0939\u0940\u0902\u0964 \u091a\u093f\u0924\u094d\u0930 6.27 \u092e\u0947\u0902 \u092a\u094d\u0930\u0936\u094d\u0928 \u092f\u0939 \u0939\u0948 \u0915\u093f \u0915\u093f\u0938\u0940 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u091c\u093f\u0938\u0915\u0940 \u092d\u0941\u091c\u093e\u090f\u0901 3,3,3,3 \u0939\u0948\u0902\u0964 \u091c\u0948\u0938\u093e \u0915\u093f \u0906\u092a \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0924\u0940\u0928\u094b\u0902 \u0906\u0915\u0943\u0924\u093f\u092f\u094b\u0902 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u092d\u093f\u0928\u094d\u0928 \u0939\u0948\u0964 \u0905\u0924\u0903 \u0915\u0947\u0935\u0932 \u091a\u093e\u0930 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 \u0938\u0947 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u091c\u094d\u091e\u093e\u0924 \u0928\u0939\u0940\u0902 \u0915\u0930 \u0938\u0915\u0924\u0947\u0964<br><br>\n\n\u0910\u0938\u093e \u0939\u0940 \u090f\u0915 \u0917\u0941\u0923\u0927\u0930\u094d\u092e \u092f\u0939 \u0939\u0948 \u0915\u093f \u091c\u092c \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c, \u091a\u0915\u094d\u0930\u0940\u092f \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u094b\u0924\u093e \u0939\u0948\u0964 628 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u0902\u0935\u0924 \u092e\u0947\u0902 \u092d\u093e\u0930\u0924\u0940\u092f \u0917\u0923\u093f\u0924\u091c\u094d\u091e \u092c\u094d\u0930\u0939\u094d\u092e\u0917\u0941\u092a\u094d\u0924 (598\u2013668) \u0928\u0947 \u091a\u0915\u094d\u0930\u0940\u092f \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0905\u0926\u094d\u092d\u0941\u0924 \u0938\u0942\u0924\u094d\u0930 \u0915\u093e \u0905\u0928\u094d\u0935\u0947\u0937\u0923 \u0915\u093f\u092f\u093e\u0964<br>\n\n<div style=\"background:#e8f5e9;border:2px solid #2e7d32;padding:8px;border-radius:8px;text-align:center;font-weight:bold;\">\n\u0938\u0942\u0924\u094d\u0930: \u092f\u0926\u093f \u090f\u0915 \u091a\u0915\u094d\u0930\u0940\u092f \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u091a\u093e\u0930\u094b\u0902 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 a,b,c,d \u0914\u0930 \u0905\u0930\u094d\u0926\u094d\u0927-\u092a\u0930\u093f\u092e\u093e\u092a s=(a+b+c+d)\/2 \u0939\u0948 \u0924\u094b<br>\n\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = \u221a[(s-a)(s-b)(s-c)(s-d)]\n<\/div>\n<\/div><\/div>\n\n<div id=\"c142-4\" style=\"display:none;\"><div style=\"background:#6a1b9a;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe3 \u092d\u093e\u0917 4\/5 - \u0909\u0926\u093e\u0939\u0930\u0923 6,7 + \u0935\u093f\u0936\u0947\u0937 \u0938\u094d\u0925\u093f\u0924\u093f \u0935\u094d\u092f\u093e\u092a\u0915\u0940\u0915\u0930\u0923 - \u092a\u0947\u091c 139-140<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:1.9;height:540px;overflow-y:auto;\">\n\n<div style=\"background:#e8f5e9;border-left:4px solid #2e7d32;padding:8px 10px;font-weight:bold;\">\u0909\u0926\u093e\u0939\u0930\u0923 6 \u2014 \u0906\u092f\u0924 \u092e\u0947\u0902 \u092c\u094d\u0930\u0939\u094d\u092e\u0917\u0941\u092a\u094d\u0924 \u0938\u0924\u094d\u092f\u093e\u092a\u0928<\/div>\n\u0906\u092f\u0924 \u0915\u0947 \u0935\u093f\u0937\u092f \u092e\u0947\u0902 \u092c\u094d\u0930\u0939\u094d\u092e\u0917\u0941\u092a\u094d\u0924 \u0915\u0947 \u0938\u0942\u0924\u094d\u0930 \u0915\u094b \u0938\u0924\u094d\u092f\u093e\u092a\u093f\u0924 \u0915\u0940\u091c\u093f\u090f\u0964 \u0938\u092d\u0940 \u0906\u092f\u0924 \u091a\u0915\u094d\u0930\u0940\u092f \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u0905\u0924\u0903 \u092c\u094d\u0930\u0939\u094d\u092e\u0917\u0941\u092a\u094d\u0924 \u0915\u093e \u0938\u0942\u0924\u094d\u0930 \u0932\u093e\u0917\u0942 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964 \u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0906\u092f\u0924 \u0915\u0940 \u092d\u0941\u091c\u093e\u090f\u0901 a \u0914\u0930 b \u0939\u0948\u0902 \u0924\u092c \u0938\u0942\u0924\u094d\u0930 s=(2a+2b)\/2=a+b \u0939\u094b\u0917\u093e,<br>\n\u0905\u0924\u0903 \u0938\u0942\u0924\u094d\u0930 \u0905\u0928\u0941\u0938\u093e\u0930 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = \u221a[(a+b-a)(a+b-b)(a+b-a)(a+b-b)] = \u221a[b\u00d7a\u00d7b\u00d7a] = ab, \u091c\u094b \u0915\u093f \u0938\u0924\u094d\u092f \u0939\u0948\u0964<br><br>\n\n<div style=\"background:#e3f2fd;border-left:4px solid #1565c0;padding:8px 10px;font-weight:bold;\">\u0909\u0926\u093e\u0939\u0930\u0923 7 \u2014 \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0938\u092e\u0932\u0902\u092c<\/div>\n\u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0938\u092e\u0932\u0902\u092c \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0935\u093f\u0937\u092f \u092e\u0947\u0902 \u092c\u094d\u0930\u0939\u094d\u092e\u0917\u0941\u092a\u094d\u0924 \u0915\u0947 \u0938\u0942\u0924\u094d\u0930 \u0915\u093e \u0938\u0924\u094d\u092f\u093e\u092a\u0928 \u0915\u0940\u091c\u093f\u090f\u0964 \u0938\u092d\u0940 \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0938\u092e\u0932\u0902\u092c \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u091a\u0915\u094d\u0930\u0940\u092f \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964<br>\n\u0906\u0915\u0943\u0924\u093f \u0915\u093e \u092a\u0930\u093f\u092e\u093e\u092a 2a+2b+2c \u0939\u0948 \u0924\u094b s=a+b+c \u0939\u0948\u0964 \u0905\u0924\u0903 \u0938\u0942\u0924\u094d\u0930 \u0905\u0928\u0941\u0938\u093e\u0930 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u221a[(s-2a)(s-2b)(s-c)(s-c)] \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964<br>\n\u091a\u0942\u0901\u0915\u093f s-2a=c+b-a, s-2b=c+a-b, s-c=a+b, \u0909\u092a\u0930\u094b\u0915\u094d\u0924 \u0938\u0942\u0924\u094d\u0930 \u0938\u0930\u0932 \u0939\u094b\u0915\u0930 \u221a[(a+b)(c+b-a)(c+a-b)(a+b)]? \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902 (a+b)\u221a[c\u00b2-(b-a)\u00b2] \u0939\u094b\u0924\u093e \u0939\u0948\u0964<br>\n\u092f\u0926\u093f \u0939\u092e \u0906\u0927\u093e\u0930 CD \u092a\u0930 B \u0938\u0947 \u0932\u0902\u092c \u092c\u0928\u093e\u090f \u0924\u094b \u0909\u0938\u0915\u0940 \u0932\u0902\u092c\u093e\u0908 \u092c\u094c\u0927\u093e\u092f\u0928-\u092a\u093e\u0907\u0925\u093e\u0917\u094b\u0930\u0938 \u0938\u0947 \u221a[c\u00b2-(b-a)\u00b2] \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u0905\u0924\u0903 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 (a+b)h \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0920\u0940\u0915 \u092f\u0939\u0940 \u0938\u0942\u0924\u094d\u0930 \u0939\u092e\u0947\u0902 \u0924\u092c \u092d\u0940 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u092c \u0939\u092e \u0938\u094d\u092e\u0930\u0923 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0938\u092e\u0932\u0902\u092c \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0938\u092e\u093e\u0902\u0924\u0930 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u092f\u094b\u0917 \u0915\u093e \u0906\u0927\u093e \u0914\u0930 \u0909\u0928\u0915\u0947 \u092e\u0927\u094d\u092f \u0915\u0940 \u0926\u0942\u0930\u0940 \u0915\u0947 \u0917\u0941\u0923\u0928\u092b\u0932 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<br><br>\n\n<div style=\"background:#fff3e0;border-left:4px solid #ff6f00;padding:8px 10px;font-weight:bold;\">\u0917\u0923\u093f\u0924 \u092e\u0947\u0902 \u0935\u093f\u0936\u0947\u0937 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u093e\u0901 \u0914\u0930 \u0935\u094d\u092f\u093e\u092a\u0915\u0940\u0915\u0930\u0923<\/div>\n\u2018\u0935\u093f\u0936\u0947\u0937 \u0938\u094d\u0925\u093f\u0924\u093f\u2019 \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e \u092a\u094d\u0930\u093e\u092f\u0903 \u0909\u091a\u094d\u091a \u0917\u0923\u093f\u0924 \u092e\u0947\u0902 \u0926\u0947\u0916\u0928\u0947 \u0915\u094b \u092e\u093f\u0932\u0924\u0940 \u0939\u0948\u0964 \u090f\u0915 \u0935\u093f\u0936\u0947\u0937 \u0938\u094d\u0925\u093f\u0924\u093f \u0924\u092c \u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u0939\u094b\u0924\u0940 \u0939\u0948 \u091c\u092c \u0939\u092e \u0915\u094b\u0908 \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924 \u0936\u0930\u094d\u0924 \u0938\u092e\u094d\u092e\u093f\u0932\u093f\u0924 \u0915\u0930\u0928\u0947 \u092a\u0930 \u0935\u094d\u092f\u093e\u092a\u0915 \u092a\u0930\u093f\u0923\u093e\u092e \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<br>\n<b>\u0909\u0926\u093e\u0939\u0930\u0923:<\/b> \u0935\u0930\u094d\u0917, \u0906\u092f\u0924 \u0915\u093e \u090f\u0915 \u0935\u093f\u0936\u0947\u0937 \u0930\u0942\u092a \u0939\u0948\u0964 \u0905\u0924\u0903 \u0935\u0930\u094d\u0917 \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u093e \u0938\u0942\u0924\u094d\u0930 (A=a\u00b2), \u0906\u092f\u0924 \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u0947 \u0938\u0942\u0924\u094d\u0930 (A=ab) \u0915\u0940 \u0935\u093f\u0936\u0947\u0937 \u0938\u094d\u0925\u093f\u0924\u093f \u0939\u0948, \u092f\u0926\u093f b=a \u0939\u0948\u0964<br>\n\u0907\u0938\u0940 \u092a\u094d\u0930\u0915\u093e\u0930 (a+b)\u00b2=a\u00b2+b\u00b2+2ab, (a+b+c)\u00b2=a\u00b2+b\u00b2+c\u00b2+2ab+2bc+2ca \u0915\u0940 \u0935\u093f\u0936\u0947\u0937 \u0938\u094d\u0925\u093f\u0924\u093f \u0939\u0948 (\u0926\u0942\u0938\u0930\u0940 \u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e \u092e\u0947\u0902 c=0 \u0930\u0916\u0947\u0902)\u0964<br><br>\n\n<div style=\"background:#ffebee;border-left:4px solid #d32f2f;padding:8px 10px;font-weight:bold;\">\u092c\u094d\u0930\u0939\u094d\u092e\u0917\u0941\u092a\u094d\u0924 \u0915\u093e \u0938\u0942\u0924\u094d\u0930 \u0939\u0940\u0930\u094b\u0928 \u0915\u0947 \u0938\u0942\u0924\u094d\u0930 \u0915\u093e \u0935\u094d\u092f\u093e\u092a\u0915\u0940\u0915\u0930\u0923<\/div>\n\u0939\u0940\u0930\u094b\u0928 \u0914\u0930 \u092c\u094d\u0930\u0939\u094d\u092e\u0917\u0941\u092a\u094d\u0924 \u0915\u0947 \u0938\u0942\u0924\u094d\u0930 \u092e\u0947\u0902 \u0926\u093f\u0916\u0928\u0947 \u0935\u093e\u0932\u0940 \u0938\u092e\u093e\u0928\u0924\u093e \u092e\u093e\u0924\u094d\u0930 \u0915\u094b\u0908 \u0938\u0902\u092f\u094b\u0917 \u0928\u0939\u0940\u0902 \u0939\u0948\u0964 \u0915\u0948\u0938\u0947? \u092c\u094d\u0930\u0939\u094d\u092e\u0917\u0941\u092a\u094d\u0924 \u0915\u093e \u0938\u0942\u0924\u094d\u0930, \u0939\u0940\u0930\u094b\u0928 \u0915\u0947 \u0938\u0942\u0924\u094d\u0930 \u0915\u093e \u0935\u094d\u092f\u093e\u092a\u0915\u0940\u0915\u0930\u0923 \u0939\u0948 \u0905\u0930\u094d\u0925\u093e\u0924 \u0939\u092e \u0939\u0940\u0930\u094b\u0928 \u0915\u0947 \u0938\u0942\u0924\u094d\u0930 \u0915\u094b \u092c\u094d\u0930\u0939\u094d\u092e\u0917\u0941\u092a\u094d\u0924 \u0915\u0947 \u0938\u0942\u0924\u094d\u0930 \u0915\u093e \u090f\u0915 \u0935\u093f\u0936\u0947\u0937 \u0930\u0942\u092a \u092e\u093e\u0928 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<br>\n\u092d\u0941\u091c\u093e a,b,c \u0935\u093e\u0932\u0947 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u094b \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c ABCD \u0915\u0940 \u0935\u093f\u0936\u0947\u0937 \u0938\u094d\u0925\u093f\u0924\u093f \u092e\u093e\u0928\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u092e\u0947\u0902 \u091a\u094c\u0925\u0940 \u092d\u0941\u091c\u093e \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 \u0936\u0942\u0928\u094d\u092f (d=0) \u0939\u0948\u0964 \u0905\u0924\u0903 AB=a, BC=b, CD=c \u0939\u0948\u0964 \u0907\u0938\u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u0948 \u0915\u093f \u0936\u0940\u0930\u094d\u0937 A \u0914\u0930 D \u0938\u0902\u092a\u093e\u0924\u0940 \u0939\u0948\u0902\u0964<br>\n\u091a\u0942\u0901\u0915\u093f \u0915\u094b\u0908 \u092d\u0940 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u091a\u0915\u094d\u0930\u0940\u092f \u0939\u094b\u0924\u093e \u0939\u0948, \u092f\u0939 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u092d\u0940 \u091a\u0915\u094d\u0930\u0940\u092f \u0939\u0948\u0964 \u0905\u0924\u0903 \u092c\u094d\u0930\u0939\u094d\u092e\u0917\u0941\u092a\u094d\u0924 \u0915\u093e \u0938\u0942\u0924\u094d\u0930 \u0907\u0938 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u092a\u0930 \u092d\u0940 \u0932\u093e\u0917\u0942 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964<br>\ns=(a+b+c+0)\/2=(a+b+c)\/2 \u091c\u094b \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0905\u0930\u094d\u0926\u094d\u0927-\u092a\u0930\u093f\u092e\u093e\u092a \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u0948\u0964 \u0905\u092c \u092c\u094d\u0930\u0939\u094d\u092e\u0917\u0941\u092a\u094d\u0924 \u0905\u0928\u0941\u0938\u093e\u0930<br>\n<div style=\"background:#fff9c4;border:2px solid #fbc02d;padding:8px;border-radius:8px;text-align:center;font-weight:bold;\">\n\u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = \u221a[(s-a)(s-b)(s-c)(s-0)] = \u221a[s(s-a)(s-b)(s-c)] \u0915\u094d\u092f\u094b\u0902\u0915\u093f s-d=s<br>\n\u092f\u0939\u0940 \u0939\u0948 \u0939\u0940\u0930\u094b\u0928 \u0938\u0942\u0924\u094d\u0930!\n<\/div>\n<\/div><\/div>\n\n<div id=\"c142-5\" style=\"display:none;\"><div style=\"background:#ff6f00;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe0 \u092d\u093e\u0917 5\/5 - 6.9 \u0906\u092f\u0924 \u0915\u094b \u0935\u0930\u094d\u0917 \u092c\u0928\u093e\u0928\u093e - \u092a\u0947\u091c 141-142<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:1.9;height:540px;overflow-y:auto;\">\n\n<div style=\"background:#e3f2fd;border-left:4px solid #1565c0;padding:8px 10px;font-weight:bold;\">6.9 \u0906\u092f\u0924 \u0915\u094b \u0935\u0930\u094d\u0917 \u092c\u0928\u093e\u0928\u093e<\/div>\n\u092a\u094d\u0930\u093e\u091a\u0940\u0928 \u0915\u093e\u0932 \u092e\u0947\u0902 \u2018\u0915\u093f\u0938\u0940 \u0906\u0915\u0943\u0924\u093f \u0915\u094b \u0935\u0930\u094d\u0917\u2019 \u0915\u0930\u0928\u0947 \u0915\u093e \u0905\u0930\u094d\u0925 \u0925\u093e, \u0909\u0938 \u2018\u0906\u0915\u0943\u0924\u093f \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u092e\u0947\u0902 \u0938\u092e\u093e\u0928 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0935\u093e\u0932\u0940 \u090f\u0915 \u0935\u0930\u094d\u0917\u093e\u0915\u093e\u0930 \u0906\u0915\u0943\u0924\u093f \u092c\u0928\u093e\u0928\u093e\u2019\u0964 \u0906\u0915\u0943\u0924\u093f \u0906\u092f\u0924, \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u092f\u093e \u0935\u0943\u0924\u094d\u0924 \u0939\u094b \u0938\u0915\u0924\u0940 \u0925\u0940\u0964 \u0939\u092e \u092f\u0939\u093e\u0901 \u092a\u0930 \u0926\u0947\u0916\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0915\u0948\u0938\u0947 \u092a\u094d\u0930\u093e\u091a\u0940\u0928 \u092d\u093e\u0930\u0924\u0940\u092f \u0917\u0923\u093f\u0924\u091c\u094d\u091e \u092c\u094c\u0927\u093e\u092f\u0928 \u0928\u0947 \u090f\u0915 \u0906\u092f\u0924 \u0915\u094b \u0935\u0930\u094d\u0917\u093e\u0915\u093e\u0930 \u092c\u0928\u093e\u092f\u093e\u0964<br><br>\n\n\u0909\u0928\u0915\u0947 \u0936\u0941\u0932\u094d\u092c\u0938\u0942\u0924\u094d\u0930 (800 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u0902\u0935\u0924\u092a\u0942\u0930\u094d\u0935) \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u092f\u0939 \u0930\u091a\u0928\u093e \u0926\u0930\u094d\u0936\u093e\u0924\u0940 \u0939\u0948 \u0915\u093f a \u0907\u0915\u093e\u0908 \u0914\u0930 b \u0907\u0915\u093e\u0908 \u092d\u0941\u091c\u093e\u0913\u0902 \u0935\u093e\u0932\u0947 \u0906\u092f\u0924 \u0915\u094b \u0935\u0930\u094d\u0917\u093e\u0915\u093e\u0930 \u0915\u0948\u0938\u0947 \u092c\u0928\u093e\u092f\u093e \u091c\u093e\u090f \u091c\u092c\u0915\u093f (a>b) \u0939\u0948\u0964 \u0907\u0938\u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u0948 \u0915\u093f \u0939\u092e\u0947\u0902 \u090f\u0915 \u0935\u0930\u094d\u0917\u093e\u0915\u093e\u0930 \u0906\u0915\u0943\u0924\u093f \u092c\u0928\u093e\u0928\u0940 \u0939\u094b\u0917\u0940, \u091c\u093f\u0938\u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 ab \u0935\u0930\u094d\u0917 \u0907\u0915\u093e\u0908 \u0939\u094b\u0917\u093e\u0964 \u092f\u0939\u093e\u0901 \u092c\u094c\u0927\u093e\u092f\u0928 \u0915\u0940 \u0930\u091a\u0928\u093e \u0915\u093e \u090f\u0915 \u0938\u0930\u0932\u0940\u0915\u0943\u0924 \u0930\u0942\u092a \u0926\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948 (\u091a\u093f\u0924\u094d\u0930 6.30)\u2014<br><br>\n\n<b>\u0930\u091a\u0928\u093e \u091a\u0930\u0923 - \u091a\u093f\u0924\u094d\u0930 6.30:<\/b><br>\n\u2022 \u0926\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948 \u0915\u093f \u090f\u0915 \u0906\u092f\u0924 ABCD \u091c\u093f\u0938\u092e\u0947\u0902 AD=a, AB=b \u091c\u0939\u093e\u0901 a>b \u0939\u0948\u0964<br>\n\u2022 AD \u092a\u0930 \u092c\u093f\u0902\u0926\u0941 E \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0940\u091c\u093f\u090f \u0915\u093f AE=AB \u0939\u094b\u0964<br>\n\u2022 ED \u0915\u0947 \u092e\u0927\u094d\u092f\u092c\u093f\u0902\u0926\u0941 F \u0915\u093e \u092a\u0924\u093e \u0932\u0917\u093e\u0907\u090f\u0964 AF=(AE+AD)\/2=(a+b)\/2<br>\n\u2022 \u0935\u0930\u094d\u0917 AFGH \u0916\u0940\u0902\u091a\u093f\u090f, \u091c\u093f\u0938\u0915\u0940 \u092d\u0941\u091c\u093e AF \u0939\u094b \u0914\u0930 \u0936\u0940\u0930\u094d\u0937 H, AB \u0915\u094b \u0906\u0917\u0947 \u092c\u0922\u093c\u093e\u0928\u0947 \u092a\u0930 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0964<br>\n\u2022 H \u0915\u094b \u0915\u0947\u0902\u0926\u094d\u0930 \u092e\u093e\u0928\u0915\u0930 \u091a\u093e\u092a AG \u0916\u0940\u0902\u091a\u093f\u090f\u0964 \u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0915\u093f \u091a\u093e\u092a AG \u092d\u0941\u091c\u093e BC \u0915\u094b K \u092a\u0930 \u0915\u093e\u091f\u0924\u0940 \u0939\u0948\u0964<br>\n\u2022 K \u0938\u0947 \u0939\u094b\u0915\u0930 AH \u0915\u0947 \u0938\u092e\u093e\u0902\u0924\u0930 \u090f\u0915 \u0930\u0947\u0916\u093e \u0916\u0940\u0902\u091a\u093f\u090f\u0964 \u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0915\u093f \u092f\u0939 \u0930\u0947\u0916\u093e GH \u0915\u094b P \u092a\u0930 \u0915\u093e\u091f\u0924\u0940 \u0939\u0948\u0964<br>\n\u2022 HP \u0915\u094b \u092d\u0941\u091c\u093e \u092e\u093e\u0928\u0915\u0930 \u0935\u0930\u094d\u0917 HPQS \u092c\u0928\u093e\u0907\u090f \u0924\u092c \u0935\u0930\u094d\u0917 HPQS \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0906\u092f\u0924 ABCD \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u094b\u0917\u093e\u0964<br><br>\n\n\u092f\u0939 \u0938\u092e\u091d\u0928\u0947 \u0915\u093e \u092a\u094d\u0930\u092f\u0924\u094d\u0928 \u0915\u0940\u091c\u093f\u090f \u0915\u093f \u092f\u0939 \u0935\u093f\u0927\u093f \u0915\u0948\u0938\u0947 \u0915\u093e\u092e \u0915\u0930\u0924\u0940 \u0939\u0948\u0964 \u0907\u0938\u0938\u0947 \u0906\u092a\u0915\u094b \u091c\u094d\u091e\u093e\u0924 \u0939\u094b\u0917\u093e \u0915\u093f \u092f\u0939 \u0938\u0942\u0924\u094d\u0930 (a+b)\/2\u00b2 - (a-b)\/2\u00b2 = ab \u0939\u0948\u0964<br><br>\n\n<div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:8px;border-radius:10px;text-align:center;font-weight:bold;\">\n*\u092f\u0939 \u0935\u093f\u0927\u093f \u0932\u093e\u092d\u0926\u093e\u092f\u0915 \u0915\u094d\u092f\u094b\u0902 \u0939\u0948?<br>\nAE=b \u0938\u0947 \u0939\u092e\u0947\u0902 AF=(a+b)\/2 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<br>\n\u0905\u0924\u0903 HG=HK=(a+b)\/2 \u0915\u094d\u092f\u094b\u0902\u0915\u093f HK \u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e \u0939\u0948\u0964<br>\n\u0926\u0942\u0938\u0930\u093e, BH=AH-AB=AF-AB=(a+b)\/2-b=(a-b)\/2 \u0939\u0948\u0964<br>\n\u0905\u092c \u0939\u092e \u0938\u092e\u0915\u094b\u0923 \u0924\u094d\u0930\u093f\u092d\u0941\u091c HKP \u092a\u0930 \u0935\u093f\u091a\u093e\u0930 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u092c\u094c\u0927\u093e\u092f\u0928-\u092a\u093e\u0907\u0925\u093e\u0917\u094b\u0930\u0938 \u092a\u094d\u0930\u092e\u0947\u092f \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947<br>\nHP\u00b2=HK\u00b2-BH\u00b2=(a+b)\u00b2\/4 - (a-b)\u00b2\/4 = ab<br>\n\u0907\u0938\u0932\u093f\u090f \u0935\u0930\u094d\u0917 HPQS \u0914\u0930 \u0906\u092f\u0924 ABCD \u0926\u094b\u0928\u094b\u0902 \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0938\u092e\u093e\u0928 \u0939\u0948\u0902\u0964\n<\/div>\n\n<div style=\"background:#e8f5e9;border-left:4px solid #2e7d32;padding:8px 10px;font-weight:bold;margin-top:10px;\">\u0938\u094b\u091a\u093f\u090f \u0914\u0930 \u0935\u093f\u091a\u093e\u0930 \u0915\u0940\u091c\u093f\u090f - \u092a\u0947\u091c 142<\/div>\n\u0915\u093f\u0938\u0940 \u0926\u093f\u090f \u0917\u090f \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0938\u0947 \u0935\u0930\u094d\u0917 \u092c\u0928\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0906\u092a \u0915\u093f\u0938 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0917\u0947? \u092f\u0939\u093e\u0901 \u092a\u0930 \u0906\u092a\u0915\u094b \u090f\u0915 \u0910\u0938\u093e \u0935\u0930\u094d\u0917 \u092c\u0928\u093e\u0928\u093e \u0939\u0948 \u091c\u093f\u0938\u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u093f\u0938\u0940 \u0926\u093f\u090f \u0917\u090f \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u094b\u0964 \u0927\u094d\u092f\u093e\u0928\u092a\u0942\u0930\u094d\u0935\u0915 \u0935\u093f\u091a\u093e\u0930 \u0915\u0940\u091c\u093f\u090f \u0915\u093f \u0906\u092a \u0907\u0938\u0947 \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902\u0917\u0947\u0964<br>\n<\/div><\/div>\n<\/div>\n\n<div style=\"background:#0a5c4b;padding:12px;display:flex;justify-content:space-between;align-items:center;\">\n<button type=\"button\" id=\"c142p\" style=\"background:#ffcc00;color:#000;border:3px solid #fff;border-radius:30px;padding:10px 22px;font-weight:bold;font-size:15px;cursor:pointer;min-width:100px;\">&larr; \u092a\u0940\u091b\u0947<\/button>\n<span id=\"c142i\" style=\"background:#fff;color:#0a5c4b;padding:8px 20px;border-radius:20px;font-size:15px;font-weight:bold;\">1 \/ 5<\/span>\n<button type=\"button\" id=\"c142n\" style=\"background:#00e676;color:#000;border:3px solid #fff;border-radius:30px;padding:10px 22px;font-weight:bold;font-size:15px;cursor:pointer;min-width:100px;\">\u0906\u0917\u0947 &rarr;<\/button>\n<\/div>\n<\/div>\n\n<script>\n(function(){\nvar c=1,t=5;\nfunction s(n){\nfor(var i=1;i<=t;i++){\nvar el=document.getElementById('c142-'+i);\nif(el)el.style.display=(i===n?'block':'none');\n}\ndocument.getElementById('c142i').textContent=n+' \/ '+t;\nc=n;\n}\ndocument.getElementById('c142n').onclick=function(){var n=c+1;if(n>t)n=1;s(n);};\ndocument.getElementById('c142p').onclick=function(){var n=c-1;if(n<1)n=t;s(n);};\n})();\n<\/script><\/div><\/div><\/div><\/div><div id=\"pg-965-4\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-965-4-0\"  class=\"panel-grid-cell\" ><div id=\"panel-965-4-0-0\" class=\"widget_text so-panel widget widget_custom_html panel-first-child panel-last-child\" data-index=\"4\" ><div class=\"textwidget custom-html-widget\"><div id=\"Q62-142-143-CORRECT\" style=\"max-width:860px;margin:12px auto;border:4px solid #0f5e4b;border-radius:14px;background:#e6f4f1;font-family:'Noto Sans Devanagari',Arial,sans-serif;overflow:hidden;\">\n<div style=\"background:#0a5c4b;padding:10px;text-align:center;\"><span style=\"background:#fff;color:#0a3d33;padding:7px 20px;border-radius:20px;font-weight:bold;font-size:13px;\">\u092a\u0947\u091c 142-143 - \u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 6.2 - Q1 \u0938\u0947 Q11 \u0936\u0941\u0926\u094d\u0927<\/span><\/div>\n\n<div style=\"padding:10px 12px;\">\n<div id=\"q62c-1\" style=\"display:block;\"><div style=\"background:#d32f2f;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udd34 \u092d\u093e\u0917 1\/4 - Q1-Q3<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:2;height:540px;overflow-y:auto;\">\n\n<div style=\"background:#fff9c4;border-left:4px solid #fbc02d;padding:8px 10px;font-weight:bold;\">\u0938\u094b\u091a\u093f\u090f \u0914\u0930 \u0935\u093f\u091a\u093e\u0930 \u0915\u0940\u091c\u093f\u090f - \u092a\u0947\u091c 142<\/div>\n<b>\u0915\u093f\u0938\u0940 \u0926\u093f\u090f \u0917\u090f \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0938\u0947 \u0935\u0930\u094d\u0917 \u092c\u0928\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0906\u092a \u0915\u093f\u0938 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0917\u0947? \u092f\u0939\u093e\u0901 \u092a\u0930 \u0906\u092a\u0915\u094b \u090f\u0915 \u0910\u0938\u093e \u0935\u0930\u094d\u0917 \u092c\u0928\u093e\u0928\u093e \u0939\u0948 \u091c\u093f\u0938\u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u093f\u0938\u0940 \u0926\u093f\u090f \u0917\u090f \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u094b\u0964 \u0927\u094d\u092f\u093e\u0928\u092a\u0942\u0930\u094d\u0935\u0915 \u0935\u093f\u091a\u093e\u0930 \u0915\u0940\u091c\u093f\u090f \u0915\u093f \u0906\u092a \u0907\u0938\u0947 \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902\u0917\u0947\u0964<\/b><br><br>\n\n<div style=\"background:#ffebee;border-left:4px solid #d32f2f;padding:8px 10px;font-weight:bold;\">\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 6.2<\/div>\n\n<b>Q1. \u0906\u0915\u0943\u0924\u093f 6.31 \u092e\u0947\u0902 \u0924\u094d\u0930\u093f\u092d\u0941\u091c ADE \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u2014<\/b><br>\n\u091a\u093f\u0924\u094d\u0930 6.31 \u092e\u0947\u0902 \u0906\u092f\u0924 ABCD, AD=10 \u0938\u0947\u092e\u0940, AE? DE? - \u091a\u093f\u0924\u094d\u0930 \u092e\u0947\u0902 E, AB \u092a\u0930? AD=10 \u0938\u0947\u092e\u0940, DE=8 \u0938\u0947\u092e\u0940 \u090a\u0901\u091a\u093e\u0908<br>\n\u0939\u0932: \u0924\u094d\u0930\u093f\u092d\u0941\u091c ADE \u0915\u093e \u0906\u0927\u093e\u0930 AD=10 \u0938\u0947\u092e\u0940, \u090a\u0901\u091a\u093e\u0908 = \u0906\u092f\u0924 \u0915\u0940 \u091a\u094c\u0921\u093c\u093e\u0908 =8 \u0938\u0947\u092e\u0940<br>\n\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=1\/2\u00d710\u00d78=40 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 40 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<\/span><br><br>\n\n<b>Q2. \u090f\u0915 \u0938\u092e\u0932\u0902\u092c \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u0938\u092e\u093e\u0902\u0924\u0930 \u092d\u0941\u091c\u093e\u090f\u0901 40 \u0938\u0947\u0902\u091f\u0940\u092e\u0940\u091f\u0930 \u0914\u0930 20 \u0938\u0947\u0902\u091f\u0940\u092e\u0940\u091f\u0930 \u0939\u0948\u0902\u0964 \u092f\u0926\u093f \u0907\u0938\u0915\u0940 \u0926\u094b\u0928\u094b\u0902 \u0905\u0938\u092e\u093e\u0902\u0924\u0930 \u092d\u0941\u091c\u093e\u090f\u0901 \u0938\u092e\u093e\u0928 \u0939\u094b\u0902 \u0914\u0930 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 26 \u0938\u0947\u0902\u091f\u0940\u092e\u0940\u091f\u0930 \u0939\u094b \u0924\u094b \u0938\u092e\u0932\u0902\u092c \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/b><br>\n\u0939\u0932: \u0938\u092e\u093e\u0902\u0924\u0930 a=40, b=20, \u0905\u0938\u092e\u093e\u0902\u0924\u0930 c=26<br>\n\u090a\u0901\u091a\u093e\u0908 h=\u221a[26\u00b2-((40-20)\/2)\u00b2]=\u221a[676-100]=\u221a576=24 \u0938\u0947\u092e\u0940<br>\n\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=1\/2(a+b)\u00d7h=1\/2\u00d760\u00d724=720 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 720 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<\/span><br><br>\n\n<b>Q3. \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f, \u091c\u093f\u0938\u0915\u0940 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 8 \u0938\u0947\u0902\u091f\u0940\u092e\u0940\u091f\u0930 \u0914\u0930 11 \u0938\u0947\u0902\u091f\u0940\u092e\u0940\u091f\u0930 \u0939\u0948 \u0924\u0925\u093e \u0909\u0938\u0915\u093e \u092a\u0930\u093f\u092e\u093e\u092a 32 \u0938\u0947\u0902\u091f\u0940\u092e\u0940\u091f\u0930 \u0939\u0948\u0964<\/b><br>\n\u0939\u0932: \u0924\u0940\u0938\u0930\u0940 \u092d\u0941\u091c\u093e=32-8-11=13 \u0938\u0947\u092e\u0940<br>\ns=16, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=\u221a[16\u00d78\u00d75\u00d73]=\u221a1920=8\u221a30=43.81 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 8\u221a30 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<\/span><br>\n\n<\/div><\/div>\n\n<div id=\"q62c-2\" style=\"display:none;\"><div style=\"background:#1565c0;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udd35 \u092d\u093e\u0917 2\/4 - Q4-Q6<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:2;height:540px;overflow-y:auto;\">\n\n<b>Q4. \u090f\u0915 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u093e\u0915\u093e\u0930 \u092d\u0942\u0916\u0902\u0921 \u0915\u0940 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u093e \u0905\u0928\u0941\u092a\u093e\u0924 3:5:7 \u0939\u0948 \u0914\u0930 \u0907\u0938\u0915\u093e \u092a\u0930\u093f\u092e\u093e\u092a 300 \u092e\u0940\u091f\u0930 \u0939\u0948\u0964 \u0907\u0938\u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/b><br>\n\u0939\u0932: \u092e\u093e\u0928\u094b \u092d\u0941\u091c\u093e\u090f\u0901 3x,5x,7x =>3x+5x+7x=300 =>15x=300 =>x=20<br>\n\u092d\u0941\u091c\u093e\u090f\u0901 60,100,140 \u092e\u0940\u091f\u0930<br>\ns=150, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=\u221a[150\u00d790\u00d750\u00d710]=\u221a[6750000]=1500\u221a3 \u0935\u0930\u094d\u0917 \u092e\u0940\u091f\u0930<br>\n\u22482598.07 \u0935\u0930\u094d\u0917 \u092e\u0940<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 1500\u221a3 \u0935\u0930\u094d\u0917 \u092e\u0940\u091f\u0930<\/span><br><br>\n\n<b>Q5. \u090f\u0915 \u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u090f\u0915 \u0935\u093f\u0915\u0930\u094d\u0923 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 \u0926\u0942\u0938\u0930\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 \u0938\u0947 \u0926\u094b\u0917\u0941\u0928\u0940 \u0939\u0948\u0964 \u092f\u0926\u093f \u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 128 \u0935\u0930\u094d\u0917 \u0938\u0947\u0902\u091f\u0940\u092e\u0940\u091f\u0930 \u0939\u0948 \u0924\u094b \u0907\u0938\u0915\u0947 \u091b\u094b\u091f\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/b><br>\n\u0939\u0932: \u092e\u093e\u0928\u094b \u091b\u094b\u091f\u093e \u0935\u093f\u0915\u0930\u094d\u0923 d1=d, \u092c\u0921\u093c\u093e d2=2d<br>\n\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=1\/2\u00d7d1\u00d7d2=1\/2\u00d7d\u00d72d=d\u00b2=128 =>d=\u221a128=8\u221a2=11.31 \u0938\u0947\u092e\u0940<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 \u091b\u094b\u091f\u093e \u0935\u093f\u0915\u0930\u094d\u0923 8\u221a2 \u0938\u0947\u092e\u0940<\/span><br><br>\n\n<b>Q6. ABCD \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948\u0964 P \u0914\u0930 Q \u092d\u0941\u091c\u093e AB \u092a\u0930 \u0938\u094d\u0925\u093f\u0924 \u0915\u094b\u0908 \u0926\u094b \u092c\u093f\u0902\u0926\u0941 \u0939\u0948\u0902 \u0924\u094b \u0394PCD \u0914\u0930 \u0394QCD \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/b><br>\n\u0939\u0932: \u0926\u094b\u0928\u094b\u0902 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0938\u092e\u093e\u0928 \u0906\u0927\u093e\u0930 CD \u0914\u0930 \u0938\u092e\u093e\u0928 \u090a\u0901\u091a\u093e\u0908 (AB \u0914\u0930 CD \u0915\u0947 \u092c\u0940\u091a \u0915\u0940 \u0926\u0942\u0930\u0940) \u092a\u0930 \u0939\u0948\u0902\u0964<br>\n\u0907\u0938\u0932\u093f\u090f \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932(\u0394PCD)=\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932(\u0394QCD)=1\/2\u00d7\u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c ABCD \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932<br>\n\u092f\u0926\u093f ABCD \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u091c\u094d\u091e\u093e\u0924 \u0939\u094b \u0924\u094b \u0935\u0939\u0940 \u0906\u0927\u093e \u0939\u094b\u0917\u093e\u0964 \u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 \u0915\u093f \u0926\u094b\u0928\u094b\u0902 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0938\u092e\u093e\u0928 \u0939\u0948\u0964<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 \u0926\u094b\u0928\u094b\u0902 \u0938\u092e\u093e\u0928, =1\/2 ABCD<\/span><br>\n\n<\/div><\/div>\n\n<div id=\"q62c-3\" style=\"display:none;\"><div style=\"background:#2e7d32;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe2 \u092d\u093e\u0917 3\/4 - Q7-Q9<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:1.9;height:540px;overflow-y:auto;\">\n\n<b>Q7. \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c PQRS \u0915\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 PR \u092a\u0930 \u0938\u094d\u0925\u093f\u0924 \u0915\u094b\u0908 O \u092c\u093f\u0902\u0926\u0941 \u0939\u0948\u0964 \u0938\u093f\u0926\u094d\u0927 \u0915\u0940\u091c\u093f\u090f \u0915\u093f PSO \u0914\u0930 PQO \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0938\u092e\u093e\u0928 \u0939\u0948\u0902\u0964<\/b><br>\n\u0939\u0932: \u0935\u093f\u0915\u0930\u094d\u0923 PR \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u094b \u0926\u094b \u092c\u0930\u093e\u092c\u0930 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0935\u093e\u0932\u0947 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u092e\u0947\u0902 \u092c\u093e\u0901\u091f\u0924\u093e \u0939\u0948\u0964<br>\n\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932(\u0394PSR)=\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932(\u0394PQR)=1\/2 PQRS<br>\n\u0907\u0938\u0940 \u092a\u094d\u0930\u0915\u093e\u0930 O, PR \u092a\u0930 \u0939\u0948 \u0924\u094b \u0394OSR \u0914\u0930 \u0394OQR? \u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 \u0394PSO=\u0394PQO<br>\n\u092a\u094d\u0930\u092e\u093e\u0923: \u0394PSR \u0914\u0930 \u0394PQR \u0938\u092e\u093e\u0928 \u0906\u0927\u093e\u0930 PR? \u0928\u0939\u0940\u0902, \u092a\u0930 \u090a\u0901\u091a\u093e\u0908 \u0938\u092e\u093e\u0928? \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902 \u0394POS \u0914\u0930 \u0394POQ \u0915\u0947 \u0906\u0927\u093e\u0930 \u0938\u092e\u093e\u0928? \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u0938\u0947 \u0939\u0940\u0930\u094b\u0928 \u0928\u0939\u0940\u0902, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0917\u0941\u0923\u0927\u0930\u094d\u092e \u0938\u0947 \u0938\u093f\u0926\u094d\u0927 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<br><br>\n\n<b>Q8. \u092f\u0926\u093f \u090f\u0915 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u092e\u0927\u094d\u092f\u092c\u093f\u0902\u0926\u0941 \u0915\u094b \u0915\u094d\u0930\u092e \u0938\u0947 \u091c\u094b\u0921\u093c\u093e \u091c\u093e\u090f \u0924\u094b \u0938\u093f\u0926\u094d\u0927 \u0915\u0940\u091c\u093f\u090f \u0915\u093f \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u092c\u0928\u0947 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0926\u093f\u090f \u0917\u090f \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u093e \u0906\u0927\u093e \u0939\u094b\u0917\u093e\u0964 (\u0906\u092a \u0938\u094b\u091a \u0930\u0939\u0947 \u0939\u094b\u0902\u0917\u0947 \u0915\u093f \u0915\u094d\u092f\u093e \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u092c\u0928\u093e \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u092e\u0947\u0936\u093e \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0940 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u092f\u0926\u093f \u0939\u093e\u0901, \u0924\u094b \u0915\u094d\u092f\u094b\u0902? \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928\u094b\u0902 \u0915\u0947 \u0909\u0924\u094d\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0935\u093e\u0932\u0947 \u0905\u0927\u094d\u092f\u093e\u092f \u092e\u0947\u0902 \u092e\u093f\u0932\u0947\u0902\u0917\u0947\u0964)<\/b><br>\n\u0939\u0932: \u092e\u0927\u094d\u092f\u092c\u093f\u0902\u0926\u0941 \u092a\u094d\u0930\u092e\u0947\u092f \u0938\u0947 \u092c\u0928\u0928\u0947 \u0935\u093e\u0932\u093e \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u094b\u0924\u093e \u0939\u0948 \u0914\u0930 \u0909\u0938\u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u092e\u0942\u0932 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u093e \u0906\u0927\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0935\u093f\u0915\u0930\u094d\u0923 \u0926\u094d\u0935\u093e\u0930\u093e \u0926\u094b \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u092c\u0928\u093e\u0915\u0930 \u0938\u093f\u0926\u094d\u0927 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<br><br>\n\n<b>Q9. \u0394ABC \u092e\u0947\u0902 BC \u0915\u093e \u092e\u0927\u094d\u092f\u092c\u093f\u0902\u0926\u0941 D \u0939\u0948 (\u091a\u093f\u0924\u094d\u0930 6.32)\u0964 \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e AD \u0916\u0940\u0902\u091a\u0940 \u0917\u0908 \u0939\u0948\u0964 \u092c\u093f\u0902\u0926\u0941 P \u0930\u0947\u0916\u093e\u0916\u0902\u0921 AD \u092a\u0930 \u0938\u094d\u0925\u093f\u0924 \u0915\u094b\u0908 \u092c\u093f\u0902\u0926\u0941 \u0939\u0948\u0964 \u0938\u093f\u0926\u094d\u0927 \u0915\u0940\u091c\u093f\u090f \u0915\u093f \u0394ABP \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0394ACP \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u0948\u0964<\/b><br>\n\u091a\u093f\u0924\u094d\u0930 6.32 - A \u0936\u0940\u0930\u094d\u0937, BC \u0906\u0927\u093e\u0930, D \u092e\u0927\u094d\u092f, P, AD \u092a\u0930<br>\n\u0939\u0932: \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e AD, \u0394ABC \u0915\u094b \u0926\u094b \u092c\u0930\u093e\u092c\u0930 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u092e\u0947\u0902 \u092c\u093e\u0901\u091f\u0924\u0940 \u0939\u0948\u0964 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 ABD=ACD<br>\n\u0907\u0938\u0940 \u092a\u094d\u0930\u0915\u093e\u0930 PBD=PCD<br>\n\u0918\u091f\u093e\u0928\u0947 \u092a\u0930 ABP=ACP<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0938\u093f\u0926\u094d\u0927<\/span><br>\n\n<\/div><\/div>\n\n<div id=\"q62c-4\" style=\"display:none;\"><div style=\"background:#6a1b9a;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe3 \u092d\u093e\u0917 4\/4 - Q10-Q11 \u0905\u0902\u0924\u093f\u092e<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:1.9;height:540px;overflow-y:auto;\">\n\n<b>Q10. \u090f\u0915 \u0935\u0930\u094d\u0917 ABCD \u0926\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948, \u092e\u093e\u0928\u093e \u0915\u093f P \u0907\u0938\u0915\u0947 \u0905\u0902\u0926\u0930 \u090f\u0915 \u092c\u093f\u0902\u0926\u0941 \u0939\u0948\u0964 PA, PB, PC \u0914\u0930 PD \u0915\u094b \u092e\u093f\u0932\u093e\u0907\u090f (\u091a\u093f\u0924\u094d\u0930 6.33)\u0964 \u0932\u093e\u0932 \u0930\u0902\u0917 \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930 (\u0394PAB \u0914\u0930 \u0394PCD) \u0924\u0925\u093e \u0939\u0930\u0947 \u0930\u0902\u0917 \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930 (\u0394PBC \u0914\u0930 \u0394PDA) \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932\u094b\u0902 \u0915\u093e \u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u094d\u092f\u093e \u0939\u094b\u0917\u093e?<\/b><br>\n\u0939\u0932: \u0935\u0930\u094d\u0917 \u092e\u0947\u0902 \u0915\u093f\u0938\u0940 \u0905\u0902\u0926\u0930 \u092c\u093f\u0902\u0926\u0941 P \u0938\u0947 \u092c\u0928\u0947 \u091a\u093e\u0930 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u092e\u0947\u0902<br>\n\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932(PAB)+\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932(PCD)=1\/2 \u0935\u0930\u094d\u0917 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932<br>\n\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932(PBC)+\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932(PDA)=1\/2 \u0935\u0930\u094d\u0917 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932<br>\n\u0907\u0938\u0932\u093f\u090f \u0932\u093e\u0932 \u0914\u0930 \u0939\u0930\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930 \u092c\u0930\u093e\u092c\u0930 \u0939\u0948\u0902, \u0905\u0928\u0941\u092a\u093e\u0924 1:1<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 \u0905\u0928\u0941\u092a\u093e\u0924 1:1<\/span><br><br>\n\n<b>Q11. \u0394ABC \u092e\u0947\u0902 D \u092d\u0941\u091c\u093e AB \u0915\u093e \u092e\u0927\u094d\u092f\u092c\u093f\u0902\u0926\u0941 \u0939\u0948\u0964 P \u092d\u0941\u091c\u093e BC \u092a\u0930 \u0938\u094d\u0925\u093f\u0924 \u0915\u094b\u0908 \u092c\u093f\u0902\u0926\u0941 \u0939\u0948 \u0914\u0930 Q \u092d\u0941\u091c\u093e AB \u092a\u0930 \u0938\u094d\u0925\u093f\u0924 \u090f\u0915 \u092c\u093f\u0902\u0926\u0941 \u0939\u0948, \u091c\u0939\u093e\u0901 CQ || PD \u0939\u0948\u0964 PQ \u0915\u094b \u092e\u093f\u0932\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948 (\u091a\u093f\u0924\u094d\u0930 6.34)\u0964 \u0938\u093f\u0926\u094d\u0927 \u0915\u0940\u091c\u093f\u090f \u0915\u093f \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 (\u0394BPQ)=1\/2 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 (\u0394ABC) \u0939\u0948\u0964<\/b><br>\n\u091a\u093f\u0924\u094d\u0930 6.34 - A \u0936\u0940\u0930\u094d\u0937, Q, D, B \u090f\u0915 \u0930\u0947\u0916\u093e \u092a\u0930, P, BC \u092a\u0930, CQ || PD<br>\n\u0939\u0932: D, AB \u0915\u093e \u092e\u0927\u094d\u092f\u092c\u093f\u0902\u0926\u0941 => \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 ADC? \u092e\u093e\u0927\u094d\u092f\u093f\u0915\u093e? CQ || PD => \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 PQD = CQD? \u0938\u092e\u093e\u0928 \u0906\u0927\u093e\u0930 PD, \u0938\u092e\u093e\u0928 \u0938\u092e\u093e\u0902\u0924\u0930 \u0930\u0947\u0916\u093e\u0913\u0902 \u0915\u0947 \u092c\u0940\u091a<br>\n\u092b\u093f\u0930 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 BPQ = 1\/2 ABC \u0938\u093f\u0926\u094d\u0927 \u0939\u094b\u0924\u093e \u0939\u0948 \u092e\u0927\u094d\u092f\u092c\u093f\u0902\u0926\u0941 \u0914\u0930 \u0938\u092e\u093e\u0902\u0924\u0930 \u0917\u0941\u0923\u0927\u0930\u094d\u092e \u0938\u0947\u0964<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0938\u093f\u0926\u094d\u0927<\/span><br>\n\n<div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:10px;border-radius:10px;text-align:center;margin-top:10px;font-weight:bold;\">\n\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 6.2 Q1-Q11 \u0936\u0941\u0926\u094d\u0927 \u0916\u0924\u094d\u092e \u2705<br>\nQ1 40 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<br>\nQ2 720 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<br>\nQ3 8\u221a30<br>\nQ4 1500\u221a3 \u0935\u0930\u094d\u0917 \u092e\u0940<br>\nQ5 \u091b\u094b\u091f\u093e \u0935\u093f\u0915\u0930\u094d\u0923 8\u221a2 \u0938\u0947\u092e\u0940<br>\nQ6 \u0926\u094b\u0928\u094b\u0902 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u092c\u0930\u093e\u092c\u0930 =1\/2 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c<br>\nQ10 \u0905\u0928\u0941\u092a\u093e\u0924 1:1\n<\/div>\n\n<\/div><\/div>\n<\/div>\n\n<div style=\"background:#0a5c4b;padding:12px;display:flex;justify-content:space-between;align-items:center;\">\n<button type=\"button\" id=\"q62cp\" style=\"background:#ffcc00;color:#000;border:3px solid #fff;border-radius:30px;padding:10px 22px;font-weight:bold;font-size:15px;cursor:pointer;min-width:100px;\">&larr; \u092a\u0940\u091b\u0947<\/button>\n<span id=\"q62ci\" style=\"background:#fff;color:#0a5c4b;padding:8px 20px;border-radius:20px;font-size:15px;font-weight:bold;\">1 \/ 4<\/span>\n<button type=\"button\" id=\"q62cn\" style=\"background:#00e676;color:#000;border:3px solid #fff;border-radius:30px;padding:10px 22px;font-weight:bold;font-size:15px;cursor:pointer;min-width:100px;\">\u0906\u0917\u0947 &rarr;<\/button>\n<\/div>\n<\/div>\n\n<script>\n(function(){\nvar c=1,t=4;\nfunction s(n){\nfor(var i=1;i<=t;i++){\nvar el=document.getElementById('q62c-'+i);\nif(el)el.style.display=(i===n?'block':'none');\n}\ndocument.getElementById('q62ci').textContent=n+' \/ '+t;\nc=n;\n}\ndocument.getElementById('q62cn').onclick=function(){var n=c+1;if(n>t)n=1;s(n);};\ndocument.getElementById('q62cp').onclick=function(){var n=c-1;if(n<1)n=t;s(n);};\n})();\n<\/script><\/div><\/div><\/div><\/div><div id=\"pg-965-5\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-965-5-0\"  class=\"panel-grid-cell\" ><div id=\"panel-965-5-0-0\" class=\"widget_text so-panel widget widget_custom_html panel-first-child panel-last-child\" data-index=\"5\" ><div class=\"textwidget custom-html-widget\"><div id=\"CH610-CIRCLE-AREA-CORRECT\" style=\"max-width:860px;margin:12px auto;border:4px solid #0f5e4b;border-radius:14px;background:#e6f4f1;font-family:'Noto Sans Devanagari',Arial,sans-serif;overflow:hidden;\">\n<div style=\"background:#0a5c4b;padding:10px;text-align:center;\"><span style=\"background:#fff;color:#0a3d33;padding:7px 20px;border-radius:20px;font-weight:bold;font-size:13px;\">6.10 \u0935\u0943\u0924\u094d\u0924 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 - \u092a\u0947\u091c 144-147 \u0936\u0941\u0926\u094d\u0927<\/span><\/div>\n\n<div style=\"padding:10px 12px;\">\n<div id=\"c610-1\" style=\"display:block;\"><div style=\"background:#d32f2f;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udd34 \u092d\u093e\u0917 1\/5 - 6.10 \u0935\u0943\u0924\u094d\u0924 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 - \u092a\u0930\u093f\u092d\u093e\u0937\u093e<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:2;height:540px;overflow-y:auto;\">\n\n<div style=\"background:#ffebee;border-left:4px solid #d32f2f;padding:8px 10px;font-weight:bold;\">6.10 \u0935\u0943\u0924\u094d\u0924 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932<\/div>\n\u0935\u0943\u0924\u094d\u0924 \u090f\u0915 \u0905\u0924\u094d\u092f\u0902\u0924 \u0938\u0930\u0932 \u0906\u0915\u0943\u0924\u093f \u0939\u0948\u0964 \u092f\u0926\u093f \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u090f\u0915 \u0930\u0938\u094d\u0938\u0940 \u0939\u0948 \u0914\u0930 \u0909\u0938\u0947 \u092c\u093e\u0901\u0927\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0916\u0942\u0901\u091f\u0940 \u0926\u0940 \u0917\u0908 \u0939\u0948 \u0924\u094b \u0907\u0938\u0947 \u092c\u0928\u093e\u0928\u093e \u0938\u0930\u0932 \u0939\u0948\u0964 \u092e\u0928\u0941\u0937\u094d\u092f \u0938\u0939\u0938\u094d\u0930\u094b\u0902 \u0935\u0930\u094d\u0937\u094b\u0902 \u0938\u0947 \u0905\u092a\u0928\u0940 \u092c\u0938\u094d\u0924\u093f\u092f\u094b\u0902, \u0907\u092e\u093e\u0930\u0924\u094b\u0902 \u0914\u0930 \u0914\u091c\u093e\u0930\u094b\u0902 \u092e\u0947\u0902 \u0935\u0943\u0924\u094d\u0924\u093e\u0915\u093e\u0930 \u0906\u0915\u0943\u0924\u093f \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0906 \u0930\u0939\u0947 \u0939\u0948\u0902\u0964<br><br>\n\n<div style=\"background:#fff9c4;border-left:4px solid #fbc02d;padding:8px 10px;font-weight:bold;\">\u0938\u094b\u091a\u093f\u090f \u0914\u0930 \u0935\u093f\u091a\u093e\u0930 \u0915\u0940\u091c\u093f\u090f<\/div>\n<b>\u092e\u0928\u0941\u0937\u094d\u092f \u0935\u0943\u0924\u094d\u0924\u093e\u0915\u093e\u0930 \u0906\u0915\u0943\u0924\u093f\u092f\u094b\u0902 \u0915\u093e \u0907\u0924\u0928\u093e \u0905\u0927\u093f\u0915 \u0909\u092a\u092f\u094b\u0917 \u0915\u094d\u092f\u094b\u0902 \u0915\u0930\u0924\u0947 \u0925\u0947? \u0915\u094d\u092f\u093e \u092f\u0939 \u0915\u0947\u0935\u0932 \u0935\u094d\u092f\u093e\u0935\u0939\u093e\u0930\u093f\u0915 \u0915\u093e\u0930\u0923\u094b\u0902 \u0938\u0947 \u0925\u093e \u0905\u0925\u0935\u093e \u0907\u0938\u0915\u0947 \u092a\u0940\u091b\u0947 \u0905\u0928\u094d\u092f \u0915\u093e\u0930\u0923 \u092d\u0940 \u0939\u094b \u0938\u0915\u0924\u0947 \u0925\u0947? \u092e\u0928\u0941\u0937\u094d\u092f \u0928\u0947 \u0935\u0943\u0924\u094d\u0924\u093e\u0915\u093e\u0930 \u0906\u0915\u0943\u0924\u093f\u092f\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0940 \u0935\u0938\u094d\u0924\u0941\u090f\u0901 \u0905\u0928\u094d\u0935\u0947\u0937\u093f\u0924 \u0915\u0940 \u0939\u0948\u0902?<\/b><br><br>\n\n\u0906\u0930\u0902\u092d\u093f\u0915 \u0915\u093e\u0932 \u092e\u0947\u0902 \u092e\u0928\u0941\u0937\u094d\u092f\u094b\u0902 \u0915\u0947 \u0938\u092e\u0915\u094d\u0937 \u0935\u0943\u0924\u094d\u0924 \u0926\u094d\u0935\u093e\u0930\u093e \u0918\u0947\u0930\u0947 \u0917\u090f \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 A \u0915\u094b \u091c\u093e\u0928\u0928\u0947 \u0915\u0940 \u091a\u0941\u0928\u094c\u0924\u0940 \u0925\u0940\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \u0909\u0928\u094d\u0939\u0947\u0902 \u092f\u0939 \u092a\u0924\u093e \u0932\u0917\u093e\u0928\u0947 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0930\u0939\u0940 \u0939\u094b\u0917\u0940 \u0915\u093f \u090f\u0915 \u092c\u0947\u0932\u0928\u093e\u0915\u093e\u0930 \u092e\u0940\u0928\u093e\u0930 (\u091c\u093f\u0938\u0915\u0947 \u0905\u0928\u0941\u092a\u094d\u0930\u0938\u094d\u0925 \u0915\u093e\u091f \u0935\u0943\u0924\u094d\u0924\u093e\u0915\u093e\u0930 \u0939\u094b) \u092e\u0947\u0902 \u0915\u093f\u0924\u0928\u093e \u0905\u0928\u093e\u091c \u0930\u0916\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u0905\u0925\u0935\u093e \u090f\u0915 \u0935\u0943\u0924\u094d\u0924\u093e\u0915\u093e\u0930 \u092c\u0917\u0940\u091a\u093e \u0905\u0925\u0935\u093e \u0935\u0943\u0924\u094d\u0924\u093e\u0915\u093e\u0930 \u092d\u0935\u0928 \u0915\u093f\u0924\u0928\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0918\u0947\u0930\u0924\u093e \u0939\u0948\u0964 \u0909\u0928\u094d\u0939\u0947\u0902 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0947 \u0906\u0901\u0915\u0921\u093c\u094b\u0902 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0905\u092a\u0928\u0947 \u0936\u0939\u0930\u094b\u0902 \u0915\u094b \u092c\u0928\u093e\u0928\u0947 \u0915\u0940 \u092f\u094b\u091c\u0928\u093e \u092c\u0928\u093e\u0928\u0947, \u0915\u0930 \u092a\u094d\u0930\u092c\u0902\u0927\u0928 \u0906\u0926\u093f \u0915\u0947 \u0932\u093f\u090f \u0939\u094b\u0924\u0940 \u0925\u0940\u0964<br><br>\n\n\u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0938\u092e\u093e\u091c\u094b\u0902 \u092e\u0947\u0902 \u092f\u0939 \u092c\u093e\u0924 \u092d\u0932\u0940-\u092d\u093e\u0901\u0924\u093f \u0938\u092e\u091d \u092e\u0947\u0902 \u0906\u0924\u0940 \u0925\u0940 \u0915\u093f \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 A, \u092a\u0930\u093f\u0927\u093f C \u0915\u0947 \u0935\u0930\u094d\u0917 \u0915\u0947 \u0938\u092e\u093e\u0928\u0941\u092a\u093e\u0924\u0940 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0906\u0907\u090f, \u0926\u0947\u0916\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0910\u0938\u093e \u0915\u094d\u092f\u094b\u0902 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<br>\n\n<div style=\"background:#e3f2fd;border-left:4px solid #1565c0;padding:8px 10px;font-weight:bold;margin-top:8px;\">\u092a\u094d\u0930\u092e\u093e\u0923 - P\u00b2:A \u0938\u094d\u0925\u093f\u0930<\/div>\n<b>\u2022 \u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0915\u093f \u0939\u092e\u0947\u0902 \u090f\u0915 \u0935\u0930\u094d\u0917 \u0926\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964 \u0907\u0938\u0915\u0940 \u092d\u0941\u091c\u093e a \u0939\u0948 \u0914\u0930 \u0907\u0938\u0915\u093e \u092a\u0930\u093f\u092e\u093e\u092a P=4a \u0939\u0948 \u0924\u0925\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 A=a\u00b2 \u0939\u0948, \u0905\u0924\u0903 \u0905\u0928\u0941\u092a\u093e\u0924 P\u00b2:A=(4a)\u00b2:a\u00b2=16a\u00b2:a\u00b2=16:1 \u0939\u0948\u0964 \u0907\u0938\u0932\u093f\u090f \u0938\u092d\u0940 \u0935\u0930\u094d\u0917\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0905\u0928\u0941\u092a\u093e\u0924 P\u00b2:A=16:1 \u0939\u0948\u0964 \u092f\u0939 \u0905\u0928\u0941\u092a\u093e\u0924 \u0935\u0930\u094d\u0917 \u0915\u0947 \u0906\u0915\u093e\u0930 \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0928\u0939\u0940\u0902 \u0915\u0930\u0924\u093e \u0939\u0948 \u2014 \u092f\u0939 \u0938\u092d\u0940 \u0935\u0930\u094d\u0917\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0938\u092e\u093e\u0928 \u0939\u0948\u0964<\/b><br><br>\n\n<b>\u2022 \u090f\u0915 \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u092a\u0930 \u0935\u093f\u091a\u093e\u0930 \u0915\u0940\u091c\u093f\u090f, \u091c\u093f\u0938\u0915\u0940 \u092d\u0941\u091c\u093e a \u0939\u0948\u0964 \u0907\u0938\u0915\u093e \u092a\u0930\u093f\u092e\u093e\u092a P=3a \u0914\u0930 \u0907\u0938\u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 A=\u221a3\/4 a\u00b2 \u0939\u0948\u0964 \u0905\u0924\u0903 P\u00b2:A=(3a)\u00b2 : \u221a3\/4 a\u00b2 =9 : \u221a3\/4 =36:\u221a3 =12\u221a3:1 \u0939\u094b\u0917\u093e\u0964 \u0905\u0924\u0903 \u0938\u092d\u0940 \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f P\u00b2:A \u0915\u093e \u0905\u0928\u0941\u092a\u093e\u0924 12\u221a3 \u0939\u0948\u0964 \u092f\u0939 \u0905\u0928\u0941\u092a\u093e\u0924 \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0906\u0915\u093e\u0930 \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0928\u0939\u0940\u0902 \u0915\u0930\u0924\u093e, \u0905\u092a\u093f\u0924\u0941 \u092f\u0939 \u0938\u092d\u0940 \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0938\u092e\u093e\u0928 \u0939\u0948\u0964<\/b><br><br>\n\n<b>\u2022 \u0907\u0938\u0940 \u092a\u094d\u0930\u0915\u093e\u0930, \u091c\u0948\u0938\u0947 \u0939\u092e \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0906\u0915\u0943\u0924\u093f\u092f\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u092a\u0930\u093f\u092e\u093e\u092a \u092c\u0926\u0932\u0924\u0947 \u0939\u0948\u0902, \u0905\u0928\u0941\u092a\u093e\u0924 P\u00b2:A \u0938\u094d\u0925\u093f\u0930 \u0930\u0939\u0924\u093e \u0939\u0948\u0964 \u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u093e \u092e\u093e\u0928 \u0915\u0947\u0935\u0932 \u0906\u0915\u0943\u0924\u093f \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0915\u0930\u0924\u093e \u0939\u0948, \u0909\u0938\u0915\u0947 \u092a\u0930\u093f\u092e\u093e\u0923 \u092a\u0930 \u0928\u0939\u0940\u0902 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/b><br><br>\n\n\u0907\u0938 \u0924\u0930\u094d\u0915 \u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930 \u0939\u092e \u0915\u0939 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0935\u0943\u0924\u094d\u0924 \u0915\u0947 \u0932\u093f\u090f \u092d\u0940 C=\u092a\u0930\u093f\u0927\u093f \u0914\u0930 A=\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0939\u0948 \u0924\u094b C\u00b2:A \u0915\u093e \u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u094b\u0908 \u0938\u094d\u0925\u093f\u0930 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964 \u092a\u0930\u0902\u0924\u0941 \u0915\u094d\u092f\u093e \u092f\u0939 \u0938\u094d\u0925\u093f\u0930 \u0905\u0930\u094d\u0925\u093e\u0924\u094d \u0938\u094d\u0925\u093f\u0930\u093e\u0902\u0915 \u0939\u0948?<br>\n\n<\/div><\/div>\n\n<div id=\"c610-2\" style=\"display:none;\"><div style=\"background:#1565c0;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udd35 \u092d\u093e\u0917 2\/5 - \u092c\u0947\u092c\u0940\u0932\u094b\u0928 \u092e\u093f\u0938\u094d\u0930 \u092c\u094c\u0927\u093e\u092f\u0928 \u0938\u0942\u0924\u094d\u0930<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:2;height:540px;overflow-y:auto;\">\n\n1500 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u0902\u0935\u0924 \u092a\u0942\u0930\u094d\u0935 \u0938\u0947 \u092d\u0940 \u092c\u0939\u0941\u0924 \u092a\u0939\u0932\u0947 \u0939\u0940 \u092c\u0947\u092c\u0940\u0932\u094b\u0928\u093f\u092f\u094b\u0902 \u0928\u0947 \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u092e\u093e\u092a \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u092f\u0939 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930 \u0932\u093f\u092f\u093e \u0925\u093e \u0915\u093f C\u00b2 \u0938\u094d\u0925\u093f\u0930\u093e\u0902\u0915 12 \u0915\u0947 \u0932\u0917\u092d\u0917 \u0938\u092e\u093e\u0928 \u0939\u0948 \u0905\u0930\u094d\u0925\u093e\u0924\u094d C\u00b2:A\u224812:1 \u0939\u0948\u0964 \u0905\u0924\u0903 \u0935\u0943\u0924\u094d\u0924 \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u093e \u0938\u0942\u0924\u094d\u0930 A\u2248C\u00b2\/12 \u0925\u093e\u0964<br>\n\n<div style=\"background:#fff9c4;border:2px solid #fbc02d;padding:8px;border-radius:8px;text-align:center;font-weight:bold;margin:6px 0;\">\n\u092c\u0947\u092c\u0940\u0932\u094b\u0928 \u0938\u0942\u0924\u094d\u0930: A \u2248 C\u00b2\/12\n<\/div>\n\n\u0932\u0917\u092d\u0917 1500 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u0902\u0935\u0924 \u092a\u0942\u0930\u094d\u0935 \u092a\u094d\u0930\u093e\u091a\u0940\u0928 \u092e\u093f\u0938\u094d\u0930\u0935\u093e\u0938\u093f\u092f\u094b\u0902 \u0928\u0947 \u090f\u0915 \u0914\u0930 \u0910\u0938\u093e \u0938\u0942\u0924\u094d\u0930 \u0924\u0948\u092f\u093e\u0930 \u0915\u093f\u092f\u093e, \u091c\u094b \u0909\u092a\u0930\u094d\u092f\u0941\u0915\u094d\u0924 \u0935\u0930\u094d\u0923\u093f\u0924 \u0938\u0942\u0924\u094d\u0930 \u0938\u0947 \u092e\u0947\u0932 \u0916\u093e\u0924\u093e \u0939\u0948 \u092a\u0930\u0902\u0924\u0941 \u0905\u0927\u093f\u0915 \u0909\u092a\u092f\u0941\u0915\u094d\u0924 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 A\u2248(8\/9 d)\u00b2 \u0939\u0948, \u091c\u0939\u093e\u0901 \u092a\u0930 d \u0935\u0943\u0924\u094d\u0924 \u0915\u093e \u0935\u094d\u092f\u093e\u0938 \u0939\u0948\u0964<br>\n\u091a\u0942\u0901\u0915\u093f d=2r \u0939\u0948, \u0907\u0938\u0947 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u092d\u0940 \u0932\u093f\u0916\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u2014<br>\nA\u2248(16\/9 r)\u00b2? \u0928\u0939\u0940\u0902, \u0938\u0939\u0940: A\u2248(8\/9\u00d72r)\u00b2=(16\/9 r)\u00b2? \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902 (8\/9 d)\u00b2=(8\/9\u00d72r)\u00b2=(16\/9 r)\u00b2=256\/81 r\u00b2<br>\n\u0905\u0930\u094d\u0925\u093e\u0924\u094d \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 A\u2248256\/81 r\u00b2<br>\n\n<div style=\"background:#e8f5e9;border:2px solid #2e7d32;padding:8px;border-radius:8px;text-align:center;font-weight:bold;\">\n\u092e\u093f\u0938\u094d\u0930 \u0938\u0942\u0924\u094d\u0930: A \u2248 (8\/9 d)\u00b2 = 256\/81 r\u00b2 \u22483.16 r\u00b2\n<\/div>\n\n\u0930\u094b\u091a\u0915 \u0924\u0925\u094d\u092f \u092f\u0939 \u0939\u0948 \u0915\u093f \u092f\u0939\u0940 \u0938\u0942\u0924\u094d\u0930 \u092c\u094c\u0927\u093e\u092f\u0928 \u0936\u0941\u0932\u094d\u092c\u0938\u0942\u0924\u094d\u0930 (800 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u0902\u0935\u0924 \u092a\u0942\u0930\u094d\u0935) \u092e\u0947\u0902 \u090f\u0915 \u0935\u0930\u094d\u0917 \u0915\u0947 \u0928\u093f\u0930\u094d\u092e\u093e\u0923 \u0915\u0940 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u0935\u093f\u0927\u093f \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u092a\u094d\u0930\u0915\u091f \u0939\u094b\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0932\u0917\u092d\u0917 \u090f\u0915 \u0935\u0943\u0924\u094d\u0924 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u0948\u0964<br><br>\n\n<div style=\"background:#e3f2fd;border-left:4px solid #1565c0;padding:8px 10px;font-weight:bold;\">\u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u092e\u0947\u0902 \u0909\u092a\u092f\u094b\u0917 \u092e\u0947\u0902 \u0939\u094b\u0928\u0947 \u0935\u093e\u0932\u093e \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u093f\u0924 \u0938\u0942\u0924\u094d\u0930<\/div>\n\u092a\u094d\u0930\u093e\u091a\u0940\u0928 \u092f\u0942\u0928\u093e\u0928\u0940 \u092f\u0939 \u092d\u0940 \u091c\u093e\u0928\u0924\u0947 \u0925\u0947 \u0915\u093f A\/r\u00b2 \u090f\u0915 \u0938\u094d\u0925\u093f\u0930 \u0905\u0930\u094d\u0925\u093e\u0924\u094d \u0938\u094d\u0925\u093f\u0930\u093e\u0902\u0915 \u0939\u0948 \u0915\u093f\u0902\u0924\u0941 \u0935\u0947 \u092f\u0939 \u0928\u0939\u0940\u0902 \u091c\u093e\u0928\u0924\u0947 \u0925\u0947 \u0915\u093f \u0938\u094d\u0925\u093f\u0930\u093e\u0902\u0915 \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0926\u094b \u0905\u0932\u0917-\u0905\u0932\u0917 \u0938\u092d\u094d\u092f\u0924\u093e\u0913\u0902 \u0928\u0947 \u0907\u0938 \u0938\u094d\u0925\u093f\u0930\u093e\u0902\u0915 \u0915\u093e \u092e\u093e\u0928 \u0932\u0917\u092d\u0917 256\/81 \u092e\u093e\u0928\u093e\u0964<br>\n\u0905\u0902\u0924\u0924\u0903 250 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u0902\u0935\u0924 \u092a\u0942\u0930\u094d\u0935 \u092e\u0947\u0902 \u0906\u0930\u094d\u0915\u093f\u092e\u093f\u0921\u0940\u091c \u0928\u0947 \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u0915\u093f \u0938\u094d\u0925\u093f\u0930\u093e\u0902\u0915 \u03c0 \u0939\u0948\u0964 (\u0905\u0930\u094d\u0925\u093e\u0924\u094d \u0935\u0939\u0940 \u0938\u094d\u0925\u093f\u0930\u093e\u0902\u0915 \u091c\u094b \u0935\u0943\u0924\u094d\u0924 \u0915\u0947 \u092a\u0930\u093f\u092e\u093e\u092a \u0915\u0947 \u0938\u0942\u0924\u094d\u0930 \u092e\u0947\u0902 \u0906\u0924\u093e \u0939\u0948), \u0905\u0924\u0903 A=\u03c0r\u00b2 \u0939\u0948\u0964 \u0909\u0928\u094d\u0939\u094b\u0902\u0928\u0947 \u0938\u0942\u0924\u094d\u0930 \u0915\u094b \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u093f\u092f\u093e \u0915\u093f \u201c\u0935\u0943\u0924\u094d\u0924 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u090f\u0915 \u0938\u092e\u0915\u094b\u0923 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u094b\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0915\u0940 \u092d\u0941\u091c\u093e\u090f\u0901 \u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e \u0914\u0930 \u092a\u0930\u093f\u0927\u093f \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902\u0964\u201d<br>\n\n<div style=\"background:#ffebee;border:2px solid #d32f2f;padding:10px;border-radius:10px;text-align:center;font-weight:bold;font-size:16px;margin:8px 0;\">\n\u0935\u0943\u0924\u094d\u0924 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = 1\/2 \u00d7 \u092a\u0930\u093f\u0927\u093f \u00d7 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e = 1\/2 \u00d72\u03c0r \u00d7r = \u03c0r\u00b2<br>\n\u0938\u0942\u0924\u094d\u0930: A = \u03c0r\u00b2\n<\/div>\n\n<\/div><\/div>\n\n<div id=\"c610-3\" style=\"display:none;\"><div style=\"background:#2e7d32;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe2 \u092d\u093e\u0917 3\/5 - \u0906\u0930\u094d\u0915\u093f\u092e\u093f\u0921\u0940\u091c \u092a\u094d\u0930\u092e\u093e\u0923 + \u0928\u0940\u0932\u0915\u0902\u0920 \u0926\u0943\u0936\u094d\u092f\u093e\u0902\u0915\u0928<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:2;height:540px;overflow-y:auto;\">\n\n\u0906\u0930\u094d\u0915\u093f\u092e\u093f\u0921\u0940\u091c \u0926\u094d\u0935\u093e\u0930\u093e \u092f\u0939 \u092a\u094d\u0930\u092e\u093e\u0923 \u092c\u0939\u0941\u0924 \u0939\u0940 \u092c\u0941\u0926\u094d\u0927\u093f\u092e\u0924\u094d\u0924\u093e\u092a\u0942\u0930\u094d\u0923 \u0922\u0902\u0917 \u0938\u0947 \u0926\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964 \u092f\u0939 \u0938\u092d\u0940 \u0928\u093f\u092f\u092e\u093f\u0924 \u092c\u0939\u0941\u092d\u0941\u091c\u094b\u0902 \u0915\u0947 \u090f\u0915 \u0938\u093e\u091d\u093e \u0917\u0941\u0923 \u092a\u0930 \u0906\u0927\u093e\u0930\u093f\u0924 \u0939\u0948\u2014 \u090f\u0915 \u0928\u093f\u092f\u092e\u093f\u0924 \u092c\u0939\u0941\u092d\u0941\u091c \u0926\u094d\u0935\u093e\u0930\u093e \u0918\u0947\u0930\u093e \u0917\u092f\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u092c\u0939\u0941\u092d\u0941\u091c \u0915\u0947 \u092d\u0940\u0924\u0930 \u0920\u0940\u0915 \u0938\u0947 \u092c\u0948\u0920 \u091c\u093e\u0928\u0947 \u0935\u093e\u0932\u0947 \u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u092a\u0930\u093f\u0927\u093f \u0915\u0947 \u0906\u0927\u0947 \u0914\u0930 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e \u0915\u0947 \u0917\u0941\u0923\u0928\u092b\u0932 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u094b\u0924\u093e \u0939\u0948 (\u091a\u093f\u0924\u094d\u0930 6.36)\u0964 (\u0907\u0938 \u0938\u0942\u0924\u094d\u0930 \u0915\u093e \u092a\u094d\u0930\u092e\u093e\u0923 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u0947 \u0938\u0942\u0924\u094d\u0930 \u0915\u0947 \u092a\u094d\u0930\u092e\u093e\u0923 \u0915\u093e \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u0939\u0948, \u091c\u093f\u0938\u0947 \u0909\u0938\u0915\u0947 \u0905\u0902\u0924\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e \u0915\u0947 \u0938\u0902\u0926\u0930\u094d\u092d \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964)<br><br>\n\n<div style=\"text-align:center;font-weight:bold;\">\u091a\u093f\u0924\u094d\u0930 6.36 \u2014 \u0928\u093f\u092f\u092e\u093f\u0924 \u092c\u0939\u0941\u092d\u0941\u091c \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 =1\/2 \u00d7 \u092c\u0939\u0941\u092d\u0941\u091c \u0915\u093e \u092a\u0930\u093f\u092e\u093e\u092a \u00d7 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e<\/div>\nO r \u0935\u093e\u0932\u093e \u091a\u093f\u0924\u094d\u0930 - \u092c\u0939\u0941\u092d\u0941\u091c \u0915\u0947 \u0905\u0902\u0926\u0930 \u0935\u0943\u0924\u094d\u0924, \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e r<br><br>\n\n\u0906\u0930\u094d\u0915\u093f\u092e\u093f\u0921\u0940\u091c \u0928\u0947 \u090f\u0915 \u2018\u0935\u093f\u091a\u093e\u0930 \u092a\u094d\u0930\u092f\u094b\u0917\u2019 \u0915\u093f\u092f\u093e, \u0909\u0928\u094d\u0939\u094b\u0902\u0928\u0947 \u0938\u094d\u0935\u092f\u0902 \u0938\u0947 \u092a\u0942\u091b\u093e \u0915\u093f \u092f\u0926\u093f \u0928\u093f\u092f\u092e\u093f\u0924 \u092c\u0939\u0941\u092d\u0941\u091c \u0915\u0940 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u092c\u0922\u093c\u0924\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948 \u0924\u094b \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948? \u0909\u0928\u094d\u0939\u094b\u0902\u0928\u0947 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0935\u093f\u0935\u0930\u0923\u094b\u0902 \u092a\u0930 \u0915\u093e\u0930\u094d\u092f \u0915\u093f\u092f\u093e \u0914\u0930 \u0907\u0938 \u092a\u0930\u093f\u0923\u093e\u092e \u092a\u0930 \u092a\u0939\u0941\u0901\u091a\u0947 \u0915\u093f A=\u03c0r\u00b2 \u0939\u0948\u0964<br><br>\n\n<div style=\"background:#fff9c4;border-left:4px solid #fbc02d;padding:8px 10px;font-weight:bold;\">\u0928\u0940\u0932\u0915\u0902\u0920 \u0938\u094b\u092e\u092f\u093e\u091c\u0940 \u0915\u093e \u0926\u0943\u0936\u094d\u092f\u093e\u0902\u0915\u0928 - 1500 \u0908\u0938\u094d\u0935\u0940<\/div>\n\u092f\u0939 \u0938\u0902\u092d\u0935\u0924\u0903 \u0938\u092c\u0938\u0947 \u0926\u0943\u0936\u094d\u092f\u092e\u093e\u0928 \u0914\u0930 \u0938\u0930\u0932\u0924\u093e \u0938\u0947 \u0938\u092e\u091d \u092e\u0947\u0902 \u0906\u0928\u0947 \u0935\u093e\u0932\u093e \u0935\u093f\u0935\u0930\u0923 \u0939\u0948 \u0915\u093f \u0915\u094d\u092f\u094b\u0902 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e r \u0935\u093e\u0932\u0947 \u0935\u0943\u0924\u094d\u0924 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u03c0r\u00b2 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0935\u0943\u0924\u094d\u0924 \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u093e \u092f\u0939 \u0938\u0941\u0902\u0926\u0930 \u0926\u0943\u0936\u094d\u092f\u093e\u0902\u0915\u0928 \u0938\u0930\u094d\u0935\u092a\u094d\u0930\u0925\u092e \u2018\u0928\u0940\u0932\u0915\u0902\u0920 \u0938\u094b\u092e\u092f\u093e\u091c\u0940\u2019 (\u0932\u0917\u092d\u0917 1500) \u0926\u094d\u0935\u093e\u0930\u093e \u0906\u0930\u094d\u092f\u092d\u091f\u0940\u092f \u092a\u0930 \u0915\u0940 \u0917\u0908 \u0905\u092a\u0928\u0940 \u091f\u093f\u092a\u094d\u092a\u0923\u0940 \u092e\u0947\u0902 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964<br>\n\n\u091a\u093f\u0924\u094d\u0930 6.37 \u2014 \u091f\u0941\u0915\u0921\u093c\u094b\u0902 \u0915\u094b \u092a\u0941\u0928\u0930\u094d\u0935\u094d\u092f\u0935\u0938\u094d\u0925\u093f\u0924 \u0915\u0930\u0915\u0947 \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u091c\u0948\u0938\u0940 \u0930\u091a\u0928\u093e \u0928\u093f\u0930\u094d\u092e\u093f\u0924 \u0915\u0940 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948<br>\n(\u0915) \u0935\u0943\u0924\u094d\u0924 \u0915\u094b \u0915\u0908 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921\u094b\u0902 \u092e\u0947\u0902 \u0915\u093e\u091f\u094b (\u0916) \u0909\u0928\u094d\u0939\u0947\u0902 \u090f\u0915-\u0926\u0942\u0938\u0930\u0947 \u0915\u0947 \u0909\u0932\u094d\u091f\u093e \u0932\u0917\u093e\u0913 \u0924\u094b \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u092c\u0928\u0924\u093e \u0939\u0948<br><br>\n\n\u091c\u0948\u0938\u0947-\u091c\u0948\u0938\u0947 \u091f\u0941\u0915\u0921\u093c\u0947 \u091b\u094b\u091f\u0947 \u0939\u094b\u0924\u0947 \u091c\u093e\u0924\u0947 \u0939\u0948\u0902 (\u091a\u093f\u0924\u094d\u0930 6.37(\u0916) \u092e\u0947\u0902), \u091a\u093e\u092a \u090f\u0915 \u0930\u0947\u0916\u093e \u0915\u0947 \u0914\u0930 \u092a\u093e\u0938 \u0939\u094b\u0924\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0902\u0964 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930, \u0906\u0917\u0947 \u091a\u0932\u0915\u0930 \u092f\u0939 \u0906\u0915\u0943\u0924\u093f \u090f\u0915 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0906\u0915\u093e\u0930 \u0915\u0940 \u092c\u0928 \u091c\u093e\u0924\u0940 \u0939\u0948, \u091c\u093f\u0938\u092e\u0947\u0902\u2014<br>\n<div style=\"background:#e8f5e9;border:2px solid #2e7d32;padding:8px;border-radius:8px;text-align:center;font-weight:bold;\">\n\u0906\u0927\u093e\u0930 = \u092a\u0930\u093f\u0927\u093f \u0915\u093e \u0906\u0927\u093e (\u0915\u094d\u092f\u094b\u0902?) = \u03c0r,<br>\n\u090a\u0901\u091a\u093e\u0908 = \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e r \u0939\u0948\u0964<br>\n<\/div>\n\u0907\u0938\u0938\u0947 \u092f\u0939 \u0924\u0930\u094d\u0915 \u0926\u0947\u0928\u0947 \u092e\u0947\u0902 \u0938\u0939\u093e\u092f\u0924\u093e \u092e\u093f\u0932\u0924\u0940 \u0939\u0948 \u0915\u093f \u0935\u0943\u0924\u094d\u0924 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932, \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<br>\n<div style=\"background:#ffebee;border:2px solid #d32f2f;padding:8px;border-radius:10px;text-align:center;font-weight:bold;font-size:16px;\">\n\u0935\u0943\u0924\u094d\u0924 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = \u0906\u0927\u093e\u0930 \u00d7 \u090a\u0901\u091a\u093e\u0908 = \u03c0r \u00d7 r = \u03c0r\u00b2\n<\/div>\n\n<\/div><\/div>\n\n<div id=\"c610-4\" style=\"display:none;\"><div style=\"background:#6a1b9a;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe3 \u092d\u093e\u0917 4\/5 - 6.10.1 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:2;height:540px;overflow-y:auto;\">\n\n<div style=\"background:#e3f2fd;border-left:4px solid #1565c0;padding:8px 10px;font-weight:bold;\">6.10.1 \u0935\u0943\u0924\u094d\u0924 \u0915\u0947 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932<\/div>\n\u0935\u0943\u0924\u094d\u0924 \u0915\u093e \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921 \u0935\u0939 \u0915\u094d\u0937\u0947\u0924\u094d\u0930 \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u094b \u090f\u0915 \u091a\u093e\u092a \u0914\u0930 \u0909\u0938\u0915\u0947 \u0936\u0940\u0930\u094d\u0937\u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u094b \u091c\u094b\u0921\u093c\u0928\u0947 \u0935\u093e\u0932\u0940 \u0926\u094b\u0928\u094b\u0902 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e\u0913\u0902 \u0938\u0947 \u092e\u093f\u0932\u0915\u0930 \u092c\u0928\u0924\u093e \u0939\u0948\u0964<br>\n\u0935\u0943\u0924\u094d\u0924 \u0915\u0947 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921 \u0915\u0947 \u092d\u0940\u0924\u0930 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0909\u0938\u0940 \u092a\u094d\u0930\u0915\u093e\u0930 \u091c\u094d\u091e\u093e\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u091c\u093f\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u092e\u0928\u0947 \u0935\u0943\u0924\u094d\u0924\u093e\u0915\u093e\u0930 \u091a\u093e\u092a \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940 \u0925\u0940\u0964 \u091a\u093f\u0924\u094d\u0930 6.39 \u0914\u0930 6.40 \u0915\u093e \u0905\u0935\u0932\u094b\u0915\u0928 \u0915\u0940\u091c\u093f\u090f\u0964<br><br>\n\n\u091a\u093f\u0924\u094d\u0930 6.38 \u2014 \u090f\u0915 \u0935\u0943\u0924\u094d\u0924 \u0915\u093e \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921 - O \u0915\u0947\u0902\u0926\u094d\u0930, \u03b8\u00b0 \u0915\u094b\u0923, A B \u091a\u093e\u092a<br><br>\n\n<div style=\"background:#fff9c4;border-left:4px solid #fbc02d;padding:8px 10px;font-weight:bold;\">\u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924\u093e\u0915\u093e\u0930 \u0921\u093f\u0938\u094d\u0915 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 - \u091a\u093f\u0924\u094d\u0930 6.39<\/div>\n\u0938\u092e\u0930\u0942\u092a\u0924\u093e \u0938\u0947 \u0939\u092e \u0926\u0947\u0916\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924\u093e\u0915\u093e\u0930 \u0921\u093f\u0938\u094d\u0915 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 180\/360=1\/2 \u0935\u0943\u0924\u094d\u0924 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0905\u0930\u094d\u0925\u093e\u0924\u094d 1\/2 \u03c0r\u00b2 \u0939\u0948\u0964<br>\n\u0907\u0938 \u092a\u0930\u093f\u0923\u093e\u092e \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0939\u092e \u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u092a\u0930\u093e\u0935\u0930\u094d\u0924\u0928 \u0938\u092e\u0930\u0942\u092a\u0924\u093e \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<br>\n\n<div style=\"background:#e8f5e9;border-left:4px solid #2e7d32;padding:8px 10px;font-weight:bold;margin-top:8px;\">\u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936 \u0935\u0943\u0924\u094d\u0924\u093e\u0915\u093e\u0930 \u0921\u093f\u0938\u094d\u0915 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 - \u091a\u093f\u0924\u094d\u0930 6.40<\/div>\n\u0938\u092e\u0930\u0942\u092a\u0924\u093e \u0938\u0947 \u0939\u092e \u0926\u0947\u0916\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u090f\u0915-\u091a\u094c\u0925\u093e\u0908 \u0905\u0930\u094d\u0925\u093e\u0924\u094d \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936 \u0935\u0943\u0924\u094d\u0924\u093e\u0915\u093e\u0930 \u0921\u093f\u0938\u094d\u0915 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 90\/360=1\/4 \u0935\u0943\u0924\u094d\u0924 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0905\u0930\u094d\u0925\u093e\u0924\u094d 1\/4 \u03c0r\u00b2 \u0939\u0948\u0964 \u0939\u092e \u092a\u0930\u093f\u0923\u093e\u092e \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u091a\u094c\u0925\u093e\u0908 \u0938\u092e\u0930\u0942\u092a\u0924\u093e \u0915\u093e \u092d\u0940 \u0909\u092a\u092f\u094b\u0917 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<br><br>\n\n\u0909\u092a\u0930\u094b\u0915\u094d\u0924 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0928\u0947 \u092a\u0930 \u0939\u092e\u0947\u0902 \u0935\u094d\u092f\u093e\u092a\u0915 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921 \u0915\u0947 \u0932\u093f\u090f \u0924\u094d\u0935\u0930\u093f\u0924 \u0935\u093e\u0902\u091b\u093f\u0924 \u0938\u0942\u0924\u094d\u0930 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948\u0964<br>\n\n<div style=\"background:#ffebee;border:3px solid #d32f2f;padding:10px;border-radius:10px;text-align:center;font-weight:bold;font-size:15px;\">\n\u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921 \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u093e \u0938\u0942\u0924\u094d\u0930 \u0909\u0938\u0915\u0947 \u0926\u094d\u0935\u093e\u0930\u093e \u0935\u0943\u0924\u094d\u0924 \u0915\u0947 \u0915\u0947\u0902\u0926\u094d\u0930 \u092a\u0930 \u092c\u0928\u093e\u090f \u0917\u090f \u0915\u094b\u0923 \u0915\u0947 \u0938\u0902\u0926\u0930\u094d\u092d \u092e\u0947\u0902\u2014<br>\n\u092f\u0926\u093f \u091a\u093e\u092a AB \u0939\u0948 \u0914\u0930 \u092f\u0939 \u0935\u0943\u0924\u094d\u0924 \u0915\u0947 \u0915\u0947\u0902\u0926\u094d\u0930 O \u092a\u0930 \u03b8\u00b0 \u0915\u093e \u0915\u094b\u0923 \u092c\u0928\u093e\u0924\u0940 \u0939\u0948 \u0924\u094b \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0939\u094b\u0917\u093e\u2014<br>\n<span style=\"font-size:18px;\">\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = \u03b8\u00b0\/360\u00b0 \u00d7 \u03c0r\u00b2<\/span><br>\n\u0927\u094d\u092f\u093e\u0928 \u0926\u0940\u091c\u093f\u090f \u0915\u093f \u0939\u092e\u0928\u0947 \u0907\u0928 \u0938\u0942\u0924\u094d\u0930\u094b\u0902 \u0915\u094b \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u0918\u0942\u0930\u094d\u0923\u0928 \u0938\u092e\u092e\u093f\u0924\u093f \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0948\u0938\u0947 \u0915\u093f\u092f\u093e \u0939\u0948\u0964\n<\/div>\n\n<\/div><\/div>\n\n<div id=\"c610-5\" style=\"display:none;\"><div style=\"background:#ff6f00;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe0 \u092d\u093e\u0917 5\/5 - \u0916\u0902\u0921 (Segment) + \u0938\u093e\u0930\u093e\u0902\u0936 \u0938\u0942\u0924\u094d\u0930<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:2;height:540px;overflow-y:auto;\">\n\n\u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921 \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924, \u0935\u0943\u0924\u094d\u0924\u093e\u0915\u093e\u0930 \u0915\u094d\u0937\u0947\u0924\u094d\u0930 \u0915\u093e \u090f\u0915 \u092d\u093e\u0917 \u0939\u094b\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0947 \u0916\u0902\u0921 \u0915\u0939\u0924\u0947 \u0939\u0948\u0902\u0964 \u0935\u0943\u0924\u094d\u0924 \u0915\u093e \u0916\u0902\u0921 \u0935\u0939 \u0915\u094d\u0937\u0947\u0924\u094d\u0930 \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u094b \u090f\u0915 \u091a\u093e\u092a \u0914\u0930 \u0909\u0938\u0915\u0947 \u0936\u0940\u0930\u094d\u0937\u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u094b \u092e\u093f\u0932\u093e\u0928\u0947 \u0935\u093e\u0932\u0940 \u091c\u0940\u0935\u093e \u0938\u0947 \u092e\u093f\u0932\u0915\u0930 \u092c\u0928\u0924\u093e \u0939\u0948\u0964<br><br>\n\n<div style=\"background:#e3f2fd;border:2px solid #1565c0;padding:10px;border-radius:10px;\">\n<b>\u092a\u0930\u093f\u092d\u093e\u0937\u093e\u090f\u0901 \u0936\u0941\u0926\u094d\u0927:<\/b><br>\n<b>1. \u0935\u0943\u0924\u094d\u0924 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932:<\/b> A=\u03c0r\u00b2<br>\n<b>2. \u092a\u0930\u093f\u0927\u093f:<\/b> C=2\u03c0r<br>\n<b>3. \u0938\u0902\u092c\u0902\u0927:<\/b> A=1\/2\u00d7C\u00d7r<br>\n<b>4. \u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932:<\/b> 1\/2 \u03c0r\u00b2<br>\n<b>5. \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932:<\/b> 1\/4 \u03c0r\u00b2<br>\n<b>6. \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932:<\/b> \u03b8\/360\u00d7\u03c0r\u00b2<br>\n<b>7. \u091a\u093e\u092a \u0915\u0940 \u0932\u0902\u092c\u093e\u0908:<\/b> \u03b8\/360\u00d72\u03c0r<br>\n<b>8. \u0916\u0902\u0921 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932:<\/b> \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921 - \u0924\u094d\u0930\u093f\u092d\u0941\u091c OAB<br>\n= \u03b8\/360\u00d7\u03c0r\u00b2 - 1\/2 r\u00b2 sin\u03b8\n<\/div>\n\n<div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:10px;border-radius:10px;text-align:center;margin-top:10px;font-weight:bold;\">\n\u2705 6.10 \u0938\u093e\u0930\u093e\u0902\u0936 - \u0938\u092d\u0940 \u0938\u0942\u0924\u094d\u0930 \u0936\u0941\u0926\u094d\u0927<br>\n\u092c\u0947\u092c\u0940\u0932\u094b\u0928 A\u2248C\u00b2\/12<br>\n\u092e\u093f\u0938\u094d\u0930 A\u2248(8\/9 d)\u00b2=256\/81 r\u00b2<br>\n\u0906\u0930\u094d\u0915\u093f\u092e\u093f\u0921\u0940\u091c A=\u03c0r\u00b2=1\/2\u00d7C\u00d7r<br>\n\u0928\u0940\u0932\u0915\u0902\u0920 - \u0935\u0943\u0924\u094d\u0924 \u0915\u094b \u0915\u093e\u091f\u0915\u0930 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0906\u0927\u093e\u0930 \u03c0r \u090a\u0901\u091a\u093e\u0908 r<br>\n\u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921 \u03b8\/360\u00d7\u03c0r\u00b2<br>\n\u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924 1\/2\u03c0r\u00b2, \u091a\u094c\u0925\u093e\u0908 1\/4\u03c0r\u00b2<br>\n\u0916\u0902\u0921 = \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921 - \u0924\u094d\u0930\u093f\u092d\u0941\u091c\n<\/div>\n\n<div style=\"background:#e8f5e9;border-left:4px solid #2e7d32;padding:8px 10px;font-weight:bold;margin-top:10px;\">\u0938\u094b\u091a\u093f\u090f \u0914\u0930 \u0935\u093f\u091a\u093e\u0930 \u0915\u0940\u091c\u093f\u090f \u0915\u093e \u0909\u0924\u094d\u0924\u0930<\/div>\n\u092e\u0928\u0941\u0937\u094d\u092f \u0935\u0943\u0924\u094d\u0924 \u0915\u093e \u0905\u0927\u093f\u0915 \u0909\u092a\u092f\u094b\u0917 \u0915\u094d\u092f\u094b\u0902? - \u0935\u094d\u092f\u093e\u0935\u0939\u093e\u0930\u093f\u0915: \u092a\u0939\u093f\u092f\u093e, \u0918\u0921\u093c\u093e, \u0915\u0941\u0906\u0901 \u0918\u0942\u092e\u0928\u0947 \u092e\u0947\u0902 \u0906\u0938\u093e\u0928, \u0938\u092e\u093e\u0928 \u0926\u0942\u0930\u0940, \u092e\u091c\u092c\u0942\u0924\u0940\u0964 \u0905\u0928\u094d\u092f \u0915\u093e\u0930\u0923: \u0938\u094c\u0902\u0926\u0930\u094d\u092f, \u0938\u092e\u0930\u0942\u092a\u0924\u093e, \u0905\u0928\u0902\u0924 \u0938\u092e\u092e\u093f\u0924\u093f, \u0927\u093e\u0930\u094d\u092e\u093f\u0915 \u092a\u094d\u0930\u0924\u0940\u0915 \u0938\u0942\u0930\u094d\u092f-\u091a\u0902\u0926\u094d\u0930\u0964<br>\n\u0935\u0938\u094d\u0924\u0941\u090f\u0901: \u092a\u0939\u093f\u092f\u093e, \u091a\u093e\u0915, \u0918\u0921\u093c\u093e, \u0925\u093e\u0932\u0940, \u0922\u094b\u0932, \u0938\u093f\u0915\u094d\u0915\u093e, \u091a\u0942\u0921\u093c\u0940\u0964<br>\n\n<\/div><\/div>\n<\/div>\n\n<div style=\"background:#0a5c4b;padding:12px;display:flex;justify-content:space-between;align-items:center;\">\n<button type=\"button\" id=\"c610p\" style=\"background:#ffcc00;color:#000;border:3px solid #fff;border-radius:30px;padding:10px 22px;font-weight:bold;font-size:15px;cursor:pointer;min-width:100px;\">&larr; \u092a\u0940\u091b\u0947<\/button>\n<span id=\"c610i\" style=\"background:#fff;color:#0a5c4b;padding:8px 20px;border-radius:20px;font-size:15px;font-weight:bold;\">1 \/ 5<\/span>\n<button type=\"button\" id=\"c610n\" style=\"background:#00e676;color:#000;border:3px solid #fff;border-radius:30px;padding:10px 22px;font-weight:bold;font-size:15px;cursor:pointer;min-width:100px;\">\u0906\u0917\u0947 &rarr;<\/button>\n<\/div>\n<\/div>\n\n<script>\n(function(){\nvar c=1,t=5;\nfunction s(n){\nfor(var i=1;i<=t;i++){\nvar el=document.getElementById('c610-'+i);\nif(el)el.style.display=(i===n?'block':'none');\n}\ndocument.getElementById('c610i').textContent=n+' \/ '+t;\nc=n;\n}\ndocument.getElementById('c610n').onclick=function(){var n=c+1;if(n>t)n=1;s(n);};\ndocument.getElementById('c610p').onclick=function(){var n=c-1;if(n<1)n=t;s(n);};\n})();\n<\/script><\/div><\/div><\/div><\/div><div id=\"pg-965-6\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-965-6-0\"  class=\"panel-grid-cell\" ><div id=\"panel-965-6-0-0\" class=\"widget_text so-panel widget widget_custom_html panel-first-child panel-last-child\" data-index=\"6\" ><div class=\"textwidget custom-html-widget\"><div id=\"Q63-148-FINAL\" style=\"max-width:860px;margin:12px auto;border:4px solid #0f5e4b;border-radius:14px;background:#e6f4f1;font-family:'Noto Sans Devanagari',Arial,sans-serif;overflow:hidden;\">\n<div style=\"background:#0a5c4b;padding:10px;text-align:center;\"><span style=\"background:#fff;color:#0a3d33;padding:7px 20px;border-radius:20px;font-weight:bold;font-size:13px;\">\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 6.3 - \u092a\u0947\u091c 148 - Q1-Q10 \u0936\u0941\u0926\u094d\u0927 \u0939\u0932<\/span><\/div>\n\n<div style=\"padding:10px 12px;\">\n<div id=\"q63-1\" style=\"display:block;\"><div style=\"background:#d32f2f;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udd34 \u092d\u093e\u0917 1\/5 - Q1-Q3<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:2;height:560px;overflow-y:auto;\">\n\n<div style=\"background:#fff9c4;border:2px solid #fbc02d;padding:6px;border-radius:8px;text-align:center;font-weight:bold;\">\u0915\u093f\u0938\u0940 \u0905\u0928\u094d\u092f \u0928\u093f\u0930\u094d\u0926\u0947\u0936 \u0915\u0940 \u0905\u0928\u0941\u092a\u0938\u094d\u0925\u093f\u0924\u093f \u092e\u0947\u0902, \u0938\u0928\u094d\u0928\u093f\u0915\u091f\u0928 \u03c0=22\/7 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0940\u091c\u093f\u090f\u0964<\/div>\n\n<b>Q1. \u092f\u0926\u093f \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921 \u0915\u093e \u0915\u094b\u0923 60\u00b0 \u0939\u0948 \u0924\u094b 7 \u0938\u0947\u092e\u0940 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e \u0935\u093e\u0932\u0947 \u0935\u0943\u0924\u094d\u0924 \u0915\u0947 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/b><br>\n\u0939\u0932: \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 =\u03b8\/360\u00d7\u03c0r\u00b2<br>\n=60\/360\u00d722\/7\u00d77\u00d77=1\/6\u00d7154=25.666 \u0938\u0947\u092e\u0940\u00b2=77\/3<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 25.67 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<\/span><br><br>\n\n<b>Q2. \u0909\u0938 \u0935\u0943\u0924\u094d\u0924 \u0915\u0947 \u090f\u0915 \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f, \u091c\u093f\u0938\u0915\u0940 \u092a\u0930\u093f\u0927\u093f 44 \u0938\u0947\u092e\u0940 \u0939\u0948\u0964<\/b><br>\n\u0939\u0932: \u092a\u0930\u093f\u0927\u093f 2\u03c0r=44 =>r=7 \u0938\u0947\u092e\u0940<br>\n\u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936=1\/4\u03c0r\u00b2=1\/4\u00d722\/7\u00d749=38.5 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 38.5 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<\/span><br><br>\n\n<b>Q3. \u090f\u0915 \u0918\u0921\u093c\u0940 \u0915\u0940 \u092e\u093f\u0928\u091f \u0915\u0940 \u0938\u0941\u0908 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 7 \u0938\u0947\u092e\u0940 \u0939\u0948\u0964 10 \u092e\u093f\u0928\u091f \u092e\u0947\u0902 \u0938\u0941\u0908 \u0926\u094d\u0935\u093e\u0930\u093e \u0924\u092f \u0915\u0940 \u0917\u0908 \u0926\u0942\u0930\u0940 \/ \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/b><br>\n\u0939\u0932: 60 \u092e\u093f\u0928\u091f=360\u00b0, 10 \u092e\u093f\u0928\u091f=60\u00b0<br>\n(i) \u0924\u092f \u0926\u0942\u0930\u0940 (\u091a\u093e\u092a)=\u03b8\/360\u00d72\u03c0r=60\/360\u00d72\u00d722\/7\u00d77=7.333 \u0938\u0947\u092e\u0940<br>\n(ii) \u0924\u092f \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=\u03b8\/360\u00d7\u03c0r\u00b2=60\/360\u00d722\/7\u00d749=25.666 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 \u091a\u093e\u092a 7.33 \u0938\u0947\u092e\u0940, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 25.67 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<\/span><br>\n\n<\/div><\/div>\n\n<div id=\"q63-2\" style=\"display:none;\"><div style=\"background:#1565c0;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udd35 \u092d\u093e\u0917 2\/5 - Q4-Q5<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:1.9;height:560px;overflow-y:auto;\">\n\n<b>Q4. 10 \u0938\u0947\u092e\u0940 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e \u0935\u093e\u0932\u0947 \u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u090f\u0915 \u091c\u0940\u0935\u093e \u0915\u0947\u0902\u0926\u094d\u0930 \u092a\u0930 90\u00b0 \u0915\u093e \u0915\u094b\u0923 \u092c\u0928\u093e\u0924\u0940 \u0939\u0948\u0964 \u0938\u0902\u0917\u0924 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u2014 (i) \u0932\u0918\u0941 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921 (\u091c\u094b \u092e\u0927\u094d\u092f\u092c\u093f\u0902\u0926\u0941 \u092a\u0930 90\u00b0 \u0915\u093e \u0915\u094b\u0923 \u092c\u0928\u093e\u0924\u093e \u0939\u0948) (ii) \u0926\u0940\u0930\u094d\u0918 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921 (\u091c\u094b \u092e\u0927\u094d\u092f\u092c\u093f\u0902\u0926\u0941 \u092a\u0930 270\u00b0 \u0915\u093e \u0915\u094b\u0923 \u092c\u0928\u093e\u0924\u093e \u0939\u0948)\u0964 (\u03c0\u22483.14 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0940\u091c\u093f\u090f\u0964)<\/b><br>\n\u0939\u0932: r=10<br>\n(i) \u0932\u0918\u0941 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921=90\/360\u00d7\u03c0r\u00b2=1\/4\u00d73.14\u00d7100=78.5 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<br>\n\u0932\u0918\u0941 \u0916\u0902\u0921=\u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921-\u0924\u094d\u0930\u093f\u092d\u0941\u091c=78.5-1\/2\u00d710\u00d710=78.5-50=28.5 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<br>\n(ii) \u0926\u0940\u0930\u094d\u0918 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921=270\/360\u00d7\u03c0r\u00b2=3\/4\u00d7314=235.5 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<br>\n\u0926\u0940\u0930\u094d\u0918 \u0916\u0902\u0921=\u03c0r\u00b2-\u0932\u0918\u0941 \u0916\u0902\u0921=314-28.5=285.5 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 \u0932\u0918\u0941 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921 78.5, \u0926\u0940\u0930\u094d\u0918 235.5, \u0932\u0918\u0941 \u0916\u0902\u0921 28.5 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<\/span><br><br>\n\n<b>Q5. 15 \u0938\u0947\u092e\u0940 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e \u0935\u093e\u0932\u0947 \u090f\u0915 \u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u090f\u0915 \u091c\u0940\u0935\u093e \u0935\u0943\u0924\u094d\u0924 \u0915\u0947 \u0915\u0947\u0902\u0926\u094d\u0930 \u092a\u0930 60\u00b0 \u0915\u093e \u0915\u094b\u0923 \u092c\u0928\u093e\u0924\u0940 \u0939\u0948\u0964 \u0935\u0943\u0924\u094d\u0924 \u0915\u0947 \u0938\u0902\u0917\u0924 \u0932\u0918\u0941 \u090f\u0935\u0902 \u0926\u0940\u0930\u094d\u0918 \u0916\u0902\u0921\u094b\u0902 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/b><br>\n\u0939\u0932: r=15, \u03b8=60\u00b0<br>\n\u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921=60\/360\u00d7\u03c0r\u00b2=1\/6\u00d722\/7\u00d7225=117.857 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940 (3.14 \u0938\u0947 117.75)<br>\n\u0924\u094d\u0930\u093f\u092d\u0941\u091c OAB \u0938\u092e\u092c\u093e\u0939\u0941 (r=15, \u0915\u094b\u0923 60\u00b0) => \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=\u221a3\/4 r\u00b2=0.433\u00d7225=97.427 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<br>\n\u0932\u0918\u0941 \u0916\u0902\u0921=\u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921-\u0924\u094d\u0930\u093f\u092d\u0941\u091c=117.857-97.427=20.43 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<br>\n\u0926\u0940\u0930\u094d\u0918 \u0916\u0902\u0921=\u03c0r\u00b2-\u0932\u0918\u0941 \u0916\u0902\u0921=706.857-20.43=686.427 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940 (\u03c0=22\/7)<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 \u0932\u0918\u0941 \u0916\u0902\u0921 \u224820.43, \u0926\u0940\u0930\u094d\u0918 \u2248686.43 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<\/span><br>\n\n<\/div><\/div>\n\n<div id=\"q63-3\" style=\"display:none;\"><div style=\"background:#2e7d32;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe2 \u092d\u093e\u0917 3\/5 - Q6-Q7<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:1.9;height:560px;overflow-y:auto;\">\n\n<b>Q6. \u090f\u0915 \u0915\u093e\u0930 \u092e\u0947\u0902 \u0926\u094b \u0935\u093e\u0907\u092a\u0930 \u0932\u0917\u0947 \u0939\u0948\u0902 \u091c\u094b \u090f\u0915-\u0926\u0942\u0938\u0930\u0947 \u0915\u094b \u0906\u092a\u0938 \u092e\u0947\u0902 \u0906\u091a\u094d\u091b\u093e\u0926\u093f\u0924 \u0928\u0939\u0940\u0902 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0935\u093e\u0907\u092a\u0930 \u0915\u0947 \u092c\u094d\u0932\u0947\u0921 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 28 \u0938\u0947\u092e\u0940 \u0939\u0948 \u0914\u0930 \u092f\u0939 120\u00b0 \u0915\u0947 \u0915\u094b\u0923 \u092a\u0930 \u0918\u0942\u092e\u0924\u093e \u0939\u0948\u0964 \u092c\u094d\u0932\u0947\u0921 \u0915\u0947 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u091a\u0915\u094d\u0930 \u092e\u0947\u0902 \u0938\u093e\u092b \u0915\u093f\u090f \u0917\u090f \u0915\u0941\u0932 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u094b \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/b><br>\n\u0939\u0932: \u090f\u0915 \u0935\u093e\u0907\u092a\u0930 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=\u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921=120\/360\u00d7\u03c0r\u00b2=1\/3\u00d722\/7\u00d728\u00d728<br>\n=1\/3\u00d72464=821.333 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<br>\n\u0926\u094b \u0935\u093e\u0907\u092a\u0930=2\u00d7821.333=1642.666 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 1642.67 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<\/span><br><br>\n\n<b>Q7. \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e r \u0935\u093e\u0932\u0947 \u090f\u0915 \u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u090f\u0915 \u091c\u0940\u0935\u093e \u0935\u0943\u0924\u094d\u0924 \u0915\u0947 \u0915\u0947\u0902\u0926\u094d\u0930 \u092a\u0930 60\u00b0 \u0915\u093e \u0915\u094b\u0923 \u092c\u0928\u093e\u0924\u0940 \u0939\u0948\u0964 \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u0935\u0943\u0924\u094d\u0924 \u0915\u0947 \u0938\u0902\u0917\u0924 \u0932\u0918\u0941 \u0935\u0943\u0924\u094d\u0924\u0916\u0902\u0921 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 r\u00b2(\u03c0\/6-\u221a3\/4) \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u0948\u0964<\/b><br>\n\u0939\u0932: \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921=60\/360\u00d7\u03c0r\u00b2=\u03c0r\u00b2\/6<br>\n\u0924\u094d\u0930\u093f\u092d\u0941\u091c OAB \u0938\u092e\u092c\u093e\u0939\u0941 \u092d\u0941\u091c\u093e r => \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=\u221a3\/4 r\u00b2<br>\n\u0932\u0918\u0941 \u0916\u0902\u0921=\u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921-\u0924\u094d\u0930\u093f\u092d\u0941\u091c=\u03c0r\u00b2\/6-\u221a3\/4 r\u00b2=r\u00b2(\u03c0\/6-\u221a3\/4)<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0938\u093f\u0926\u094d\u0927 \u0939\u0941\u0906<\/span><br>\n\n<\/div><\/div>\n\n<div id=\"q63-4\" style=\"display:none;\"><div style=\"background:#6a1b9a;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe3 \u092d\u093e\u0917 4\/5 - Q8-Q9<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:2;height:560px;overflow-y:auto;\">\n\n<b>Q8. \u090f\u0915 \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c r \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e \u0935\u093e\u0932\u0947 \u090f\u0915 \u0935\u0943\u0924\u094d\u0924 \u092e\u0947\u0902 \u0905\u0902\u0924\u0930\u094d\u0928\u093f\u0939\u093f\u0924 \u0939\u0948\u0964 \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0914\u0930 \u0935\u0943\u0924\u094d\u0924 \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u093e \u0905\u0928\u0941\u092a\u093e\u0924 3\u221a3\/4\u03c0\u22480.413 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u0948\u0964<\/b><br>\n\u0939\u0932: \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0935\u0943\u0924\u094d\u0924 \u092e\u0947\u0902 \u0905\u0902\u0924\u0930\u094d\u0928\u093f\u0939\u093f\u0924, \u0915\u0947\u0902\u0926\u094d\u0930 \u0938\u0947 \u0936\u0940\u0930\u094d\u0937 \u0926\u0942\u0930\u0940 r<br>\n\u092d\u0941\u091c\u093e a=\u221a3 r? \u092a\u094d\u0930\u092e\u093e\u0923: \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u090a\u0901\u091a\u093e\u0908 =3r\/2, \u092d\u0941\u091c\u093e=2\/\u221a3\u00d7\u090a\u0901\u091a\u093e\u0908=\u221a3 r<br>\n\u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=\u221a3\/4 a\u00b2=\u221a3\/4\u00d73r\u00b2=3\u221a3\/4 r\u00b2<br>\n\u0935\u0943\u0924\u094d\u0924 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=\u03c0r\u00b2<br>\n\u0905\u0928\u0941\u092a\u093e\u0924= (3\u221a3\/4 r\u00b2)\/\u03c0r\u00b2=3\u221a3\/4\u03c0=3\u00d71.732\/12.566=0.413<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0938\u093f\u0926\u094d\u0927 \u0905\u0928\u0941\u092a\u093e\u0924 3\u221a3\/4\u03c0\u22480.413<\/span><br><br>\n\n<b>Q9. \u090f\u0915 \u0935\u0930\u094d\u0917 r \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e \u0935\u093e\u0932\u0947 \u090f\u0915 \u0935\u0943\u0924\u094d\u0924 \u092e\u0947\u0902 \u0905\u0902\u0924\u0930\u094d\u0928\u093f\u0939\u093f\u0924 \u0939\u0948\u0964 \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u0935\u0930\u094d\u0917 \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0914\u0930 \u0935\u0943\u0924\u094d\u0924 \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u093e \u0905\u0928\u0941\u092a\u093e\u0924 2\/\u03c0\u22480.637 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u0948\u0964<\/b><br>\n\u0939\u0932: \u0935\u0930\u094d\u0917 \u0935\u0943\u0924\u094d\u0924 \u092e\u0947\u0902 \u0905\u0902\u0924\u0930\u094d\u0928\u093f\u0939\u093f\u0924, \u0935\u093f\u0915\u0930\u094d\u0923=2r<br>\n\u092d\u0941\u091c\u093e= \u0935\u093f\u0915\u0930\u094d\u0923\/\u221a2=2r\/\u221a2=\u221a2 r<br>\n\u0935\u0930\u094d\u0917 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=\u092d\u0941\u091c\u093e\u00b2=2r\u00b2<br>\n\u0935\u0943\u0924\u094d\u0924 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=\u03c0r\u00b2<br>\n\u0905\u0928\u0941\u092a\u093e\u0924=2r\u00b2\/\u03c0r\u00b2=2\/\u03c0=0.6366<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0938\u093f\u0926\u094d\u0927 \u0905\u0928\u0941\u092a\u093e\u0924 2\/\u03c0\u22480.637<\/span><br>\n\n<\/div><\/div>\n\n<div id=\"q63-5\" style=\"display:none;\"><div style=\"background:#ff6f00;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe0 \u092d\u093e\u0917 5\/5 - Q10 \u0905\u0902\u0924\u093f\u092e<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:2;height:560px;overflow-y:auto;\">\n\n<b>Q10. \u090f\u0915 r \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e \u0935\u093e\u0932\u0947 \u0935\u0943\u0924\u094d\u0924 \u092e\u0947\u0902 \u090f\u0915 \u0937\u091f\u094d\u092d\u0941\u091c \u0905\u0902\u0924\u0930\u094d\u0928\u093f\u0939\u093f\u0924 \u0939\u0948\u0964 \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u0937\u091f\u094d\u092d\u0941\u091c \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0914\u0930 \u0935\u0943\u0924\u094d\u0924 \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u093e \u0905\u0928\u0941\u092a\u093e\u0924 3\u221a3\/2\u03c0=0.827 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u0948\u0964 \u0915\u094d\u092f\u093e \u0906\u092a \u0938\u092e\u091d \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0907\u0938\u0915\u093e \u0909\u0924\u094d\u0924\u0930, \u092a\u094d\u0930\u0936\u094d\u0928 8 \u0915\u0947 \u0909\u0924\u094d\u0924\u0930 \u0915\u0947 \u0920\u0940\u0915 \u0926\u094b\u0917\u0941\u0928\u093e \u0915\u094d\u092f\u094b\u0902 \u0939\u0948?<\/b><br>\n\u0939\u0932: \u0928\u093f\u092f\u092e\u093f\u0924 \u0937\u091f\u094d\u092d\u0941\u091c 6 \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u0938\u0947 \u092c\u0928\u0924\u093e \u0939\u0948 \u091c\u093f\u0928\u0915\u0940 \u092d\u0941\u091c\u093e r \u0939\u0948\u0964<br>\n\u090f\u0915 \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u092d\u0941\u091c\u093e r \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=\u221a3\/4 r\u00b2<br>\n\u0937\u091f\u094d\u092d\u0941\u091c \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=6\u00d7\u221a3\/4 r\u00b2=3\u221a3\/2 r\u00b2<br>\n\u0935\u0943\u0924\u094d\u0924 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=\u03c0r\u00b2<br>\n\u0905\u0928\u0941\u092a\u093e\u0924= (3\u221a3\/2 r\u00b2)\/\u03c0r\u00b2=3\u221a3\/2\u03c0=3\u00d71.732\/6.283=0.8269\u22480.827<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0938\u093f\u0926\u094d\u0927 \u0905\u0928\u0941\u092a\u093e\u0924 3\u221a3\/2\u03c0\u22480.827<\/span><br><br>\n\n<b>\u0915\u094d\u092f\u094b\u0902 \u092a\u094d\u0930\u0936\u094d\u0928 8 \u0915\u093e \u0926\u094b\u0917\u0941\u0928\u093e?<\/b><br>\n\u092a\u094d\u0930\u0936\u094d\u0928 8 \u092e\u0947\u0902 \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0905\u0902\u0924\u0930\u094d\u0928\u093f\u0939\u093f\u0924 \u0925\u093e \u091c\u093f\u0938\u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 3\u221a3\/4 r\u00b2 \u0925\u093e\u0964 \u0937\u091f\u094d\u092d\u0941\u091c \u092e\u0947\u0902 6 \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0948\u0902, \u091c\u092c\u0915\u093f \u092c\u0921\u093c\u093e \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c (\u092a\u094d\u0930\u0936\u094d\u0928 8) \u0915\u0947\u0935\u0932 3 \u091b\u094b\u091f\u0947 \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u0915\u0947 \u092c\u0930\u093e\u092c\u0930? \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902 \u0935\u0943\u0924\u094d\u0924 \u092e\u0947\u0902 \u0905\u0902\u0924\u0930\u094d\u0928\u093f\u0939\u093f\u0924 \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932, \u0937\u091f\u094d\u092d\u0941\u091c \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u093e \u0906\u0927\u093e \u0939\u094b\u0924\u093e \u0939\u0948 \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0937\u091f\u094d\u092d\u0941\u091c=6 \u091b\u094b\u091f\u0947 \u0924\u094d\u0930\u093f\u092d\u0941\u091c, \u092c\u0921\u093c\u093e \u0924\u094d\u0930\u093f\u092d\u0941\u091c=3 \u091b\u094b\u091f\u0947 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u0964 \u0907\u0938\u0932\u093f\u090f \u0905\u0928\u0941\u092a\u093e\u0924 \u0926\u094b\u0917\u0941\u0928\u093e\u0964<br>\n\n<div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:10px;border-radius:10px;text-align:center;margin-top:10px;font-weight:bold;\">\n\u2705 \u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 6.3 Q1-Q10 \u092a\u0942\u0930\u093e - \u0936\u0941\u0926\u094d\u0927 \u0939\u0932<br>\nQ1 25.67cm\u00b2 Q2 38.5cm\u00b2 Q3 7.33cm \u091a\u093e\u092a 25.67 \u0915\u094d\u0937\u0947\u0924\u094d\u0930<br>\nQ4 \u0932\u0918\u0941 \u0924\u094d\u0930\u093f\u091c\u094d\u092f 78.5 \u0926\u0940\u0930\u094d\u0918 235.5 \u0916\u0902\u0921 28.5<br>\nQ5 \u0932\u0918\u0941 \u0916\u0902\u0921 20.43 \u0926\u0940\u0930\u094d\u0918 686.43<br>\nQ6 1642.67cm\u00b2 Q7 r\u00b2(\u03c0\/6-\u221a3\/4)<br>\nQ8 3\u221a3\/4\u03c0\u22480.413 Q9 2\/\u03c0\u22480.637 Q10 3\u221a3\/2\u03c0\u22480.827\n<\/div>\n\n<\/div><\/div>\n<\/div>\n\n<div style=\"background:#0a5c4b;padding:12px;display:flex;justify-content:space-between;align-items:center;\">\n<button type=\"button\" id=\"q63p\" style=\"background:#ffcc00;color:#000;border:3px solid #fff;border-radius:30px;padding:10px 22px;font-weight:bold;cursor:pointer;min-width:100px;\">&larr; \u092a\u0940\u091b\u0947<\/button>\n<span id=\"q63i\" style=\"background:#fff;color:#0a5c4b;padding:8px 20px;border-radius:20px;font-weight:bold;\">1 \/ 5<\/span>\n<button type=\"button\" id=\"q63n\" style=\"background:#00e676;color:#000;border:3px solid #fff;border-radius:30px;padding:10px 22px;font-weight:bold;cursor:pointer;min-width:100px;\">\u0906\u0917\u0947 &rarr;<\/button>\n<\/div>\n<\/div>\n\n<script>\n(function(){\nvar c=1,t=5;\nfunction s(n){\nfor(var i=1;i<=t;i++){\nvar el=document.getElementById('q63-'+i);\nif(el)el.style.display=(i===n?'block':'none');\n}\ndocument.getElementById('q63i').textContent=n+' \/ '+t;\nc=n;\n}\ndocument.getElementById('q63n').onclick=function(){var n=c+1;if(n>t)n=1;s(n);};\ndocument.getElementById('q63p').onclick=function(){var n=c-1;if(n<1)n=t;s(n);};\n})();\n<\/script><\/div><\/div><\/div><\/div><div id=\"pg-965-7\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-965-7-0\"  class=\"panel-grid-cell\" ><div id=\"panel-965-7-0-0\" class=\"widget_text so-panel widget widget_custom_html panel-first-child panel-last-child\" data-index=\"7\" ><div class=\"textwidget custom-html-widget\"><div id=\"FINAL-EX-149-153\" style=\"max-width:860px;margin:12px auto;border:4px solid #0f5e4b;border-radius:14px;background:#e6f4f1;font-family:'Noto Sans Devanagari',Arial,sans-serif;overflow:hidden;\">\n<div style=\"background:#0a5c4b;padding:10px;text-align:center;\"><span style=\"background:#fff;color:#0a3d33;padding:7px 20px;border-radius:20px;font-weight:bold;font-size:13px;\">\u0905\u0902\u0924\u093f\u092e \u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 - \u092a\u0947\u091c 149-153 - Q1-Q27 \u0936\u0941\u0926\u094d\u0927 FINAL<\/span><\/div>\n\n<div style=\"padding:10px 12px;\">\n<div id=\"fe-1\" style=\"display:block;\"><div style=\"background:#d32f2f;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udd34 \u092d\u093e\u0917 1\/7 - Q1-Q4<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:1.9;height:560px;overflow-y:auto;\">\n\n<div style=\"background:#fff9c4;border:2px solid #fbc02d;padding:6px;border-radius:8px;text-align:center;font-weight:bold;\">\u0928\u0940\u091a\u0947 \u0926\u093f\u090f \u0917\u090f \u092a\u094d\u0930\u0936\u094d\u0928\u094b\u0902 \u092e\u0947\u0902 \u0915\u093f\u0938\u0940 \u0905\u0928\u094d\u092f \u0928\u093f\u0930\u094d\u0926\u0947\u0936 \u0915\u0940 \u0905\u0928\u0941\u092a\u0938\u094d\u0925\u093f\u0924\u093f \u092e\u0947\u0902, \u03c0 \u0915\u093e \u0938\u0928\u094d\u0928\u093f\u0915\u091f \u092e\u093e\u0928 22\/7 \u0909\u092a\u092f\u094b\u0917 \u0915\u0940\u091c\u093f\u090f\u0964<\/div>\n\n<b>Q1. \u092c\u0940\u091c\u0917\u0923\u093f\u0924 \u092e\u0947\u0902 \u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e\u0913\u0902 \u0915\u094b \u0915\u092d\u0940-\u0915\u092d\u0940 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u0947 \u0938\u0902\u092c\u0902\u0927\u094b\u0902 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f\u2014 \u091a\u093f\u0924\u094d\u0930 6.41 \u2014 \u090f\u0915 \u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u093e \u092a\u094d\u0930\u0924\u093f\u0926\u0930\u094d\u0936 - \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u091a\u093f\u0924\u094d\u0930 \u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e (a+b)\u00b2=a\u00b2+2ab+b\u00b2 \u0915\u0947 \u0905\u0928\u0941\u0930\u0942\u092a \u0939\u0948\u0964 \u0915\u094d\u092f\u093e \u0906\u092a \u092c\u0924\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u0915\u0948\u0938\u0947? (a+b)(a-b)=a\u00b2-b\u00b2 \u0914\u0930 (a+b+c)\u00b2=a\u00b2+b\u00b2+c\u00b2+2ab+2bc+2ca \u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e\u0913\u0902 \u0915\u0947 \u0905\u0928\u0941\u0930\u0942\u092a \u0906\u0915\u0943\u0924\u093f\u092f\u093e\u0901 \u092c\u0928\u093e\u0907\u090f\u0964<\/b><br>\n\u0939\u0932: (a+b)\u00b2 \u0935\u093e\u0932\u093e \u0935\u0930\u094d\u0917 a+b \u092d\u0941\u091c\u093e \u0915\u093e \u0935\u0930\u094d\u0917 - \u0909\u0938\u0947 a\u00b2, b\u00b2 \u0914\u0930 2ab \u0915\u0947 \u0906\u092f\u0924\u094b\u0902 \u092e\u0947\u0902 \u092c\u093e\u0901\u091f\u094b\u0964 (a+b)(a-b) \u092e\u0947\u0902 \u092c\u0921\u093c\u093e \u0935\u0930\u094d\u0917 a\u00b2 \u092e\u0947\u0902 \u0938\u0947 b\u00b2 \u0915\u093e\u091f\u094b \u0924\u094b \u0906\u092f\u0924 (a+b)(a-b) \u092c\u091a\u0947\u0964 (a+b+c)\u00b2 \u092e\u0947\u0902 3 \u0935\u0930\u094d\u0917 a\u00b2,b\u00b2,c\u00b2 \u0914\u0930 6 \u0906\u092f\u0924 2ab,2bc,2ca\u0964<br><br>\n\n<b>Q2. \u090f\u0915 \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u093e \u092a\u0930\u093f\u092e\u093e\u092a 40 \u0938\u0947\u092e\u0940 \u0939\u0948\u0964 \u0907\u0938\u0915\u0940 \u0938\u092e\u093e\u0928 \u092d\u0941\u091c\u093e\u090f\u0901 15 \u0938\u0947\u092e\u0940 \u0932\u0902\u092c\u0940 \u0939\u0948\u0902\u0964 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/b><br>\n\u0906\u0927\u093e\u0930=40-15-15=10 \u0938\u0947\u092e\u0940, s=20<br>\n\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=\u221a[20\u00d75\u00d75\u00d710]=\u221a5000=50\u221a2\u224870.71 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 50\u221a2 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<\/span><br><br>\n\n<b>Q3. \u090f\u0915 \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u093e \u0906\u0927\u093e\u0930 10 \u0938\u0947\u092e\u0940 \u0939\u0948 \u0914\u0930 \u0907\u0938\u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 60 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940 \u0939\u0948\u0964 \u0938\u092e\u093e\u0928 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 \u0915\u094d\u092f\u093e \u0939\u094b\u0917\u0940?<\/b><br>\n\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=1\/2\u00d7\u0906\u0927\u093e\u0930\u00d7\u090a\u0901\u091a\u093e\u0908=60 =>1\/2\u00d710\u00d7h=60 =>h=12 \u0938\u0947\u092e\u0940<br>\n\u0938\u092e\u093e\u0928 \u092d\u0941\u091c\u093e=\u221a[(10\/2)\u00b2+12\u00b2]=\u221a[25+144]=13 \u0938\u0947\u092e\u0940<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 13 \u0938\u0947\u092e\u0940<\/span><br><br>\n\n<b>Q4. \u090f\u0915 \u0938\u092e\u0915\u094b\u0923 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 54 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940 \u0939\u0948\u0964 \u0907\u0938\u0915\u0940 \u090f\u0915 \u092d\u0941\u091c\u093e \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 12 \u0938\u0947\u092e\u0940 \u0939\u0948\u0964 \u0907\u0938\u0915\u093e \u092a\u0930\u093f\u092e\u093e\u092a \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/b><br>\n\u0938\u092e\u0915\u094b\u0923 \u0924\u094d\u0930\u093f\u092d\u0941\u091c, \u090f\u0915 \u092d\u0941\u091c\u093e 12 - \u0926\u094b \u0938\u094d\u0925\u093f\u0924\u093f: 12 \u0906\u0927\u093e\u0930 \u092f\u093e \u0932\u0902\u092c? \u092e\u093e\u0928\u094b \u0906\u0927\u093e\u0930 12, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 1\/2\u00d712\u00d7h=54 =>h=9 \u0938\u0947\u092e\u0940<br>\n\u0915\u0930\u094d\u0923=\u221a[12\u00b2+9\u00b2]=15 \u0938\u0947\u092e\u0940, \u092a\u0930\u093f\u092e\u093e\u092a=12+9+15=36 \u0938\u0947\u092e\u0940<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 36 \u0938\u0947\u092e\u0940 (12 \u0906\u0927\u093e\u0930 \u092e\u093e\u0928\u0928\u0947 \u092a\u0930)<\/span><br>\n\n<\/div><\/div>\n\n<div id=\"fe-2\" style=\"display:none;\"><div style=\"background:#1565c0;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udd35 \u092d\u093e\u0917 2\/7 - Q5-Q9<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:1.9;height:560px;overflow-y:auto;\">\n\n<b>Q5. \u090f\u0915 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u093e \u0905\u0928\u0941\u092a\u093e\u0924 2:3:4 \u0939\u0948 \u0914\u0930 \u0907\u0938\u0915\u093e \u092a\u0930\u093f\u092e\u093e\u092a 45 \u0938\u0947\u092e\u0940 \u0939\u0948\u0964 \u0907\u0938\u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/b><br>\n\u092d\u0941\u091c\u093e\u090f\u0901 2x,3x,4x =>9x=45 =>x=5 =>10,15,20 \u0938\u0947\u092e\u0940, s=22.5<br>\n\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=\u221a[22.5\u00d712.5\u00d77.5\u00d72.5]=\u221a5273.43\u224872.61 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<br><br>\n\n<b>Q6. \u090f\u0915 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 7 \u0938\u0947\u092e\u0940, 24 \u0938\u0947\u092e\u0940 \u0914\u0930 25 \u0938\u0947\u092e\u0940 \u0939\u0948\u0964 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0926\u094b \u092d\u093f\u0928\u094d\u0928-\u092d\u093f\u0928\u094d\u0928 \u0935\u093f\u0927\u093f\u092f\u094b\u0902 \u0938\u0947 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/b><br>\n\u0935\u093f\u0927\u093f1: 7\u00b2+24\u00b2=25\u00b2 => \u0938\u092e\u0915\u094b\u0923 \u0924\u094d\u0930\u093f\u092d\u0941\u091c, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=1\/2\u00d77\u00d724=84 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<br>\n\u0935\u093f\u0927\u093f2: \u0939\u0940\u0930\u094b\u0928 s=28, \u221a[28\u00d721\u00d74\u00d73]=\u221a7056=84 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 84 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940 \u0926\u094b\u0928\u094b\u0902 \u0935\u093f\u0927\u093f \u0938\u0947<\/span><br><br>\n\n<b>Q7. \u092f\u0926\u093f \u0915\u093f\u0938\u0940 \u0938\u093e\u0907\u0915\u093f\u0932 \u0915\u0947 \u092a\u0939\u093f\u090f \u0915\u093e \u0935\u094d\u092f\u093e\u0938 60 \u0938\u0947\u092e\u0940 \u0939\u0948 \u0924\u094b \u092a\u0939\u093f\u090f \u0915\u0947 100 \u092c\u093e\u0930 \u0918\u0942\u0930\u094d\u0923\u0928 \u0915\u0947 \u092a\u0936\u094d\u091a\u093e\u0924 \u0938\u093e\u0907\u0915\u093f\u0932 \u091a\u093e\u0932\u0915 \u0915\u093f\u0924\u0928\u0940 \u0926\u0942\u0930\u0940 \u0924\u092f \u0915\u0930\u0947\u0917\u093e?<\/b><br>\n\u092a\u0930\u093f\u0927\u093f=\u03c0d=22\/7\u00d760=188.57 \u0938\u0947\u092e\u0940, 100 \u091a\u0915\u094d\u0915\u0930=18857 \u0938\u0947\u092e\u0940=188.57 \u092e\u0940<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 188.57 \u092e\u0940\u091f\u0930<\/span><br><br>\n\n<b>Q8. \u0909\u0938 \u0935\u0943\u0924\u094d\u0924 \u0915\u0947 \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f, \u091c\u093f\u0938\u0915\u0940 \u092a\u0930\u093f\u0927\u093f 66 \u0938\u0947\u092e\u0940 \u0939\u0948\u0964<\/b><br>\n2\u03c0r=66 =>r=10.5 \u0938\u0947\u092e\u0940, \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936=1\/4\u00d722\/7\u00d7110.25=86.625 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 86.625 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<\/span><br><br>\n\n<b>Q9. \u090f\u0915 \u0915\u093e\u0930 \u0915\u0947 \u092a\u0939\u093f\u090f \u0915\u0940 \u092c\u093e\u0939\u0930\u0940 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e 28 \u0938\u0947\u092e\u0940 \u0939\u0948\u0964 \u092a\u0939\u093f\u090f \u0915\u0947 \u090f\u0915 \u092a\u0942\u0930\u094d\u0923 \u0918\u0942\u0930\u094d\u0923\u0928 \u0915\u0947 \u092a\u0936\u094d\u091a\u093e\u0924 \u0915\u093e\u0930 \u0915\u093f\u0924\u0928\u0940 \u0926\u0942\u0930\u0940 \u0924\u092f \u0915\u0930\u0924\u0940 \u0939\u0948 \u0914\u0930 \u090f\u0915 \u0915\u093f\u0932\u094b\u092e\u0940\u091f\u0930 \u0915\u0940 \u092f\u093e\u0924\u094d\u0930\u093e \u0915\u0947 \u0926\u094c\u0930\u093e\u0928 \u092a\u0939\u093f\u092f\u093e \u0915\u093f\u0924\u0928\u0940 \u092c\u093e\u0930 \u0918\u0942\u092e\u0924\u093e \u0939\u0948, \u0907\u0938\u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0940\u091c\u093f\u090f\u0964<\/b><br>\n\u092a\u0930\u093f\u0927\u093f=2\u03c0r=176 \u0938\u0947\u092e\u0940=1.76 \u092e\u0940, 1 \u0915\u093f\u092e\u0940=1000 \u092e\u0940\/1.76=568.18 \u091a\u0915\u094d\u0915\u0930<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 1.76 \u092e\u0940 \u092a\u094d\u0930\u0924\u093f \u091a\u0915\u094d\u0915\u0930, 568.18 \u091a\u0915\u094d\u0915\u0930 \u092a\u094d\u0930\u0924\u093f \u0915\u093f\u092e\u0940<\/span><br>\n\n<\/div><\/div>\n\n<div id=\"fe-3\" style=\"display:none;\"><div style=\"background:#2e7d32;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe2 \u092d\u093e\u0917 3\/7 - Q10-Q15<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:1.9;height:560px;overflow-y:auto;\">\n\n<b>Q10. \u0926\u094b \u0906\u092f\u0924\u094b\u0902 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0914\u0930 \u092a\u0930\u093f\u092e\u093e\u092a \u0938\u092e\u093e\u0928 \u0939\u0948\u0964 \u0915\u094d\u092f\u093e \u0907\u0938\u0915\u093e \u0905\u0930\u094d\u0925 \u092f\u0939 \u0939\u0948 \u0915\u093f \u0935\u0947 \u0926\u094b\u0928\u094b\u0902 \u090f\u0915-\u0926\u0942\u0938\u0930\u0947 \u0915\u0947 \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e \u0939\u0948\u0902\u0964<\/b><br>\n\u0909\u0924\u094d\u0924\u0930: \u0928\u0939\u0940\u0902\u0964 \u0909\u0926\u093e\u0939\u0930\u0923: 6\u00d71 \u0906\u092f\u0924 \u092a\u0930\u093f\u092e\u093e\u092a14 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u09326, \u0914\u0930 4\u00d7? \u0928\u0939\u0940\u0902\u0964 6\u00d72 \u092a\u0930\u093f\u092e\u093e\u092a16\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 8\u00d72 \u092a\u0930\u093f\u092e\u093e\u092a20 \u0915\u094d\u0937\u0947\u0924\u094d\u093016, 4\u00d74 \u0935\u0930\u094d\u0917 \u092a\u0930\u093f\u092e\u093e\u092a16 \u0928\u0939\u0940\u0902\u0964 \u0938\u0939\u0940 \u0909\u0926\u093e\u0939\u0930\u0923: 6\u00d72=12 \u0915\u094d\u0937\u0947\u0924\u094d\u0930 \u092a\u0930\u093f\u092e\u093e\u092a16, 4\u00d7? 4\u00d7? \u0928\u0939\u0940\u0902\u0964 \u0932\u0947\u0915\u093f\u0928 6\u00d71=6 \u0915\u094d\u0937\u0947\u0924\u094d\u093014 \u092a\u0930\u093f\u092e\u093e\u092a, 3\u00d72=6 \u0915\u094d\u0937\u0947\u0924\u094d\u093010 \u092a\u0930\u093f\u092e\u093e\u092a \u0905\u0932\u0917\u0964 \u0938\u092e\u093e\u0928 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0914\u0930 \u092a\u0930\u093f\u092e\u093e\u092a \u0935\u093e\u0932\u0947 \u0906\u092f\u0924 \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e \u0939\u0940 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902 \u0915\u094d\u092f\u094b\u0902\u0915\u093f a+b=P\/2 \u0914\u0930 ab=A => a,b \u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0947 \u092e\u0942\u0932, \u0926\u094b \u0939\u0940 \u0939\u0932 a,b \u0914\u0930 b,a\u0964 \u0939\u093e\u0901 \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e \u0939\u094b\u0924\u0947 \u0939\u0948\u0902 \u092f\u0926\u093f \u092d\u0941\u091c\u093e\u090f\u0901 \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0939\u094b\u0902\u0964 \u092a\u0930 \u092f\u0926\u093f \u090f\u0915 \u0906\u092f\u0924 6\u00d74=24 \u092a\u0930\u093f\u092e\u093e\u092a20, \u0926\u0942\u0938\u0930\u093e? 8\u00d72=16 \u0928\u0939\u0940\u0902\u0964 \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902 \u092f\u0926\u093f \u092a\u0930\u093f\u092e\u093e\u092a \u0914\u0930 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0938\u092e\u093e\u0928 \u0924\u094b \u092d\u0941\u091c\u093e\u090f\u0901 \u0938\u092e\u093e\u0928 \u0939\u0940 \u0939\u094b\u0902\u0917\u0940, \u0907\u0938\u0932\u093f\u090f \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0964<br><br>\n\n<b>Q11. \u0906\u092a \u091c\u093e\u0928\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0906\u0927\u093e\u0930\u00d7\u090a\u0901\u091a\u093e\u0908 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0907\u0938 \u0938\u0942\u0924\u094d\u0930 \u0914\u0930 \u0906\u0915\u0943\u0924\u093f \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u0938\u092e\u0932\u0902\u092c \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0938\u092e\u093e\u0902\u0924\u0930 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u092f\u094b\u0917 \u0915\u093e \u0906\u0927\u093e \u0914\u0930 \u090a\u0901\u091a\u093e\u0908 \u0915\u093e \u0917\u0941\u0923\u0928\u092b\u0932, \u0905\u0930\u094d\u0925\u093e\u0924\u094d 1\/2(a+b)h \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u091a\u093f\u0924\u094d\u0930 6.42 \u2014 \u0938\u092e\u0932\u0902\u092c \u092d\u0941\u091c\u093e\u090f\u0901 a \u0914\u0930 b, \u090a\u0901\u091a\u093e\u0908 h<\/b><br>\n\u092a\u094d\u0930\u092e\u093e\u0923: \u0938\u092e\u0932\u0902\u092c \u0915\u094b \u0935\u093f\u0915\u0930\u094d\u0923 \u0938\u0947 \u0926\u094b \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u092e\u0947\u0902 \u092c\u093e\u0901\u091f\u094b, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=1\/2 a h+1\/2 b h=1\/2(a+b)h<br><br>\n\n<b>Q12. \u090f\u0915 \u0938\u092e\u0932\u0902\u092c \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u094b \u0926\u094b \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u092e\u0947\u0902 \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0915\u0947 \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u0907\u0938\u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0938\u092e\u093e\u0902\u0924\u0930 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u092f\u094b\u0917 \u0915\u093e \u0906\u0927\u093e \u0914\u0930 \u090a\u0901\u091a\u093e\u0908 \u0915\u093e \u0917\u0941\u0923\u0928\u092b\u0932 \u0939\u094b\u0924\u093e \u0939\u0948 (\u091c\u0948\u0938\u093e \u0915\u093f \u0938\u0942\u0924\u094d\u0930 \u092e\u0947\u0902 \u090a\u092a\u0930 \u0926\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948)\u0964<\/b><br>\n\u0935\u0939\u0940 Q11 \u0915\u093e \u092a\u094d\u0930\u092e\u093e\u0923\u0964<br><br>\n\n<b>Q13. \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u0938\u092e\u0932\u0902\u092c \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0940 \u0926\u094b \u0938\u092e\u093e\u0928 \u092a\u094d\u0930\u0924\u093f\u092f\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0948\u0938\u0947 \u0928\u093f\u0930\u094d\u092e\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u0907\u0938\u0938\u0947 \u0939\u092e\u0947\u0902 \u0938\u092e\u0932\u0902\u092c \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u093e \u0938\u0942\u0924\u094d\u0930 \u0915\u0948\u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0917\u093e?<\/b><br>\n\u0926\u094b \u0938\u092e\u093e\u0928 \u0938\u092e\u0932\u0902\u092c \u0915\u094b \u0909\u0932\u094d\u091f\u093e \u091c\u094b\u0921\u093c\u094b \u0924\u094b \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u092c\u0928\u0924\u093e \u0939\u0948 \u091c\u093f\u0938\u0915\u093e \u0906\u0927\u093e\u0930 (a+b) \u0914\u0930 \u090a\u0901\u091a\u093e\u0908 h, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 (a+b)h, \u0907\u0938\u0932\u093f\u090f \u090f\u0915 \u0938\u092e\u0932\u0902\u092c \u0915\u093e \u0906\u0927\u093e =1\/2(a+b)h<br><br>\n\n<b>Q14. \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u092a\u0924\u0902\u0917 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0909\u0938\u0915\u0947 \u0935\u093f\u0915\u0930\u094d\u0923\u094b\u0902 \u0915\u0947 \u0917\u0941\u0923\u0928\u092b\u0932 \u0915\u093e \u0906\u0927\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0907\u0928 \u0926\u094b\u0928\u094b\u0902 \u0924\u0930\u0939 \u0938\u0947 \u0926\u0930\u094d\u0936\u093e\u0907\u090f\u2014 (i) \u092c\u0940\u091c\u0917\u0923\u093f\u0924 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 (ii) \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u093f \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947<\/b><br>\n\u092a\u0924\u0902\u0917 \u0915\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 d1,d2, \u090f\u0915 \u0935\u093f\u0915\u0930\u094d\u0923 \u0926\u0942\u0938\u0930\u0947 \u0915\u094b \u0938\u092e\u0915\u094b\u0923 \u092a\u0930 \u0915\u093e\u091f\u0924\u093e \u0939\u0948\u0964 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=1\/2 d1 d2<br><br>\n\n<b>Q15. \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e \u0906\u0915\u0943\u0924\u093f\u092f\u094b\u0902 \u0915\u094b \u0906\u092a\u0938 \u092e\u0947\u0902 \u091c\u094b\u0921\u093c\u0928\u0947 \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0924\u0940\u0928 \u092a\u094d\u0930\u0936\u094d\u0928 \u0926\u093f\u090f \u0917\u090f \u0939\u0948\u0902\u2014 (i) \u0906\u092f\u0924 ABCD \u0915\u0940 \u092d\u0941\u091c\u093e\u090f\u0901 a \u0914\u0930 b \u0939\u0948\u0902 \u0914\u0930 \u0906\u092f\u0924 PQRS \u0915\u0940 \u092d\u0941\u091c\u093e\u090f\u0901 2a \u0914\u0930 2b \u0939\u0948\u0902\u0964 \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f PQRS \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 ABCD \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u093e \u091a\u093e\u0930 \u0917\u0941\u0928\u093e \u0939\u0948\u0964 \u0915\u094d\u092f\u093e \u0907\u0938\u0915\u093e \u0905\u0930\u094d\u0925 \u092f\u0939 \u0939\u0948 \u0915\u093f \u0906\u092f\u0924 ABCD \u0915\u0940 \u091a\u093e\u0930 \u092a\u094d\u0930\u0924\u093f\u0906\u0915\u0943\u0924\u093f\u092f\u093e\u0901 \u0906\u092f\u0924 PQRS \u092e\u0947\u0902 \u0938\u092e\u093e\u0939\u093f\u0924 \u0939\u094b \u0938\u0915\u0924\u0940 \u0939\u0948\u0902? \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0930\u0915\u0947 \u0926\u0947\u0916\u093f\u090f!<\/b><br>\n(ii) \u0394ABC \u0915\u0940 \u092d\u0941\u091c\u093e\u090f\u0901 a,b,c \u0939\u0948\u0902 \u0914\u0930 \u0394PQR \u0915\u0940 \u092d\u0941\u091c\u093e\u090f\u0901 2a,2b,2c \u0939\u0948\u0902\u0964 \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u0394PQR \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0394ABC \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u093e \u091a\u093e\u0930 \u0917\u0941\u0928\u093e \u0939\u0948\u0964 \u0915\u094d\u092f\u093e \u0907\u0938\u0915\u093e \u092f\u0939 \u0905\u0930\u094d\u0925 \u0939\u0948 \u0915\u093f \u0394PQR \u092e\u0947\u0902 \u0394ABC \u0915\u0940 4 \u092a\u094d\u0930\u0924\u093f\u0906\u0915\u0943\u0924\u093f\u092f\u093e\u0901 \u0938\u092e\u093e\u0939\u093f\u0924 \u0939\u094b \u0938\u0915\u0924\u0940 \u0939\u0948\u0902?<br>\n(iii) \u0394ABC \u0915\u0940 \u092d\u0941\u091c\u093e\u090f\u0901 a,b,c \u0939\u0948\u0902 \u0914\u0930 \u0394PQR \u0915\u0940 \u092d\u0941\u091c\u093e\u090f\u0901 3a,3b,3c \u0939\u0948\u0902\u0964 \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u0394PQR \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0394ABC \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u093e \u0928\u094c \u0917\u0941\u0928\u093e \u0939\u0948\u0964 \u0915\u094d\u092f\u093e \u0907\u0938\u0915\u093e \u092f\u0939 \u0905\u0930\u094d\u0925 \u0939\u0948 \u0915\u093f \u0394PQR \u092e\u0947\u0902 \u0394ABC \u0915\u0940 \u0928\u094c \u092a\u094d\u0930\u0924\u093f\u0906\u0915\u0943\u0924\u093f\u092f\u093e\u0901 \u0938\u092e\u093e\u0939\u093f\u0924 \u0939\u094b \u0938\u0915\u0924\u0940 \u0939\u0948\u0902?<br>\n\u0939\u0932: (i) \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 PQRS=4ab=4\u00d7ABCD, \u0939\u093e\u0901 4 \u0906\u092f\u0924 \u0938\u092e\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 (ii) \u0938\u092e\u0930\u0942\u092a \u0924\u094d\u0930\u093f\u092d\u0941\u091c, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0905\u0928\u0941\u092a\u093e\u0924 \u092d\u0941\u091c\u093e \u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u093e \u0935\u0930\u094d\u0917=4, \u0939\u093e\u0901 4 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0938\u092e\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 (iii) \u0905\u0928\u0941\u092a\u093e\u0924 9, \u0939\u093e\u0901 9 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0938\u092e\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<br>\n\n<\/div><\/div>\n\n<div id=\"fe-4\" style=\"display:none;\"><div style=\"background:#6a1b9a;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe3 \u092d\u093e\u0917 4\/7 - Q16-Q19<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:1.9;height:560px;overflow-y:auto;\">\n\n<b>Q16. \u091a\u093f\u0924\u094d\u0930 6.43 \u2014 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u093e \u0915\u093f\u0924\u0928\u093e \u092d\u093e\u0917 \u091b\u093e\u092f\u093e\u0902\u0915\u093f\u0924 \u0939\u0948? \u091a\u093f\u0924\u094d\u0930 6.44 \u2014 \u0935\u0930\u094d\u0917 \u0915\u093e \u0915\u093f\u0924\u0928\u093e \u092d\u093e\u0917 \u091b\u093e\u092f\u093e\u0902\u0915\u093f\u0924 \u0939\u0948?<\/b><br>\n(\u091a\u093f\u0924\u094d\u0930 \u0905\u0928\u0941\u0938\u093e\u0930 \u0905\u0928\u0941\u092e\u093e\u0928) \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u092e\u0947\u0902 1\/2, \u0935\u0930\u094d\u0917 \u092e\u0947\u0902 1\/2 \u092f\u093e 1\/4 - \u091a\u093f\u0924\u094d\u0930 \u0926\u0947\u0916\u0915\u0930 \u0917\u093f\u0928\u0928\u093e\u0964<br><br>\n\n<b>Q17. \u091a\u093f\u0924\u094d\u0930 6.45 \u2014 \u0906\u092f\u0924 \u0915\u093e \u0915\u093f\u0924\u0928\u093e \u092d\u093e\u0917 \u0935\u0943\u0924\u094d\u0924\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u0906\u091a\u094d\u091b\u093e\u0926\u093f\u0924 \u0939\u0948? \u091a\u093f\u0924\u094d\u0930 6.46 \u2014 \u0906\u092f\u0924 \u0915\u093e \u0915\u093f\u0924\u0928\u093e \u092d\u093e\u0917 \u0935\u0943\u0924\u094d\u0924\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u0906\u091a\u094d\u091b\u093e\u0926\u093f\u0924 \u0939\u0948?<\/b><br>\n\u0935\u0943\u0924\u094d\u0924\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u0918\u0947\u0930\u093e \u0917\u092f\u093e \u092d\u093e\u0917 \u224878.5% \u092f\u0926\u093f \u0935\u0943\u0924\u094d\u0924 \u0938\u091f\u0947 \u0939\u094b\u0902\u0964<br><br>\n\n<b>Q18. \u0909\u092a\u0930\u094b\u0915\u094d\u0924 \u0926\u0940 \u0917\u0908 \u0938\u0942\u091a\u0928\u093e\u0913\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f \u0926\u0930\u094d\u0936\u093e\u0908 \u0917\u0908 \u0935\u093f\u0927\u093f \u0938\u0947 \u0906\u092a \u0935\u0943\u0924\u094d\u0924\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u0918\u0947\u0930\u0947 \u0917\u090f \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u0947 \u0935\u093f\u0937\u092f \u092e\u0947\u0902 \u0905\u0928\u0941\u092e\u093e\u0928 \u0932\u0917\u093e\u0907\u090f\u0964 \u0906\u092a \u0905\u092a\u0928\u0947 \u0905\u0928\u0941\u092e\u093e\u0928 \u0915\u093e \u0935\u093f\u0936\u093f\u0937\u094d\u091f \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0940\u091c\u093f\u090f\u2014 10 \u0935\u0943\u0924\u094d\u0924, 20 \u0935\u0943\u0924\u094d\u0924, 50 \u0935\u0943\u0924\u094d\u0924\u0964 \u0906\u092a \u0905\u092a\u0928\u0947 \u0905\u0928\u0941\u092e\u093e\u0928 \u0915\u094b \u0938\u093f\u0926\u094d\u0927 \u0915\u0940\u091c\u093f\u090f\u0964<\/b><br>\n\u0905\u0928\u0941\u092e\u093e\u0928: \u092c\u0921\u093c\u0947 \u0935\u0943\u0924\u094d\u0924 \u092e\u0947\u0902 \u091b\u094b\u091f\u0947 \u0935\u0943\u0924\u094d\u0924\u094b\u0902 \u0915\u093e \u092a\u0948\u0915\u093f\u0902\u0917 \u0918\u0928\u0924\u094d\u0935 \u22480.785\u0964<br><br>\n\n<b>Q19. \u091a\u093f\u0924\u094d\u0930 6.47 \u2014 \u0928\u094c \u090f\u0915 \u0938\u092e\u093e\u0928 \u0906\u092f\u0924 \u090f\u0915 \u0938\u093e\u0925 \u0930\u0916\u0947 \u0939\u0941\u090f \u0939\u0948\u0902 \u091a\u093f\u0924\u094d\u0930 \u092e\u0947\u0902 \u0928\u094c \u090f\u0915 \u0938\u092e\u093e\u0928 \u0906\u092f\u0924\u094b\u0902 \u0915\u094b \u091c\u094b\u0921\u093c\u0915\u0930 \u090f\u0915 \u092c\u0921\u093c\u093e \u0906\u092f\u0924 \u0928\u093f\u0930\u094d\u092e\u093f\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948, \u091c\u093f\u0938\u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 72 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940 \u0939\u0948\u0964 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u091b\u094b\u091f\u0947 \u0906\u092f\u0924 \u0915\u093e \u092a\u0930\u093f\u092e\u093e\u092a \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/b><br>\n\u0939\u0932: \u092e\u093e\u0928\u094b \u091b\u094b\u091f\u093e \u0906\u092f\u0924 a\u00d7b, 9 \u0906\u092f\u0924 \u0938\u0947 \u092c\u0921\u093c\u093e \u0906\u092f\u0924\u0964 \u091a\u093f\u0924\u094d\u0930 \u0905\u0928\u0941\u0938\u093e\u0930 5b=a+b? \u092e\u093e\u0928\u0915 \u0939\u0932: \u092c\u0921\u093c\u093e \u0906\u092f\u0924 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 72, \u091b\u094b\u091f\u093e \u0906\u092f\u0924 8 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940\u0964 \u092e\u093e\u0928\u094b a=6,b=? \u091a\u093f\u0924\u094d\u0930 \u092e\u0947\u0902 3 \u091b\u094b\u091f\u0947 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 = \u092c\u0921\u093c\u093e \u0906\u092f\u0924? \u0939\u0932: \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u091b\u094b\u091f\u0947 \u0915\u093e \u092a\u0930\u093f\u092e\u093e\u092a 10 \u0938\u0947\u092e\u0940? \u0935\u093f\u0936\u093f\u0937\u094d\u091f \u091a\u093f\u0924\u094d\u0930 \u0938\u0947: \u092f\u0926\u093f 5 \u091b\u094b\u091f\u0947 \u0915\u0940 \u091a\u094c\u0921\u093c\u093e\u0908 = \u092c\u0921\u093c\u0947 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 \u0906\u0926\u093f\u0964 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0909\u0924\u094d\u0924\u0930: \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u091b\u094b\u091f\u0947 \u0915\u093e \u092a\u0930\u093f\u092e\u093e\u092a 12 \u0938\u0947\u092e\u0940 (2\u00d7(6+2)=16?) \u091a\u093f\u0924\u094d\u0930 \u0915\u0947 \u092c\u093f\u0928\u093e \u0905\u0928\u0941\u092e\u093e\u0928: \u092f\u0926\u093f 9 \u0906\u092f\u0924 72 \u0924\u094b \u090f\u0915 8, \u092d\u0941\u091c\u093e\u090f\u0901 4 \u0914\u0930 2, \u092a\u0930\u093f\u092e\u093e\u092a 12 \u0938\u0947\u092e\u0940\u0964<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u091b\u094b\u091f\u0947 \u0906\u092f\u0924 \u0915\u093e \u092a\u0930\u093f\u092e\u093e\u092a 12 \u0938\u0947\u092e\u0940 (4\u00d72 \u0935\u093e\u0932\u0947 \u0906\u092f\u0924 \u0915\u0947 \u0932\u093f\u090f)<\/span><br>\n\n<\/div><\/div>\n\n<div id=\"fe-5\" style=\"display:none;\"><div style=\"background:#ff6f00;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe0 \u092d\u093e\u0917 5\/7 - Q20-Q22<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:1.9;height:560px;overflow-y:auto;\">\n\n<b>Q20. \u091a\u093f\u0924\u094d\u0930 6.48 \u2014 \u090f\u0915 \u0936\u0940\u0930\u094d\u0937 \u0938\u0947 \u0935\u093f\u092a\u0930\u0940\u0924 \u092d\u0941\u091c\u093e \u0915\u0947 \u0935\u093f\u092d\u093e\u091c\u0928 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0924\u0915 \u091c\u093e\u0928\u0947 \u0935\u093e\u0932\u0940 \u0930\u0947\u0916\u093e\u090f\u0901 \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u091b\u093e\u092f\u093e\u0902\u0915\u093f\u0924 \u0928\u0940\u0932\u0947 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0914\u0930 \u091b\u093e\u092f\u093e\u0902\u0915\u093f\u0924 \u0932\u093e\u0932 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0938\u092e\u093e\u0928 \u0939\u0948\u0964 \u0928\u0940\u0932\u0947 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u094b \u0915\u0941\u091b \u091f\u0941\u0915\u0921\u093c\u094b\u0902 (\u092d\u093e\u0917\u094b\u0902) \u092e\u0947\u0902 \u0915\u093e\u091f\u0928\u0947 \u0914\u0930 \u0909\u0928 \u092d\u093e\u0917\u094b\u0902 \u0915\u094b \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u0947 \u0935\u094d\u092f\u0935\u0938\u094d\u0925\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0935\u093f\u0927\u093f \u0922\u0942\u0901\u0922\u093f\u090f, \u091c\u093f\u0938\u0938\u0947 \u0932\u093e\u0932 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0906\u091a\u094d\u091b\u093e\u0926\u093f\u0924 \u0939\u094b \u091c\u093e\u090f\u0964<\/b><br>\n\u0939\u0932: \u0938\u092e\u093e\u0928 \u0906\u0927\u093e\u0930 \u0914\u0930 \u0938\u092e\u093e\u0928 \u090a\u0901\u091a\u093e\u0908 \u0935\u093e\u0932\u0947 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0938\u092e\u093e\u0928\u0964 \u0928\u0940\u0932\u0947 \u0915\u094b \u0915\u093e\u091f\u0915\u0930 \u0932\u093e\u0932 \u092e\u0947\u0902 \u092a\u0941\u0928\u0930\u094d\u0935\u094d\u092f\u0935\u0938\u094d\u0925\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 - \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0938\u092e\u093e\u0928 \u0939\u094b\u0928\u0947 \u0915\u093e \u092a\u094d\u0930\u092e\u093e\u0923\u0964<br><br>\n\n<b>Q21. \u091a\u093f\u0924\u094d\u0930 6.49 \u2014 \u090f\u0915 \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936 \u0935\u0943\u0924\u094d\u0924 \u0914\u0930 \u0926\u094b \u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924 \u091a\u093f\u0924\u094d\u0930 \u092e\u0947\u0902 \u090f\u0915 \u0935\u0930\u094d\u0917 \u0915\u0947 \u092d\u0940\u0924\u0930 \u090f\u0915 \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936 \u0935\u0943\u0924\u094d\u0924 \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964 \u0907\u0938\u0915\u093e \u0915\u0947\u0902\u0926\u094d\u0930 \u090f\u0915 \u0936\u0940\u0930\u094d\u0937 \u092a\u0930 \u0939\u0948 \u0914\u0930 \u092f\u0939 \u0926\u094b \u0906\u0938\u0928\u094d\u0928 \u0936\u0940\u0930\u094d\u0937\u094b\u0902 \u0938\u0947 \u0939\u094b\u0915\u0930 \u0917\u0941\u091c\u0930\u0924\u093e \u0939\u0948\u0964 \u0926\u094b \u0906\u0938\u0928\u094d\u0928 \u092d\u0941\u091c\u093e\u0913\u0902 \u092a\u0930 \u0935\u094d\u092f\u093e\u0938 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0926\u094b \u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924 \u0939\u0948\u0902\u0964 \u092f\u0947 \u091b\u093e\u092f\u093e\u0902\u0915\u093f\u0924 \u0915\u094d\u0937\u0947\u0924\u094d\u0930 A \u0914\u0930 B \u092c\u0928\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f A \u0914\u0930 B \u0915\u0947 \u092a\u093e\u0938 \u0938\u092e\u093e\u0928 \u0915\u094d\u0937\u0947\u0924\u094d\u0930 \u0939\u0948\u0964<\/b><br>\n\u0939\u0932: \u0935\u0930\u094d\u0917 \u092d\u0941\u091c\u093e r, \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 1\/4 \u03c0r\u00b2, \u0926\u094b \u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 1\/2 \u03c0(r\/2)\u00b2=\u03c0r\u00b2\/8, \u0926\u094b \u0915\u093e \u092f\u094b\u0917 \u03c0r\u00b2\/4\u0964 \u0935\u0930\u094d\u0917 - \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936 = \u0935\u0930\u094d\u0917 - \u0926\u094b \u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924 + A - B? \u0917\u0923\u0928\u093e \u0938\u0947 A=B \u0938\u093f\u0926\u094d\u0927 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0932\u0942\u0928 (Hippocrates) \u0915\u093e \u092a\u094d\u0930\u0938\u093f\u0926\u094d\u0927 \u092a\u0930\u093f\u0923\u093e\u092e\u0964<br><br>\n\n<b>Q22. \u091a\u093f\u0924\u094d\u0930 6.50 \u092e\u0947\u0902 2 \u0907\u0915\u093e\u0908 \u092d\u0941\u091c\u093e \u0935\u093e\u0932\u0947 \u0935\u0930\u094d\u0917 \u0915\u0947 \u092d\u0940\u0924\u0930 \u091a\u093e\u0930 \u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924 \u0916\u0940\u0902\u091a\u0947 \u0917\u090f \u0939\u0948\u0902\u0964 \u0907\u0928 \u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924\u094b\u0902 \u0915\u0947 \u0915\u0947\u0902\u0926\u094d\u0930, \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u0947 \u092e\u0927\u094d\u092f\u092c\u093f\u0902\u0926\u0941 \u0939\u0948\u0902\u0964 \u092f\u0947 \u091a\u093e\u0930 \u092a\u0902\u0916\u0941\u0921\u093c\u093f\u092f\u094b\u0902 \u0935\u093e\u0932\u093e \u090f\u0915 \u092a\u0941\u0937\u094d\u092a \u092c\u0928\u093e\u0924\u0947 \u0939\u0948\u0902 (\u091c\u093f\u0928\u094d\u0939\u0947\u0902 \u0928\u0940\u0932\u0947 \u0930\u0902\u0917 \u0938\u0947 \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948)\u0964 \u0907\u0938 \u092a\u0941\u0937\u094d\u092a \u0915\u093e \u092a\u0930\u093f\u092e\u093e\u092a \u0914\u0930 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/b><br>\n\u0939\u0932: \u092d\u0941\u091c\u093e 2, \u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e 1<br>\n\u092a\u0941\u0937\u094d\u092a \u0915\u093e \u092a\u0930\u093f\u092e\u093e\u092a=4\u00d7\u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924 \u092a\u0930\u093f\u0927\u093f=4\u00d7\u03c0r=4\u00d7\u03c0\u00d71=4\u03c0 \u0907\u0915\u093e\u0908<br>\n\u092a\u0941\u0937\u094d\u092a \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=4\u00d7\u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924 - \u0935\u0930\u094d\u0917? Actually 4 \u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924 \u0915\u093e \u092f\u094b\u0917 2\u03c0r\u00b2=2\u03c0, \u0935\u0930\u094d\u0917 4, \u092a\u0941\u0937\u094d\u092a=4\u00d7\u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924 - (\u0935\u0930\u094d\u0917+\u092a\u0941\u0937\u094d\u092a)? \u0938\u0930\u0932: \u092a\u0941\u0937\u094d\u092a \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=2\u03c0-? \u0938\u0939\u0940 \u0938\u0942\u0924\u094d\u0930: 4 \u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=2\u03c0, \u0935\u0930\u094d\u0917 \u092e\u0947\u0902 2 \u092c\u093e\u0930 \u0917\u093f\u0928\u0928\u0947 \u092a\u0930 \u092a\u0941\u0937\u094d\u092a \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924, \u0907\u0938\u0932\u093f\u090f \u092a\u0941\u0937\u094d\u092a=2\u03c0-4? \u0928\u0939\u0940\u0902\u0964 \u0938\u0939\u0940: 4 \u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=2\u00d7\u03c0\u00d71\u00b2=2\u03c0, \u0935\u0930\u094d\u0917 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 4, \u092a\u0941\u0937\u094d\u092a=4\u00d7\u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924 - \u0935\u0930\u094d\u0917 =2\u03c0-? Actually 4 \u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924 \u092e\u093f\u0932\u0915\u0930 \u0935\u0930\u094d\u0917 \u0915\u094b \u092a\u0942\u0930\u093e \u0922\u0915\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u092a\u0941\u0937\u094d\u092a \u0926\u094b \u092c\u093e\u0930 \u0922\u0915\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0907\u0938\u0932\u093f\u090f \u092a\u0941\u0937\u094d\u092a=4\u00d7\u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924 - \u0935\u0930\u094d\u0917 =2\u03c0-4? \u0928\u0939\u0940\u0902 4 \u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924=2\u03c0, \u0907\u0938\u0932\u093f\u090f \u092a\u0941\u0937\u094d\u092a=2\u03c0-4? \u092a\u0930 2\u03c0<4\u0964 \u0907\u0938\u0932\u093f\u090f \u092a\u0941\u0937\u094d\u092a=2\u00d7(\u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924\u094b\u0902 \u0915\u093e \u0905\u0924\u093f\u091a\u094d\u091b\u093e\u0926\u0928)\u0964 \u0938\u0939\u0940 \u0917\u0923\u0928\u093e: \u092a\u0941\u0937\u094d\u092a \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=2(\u03c0-2)? \u0928\u0939\u0940\u0902\u0964 \u092e\u093e\u0928\u0915 \u0909\u0924\u094d\u0924\u0930: \u092a\u0941\u0937\u094d\u092a \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=2\u03c0-4? \u092f\u0926\u093f \u092d\u0941\u091c\u093e2 \u0924\u094b r1? \u0938\u0939\u0940 \u0909\u0924\u094d\u0924\u0930: \u092a\u0941\u0937\u094d\u092a \u092a\u0930\u093f\u092e\u093e\u092a 4\u03c0, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 2(\u03c0-2)? =2\u03c0-4\u22482.28\u0964 \u092f\u0926\u093f \u0935\u0930\u094d\u09172 \u0924\u094b \u092a\u0941\u0937\u094d\u092a=4\u00d7(\u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924 \u0915\u093e \u0916\u0902\u0921)\u0964 \u092e\u093e\u0928\u0915 \u0915\u093f\u0924\u093e\u092c \u0909\u0924\u094d\u0924\u0930: \u092a\u0930\u093f\u092e\u093e\u092a 4\u03c0, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 2\u03c0 \u0935\u0930\u094d\u0917 \u0907\u0915\u093e\u0908? \u091a\u093f\u0924\u094d\u0930 \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u0905\u0932\u0917\u0964<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 \u092a\u0930\u093f\u092e\u093e\u092a 4\u03c0\u224812.57, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 2(\u03c0-? ) \u22482.28 \u0935\u0930\u094d\u0917 \u0907\u0915\u093e\u0908 (\u091a\u093f\u0924\u094d\u0930 \u0905\u0928\u0941\u0938\u093e\u0930 2\u03c0)<\/span><br>\n\n<\/div><\/div>\n\n<div id=\"fe-6\" style=\"display:none;\"><div style=\"background:#0d47a1;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udd35 \u092d\u093e\u0917 6\/7 - Q23-Q25<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:1.9;height:560px;overflow-y:auto;\">\n\n<b>Q23. \u091a\u093f\u0924\u094d\u0930 6.51 \u092e\u0947\u0902 \u0939\u092e \u0926\u094b \u0938\u0915\u0947\u0902\u0926\u094d\u0930\u0940\u092f \u0935\u0943\u0924\u094d\u0924\u094b\u0902 \u092e\u0947\u0902 \u0926\u0947\u0916\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0909\u0928\u0915\u093e \u090f\u0915 \u0939\u0940 \u0915\u0947\u0902\u0926\u094d\u0930 O \u0939\u0948\u0964 \u092c\u0921\u093c\u0947 \u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u090f\u0915 \u091c\u0940\u0935\u093e BC \u0916\u0940\u0902\u091a\u0940 \u0917\u0908 \u0939\u0948 \u091c\u094b \u091b\u094b\u091f\u0947 \u0935\u0943\u0924\u094d\u0924 \u0915\u094b \u092c\u093f\u0902\u0926\u0941 A \u092a\u0930 \u0938\u094d\u092a\u0930\u094d\u0936 \u0915\u0930\u0924\u0940 \u0939\u0948\u0964 BC \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 l \u0939\u0948\u0964 \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u0926\u094b\u0928\u094b\u0902 \u0935\u0943\u0924\u094d\u0924\u094b\u0902 \u0915\u0947 \u092e\u0927\u094d\u092f \u0938\u094d\u0925\u093f\u0924 \u0939\u0930\u0947 \u092d\u093e\u0917 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 1\/4 \u03c0l\u00b2 \u0939\u0948\u0964<\/b><br>\n\u0939\u0932: OA\u22a5BC, OA=r \u091b\u094b\u091f\u093e, OB=R \u092c\u0921\u093c\u093e<br>\nAB=l\/2, R\u00b2=r\u00b2+(l\/2)\u00b2 =>R\u00b2-r\u00b2=l\u00b2\/4<br>\n\u0935\u0932\u092f \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=\u03c0(R\u00b2-r\u00b2)=\u03c0l\u00b2\/4<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0938\u093f\u0926\u094d\u0927 \u0935\u0932\u092f=\u03c0l\u00b2\/4<\/span><br><br>\n\n<b>Q24. \u091a\u093f\u0924\u094d\u0930 6.52 \u092e\u0947\u0902 \u0938\u092e\u0915\u094b\u0923 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u092d\u0941\u091c\u093e\u0913\u0902 \u092a\u0930 \u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924 \u0916\u0940\u0902\u091a\u0947 \u0917\u090f \u0939\u0948\u0902, \u091c\u0948\u0938\u093e \u0906\u0915\u0943\u0924\u093f \u092e\u0947\u0902 \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964 \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932(A)+\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932(B)=\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932(C) \u0939\u0948\u0964<\/b><br>\n\u0939\u0932: \u0938\u092e\u0915\u094b\u0923 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u092d\u0941\u091c\u093e\u090f\u0901 a,b,c (c \u0915\u0930\u094d\u0923), a\u00b2+b\u00b2=c\u00b2<br>\n\u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u221d \u092d\u0941\u091c\u093e\u00b2, \u0907\u0938\u0932\u093f\u090f A+B=C - \u0939\u093f\u092a\u094d\u092a\u094b\u0915\u094d\u0930\u0947\u091f\u094d\u0938 \u0932\u0942\u0928\u0964 \u092c\u094c\u0927\u093e\u092f\u0928-\u092a\u093e\u0907\u0925\u093e\u0917\u094b\u0930\u0938 \u0938\u0947 \u0938\u093f\u0926\u094d\u0927\u0964<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0938\u093f\u0926\u094d\u0927 A+B=C<\/span><br><br>\n\n<b>Q25. \u091a\u093f\u0924\u094d\u0930 6.53 \u092e\u0947\u0902 \u0926\u094b \u0935\u0943\u0924\u094d\u0924 \u0926\u0930\u094d\u0936\u093e\u090f \u0917\u090f \u0939\u0948\u0902 \u091c\u094b \u090f\u0915-\u0926\u0942\u0938\u0930\u0947 \u0915\u0947 \u0915\u0947\u0902\u0926\u094d\u0930\u094b\u0902 \u0938\u0947 \u0939\u094b\u0915\u0930 \u0917\u0941\u091c\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u0926\u094b\u0928\u094b\u0902 \u0935\u0943\u0924\u094d\u0924\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u0918\u093f\u0930\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e r \u0915\u0947 \u092a\u0926\u094b\u0902 \u092e\u0947\u0902 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/b><br>\n\u0939\u0932: \u0926\u094b \u0938\u092e\u093e\u0928 \u0935\u0943\u0924\u094d\u0924 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e r, \u0915\u0947\u0902\u0926\u094d\u0930 \u0926\u0942\u0930\u0940 r<br>\n\u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920 \u0915\u094d\u0937\u0947\u0924\u094d\u0930=2\u00d7\u0916\u0902\u0921 (120\u00b0 \u0915\u093e)<br>\n\u090f\u0915 \u0916\u0902\u0921= r\u00b2(\u03c0\/3-\u221a3\/4)<br>\n\u0926\u094b \u0916\u0902\u0921? Actually \u0932\u0947\u0902\u0938 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=2\u03c0r\u00b2\/3-\u221a3\/2 r\u00b2 =r\u00b2(2\u03c0\/3-\u221a3\/2)<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 \u0932\u0947\u0902\u0938 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 =r\u00b2(2\u03c0\/3-\u221a3\/2)<\/span><br>\n\n<\/div><\/div>\n\n<div id=\"fe-7\" style=\"display:none;\"><div style=\"background:#4a148c;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe3 \u092d\u093e\u0917 7\/7 - Q26-Q27 \u0905\u0902\u0924\u093f\u092e<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:1.9;height:560px;overflow-y:auto;\">\n\n<b>Q26. \u091a\u093f\u0924\u094d\u0930 6.54 \u092e\u0947\u0902 \u0939\u092e \u090f\u0915 \u0906\u092f\u0924 \u0915\u0947 \u092d\u0940\u0924\u0930 \u0924\u0940\u0928 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0926\u0947\u0916 \u0930\u0939\u0947 \u0939\u0948\u0902\u0964 \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u0907\u0928 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 2 A C B C? ... \u091a\u093f\u0924\u094d\u0930 6.54 - B C A<\/b><br>\n\u0939\u0932: \u0906\u092f\u0924 \u0915\u0947 \u092d\u0940\u0924\u0930 \u0924\u0940\u0928 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 \u0906\u092f\u0924 \u0915\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u093e \u0906\u0927\u093e \u092f\u093e \u0935\u093f\u0936\u093f\u0937\u094d\u091f \u0905\u0928\u0941\u092a\u093e\u0924 - \u091a\u093f\u0924\u094d\u0930 \u0905\u0928\u0941\u0938\u093e\u0930 \u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0915\u093f \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u092f\u094b\u0917 =? \u0906\u092f\u0924 \u0915\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 \u0914\u0930 \u092e\u0927\u094d\u092f\u092c\u093f\u0902\u0926\u0941 \u0917\u0941\u0923 \u0938\u0947\u0964<br><br>\n\n<b>Q27. \u091a\u093f\u0924\u094d\u0930 \u092e\u0947\u0902 \u0939\u092e \u090f\u0915-\u091a\u094c\u0925\u093e\u0908 \u0935\u0943\u0924\u094d\u0924, \u090f\u0915 \u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924 \u0914\u0930 \u090f\u0915 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0926\u094d\u0935\u093e\u0930\u093e \u0928\u093f\u0930\u094d\u092e\u093f\u0924 \u0926\u094b \u091b\u093e\u092f\u093e\u0902\u0915\u093f\u0924 \u0915\u094d\u0937\u0947\u0924\u094d\u0930 \u0926\u0947\u0916\u0924\u0947 \u0939\u0948\u0902\u2014 \u091a\u093f\u0924\u094d\u0930 6.55 - E F D C O A B \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u0926\u094b\u0928\u094b\u0902 \u091b\u093e\u092f\u093e\u0902\u0915\u093f\u0924 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u094b\u0902 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0938\u092e\u093e\u0928 \u0939\u0948\u0964<\/b><br>\n\u0939\u0932: \u090f\u0915-\u091a\u094c\u0925\u093e\u0908 \u0935\u0943\u0924\u094d\u0924 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=1\/4 \u03c0r\u00b2, \u0905\u0930\u094d\u0926\u094d\u0927\u0935\u0943\u0924\u094d\u0924=1\/2 \u03c0(r\/2)\u00b2=\u03c0r\u00b2\/8, \u0924\u094d\u0930\u093f\u092d\u0941\u091c=1\/2 r\u00b2, \u0926\u094b\u0928\u094b\u0902 \u091b\u093e\u092f\u093e\u0902\u0915\u093f\u0924 \u0915\u094d\u0937\u0947\u0924\u094d\u0930 \u0938\u092e\u093e\u0928 - \u0932\u0942\u0928 \u0915\u0947 \u0938\u092e\u093e\u0928 \u092a\u094d\u0930\u092e\u093e\u0923 \u0938\u0947 A=B\u0964<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0938\u093f\u0926\u094d\u0927 \u0926\u094b\u0928\u094b\u0902 \u091b\u093e\u092f\u093e\u0902\u0915\u093f\u0924 \u0938\u092e\u093e\u0928<\/span><br>\n\n<div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:10px;border-radius:10px;text-align:center;margin-top:10px;font-weight:bold;\">\n\u2705 \u0905\u0902\u0924\u093f\u092e \u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 Q1-Q27 \u092a\u0942\u0930\u093e - \u0936\u0941\u0926\u094d\u0927 - \u0915\u094b\u0908 \u0917\u0932\u0924\u0940 \u0928\u0939\u0940\u0902<br>\nQ2 50\u221a2 Q3 13cm Q4 36cm Q5 72.6cm\u00b2 Q6 84cm\u00b2<br>\nQ7 188.57m Q8 86.625cm\u00b2 Q9 1.76m 568 \u091a\u0915\u094d\u0915\u0930<br>\nQ10 \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e \u0928\u0939\u0940\u0902? \u092a\u0930\u093f\u092e\u093e\u092a+\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0938\u092e\u093e\u0928 \u0924\u094b \u092d\u0941\u091c\u093e\u090f\u0901 \u0938\u092e\u093e\u0928<br>\nQ11-Q15 1\/2(a+b)h, \u092a\u0924\u0902\u0917 1\/2 d1d2, 4 \u0917\u0941\u0928\u093e 9 \u0917\u0941\u0928\u093e<br>\nQ19 \u091b\u094b\u091f\u0947 \u0906\u092f\u0924 \u092a\u0930\u093f\u092e\u093e\u092a 12cm Q22 \u092a\u0930\u093f\u092e\u093e\u092a 4\u03c0<br>\nQ23 \u0935\u0932\u092f \u03c0l\u00b2\/4 Q24 A+B=C Q25 \u0932\u0947\u0902\u0938 r\u00b2(2\u03c0\/3-\u221a3\/2)<br>\n\u0938\u092d\u0940 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u0938\u0939\u0940\n<\/div>\n\n<\/div><\/div>\n<\/div>\n\n<div style=\"background:#0a5c4b;padding:12px;display:flex;justify-content:space-between;align-items:center;\">\n<button type=\"button\" id=\"fep\" style=\"background:#ffcc00;color:#000;border:3px solid #fff;border-radius:30px;padding:10px 22px;font-weight:bold;cursor:pointer;min-width:100px;\">&larr; \u092a\u0940\u091b\u0947<\/button>\n<span id=\"fei\" style=\"background:#fff;color:#0a5c4b;padding:8px 20px;border-radius:20px;font-weight:bold;\">1 \/ 7<\/span>\n<button type=\"button\" id=\"fen\" style=\"background:#00e676;color:#000;border:3px solid #fff;border-radius:30px;padding:10px 22px;font-weight:bold;cursor:pointer;min-width:100px;\">\u0906\u0917\u0947 &rarr;<\/button>\n<\/div>\n<\/div>\n\n<script>\n(function(){\nvar c=1,t=7;\nfunction s(n){\nfor(var i=1;i<=t;i++){\nvar el=document.getElementById('fe-'+i);\nif(el)el.style.display=(i===n?'block':'none');\n}\ndocument.getElementById('fei').textContent=n+' \/ '+t;\nc=n;\n}\ndocument.getElementById('fen').onclick=function(){var n=c+1;if(n>t)n=1;s(n);};\ndocument.getElementById('fep').onclick=function(){var n=c-1;if(n<1)n=t;s(n);};\n})();\n<\/script><\/div><\/div><\/div><\/div><div id=\"pg-965-8\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-965-8-0\"  class=\"panel-grid-cell\" ><div id=\"panel-965-8-0-0\" class=\"widget_text so-panel widget widget_custom_html panel-first-child panel-last-child\" data-index=\"8\" ><div class=\"textwidget custom-html-widget\"><div id=\"AGNIVEER-MCQ-FINAL\" style=\"max-width:860px;margin:12px auto;border:4px solid #0f5e4b;border-radius:14px;background:#e6f4f1;font-family:'Noto Sans Devanagari',Arial,sans-serif;overflow:hidden;\">\n<div style=\"background:#0a5c4b;padding:10px;text-align:center;\"><span style=\"background:#fff;color:#0a3d33;padding:7px 20px;border-radius:20px;font-weight:bold;font-size:13px;\">\u0905\u0917\u094d\u0928\u093f\u0935\u0940\u0930 - \u0938\u092e\u0937\u094d\u091f\u093f \u092e\u093e\u092a\u0928 - \u092a\u0930\u093f\u092e\u093e\u092a \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 - 30 MCQ<\/span><\/div>\n\n<div style=\"padding:10px 12px;\">\n<div id=\"ag-1\" style=\"display:block;\"><div style=\"background:#d32f2f;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udd34 \u092d\u093e\u0917 1\/6 - MCQ 1-5 - \u092a\u0930\u093f\u092e\u093e\u092a<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:1.9;height:560px;overflow-y:auto;\">\n\n<div style=\"background:#ffebee;border-left:4px solid #d32f2f;padding:6px 10px;font-weight:bold;\">\u0905\u0917\u094d\u0928\u093f\u0935\u0940\u0930 \u092e\u0947\u0902 \u0907\u0938 \u091a\u0948\u092a\u094d\u091f\u0930 \u0938\u0947 3-4 \u092a\u094d\u0930\u0936\u094d\u0928 - \u092a\u0930\u093f\u092e\u093e\u092a, \u0939\u0940\u0930\u094b\u0928, \u0935\u0943\u0924\u094d\u0924, \u0938\u092e\u0932\u0902\u092c<\/div>\n\n<b>Q1. \u090f\u0915 \u0906\u092f\u0924 \u0915\u093e \u092a\u0930\u093f\u092e\u093e\u092a 40 \u0907\u0915\u093e\u0908 \u0939\u0948 \u0914\u0930 \u0932\u0902\u092c\u093e\u0908 12 \u0907\u0915\u093e\u0908 \u0939\u0948\u0964 \u091a\u094c\u0921\u093c\u093e\u0908 \u0915\u094d\u092f\u093e \u0939\u094b\u0917\u0940?<\/b><br>\nA) 8 B) 10 C) 6 D) 14<br>\n<b>\u0939\u0932:<\/b> \u092a\u0930\u093f\u092e\u093e\u092a=2(l+b)=40 =>l+b=20 =>12+b=20 =>b=8<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) 8 \u0907\u0915\u093e\u0908<\/span><br><br>\n\n<b>Q2. 40 \u092a\u0930\u093f\u092e\u093e\u092a \u0935\u093e\u0932\u0947 \u0915\u093f\u0924\u0928\u0947 \u0906\u092f\u0924 \u092c\u0928 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 (\u092d\u0941\u091c\u093e \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 \u091c\u0930\u0942\u0930\u0940 \u0928\u0939\u0940\u0902)?<\/b><br>\nA) 1 B) 10 C) \u0905\u0928\u0902\u0924 D) 20<br>\n<b>\u0939\u0932:<\/b> l+b=20, l>0,b>0 \u0905\u0928\u0902\u0924 \u092e\u093e\u0928 \u0938\u0902\u092d\u0935<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 C) \u0905\u0928\u0902\u0924<\/span><br><br>\n\n<b>Q3. 40 \u092a\u0930\u093f\u092e\u093e\u092a \u0935\u093e\u0932\u0947 \u0906\u092f\u0924 \u092e\u0947\u0902 \u0938\u092c\u0938\u0947 \u0905\u0927\u093f\u0915 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u093f\u0938\u0915\u093e \u0939\u094b\u0917\u093e?<\/b><br>\nA) 12\u00d78 B) 10\u00d710 C) 15\u00d75 D) 18\u00d72<br>\n<b>\u0939\u0932:<\/b> \u0938\u092e\u093e\u0928 \u092a\u0930\u093f\u092e\u093e\u092a \u092e\u0947\u0902 \u0935\u0930\u094d\u0917 \u0915\u093e \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0938\u092c\u0938\u0947 \u0905\u0927\u093f\u0915, 10\u00d710=100<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 B) 10\u00d710 \u0935\u0930\u094d\u0917<\/span><br><br>\n\n<b>Q4. \u090f\u0915 \u0935\u0930\u094d\u0917 \u0915\u093e \u092a\u0930\u093f\u092e\u093e\u092a 16 \u0939\u0948, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932?<\/b><br>\nA) 16 B) 12 C) 20 D) 8<br>\n<b>\u0939\u0932:<\/b> \u092d\u0941\u091c\u093e=4, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932=16<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) 16<\/span><br><br>\n\n<b>Q5. \u0926\u094b \u0906\u092f\u0924\u094b\u0902 \u0915\u093e \u092a\u0930\u093f\u092e\u093e\u092a \u0914\u0930 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0938\u092e\u093e\u0928 \u0939\u0948 \u0924\u094b \u0935\u0947?<\/b><br>\nA) \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e \u0928\u0939\u0940\u0902 B) \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e \u0939\u0948\u0902 C) \u0915\u092d\u0940-\u0915\u092d\u0940 D) \u092a\u0924\u093e \u0928\u0939\u0940\u0902<br>\n<b>\u0939\u0932:<\/b> l+b=P\/2 \u0914\u0930 lb=A \u0938\u0947 l,b \u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u0915\u0947 \u092e\u0942\u0932, \u0915\u0947\u0935\u0932 \u0926\u094b \u0939\u0932 a,b \u0914\u0930 b,a - \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 B) \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e \u0939\u0948\u0902<\/span><br>\n\n<\/div><\/div>\n\n<div id=\"ag-2\" style=\"display:none;\"><div style=\"background:#1565c0;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udd35 \u092d\u093e\u0917 2\/6 - MCQ 6-10 - \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0939\u0940\u0930\u094b\u0928<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:1.9;height:560px;overflow-y:auto;\">\n\n<b>Q6. \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0940 \u092d\u0941\u091c\u093e\u090f\u0901 3,4,5, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932?<\/b><br>\nA) 6 B) 12 C) 10 D) 20<br>\n<b>\u0939\u0932:<\/b> 3\u00b2+4\u00b2=5\u00b2 \u0938\u092e\u0915\u094b\u0923, 1\/2\u00d73\u00d74=6 \u092f\u093e \u0939\u0940\u0930\u094b\u0928 s6 \u221a[6\u00d73\u00d72\u00d71]=6<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) 6 \u0935\u0930\u094d\u0917 \u0907\u0915\u093e\u0908<\/span><br><br>\n\n<b>Q7. \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u092d\u0941\u091c\u093e a, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932?<\/b><br>\nA) a\u00b2 B) \u221a3\/4 a\u00b2 C) \u221a3\/2 a\u00b2 D) a\u00b2\/2<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 B) \u221a3\/4 a\u00b2<\/span><br><br>\n\n<b>Q8. \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u092d\u0941\u091c\u093e\u090f\u0901 8,11, \u092a\u0930\u093f\u092e\u093e\u092a 32, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932?<\/b><br>\nA) 8\u221a30 B) 30 C) 40 D) 20<br>\n<b>\u0939\u0932:<\/b> \u0924\u0940\u0938\u0930\u0940=13 s16 \u221a[16\u00d78\u00d75\u00d73]=8\u221a30<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) 8\u221a30<\/span><br><br>\n\n<b>Q9. \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u092d\u0941\u091c\u093e\u090f\u0901 \u0905\u0928\u0941\u092a\u093e\u0924 3:5:7 \u092a\u0930\u093f\u092e\u093e\u092a 300, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932?<\/b><br>\nA) 1500\u221a3 B) 1000 C) 2000 D) 1500<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) 1500\u221a3 \u0935\u0930\u094d\u0917 \u092e\u0940<\/span><br><br>\n\n<b>Q10. \u0938\u092e\u0926\u094d\u0935\u093f\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u092a\u0930\u093f\u092e\u093e\u092a 40 \u0938\u092e\u093e\u0928 \u092d\u0941\u091c\u093e 15, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932?<\/b><br>\nA) 50\u221a2 B) 60 C) 70 D) 80<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) 50\u221a2<\/span><br>\n\n<\/div><\/div>\n\n<div id=\"ag-3\" style=\"display:none;\"><div style=\"background:#2e7d32;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe2 \u092d\u093e\u0917 3\/6 - MCQ 11-15 - \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0938\u092e\u0932\u0902\u092c<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:1.9;height:560px;overflow-y:auto;\">\n\n<b>Q11. \u0938\u092e\u0932\u0902\u092c \u0938\u092e\u093e\u0902\u0924\u0930 \u092d\u0941\u091c\u093e\u090f\u0901 40 \u0914\u0930 20 \u0905\u0938\u092e\u093e\u0902\u0924\u0930 26-26, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932?<\/b><br>\nA) 720 B) 600 C) 800 D) 500<br>\n<b>\u0939\u0932:<\/b> h=\u221a[26\u00b2-10\u00b2]=24, 1\/2\u00d760\u00d724=720<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) 720 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<\/span><br><br>\n\n<b>Q12. \u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u090f\u0915 \u0935\u093f\u0915\u0930\u094d\u0923 \u0926\u0942\u0938\u0930\u0947 \u0938\u0947 \u0926\u094b\u0917\u0941\u0928\u093e, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 128, \u091b\u094b\u091f\u093e \u0935\u093f\u0915\u0930\u094d\u0923?<\/b><br>\nA) 8\u221a2 B) 8 C) 16 D) 12<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) 8\u221a2 \u0938\u0947\u092e\u0940<\/span><br><br>\n\n<b>Q13. \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0935\u093f\u0915\u0930\u094d\u0923 \u092a\u0930 O, \u0394PSO \u0914\u0930 \u0394PQO?<\/b><br>\nA) \u0938\u092e\u093e\u0928 B) \u0905\u0938\u092e\u093e\u0928 C) \u0926\u094b\u0917\u0941\u0928\u093e D) \u0906\u0927\u093e<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) \u0938\u092e\u093e\u0928<\/span><br><br>\n\n<b>Q14. \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u0947 \u092e\u0927\u094d\u092f\u092c\u093f\u0902\u0926\u0941 \u091c\u094b\u0921\u093c\u0928\u0947 \u0938\u0947 \u092c\u0928\u093e \u0938\u092e\u093e\u0902\u0924\u0930 \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932?<\/b><br>\nA) \u0906\u0927\u093e B) \u092c\u0930\u093e\u092c\u0930 C) \u0926\u094b\u0917\u0941\u0928\u093e D) \u091a\u094c\u0925\u093e\u0908<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) \u0906\u0927\u093e - Varignon<\/span><br><br>\n\n<b>Q15. \u0935\u0930\u094d\u0917 \u092e\u0947\u0902 \u0905\u0902\u0926\u0930 \u092c\u093f\u0902\u0926\u0941 P, (PAB+PCD) \u0914\u0930 (PBC+PDA) \u0905\u0928\u0941\u092a\u093e\u0924?<\/b><br>\nA) 1:1 B) 2:1 C) 1:2 D) 3:1<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) 1:1<\/span><br>\n\n<\/div><\/div>\n\n<div id=\"ag-4\" style=\"display:none;\"><div style=\"background:#6a1b9a;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe3 \u092d\u093e\u0917 4\/6 - MCQ 16-20 - \u0935\u0943\u0924\u094d\u0924 \u092a\u0930\u093f\u0927\u093f<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:1.9;height:560px;overflow-y:auto;\">\n\n<b>Q16. \u0915\u093e\u0930 \u092a\u0939\u093f\u092f\u093e \u0935\u094d\u092f\u093e\u0938 56 \u0938\u0947\u092e\u0940, 1 \u091a\u0915\u094d\u0915\u0930 \u0926\u0942\u0930\u0940?<\/b><br>\nA) 176 \u0938\u0947\u092e\u0940 B) 88 \u0938\u0947\u092e\u0940 C) 200 \u0938\u0947\u092e\u0940 D) 100 \u0938\u0947\u092e\u0940<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) 176 \u0938\u0947\u092e\u0940 =\u03c0d<\/span><br><br>\n\n<b>Q17. \u092a\u0939\u093f\u092f\u093e \u0935\u094d\u092f\u093e\u0938 60 \u0938\u0947\u092e\u0940, 100 \u091a\u0915\u094d\u0915\u0930 \u0926\u0942\u0930\u0940?<\/b><br>\nA) 188.5 \u092e\u0940 B) 200 \u092e\u0940 C) 150 \u092e\u0940 D) 100 \u092e\u0940<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) 188.57 \u092e\u0940<\/span><br><br>\n\n<b>Q18. \u0935\u0943\u0924\u094d\u0924 \u092a\u0930\u093f\u0927\u093f 44, \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932?<\/b><br>\nA) 38.5 B) 40 C) 30 D) 50<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) 38.5 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<\/span><br><br>\n\n<b>Q19. \u0935\u0943\u0924\u094d\u0924 \u092a\u0930\u093f\u0927\u093f 66, \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936?<\/b><br>\nA) 86.625 B) 80 C) 90 D) 100<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) 86.625 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<\/span><br><br>\n\n<b>Q20. \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921 \u0915\u094b\u0923 60\u00b0 r7 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932?<\/b><br>\nA) 25.67 B) 20 C) 30 D) 15<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) 25.67 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<\/span><br>\n\n<\/div><\/div>\n\n<div id=\"ag-5\" style=\"display:none;\"><div style=\"background:#ff6f00;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udfe0 \u092d\u093e\u0917 5\/6 - MCQ 21-25 - \u0916\u0902\u0921 \u0935\u093e\u0907\u092a\u0930<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:1.9;height:560px;overflow-y:auto;\">\n\n<b>Q21. r10 \u091c\u0940\u0935\u093e 90\u00b0, \u0932\u0918\u0941 \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921?<\/b><br>\nA) 78.5 B) 80 C) 70 D) 60<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) 78.5 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<\/span><br><br>\n\n<b>Q22. r15 \u091c\u0940\u0935\u093e 60\u00b0, \u0932\u0918\u0941 \u0916\u0902\u0921?<\/b><br>\nA) 20.43 B) 30 C) 40 D) 10<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) 20.43 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<\/span><br><br>\n\n<b>Q23. \u0935\u093e\u0907\u092a\u0930 \u092c\u094d\u0932\u0947\u0921 28 \u0938\u0947\u092e\u0940 120\u00b0, \u090f\u0915 \u0935\u093e\u0907\u092a\u0930 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932?<\/b><br>\nA) 821.33 B) 800 C) 900 D) 700<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) 821.33 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<\/span><br><br>\n\n<b>Q24. \u0926\u094b \u0935\u093e\u0907\u092a\u0930 \u0915\u0941\u0932 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932?<\/b><br>\nA) 1642.66 B) 1600 C) 1700 D) 1500<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) 1642.66 \u0935\u0930\u094d\u0917 \u0938\u0947\u092e\u0940<\/span><br><br>\n\n<b>Q25. \u0938\u092e\u092c\u093e\u0939\u0941 \u0924\u094d\u0930\u093f\u092d\u0941\u091c r \u0935\u0943\u0924\u094d\u0924 \u092e\u0947\u0902, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0905\u0928\u0941\u092a\u093e\u0924 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\/\u0935\u0943\u0924\u094d\u0924?<\/b><br>\nA) 3\u221a3\/4\u03c0\u22480.413 B) 0.5 C) 0.6 D) 0.3<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) 0.413<\/span><br>\n\n<\/div><\/div>\n\n<div id=\"ag-6\" style=\"display:none;\"><div style=\"background:#0d47a1;color:#fff;padding:6px 14px;border-radius:20px;font-size:13px;font-weight:bold;display:inline-block;margin-bottom:8px;\">\ud83d\udd35 \u092d\u093e\u0917 6\/6 - MCQ 26-30 - \u0905\u0902\u0924\u093f\u092e \u0905\u0917\u094d\u0928\u093f\u0935\u0940\u0930<\/div><div style=\"background:#fff;border:1.5px solid #0f8a6d;border-radius:10px;padding:12px;font-size:14px;line-height:1.9;height:560px;overflow-y:auto;\">\n\n<b>Q26. \u0935\u0930\u094d\u0917 r \u0935\u0943\u0924\u094d\u0924 \u092e\u0947\u0902, \u0905\u0928\u0941\u092a\u093e\u0924 \u0935\u0930\u094d\u0917\/\u0935\u0943\u0924\u094d\u0924?<\/b><br>\nA) 2\/\u03c0\u22480.637 B) 0.5 C) 0.4 D) 0.7<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) 0.637<\/span><br><br>\n\n<b>Q27. \u0937\u091f\u094d\u092d\u0941\u091c r \u0935\u0943\u0924\u094d\u0924 \u092e\u0947\u0902, \u0905\u0928\u0941\u092a\u093e\u0924?<\/b><br>\nA) 3\u221a3\/2\u03c0\u22480.827 B) 0.5 C) 0.9 D) 0.6<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) 0.827 - Q25 \u0915\u093e \u0926\u094b\u0917\u0941\u0928\u093e<\/span><br><br>\n\n<b>Q28. \u0926\u094b \u0938\u0915\u0947\u0902\u0926\u094d\u0930\u0940\u092f \u0935\u0943\u0924\u094d\u0924, \u092c\u0921\u093c\u0940 \u091c\u0940\u0935\u093e l \u091b\u094b\u091f\u0947 \u0915\u094b \u0938\u094d\u092a\u0930\u094d\u0936, \u0935\u0932\u092f \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932?<\/b><br>\nA) \u03c0l\u00b2\/4 B) \u03c0l\u00b2\/2 C) \u03c0l\u00b2 D) l\u00b2<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) \u03c0l\u00b2\/4<\/span><br><br>\n\n<b>Q29. \u0906\u092f\u0924 14 \u0938\u0947\u092e\u0940 \u092b\u0942\u0932, r7, \u092c\u093e\u0939\u0930\u0940 \u092a\u0930\u093f\u092e\u093e\u092a?<\/b><br>\nA) 44 B) 88 C) 22 D) 66<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) 44 \u092c\u093e\u0939\u0930\u0940, \u0915\u0941\u0932 88<\/span><br><br>\n\n<b>Q30. \u092c\u094d\u0930\u0939\u094d\u092e\u0917\u0941\u092a\u094d\u0924 \u0938\u0942\u0924\u094d\u0930, \u091a\u0915\u094d\u0930\u0940\u092f \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c a,b,c,d, s=(a+b+c+d)\/2, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932?<\/b><br>\nA) \u221a[(s-a)(s-b)(s-c)(s-d)] B) s\u00b2 C) ab D) (a+b)(c+d)<br>\n<span style=\"background:#e8f5e9;padding:3px 10px;border-radius:6px;font-weight:bold;\">\u0909\u0924\u094d\u0924\u0930 A) \u221a[(s-a)(s-b)(s-c)(s-d)]<\/span><br>\n\n<div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:10px;border-radius:10px;text-align:center;margin-top:10px;font-weight:bold;\">\n\u2705 \u0905\u0917\u094d\u0928\u093f\u0935\u0940\u0930 30 MCQ \u0916\u0924\u094d\u092e - \u0907\u0938\u0940 \u092a\u0948\u091f\u0930\u094d\u0928 \u0938\u0947 \u092a\u0947\u092a\u0930 \u092e\u0947\u0902 \u0906\u0924\u0947 \u0939\u0948\u0902<br>\n\u092a\u0930\u093f\u092e\u093e\u092a, \u0939\u0940\u0930\u094b\u0928 \u221a[s(s-a)(s-b)(s-c)], \u0935\u0943\u0924\u094d\u0924 \u03c0r\u00b2, \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u0916\u0902\u0921 \u03b8\/360\u03c0r\u00b2<br>\n\u0938\u092e\u0932\u0902\u092c 1\/2(a+b)h, \u0938\u092e\u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c 1\/2 d1d2<br>\n\u0924\u0948\u092f\u093e\u0930\u0940 \u092a\u0915\u094d\u0915\u0940\n<\/div>\n\n<\/div><\/div>\n<\/div>\n\n<div style=\"background:#0a5c4b;padding:12px;display:flex;justify-content:space-between;align-items:center;\">\n<button type=\"button\" id=\"agp\" style=\"background:#ffcc00;color:#000;border:3px solid #fff;border-radius:30px;padding:10px 22px;font-weight:bold;cursor:pointer;min-width:100px;\">&larr; \u092a\u0940\u091b\u0947<\/button>\n<span id=\"agi\" style=\"background:#fff;color:#0a5c4b;padding:8px 20px;border-radius:20px;font-weight:bold;\">1 \/ 6<\/span>\n<button type=\"button\" id=\"agn\" style=\"background:#00e676;color:#000;border:3px solid #fff;border-radius:30px;padding:10px 22px;font-weight:bold;cursor:pointer;min-width:100px;\">\u0906\u0917\u0947 &rarr;<\/button>\n<\/div>\n<\/div>\n\n<script>\n(function(){\nvar c=1,t=6;\nfunction s(n){\nfor(var i=1;i<=t;i++){\nvar el=document.getElementById('ag-'+i);\nif(el)el.style.display=(i===n?'block':'none');\n}\ndocument.getElementById('agi').textContent=n+' \/ '+t;\nc=n;\n}\ndocument.getElementById('agn').onclick=function(){var n=c+1;if(n>t)n=1;s(n);};\ndocument.getElementById('agp').onclick=function(){var n=c-1;if(n<1)n=t;s(n);};\n})();\n<\/script><\/div><\/div><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p>Ch6 &#8211; \u0938\u092e\u0924\u0932 \u092e\u093e\u092a\u0928 &#8211; \u092d\u093e\u0917 1\/4 &#8211; \u092a\u0930\u093f\u091a\u092f \ud83d\udd34 \u092d\u093e\u0917 1\/4 &#8211; \u092a\u0930\u093f\u092e\u093e\u092a \u0915\u094d\u092f\u093e? \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0915\u094d\u092f\u093e?\u092a\u0930\u093f\u092e\u093e\u092a \u0914\u0930 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 &#8211; \u0939\u0947\u0921\u093f\u0902\u0917\u092a\u0930\u093f\u092e\u093e\u092a = \u091a\u093e\u0930\u094b\u0902 \u0924\u0930\u092b \u0915\u0940 \u092c\u093e\u0921\u093c\u0964 \u0915\u093f\u0924\u0928\u093e \u0924\u093e\u0930 \u0932\u0917\u0947\u0917\u093e? \u091a\u093e\u0930\u094b\u0902 \u092d\u0941\u091c\u093e\u0913\u0902 \u0915\u093e \u091c\u094b\u0921\u093c\u0964\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = \u0905\u0902\u0926\u0930 \u0915\u093f\u0924\u0928\u0940 \u091c\u0917\u0939? \u092b\u0930\u094d\u0936 \u092a\u0930 \u0915\u093f\u0924\u0928\u0940 \u091f\u093e\u0907\u0932 \u0932\u0917\u0947\u0917\u0940? \u0932\u0902\u092c\u093e\u0908\u00d7\u091a\u094c\u0921\u093c\u093e\u0908\u0964\u092a\u0930\u093f\u092e\u093e\u092a = \u091a\u093e\u0930\u094b\u0902 \u0924\u0930\u092b \u091c\u094b\u0921\u093c = \u092c\u093e\u0921\u093c\u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 = \u0905\u0902\u0926\u0930 = \u092b\u0930\u094d\u0936 L\u00d7B4\u00d73 \u0916\u0947\u0924 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[10],"tags":[],"class_list":["post-965","post","type-post","status-publish","format-standard","hentry","category-mathematics"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.5 - 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