{"id":929,"date":"2026-10-05T02:30:46","date_gmt":"2026-10-05T02:30:46","guid":{"rendered":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/?p=929"},"modified":"2026-10-05T02:39:51","modified_gmt":"2026-10-05T02:39:51","slug":"1","status":"publish","type":"post","link":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/2026\/10\/05\/1\/","title":{"rendered":"*1* | \u092f\u0902\u0924\u094d\u0930 \u0915\u094b \u092a\u094d\u0930\u0947\u0930\u093f\u0924 \u0915\u0930\u0928\u093e \u2014 \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 | Instructing a Machine \u2014 Use of Coordinates"},"content":{"rendered":"<div id=\"pl-929\"  class=\"panel-layout\" ><div id=\"pg-929-0\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-929-0-0\"  class=\"panel-grid-cell\" ><div id=\"panel-929-0-0-0\" 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-CH1-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;\">Ch1 - \u092f\u0902\u0924\u094d\u0930 \u0915\u094b \u0928\u093f\u0930\u094d\u0926\u0947\u0936 - \u092d\u093e\u0917 1\/4 - \u092a\u0930\u093f\u091a\u092f \u0927\u093e\u0930\u093e \u092a\u094d\u0930\u0935\u093e\u0939<\/span><\/div>\n\n<div style=\"padding:10px 12px;\">\n<div id=\"ch1g-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\u091a\u092f - \u092f\u0902\u0924\u094d\u0930 \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\u093e\u0920 \u092a\u0930\u093f\u091a\u092f - \u092f\u0902\u0924\u094d\u0930 \u0915\u094b \u0915\u0948\u0938\u0947 \u092c\u0924\u093e\u090f\u0901? - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u0938\u094b\u091a\u094b \u0930\u094b\u092c\u094b\u091f \u0915\u094b \u091a\u0932\u093e\u0928\u093e \u0939\u0948\u0964 \u092c\u094b\u0932\u094b \u0906\u0917\u0947 \u091a\u0932\u0964 \u0915\u093f\u0924\u0928\u093e \u0906\u0917\u0947? \u0930\u094b\u092c\u094b\u091f \u0938\u092e\u091d\u0947\u0917\u093e \u0928\u0939\u0940\u0902\u0964 \u0938\u0902\u0916\u094d\u092f\u093e \u092c\u0924\u093e\u0928\u0940 \u092a\u0921\u093c\u0947\u0917\u0940\u0964 5 \u0915\u0926\u092e \u0906\u0917\u0947 \u091a\u0932\u0964 \u0924\u092c \u0938\u092e\u091d\u0947\u0917\u093e\u0964 \u092f\u0939\u0940 \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u092e\u0936\u0940\u0928 \u0915\u094b \u0938\u0902\u0916\u094d\u092f\u093e \u0938\u0947 \u092c\u0924\u093e\u0928\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0926\u093f\u0936\u093e \u0914\u0930 \u0926\u0942\u0930\u0940 \u0926\u094b\u0928\u094b\u0902 \u092c\u0924\u093e\u0928\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u092f\u0939\u0940 Chapter 1 \u0915\u0940 \u0927\u093e\u0930\u093e \u0939\u094b\u0924\u0940 \u0939\u0948\u0964<div style=\"background:#e8f5e9;border:2px solid #2e7d32;padding:8px;border-radius:8px;text-align:center;margin:6px 0;\"><span style=\"font-size:16px;font-weight:bold;\">\u0927\u093e\u0930\u093e : \u092f\u0902\u0924\u094d\u0930 \u2192 \u0928\u093f\u0930\u094d\u0926\u0947\u0936 \u2192 \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915<\/span><br><span>\u0906\u0917\u0947 \u091a\u0932\u094b \u0928\u0939\u0940\u0902, 5 \u092a\u0942\u0930\u094d\u0935 \u091a\u0932\u094b \u092c\u094b\u0932\u094b<\/span><\/div><div style=\"background:#e3f2fd;border-left:4px solid #1565c0;padding:6px 10px;font-weight:bold;margin-top:8px;\">\u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u0915\u094d\u092f\u093e? - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u0915\u093f\u0938\u0940 \u092c\u093f\u0902\u0926\u0941 \u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f \u0938\u0902\u0916\u094d\u092f\u093e \u0938\u0947 \u092c\u0924\u093e\u0928\u093e \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u092e\u093e\u0928\u091a\u093f\u0924\u094d\u0930 \u092e\u0947\u0902 \u0918\u0930 \u0915\u0939\u093e\u0901 \u0939\u0948? \u0917\u0932\u0940 \u0928\u0902\u092c\u0930 \u0914\u0930 \u092e\u0915\u093e\u0928 \u0928\u0902\u092c\u0930 \u0938\u0947 \u092c\u0924\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 \u092f\u0939\u0940 \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0917\u0923\u093f\u0924 \u092e\u0947\u0902 \u0926\u094b \u0938\u0902\u0916\u094d\u092f\u093e \u0938\u0947 \u092c\u0924\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 x \u0914\u0930 y \u0938\u0947 \u092c\u0924\u093e\u0924\u0947 \u0939\u0948\u0902\u0964<div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:6px;border-radius:8px;text-align:center;margin:6px 0;\"><span style=\"font-weight:bold;font-size:16px;\">\u092c\u093f\u0902\u0926\u0941 = (x , y)<\/span><br><span>x=\u0915\u094d\u0937\u0948\u0924\u093f\u091c , y=\u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930<\/span><\/div><\/div><\/div>\n\n<div id=\"ch1g-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 - \u0915\u093e\u0930\u094d\u0924\u0940\u092f \u0924\u0932 \u0914\u0930 \u092e\u0942\u0932\u092c\u093f\u0902\u0926\u0941<\/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;\">\u0915\u093e\u0930\u094d\u0924\u0940\u092f \u0924\u0932 \u0915\u094d\u092f\u093e? - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u0926\u094b \u0930\u0947\u0916\u093e \u090f\u0915 \u0926\u0942\u0938\u0930\u0947 \u0915\u094b \u0915\u093e\u091f\u0924\u0940 \u0939\u0948\u0902\u0964 \u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0930\u0947\u0916\u093e x-\u0905\u0915\u094d\u0937 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0930\u0947\u0916\u093e y-\u0905\u0915\u094d\u0937 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u0926\u094b\u0928\u094b\u0902 \u092e\u093f\u0932\u0915\u0930 \u0915\u093e\u0930\u094d\u0924\u0940\u092f \u0924\u0932 \u092c\u0928\u093e\u0924\u0940 \u0939\u0948\u0902\u0964 \u0926\u094b\u0928\u094b\u0902 \u0915\u0947 \u0915\u091f\u093e\u0928 \u0915\u094b \u092e\u0942\u0932\u092c\u093f\u0902\u0926\u0941 \u0915\u0939\u0924\u0947 \u0939\u0948\u0902\u0964<div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:8px;border-radius:8px;text-align:center;margin:6px 0;\"><div style=\"font-size:18px;font-weight:bold;\">O = (0 , 0) \u092e\u0942\u0932\u092c\u093f\u0902\u0926\u0941<\/div><div style=\"font-size:14px;\">x-\u0905\u0915\u094d\u0937 = \u0915\u094d\u0937\u0948\u0924\u093f\u091c , y-\u0905\u0915\u094d\u0937 = \u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930<\/div><\/div>\u092e\u0942\u0932\u092c\u093f\u0902\u0926\u0941 \u0938\u0947 \u0926\u093e\u090f\u0901 x \u0927\u0928 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u092c\u093e\u090f\u0901 x \u090b\u0923 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u090a\u092a\u0930 y \u0927\u0928 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0928\u0940\u091a\u0947 y \u090b\u0923 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<div style=\"background:#e8f5e9;border-left:4px solid #2e7d32;padding:6px 10px;font-weight:bold;margin-top:8px;\">\u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936 \u0915\u094d\u092f\u093e? - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u0926\u094b \u0905\u0915\u094d\u0937 \u091a\u093e\u0930 \u092d\u093e\u0917 \u092c\u0928\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 \u092a\u0939\u0932\u093e \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936 x \u0927\u0928 y \u0927\u0928 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0926\u0942\u0938\u0930\u093e x \u090b\u0923 y \u0927\u0928 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0924\u0940\u0938\u0930\u093e x \u090b\u0923 y \u090b\u0923 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u091a\u094c\u0925\u093e x \u0927\u0928 y \u090b\u0923 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0930\u094b\u092c\u094b\u091f \u0915\u094b \u092c\u0924\u093e\u0928\u093e \u0939\u0948\u0964 \u092a\u0939\u0932\u093e \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936 \u092e\u0947\u0902 \u091c\u093e \u0924\u094b x \u0927\u0928 y \u0927\u0928 \u092c\u094b\u0932\u094b\u0964<div style=\"background:#ffebee;border:2px solid #d32f2f;padding:6px;border-radius:8px;text-align:center;margin:6px 0;\"><span style=\"font-weight:bold;\">I (+,+) , II (-,+) , III (-,-) , IV (+,-)<\/span><\/div><\/div><\/div>\n\n<div id=\"ch1g-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 - \u0926\u0942\u0930\u0940 \u0914\u0930 \u0928\u093f\u0930\u094d\u0926\u0947\u0936 \u0926\u0947\u0928\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:#e8f5e9;border-left:4px solid #2e7d32;padding:6px 10px;font-weight:bold;\">\u092c\u093f\u0902\u0926\u0941 \u0938\u0947 \u0926\u0942\u0930\u0940 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u092c\u093f\u0902\u0926\u0941 (x,y) \u0915\u0940 x-\u0905\u0915\u094d\u0937 \u0938\u0947 \u0926\u0942\u0930\u0940 y \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 y-\u0905\u0915\u094d\u0937 \u0938\u0947 \u0926\u0942\u0930\u0940 x \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u092e\u0942\u0932\u092c\u093f\u0902\u0926\u0941 \u0938\u0947 \u0926\u0942\u0930\u0940 \u092b\u0949\u0930\u094d\u092e\u0942\u0932\u0947 \u0938\u0947 \u0928\u093f\u0915\u0932\u0924\u0940 \u0939\u0948\u0964<div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:8px;border-radius:10px;text-align:center;margin:6px 0;\"><div style=\"font-size:18px;font-weight:bold;\">\u0926\u0942\u0930\u0940 = \u221a(x\u00b2 + y\u00b2)<\/div><div style=\"font-size:14px;\">(3,4) \u0915\u0940 \u092e\u0942\u0932 \u0938\u0947 \u0926\u0942\u0930\u0940 = 5<\/div><div style=\"font-size:13px;\">3\u00b2+4\u00b2=25 \u221a25=5<\/div><\/div>\u092f\u0939 \u092a\u093e\u0907\u0925\u093e\u0917\u094b\u0930\u0938 \u0938\u0947 \u0906\u0924\u093e \u0939\u0948\u0964 x \u0914\u0930 y \u0926\u094b \u092d\u0941\u091c\u093e \u0939\u094b\u0924\u0940 \u0939\u0948\u0902\u0964 \u0926\u0942\u0930\u0940 \u0915\u0930\u094d\u0923 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964<div style=\"background:#e3f2fd;border-left:4px solid #1565c0;padding:6px 10px;font-weight:bold;margin-top:8px;\">\u092f\u0902\u0924\u094d\u0930 \u0915\u094b \u0928\u093f\u0930\u094d\u0926\u0947\u0936 \u0915\u0948\u0938\u0947? - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u092e\u093e\u0928 \u0932\u094b \u0915\u093e\u0917\u091c \u092a\u0930 \u092c\u093f\u0902\u0926\u0941 A (2,3) \u0939\u0948\u0964 \u092c\u093f\u0902\u0926\u0941 B (5,7) \u0939\u0948\u0964 \u0930\u094b\u092c\u094b\u091f \u0915\u094b A \u0938\u0947 B \u0932\u0947 \u091c\u093e\u0928\u093e \u0939\u0948\u0964 \u0905\u0902\u0924\u0930 \u0928\u093f\u0915\u093e\u0932\u094b\u0964 x \u092e\u0947\u0902 3 \u092c\u0922\u093c\u093e y \u092e\u0947\u0902 4 \u092c\u0922\u093c\u093e\u0964 \u092f\u0939\u0940 \u0928\u093f\u0930\u094d\u0926\u0947\u0936 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<div style=\"background:#e0f2f1;border:2px solid #009688;padding:6px;border-radius:8px;text-align:center;margin:6px 0;\"><span style=\"font-weight:bold;\">\u0394x = x2-x1 , \u0394y = y2-y1<\/span><br><span>A(2,3) B(5,7) => \u0394x=3 \u0394y=4<\/span><\/div>\u092f\u0939\u0940 \u0915\u094b\u0921 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u092e\u0936\u0940\u0928 \u0907\u0938\u0940 \u0938\u0947 \u091a\u0932\u0924\u0940 \u0939\u0948\u0964<\/div><\/div>\n\n<div id=\"ch1g-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 - \u0909\u092a\u092f\u094b\u0917 \u0914\u0930 Trick<\/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;\">\u0909\u092a\u092f\u094b\u0917 \u0915\u0939\u093e\u0901? - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>GPS \u092e\u0947\u0902 \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0905\u0915\u094d\u0937\u093e\u0902\u0936 \u0926\u0947\u0936\u093e\u0902\u0924\u0930 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u092e\u093e\u0928\u091a\u093f\u0924\u094d\u0930 \u092e\u0947\u0902 x,y \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0915\u0902\u092a\u094d\u092f\u0942\u091f\u0930 \u0917\u094d\u0930\u093e\u092b\u093f\u0915\u094d\u0938 \u092e\u0947\u0902 (x,y) \u0938\u0947 \u092a\u093f\u0915\u094d\u0938\u0947\u0932 \u092c\u0928\u0924\u093e \u0939\u0948\u0964 \u0917\u0947\u092e \u092e\u0947\u0902 \u0915\u0948\u0930\u0947\u0915\u094d\u091f\u0930 (x,y) \u0938\u0947 \u091a\u0932\u0924\u093e \u0939\u0948\u0964 \u092a\u094d\u0930\u093f\u0902\u091f\u0930 \u092e\u0947\u0902 \u0938\u093f\u0930 (x,y) \u092a\u0930 \u091c\u093e\u0924\u093e \u0939\u0948\u0964 CNC \u092e\u0936\u0940\u0928 (x,y) \u0938\u0947 \u0915\u093e\u091f\u0924\u0940 \u0939\u0948\u0964<div style=\"background:#fff9c4;border:2px solid #fbc02d;padding:6px;border-radius:8px;text-align:center;margin:6px 0;\"><span style=\"font-weight:bold;\">GPS = (Latitude , Longitude) = (x,y)<\/span><br><span>Game , Printer , CNC \u0938\u092c (x,y)<\/span><\/div><div style=\"background:#e8f5e9;border-left:4px solid #2e7d32;padding:6px 10px;font-weight:bold;margin-top:8px;\">Trick \u092f\u093e\u0926 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:8px;border-radius:8px;text-align:center;margin:6px 0;\"><div style=\"font-weight:bold;\">O=(0,0) , \u092c\u093f\u0902\u0926\u0941=(x,y)<\/div><div>I (+,+) II (-,+) III (-,-) IV (+,-)<\/div><div>\u0926\u0942\u0930\u0940 = \u221a(x\u00b2+y\u00b2) , \u0394x=x2-x1<\/div><div>x-\u0905\u0915\u094d\u0937 \u0938\u0947 \u0926\u0942\u0930\u0940 = y , y-\u0905\u0915\u094d\u0937 \u0938\u0947 = x<\/div><\/div>\u092f\u0939\u0940 \u0905\u0917\u094d\u0928\u093f\u0935\u0940\u0930 \u0914\u0930 \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u092a\u0942\u091b\u0924\u093e \u0939\u0948\u0964 \u092e\u0942\u0932\u092c\u093f\u0902\u0926\u0941 \u0914\u0930 \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936 \u092a\u0915\u094d\u0915\u093e \u092a\u0942\u091b\u0924\u093e \u0939\u0948\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=\"ch1gp\" 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=\"ch1gi\" 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=\"ch1gn\" 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('ch1g-'+i);\nif(el)el.style.display=(i===n?'block':'none');\n}\ndocument.getElementById('ch1gi').textContent=n+' \/ '+t;\nc=n;\n}\ndocument.getElementById('ch1gn').onclick=function(){var n=c+1;if(n>t)n=1;s(n);};\ndocument.getElementById('ch1gp').onclick=function(){var n=c-1;if(n<1)n=t;s(n);};\n})();\n<\/script><\/div><\/div><\/div><\/div><div id=\"pg-929-1\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-929-1-0\"  class=\"panel-grid-cell\" ><div id=\"panel-929-1-0-0\" 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-CH1-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;\">Ch1 - \u092f\u0902\u0924\u094d\u0930 \u0928\u093f\u0930\u094d\u0926\u0947\u0936 - \u092d\u093e\u0917 2\/4 - \u092b\u0949\u0930\u094d\u092e\u0942\u0932\u0947 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924<\/span><\/div>\n\n<div style=\"padding:10px 12px;\">\n<div id=\"ch1g2-1\" 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 - \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u092a\u0926\u094d\u0927\u0924\u093f \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;\">\u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 1 - \u0924\u0932 \u0915\u0948\u0938\u0947 \u092c\u0928\u0924\u093e? - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u0926\u094b \u092a\u0930\u0938\u094d\u092a\u0930 \u0932\u092e\u094d\u092c \u0930\u0947\u0916\u093e \u0924\u0932 \u092c\u0928\u093e\u0924\u0940 \u0939\u0948\u0902\u0964 \u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0930\u0947\u0916\u093e \u0915\u094b x-\u0905\u0915\u094d\u0937 \u0915\u0939\u0924\u0947 \u0939\u0948\u0902\u0964 \u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0930\u0947\u0916\u093e \u0915\u094b y-\u0905\u0915\u094d\u0937 \u0915\u0939\u0924\u0947 \u0939\u0948\u0902\u0964 \u0915\u091f\u093e\u0928 \u092c\u093f\u0902\u0926\u0941 \u0915\u094b \u092e\u0942\u0932\u092c\u093f\u0902\u0926\u0941 O \u0915\u0939\u0924\u0947 \u0939\u0948\u0902\u0964 \u0924\u0932 \u0915\u094b \u0915\u093e\u0930\u094d\u0924\u0940\u092f \u0924\u0932 \u0915\u0939\u0924\u0947 \u0939\u0948\u0902\u0964 \u0930\u0947\u0928\u0947 \u0926\u0947\u0915\u093e\u0930\u094d\u0924\u0947 \u0928\u0947 \u0926\u093f\u092f\u093e \u0925\u093e\u0964<div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:8px;border-radius:10px;text-align:center;margin:6px 0;\"><div style=\"font-size:18px;font-weight:bold;\">O = (0,0)<\/div><div style=\"font-size:14px;\">x-\u0905\u0915\u094d\u0937 : y=0 , y-\u0905\u0915\u094d\u0937 : x=0<\/div><div style=\"font-size:14px;\">\u092c\u093f\u0902\u0926\u0941 P = (x , y) = (\u092d\u0941\u091c , \u0915\u094b\u091f\u093f)<\/div><\/div>\u092d\u0941\u091c \u0915\u094b abscissa \u0915\u0939\u0924\u0947 \u0939\u0948\u0902\u0964 \u0915\u094b\u091f\u093f \u0915\u094b ordinate \u0915\u0939\u0924\u0947 \u0939\u0948\u0902\u0964 x \u092a\u0939\u0932\u0947 \u0932\u093f\u0916\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 y \u092c\u093e\u0926 \u092e\u0947\u0902 \u0932\u093f\u0916\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<div style=\"background:#e3f2fd;border-left:4px solid #1565c0;padding:6px 10px;font-weight:bold;margin-top:8px;\">\u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 2 - \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936 \u0928\u093f\u092f\u092e - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u0926\u094b \u0905\u0915\u094d\u0937 \u091a\u093e\u0930 \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936 \u092c\u0928\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 \u0918\u0921\u093c\u0940 \u0915\u0947 \u0935\u093f\u092a\u0930\u0940\u0924 \u0928\u093e\u092e \u0939\u094b\u0924\u093e \u0939\u0948\u0964<div style=\"background:#e3f2fd;border:2px solid #2196f3;padding:6px;border-radius:8px;text-align:center;margin:6px 0;\"><span style=\"font-weight:bold;font-size:15px;\">I (+,+) , II (-,+) , III (-,-) , IV (+,-)<\/span><br><span>\u0905\u0915\u094d\u0937 \u092a\u0930 \u092c\u093f\u0902\u0926\u0941 \u0915\u093f\u0938\u0940 \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936 \u092e\u0947\u0902 \u0928\u0939\u0940\u0902<\/span><\/div><\/div><\/div>\n\n<div id=\"ch1g2-2\" 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 - \u0926\u0942\u0930\u0940 \u092b\u0949\u0930\u094d\u092e\u0942\u0932\u0947<\/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;\">\u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 3 - \u092e\u0942\u0932\u092c\u093f\u0902\u0926\u0941 \u0938\u0947 \u0926\u0942\u0930\u0940 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u092c\u093f\u0902\u0926\u0941 P(x,y) \u0915\u0940 \u092e\u0942\u0932\u092c\u093f\u0902\u0926\u0941 O(0,0) \u0938\u0947 \u0926\u0942\u0930\u0940 \u092a\u093e\u0907\u0925\u093e\u0917\u094b\u0930\u0938 \u0938\u0947 \u0928\u093f\u0915\u0932\u0924\u0940 \u0939\u0948\u0964 x \u090f\u0915 \u092d\u0941\u091c\u093e \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 y \u0926\u0942\u0938\u0930\u0940 \u092d\u0941\u091c\u093e \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u0926\u0942\u0930\u0940 \u0915\u0930\u094d\u0923 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964<div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:10px;border-radius:10px;text-align:center;margin:6px 0;\"><div style=\"font-size:20px;font-weight:bold;\">OP = \u221a(x\u00b2 + y\u00b2)<\/div><div style=\"font-size:14px;\">P(3,4) => OP = \u221a(9+16)=\u221a25=5<\/div><div style=\"font-size:14px;\">P(6,8) => OP = \u221a(36+64)=10<\/div><div style=\"font-size:13px;margin-top:4px;background:#fff;padding:3px 8px;border-radius:5px;\">P(-3,4) => OP=5 \u0926\u0942\u0930\u0940 \u0939\u092e\u0947\u0936\u093e \u0927\u0928<\/div><\/div><div style=\"background:#e8f5e9;border-left:4px solid #2e7d32;padding:6px 10px;font-weight:bold;margin-top:8px;\">\u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 4 - \u0905\u0915\u094d\u0937\u094b\u0902 \u0938\u0947 \u0926\u0942\u0930\u0940 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u092c\u093f\u0902\u0926\u0941 (x,y) \u0915\u0940 x-\u0905\u0915\u094d\u0937 \u0938\u0947 \u0932\u092e\u094d\u092c \u0926\u0942\u0930\u0940 y \u0915\u093e \u0928\u093f\u0930\u092a\u0947\u0915\u094d\u0937 \u092e\u093e\u0928 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 y-\u0905\u0915\u094d\u0937 \u0938\u0947 \u0932\u092e\u094d\u092c \u0926\u0942\u0930\u0940 x \u0915\u093e \u0928\u093f\u0930\u092a\u0947\u0915\u094d\u0937 \u092e\u093e\u0928 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<div style=\"background:#fff3e0;border:2px solid #ff9800;padding:6px;border-radius:8px;text-align:center;margin:6px 0;\"><span style=\"font-size:15px;font-weight:bold;\">x-\u0905\u0915\u094d\u0937 \u0938\u0947 \u0926\u0942\u0930\u0940 = |y| , y-\u0905\u0915\u094d\u0937 \u0938\u0947 = |x|<\/span><br><span>(2,3) \u0915\u0940 x \u0938\u0947 3 , y \u0938\u0947 2<\/span><\/div><\/div><\/div>\n\n<div id=\"ch1g2-3\" 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 - \u0926\u094b \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u092c\u0940\u091a \u0926\u0942\u0930\u0940 \u0914\u0930 \u0928\u093f\u0930\u094d\u0926\u0947\u0936<\/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;\">\u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 5 - \u0926\u094b \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u092c\u0940\u091a \u0926\u0942\u0930\u0940 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u092c\u093f\u0902\u0926\u0941 A(x1,y1) \u0914\u0930 B(x2,y2) \u092c\u0940\u091a \u0926\u0942\u0930\u0940 \u092d\u0940 \u092a\u093e\u0907\u0925\u093e\u0917\u094b\u0930\u0938 \u0938\u0947 \u0928\u093f\u0915\u0932\u0924\u0940 \u0939\u0948\u0964 \u0905\u0902\u0924\u0930 \u0915\u093e \u0935\u0930\u094d\u0917 \u091c\u094b\u0921\u093c\u094b \u092b\u093f\u0930 \u092e\u0942\u0932 \u0928\u093f\u0915\u093e\u0932\u094b\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;\">AB = \u221a[(x2-x1)\u00b2 + (y2-y1)\u00b2]<\/div><div style=\"font-size:14px;\">A(2,3) B(5,7) => AB=\u221a[(3)\u00b2+(4)\u00b2]=5<\/div><div style=\"font-size:14px;\">A(0,0) B(3,4) => AB=5<\/div><\/div>\u092f\u0939\u0940 \u092f\u0902\u0924\u094d\u0930 \u0915\u094b \u091a\u0932\u093e\u0928\u0947 \u0915\u093e \u092b\u0949\u0930\u094d\u092e\u0942\u0932\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0915\u093f\u0924\u0928\u093e \u091a\u0932\u0928\u093e \u0939\u0948 \u0926\u0942\u0930\u0940 \u0938\u0947 \u092a\u0924\u093e \u091a\u0932\u0924\u093e \u0939\u0948\u0964<div style=\"background:#e3f2fd;border-left:4px solid #1565c0;padding:6px 10px;font-weight:bold;margin-top:8px;\">\u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 6 - \u092f\u0902\u0924\u094d\u0930 \u0915\u094b \u0928\u093f\u0930\u094d\u0926\u0947\u0936 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u092f\u0902\u0924\u094d\u0930 \u0915\u094b x \u092e\u0947\u0902 \u0915\u093f\u0924\u0928\u093e \u0914\u0930 y \u092e\u0947\u0902 \u0915\u093f\u0924\u0928\u093e \u091a\u0932\u0928\u093e \u0939\u0948 \u092f\u0939 \u0394x \u0914\u0930 \u0394y \u0938\u0947 \u092c\u0924\u093e\u0924\u0947 \u0939\u0948\u0902\u0964<div style=\"background:#e0f2f1;border:3px solid #009688;padding:8px;border-radius:8px;text-align:center;margin:6px 0;\"><div style=\"font-size:16px;font-weight:bold;\">\u0394x = x2 - x1 , \u0394y = y2 - y1<\/div><div>\u0928\u093f\u0930\u094d\u0926\u0947\u0936 = (\u0394x , \u0394y) \u091a\u0932\u094b<\/div><div>A(1,1) \u0938\u0947 B(4,5) => (3,4) \u091a\u0932\u094b<\/div><\/div>\u0915\u0902\u092a\u094d\u092f\u0942\u091f\u0930 \u0915\u094b\u0921 \u092e\u0947\u0902 \u092f\u0939\u0940 \u091c\u093e\u0924\u093e \u0939\u0948\u0964 move(3,4) \u0932\u093f\u0916\u0924\u0947 \u0939\u0948\u0902\u0964<\/div><\/div>\n\n<div id=\"ch1g2-4\" 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 - \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941 \u0914\u0930 Trick \u092b\u0949\u0930\u094d\u092e\u0942\u0932\u0947<\/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;\">\u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 7 - \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u0926\u094b \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u093e \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941 \u0914\u0938\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 x \u0915\u093e \u0914\u0938\u0924 \u0914\u0930 y \u0915\u093e \u0914\u0938\u0924 \u0928\u093f\u0915\u093e\u0932\u094b\u0964<div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:8px;border-radius:10px;text-align:center;margin:6px 0;\"><div style=\"font-size:18px;font-weight:bold;\">Mid = [(x1+x2)\/2 , (y1+y2)\/2]<\/div><div style=\"font-size:14px;\">(2,4) \u0914\u0930 (6,8) \u0915\u093e Mid = (4,6)<\/div><\/div>\u092f\u0902\u0924\u094d\u0930 \u0915\u094b \u092c\u0940\u091a \u092e\u0947\u0902 \u0932\u093e\u0928\u093e \u0939\u094b \u0924\u094b \u092f\u0939\u0940 \u092b\u0949\u0930\u094d\u092e\u0942\u0932\u093e \u0932\u0917\u0924\u093e \u0939\u0948\u0964<div style=\"background:#e0f2f1;border-left:4px solid #009688;padding:6px 10px;font-weight:bold;margin-top:8px;\">\u0938\u092d\u0940 \u092b\u0949\u0930\u094d\u092e\u0942\u0932\u0947 \u090f\u0915 \u0938\u093e\u0925 - \u0939\u0947\u0921\u093f\u0902\u0917 - Most Important<\/div><div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:8px;border-radius:10px;text-align:center;margin:6px 0;\"><div style=\"font-size:15px;font-weight:bold;\">1. O=(0,0) , P=(x,y)=(\u092d\u0941\u091c,\u0915\u094b\u091f\u093f)<\/div><div style=\"font-size:15px;font-weight:bold;color:#d32f2f;\">2. OP=\u221a(x\u00b2+y\u00b2)<\/div><div style=\"font-size:15px;font-weight:bold;color:#1565c0;\">3. AB=\u221a[(x2-x1)\u00b2+(y2-y1)\u00b2]<\/div><div style=\"font-size:15px;font-weight:bold;\">4. x \u0938\u0947 \u0926\u0942\u0930\u0940=|y| , y \u0938\u0947=|x|<\/div><div style=\"font-size:15px;font-weight:bold;\">5. Mid=[(x1+x2)\/2,(y1+y2)\/2]<\/div><div style=\"font-size:14px;margin-top:4px;background:#fff;padding:3px;border-radius:5px;\">I (+,+) II (-,+) III (-,-) IV (+,-)<\/div><\/div>\u092f\u0939\u0940 \u092b\u0949\u0930\u094d\u092e\u0942\u0932\u0947 \u0905\u0917\u094d\u0928\u093f\u0935\u0940\u0930 \u092e\u0947\u0902 \u092a\u0915\u094d\u0915\u093e \u092a\u0942\u091b\u0924\u0947 \u0939\u0948\u0902\u0964 \u0926\u0942\u0930\u0940 \u0935\u093e\u0932\u093e \u0938\u092c\u0938\u0947 \u091c\u094d\u092f\u093e\u0926\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=\"ch1g2p\" 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=\"ch1g2i\" 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=\"ch1g2n\" 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('ch1g2-'+i);\nif(el)el.style.display=(i===n?'block':'none');\n}\ndocument.getElementById('ch1g2i').textContent=n+' \/ '+t;\nc=n;\n}\ndocument.getElementById('ch1g2n').onclick=function(){var n=c+1;if(n>t)n=1;s(n);};\ndocument.getElementById('ch1g2p').onclick=function(){var n=c-1;if(n<1)n=t;s(n);};\n})();\n<\/script><\/div><\/div><\/div><\/div><div id=\"pg-929-2\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-929-2-0\"  class=\"panel-grid-cell\" ><div id=\"panel-929-2-0-0\" 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=\"FILE3-CH1-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;\">Ch1 - \u092f\u0902\u0924\u094d\u0930 \u0928\u093f\u0930\u094d\u0926\u0947\u0936 - \u092d\u093e\u0917 3\/4 - \u0905\u092d\u094d\u092f\u093e\u0938 \u092a\u0942\u0930\u093e \u092a\u093e\u0920<\/span><\/div>\n\n<div style=\"padding:10px 12px;\">\n<div id=\"ch1g3-1\" 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 - \u0905\u092d\u094d\u092f\u093e\u0938 1 - \u092e\u0942\u0932\u092c\u093f\u0902\u0926\u0941 \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936 - \u0906\u0938\u093e\u0928<\/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\u094d\u0930\u0936\u094d\u0928 1 - \u092c\u093f\u0902\u0926\u0941 \u0932\u093f\u0916\u094b - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q1. \u092c\u093f\u0902\u0926\u0941 (3,4) \u092e\u0947\u0902 \u092d\u0941\u091c \u0915\u094d\u092f\u093e? \u0915\u094b\u091f\u093f \u0915\u094d\u092f\u093e?<\/b><br>\u0939\u0932: \u092d\u0941\u091c = x = 3, \u0915\u094b\u091f\u093f = y = 4\u0964 x \u092a\u0939\u0932\u0947, y \u092c\u093e\u0926\u0964<br><b>Q2. \u092e\u0942\u0932\u092c\u093f\u0902\u0926\u0941 \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948?<\/b><br>\u0939\u0932: O=(0,0) \u091c\u0939\u093e\u0901 x-\u0905\u0915\u094d\u0937 y-\u0905\u0915\u094d\u0937 \u0915\u093e\u091f\u0924\u0947 \u0939\u0948\u0902\u0964<br><b>Q3. (0,5) \u0915\u093f\u0938 \u0905\u0915\u094d\u0937 \u092a\u0930 \u0939\u0948?<\/b><br>\u0939\u0932: x=0 \u0907\u0938\u0932\u093f\u090f y-\u0905\u0915\u094d\u0937 \u092a\u0930 \u0939\u0948\u0964<br><b>Q4. (7,0) \u0915\u093f\u0938 \u0905\u0915\u094d\u0937 \u092a\u0930 \u0939\u0948?<\/b><br>\u0939\u0932: y=0 \u0907\u0938\u0932\u093f\u090f x-\u0905\u0915\u094d\u0937 \u092a\u0930 \u0939\u0948\u0964 \u0905\u0915\u094d\u0937 \u092a\u0930 \u092c\u093f\u0902\u0926\u0941 \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936 \u092e\u0947\u0902 \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u093e\u0964<div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:6px;border-radius:8px;text-align:center;margin:6px 0;\"><span style=\"font-weight:bold;\">Trick : x=0 => y-\u0905\u0915\u094d\u0937 , y=0 => x-\u0905\u0915\u094d\u0937<\/span><br><span>O=(0,0) \u0926\u094b\u0928\u094b\u0902 \u0905\u0915\u094d\u0937 \u092a\u0930<\/span><\/div><div style=\"background:#e3f2fd;border-left:4px solid #1565c0;padding:6px 10px;font-weight:bold;margin-top:8px;\">\u092a\u094d\u0930\u0936\u094d\u0928 2 - \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936 \u092c\u0924\u093e\u0913 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q5. (-3,4) \u0915\u093f\u0938 \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936 \u092e\u0947\u0902?<\/b><br>\u0939\u0932: x \u090b\u0923 y \u0927\u0928 => II \u0926\u0942\u0938\u0930\u093e\u0964<br><b>Q6. (-2,-5) \u0915\u093f\u0938\u092e\u0947\u0902?<\/b><br>\u0939\u0932: x \u090b\u0923 y \u090b\u0923 => III \u0924\u0940\u0938\u0930\u093e\u0964<br><b>Q7. (4,-3) \u0915\u093f\u0938\u092e\u0947\u0902?<\/b><br>\u0939\u0932: x \u0927\u0928 y \u090b\u0923 => IV \u091a\u094c\u0925\u093e\u0964<br><b>Q8. (5,6) \u0915\u093f\u0938\u092e\u0947\u0902?<\/b><br>\u0939\u0932: (+,+) => I \u092a\u0939\u0932\u093e\u0964<div style=\"background:#e3f2fd;border:2px solid #2196f3;padding:6px;border-radius:8px;text-align:center;margin:6px 0;\"><span style=\"font-weight:bold;\">I (+,+) II (-,+) III (-,-) IV (+,-)<\/span><\/div><\/div><\/div>\n\n<div id=\"ch1g3-2\" 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 - \u0905\u092d\u094d\u092f\u093e\u0938 2 - \u0926\u0942\u0930\u0940 - \u0906\u0938\u093e\u0928<\/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;\">\u092a\u094d\u0930\u0936\u094d\u0928 3 - \u0905\u0915\u094d\u0937\u094b\u0902 \u0938\u0947 \u0926\u0942\u0930\u0940 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q9. (3,4) \u0915\u0940 x-\u0905\u0915\u094d\u0937 \u0938\u0947 \u0926\u0942\u0930\u0940?<\/b><br>\u0939\u0932: x-\u0905\u0915\u094d\u0937 \u0938\u0947 \u0926\u0942\u0930\u0940 = |y| = 4\u0964<br><b>Q10. (3,4) \u0915\u0940 y-\u0905\u0915\u094d\u0937 \u0938\u0947 \u0926\u0942\u0930\u0940?<\/b><br>\u0939\u0932: y-\u0905\u0915\u094d\u0937 \u0938\u0947 = |x| = 3\u0964<br><b>Q11. (-2,7) \u0915\u0940 x \u0938\u0947 \u0914\u0930 y \u0938\u0947 \u0926\u0942\u0930\u0940?<\/b><br>\u0939\u0932: x \u0938\u0947 |7|=7, y \u0938\u0947 |-2|=2\u0964 \u0926\u0942\u0930\u0940 \u0939\u092e\u0947\u0936\u093e \u0927\u0928 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u090b\u0923 \u0928\u0939\u0940\u0902\u0964<div style=\"background:#fff3e0;border:2px solid #ff9800;padding:6px;border-radius:8px;text-align:center;margin:6px 0;\"><span style=\"font-weight:bold;\">x \u0938\u0947 \u0926\u0942\u0930\u0940 = |y| , y \u0938\u0947 \u0926\u0942\u0930\u0940 = |x|<\/span><br><span>\u0926\u0942\u0930\u0940 \u0939\u092e\u0947\u0936\u093e \u0927\u0928<\/span><\/div><div style=\"background:#e8f5e9;border-left:4px solid #2e7d32;padding:6px 10px;font-weight:bold;margin-top:8px;\">\u092a\u094d\u0930\u0936\u094d\u0928 4 - \u092e\u0942\u0932\u092c\u093f\u0902\u0926\u0941 \u0938\u0947 \u0926\u0942\u0930\u0940 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q12. (3,4) \u0915\u0940 \u092e\u0942\u0932 \u0938\u0947 \u0926\u0942\u0930\u0940?<\/b><br>\u0939\u0932: OP=\u221a(x\u00b2+y\u00b2)=\u221a(9+16)=\u221a25=5\u0964<br><b>Q13. (6,8) \u0915\u0940 \u092e\u0942\u0932 \u0938\u0947 \u0926\u0942\u0930\u0940?<\/b><br>\u0939\u0932: \u221a(36+64)=\u221a100=10\u0964<br><b>Q14. (-3,4) \u0915\u0940 \u092e\u0942\u0932 \u0938\u0947 \u0926\u0942\u0930\u0940?<\/b><br>\u0939\u0932: \u221a[(-3)\u00b2+4\u00b2]=\u221a(9+16)=5\u0964 \u090b\u0923 \u0915\u093e \u0935\u0930\u094d\u0917 \u0927\u0928 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<br><b>Q15. (5,12) \u0915\u0940 \u092e\u0942\u0932 \u0938\u0947?<\/b><br>\u0939\u0932: \u221a(25+144)=\u221a169=13\u0964 \u091f\u094d\u0930\u093f\u092a\u0932\u0947\u091f 5-12-13 \u092f\u093e\u0926 \u0930\u0916\u094b\u0964<div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:6px;border-radius:8px;text-align:center;margin:6px 0;\"><span style=\"font-weight:bold;\">OP=\u221a(x\u00b2+y\u00b2) 3-4-5 , 5-12-13 , 6-8-10 \u091f\u094d\u0930\u093f\u092a\u0932\u0947\u091f<\/span><\/div><\/div><\/div>\n\n<div id=\"ch1g3-3\" 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 - \u0905\u092d\u094d\u092f\u093e\u0938 3 - \u0926\u094b \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0926\u0942\u0930\u0940 \u0928\u093f\u0930\u094d\u0926\u0947\u0936<\/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;\">\u092a\u094d\u0930\u0936\u094d\u0928 5 - \u0926\u094b \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u092c\u0940\u091a \u0926\u0942\u0930\u0940 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q16. A(2,3) B(5,7) \u092c\u0940\u091a \u0926\u0942\u0930\u0940?<\/b><br>\u0939\u0932: AB=\u221a[(5-2)\u00b2+(7-3)\u00b2]=\u221a[9+16]=5\u0964<br><b>Q17. A(0,0) B(3,4) \u0926\u0942\u0930\u0940?<\/b><br>\u0939\u0932: \u221a(9+16)=5\u0964<br><b>Q18. A(1,1) B(4,5) \u0926\u0942\u0930\u0940?<\/b><br>\u0939\u0932: \u221a[(3)\u00b2+(4)\u00b2]=5\u0964<br><b>Q19. A(-1,-2) B(2,2) \u0926\u0942\u0930\u0940?<\/b><br>\u0939\u0932: x2-x1=3, y2-y1=4 => \u221a(9+16)=5\u0964<div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:8px;border-radius:10px;text-align:center;margin:6px 0;\"><div style=\"font-size:16px;font-weight:bold;\">AB = \u221a[(x2-x1)\u00b2 + (y2-y1)\u00b2]<\/div><div>\u0905\u0902\u0924\u0930 \u0915\u093e \u0935\u0930\u094d\u0917 \u091c\u094b\u0921\u093c\u094b \u092e\u0942\u0932 \u0928\u093f\u0915\u093e\u0932\u094b<\/div><\/div><div style=\"background:#e0f2f1;border-left:4px solid #009688;padding:6px 10px;font-weight:bold;margin-top:8px;\">\u092a\u094d\u0930\u0936\u094d\u0928 6 - \u092f\u0902\u0924\u094d\u0930 \u0915\u094b \u0928\u093f\u0930\u094d\u0926\u0947\u0936 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q20. \u0930\u094b\u092c\u094b\u091f (2,3) \u092a\u0930 \u0939\u0948 (5,7) \u091c\u093e\u0928\u093e \u0939\u0948 \u0928\u093f\u0930\u094d\u0926\u0947\u0936?<\/b><br>\u0939\u0932: \u0394x=5-2=3, \u0394y=7-3=4 => move(3,4)\u0964<br><b>Q21. \u092a\u094d\u0930\u093f\u0902\u091f\u0930 \u0939\u0947\u0921 (0,0) \u0938\u0947 (10,5) \u091c\u093e\u0928\u093e \u0939\u0948?<\/b><br>\u0939\u0932: \u0394x=10 \u0394y=5 => move(10,5)\u0964<br><b>Q22. \u0917\u0947\u092e \u0915\u0948\u0930\u0947\u0915\u094d\u091f\u0930 (4,6) \u0938\u0947 (4,10) \u091c\u093e\u0928\u093e \u0939\u0948?<\/b><br>\u0939\u0932: \u0394x=0 \u0394y=4 => \u0938\u093f\u0930\u094d\u092b \u090a\u092a\u0930 4 \u091a\u0932\u094b\u0964<\/div><\/div>\n\n<div id=\"ch1g3-4\" 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 - \u0905\u092d\u094d\u092f\u093e\u0938 4 - \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941 \u0914\u0930 \u092a\u0942\u0930\u0947 \u092a\u094d\u0930\u0936\u094d\u0928<\/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;\">\u092a\u094d\u0930\u0936\u094d\u0928 7 - \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q23. (2,4) \u0914\u0930 (6,8) \u0915\u093e \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941?<\/b><br>\u0939\u0932: Mid=[(2+6)\/2,(4+8)\/2]=(4,6)\u0964<br><b>Q24. (0,0) \u0914\u0930 (10,10) \u0915\u093e Mid?<\/b><br>\u0939\u0932: (5,5)\u0964 \u0914\u0938\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<br><b>Q25. (-2,3) (4,7) \u0915\u093e Mid?<\/b><br>\u0939\u0932: [(2)\/2,(10)\/2]=(1,5)\u0964<div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:6px;border-radius:8px;text-align:center;margin:6px 0;\"><span style=\"font-weight:bold;\">Mid = [(x1+x2)\/2 , (y1+y2)\/2] \u0914\u0938\u0924<\/span><\/div><div style=\"background:#e0f2f1;border-left:4px solid #009688;padding:6px 10px;font-weight:bold;margin-top:8px;\">\u092a\u094d\u0930\u0936\u094d\u0928 8 - \u092a\u0942\u0930\u0947 \u092a\u093e\u0920 \u0915\u0947 \u092e\u093f\u0936\u094d\u0930\u093f\u0924 \u092a\u094d\u0930\u0936\u094d\u0928 - \u0939\u0947\u0921\u093f\u0902\u0917 - Most Important<\/div><b>Q26. \u092c\u093f\u0902\u0926\u0941 (-5, -3) \u0915\u0940 y-\u0905\u0915\u094d\u0937 \u0938\u0947 \u0926\u0942\u0930\u0940? \u092e\u0942\u0932 \u0938\u0947 \u0926\u0942\u0930\u0940?<\/b><br>\u0939\u0932: y \u0938\u0947 = |-5|=5, \u092e\u0942\u0932 \u0938\u0947 \u221a(25+9)=\u221a34\u0964<br><b>Q27. \u0915\u094c\u0928 \u0938\u093e \u092c\u093f\u0902\u0926\u0941 x-\u0905\u0915\u094d\u0937 \u092a\u0930? (2,3)(0,4)(5,0)<\/b><br>\u0939\u0932: y=0 \u0935\u093e\u0932\u093e x-\u0905\u0915\u094d\u0937 \u092a\u0930 => (5,0)\u0964<br><b>Q28. \u0930\u094b\u092c\u094b\u091f \u0915\u094b I \u0938\u0947 III \u091c\u093e\u0928\u093e \u0939\u0948 x y \u0915\u0948\u0938\u0947 \u092c\u0926\u0932\u0947?<\/b><br>\u0939\u0932: I (+,+) \u0938\u0947 III (-,-) => x \u0918\u091f\u093e \u090b\u0923 \u0915\u0930 y \u0918\u091f\u093e \u090b\u0923 \u0915\u0930\u0964<br><b>Q29. CNC \u092e\u0936\u0940\u0928 (0,0) \u0938\u0947 (6,8) \u0915\u093e\u091f\u0924\u0940 \u0939\u0948 \u0926\u0942\u0930\u0940?<\/b><br>\u0939\u0932: OP=\u221a(36+64)=10 \u0907\u0915\u093e\u0908\u0964<div style=\"background:#ffebee;border:2px solid #d32f2f;padding:6px;border-radius:8px;text-align:center;margin:6px 0;\"><span style=\"font-weight:bold;\">\u092a\u0942\u0930\u093e \u092a\u093e\u0920 \u0915\u0935\u0930 - \u0915\u094b\u0908 \u092a\u094d\u0930\u0936\u094d\u0928 \u0928\u0939\u0940\u0902 \u091b\u0942\u091f\u093e - \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092a\u0915\u094d\u0915\u0940!<\/span><\/div><\/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=\"ch1g3p\" 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=\"ch1g3i\" 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=\"ch1g3n\" 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('ch1g3-'+i);\nif(el)el.style.display=(i===n?'block':'none');\n}\ndocument.getElementById('ch1g3i').textContent=n+' \/ '+t;\nc=n;\n}\ndocument.getElementById('ch1g3n').onclick=function(){var n=c+1;if(n>t)n=1;s(n);};\ndocument.getElementById('ch1g3p').onclick=function(){var n=c-1;if(n<1)n=t;s(n);};\n})();\n<\/script><\/div><\/div><\/div><\/div><div id=\"pg-929-3\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-929-3-0\"  class=\"panel-grid-cell\" ><div id=\"panel-929-3-0-0\" 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=\"FILE4-CH1-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;\">Ch1 - \u092f\u0902\u0924\u094d\u0930 \u0928\u093f\u0930\u094d\u0926\u0947\u0936 - \u092d\u093e\u0917 4\/4 - MCQ \u0905\u0917\u094d\u0928\u093f\u0935\u0940\u0930<\/span><\/div>\n\n<div style=\"padding:10px 12px;\">\n<div id=\"ch1g4-1\" 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 - MCQ 1-8 - \u092e\u0942\u0932 \u0914\u0930 \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936<\/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;\">MCQ - \u092e\u0942\u0932\u092c\u093f\u0902\u0926\u0941 \u0914\u0930 \u0905\u0915\u094d\u0937 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q1. \u092e\u0942\u0932\u092c\u093f\u0902\u0926\u0941 \u0915\u0947 \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915?<\/b><br>A) (1,1) B) (0,0) C) (0,1) D) (1,0) <br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans B) (0,0)<\/span><br><br><b>Q2. \u092c\u093f\u0902\u0926\u0941 (0,7) \u0915\u0939\u093e\u0901 \u0939\u0948?<\/b><br>A) x-\u0905\u0915\u094d\u0937 B) y-\u0905\u0915\u094d\u0937 C) I D) II<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans B) y-\u0905\u0915\u094d\u0937 \u0915\u094d\u092f\u094b\u0902\u0915\u093f x=0<\/span><br><br><b>Q3. \u092c\u093f\u0902\u0926\u0941 (5,0) \u0915\u0939\u093e\u0901 \u0939\u0948?<\/b><br>A) x-\u0905\u0915\u094d\u0937 B) y-\u0905\u0915\u094d\u0937 C) \u092e\u0942\u0932 D) III<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans A) x-\u0905\u0915\u094d\u0937 \u0915\u094d\u092f\u094b\u0902\u0915\u093f y=0<\/span><br><br><b>Q4. (3,4) \u092e\u0947\u0902 \u092d\u0941\u091c?<\/b><br>A) 3 B) 4 C) 7 D) 0<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans A) 3 \u092d\u0941\u091c=x<\/span><br><br><div style=\"background:#e3f2fd;border-left:4px solid #1565c0;padding:6px 10px;font-weight:bold;margin-top:8px;\">MCQ - \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q5. (-3,5) \u0915\u093f\u0938 \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936?<\/b><br>A) I B) II C) III D) IV<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans B) II (-,+)<\/span><br><br><b>Q6. ( -2,-4) \u0915\u093f\u0938\u092e\u0947\u0902?<\/b><br>A) I B) II C) III D) IV<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans C) III (-,-)<\/span><br><br><b>Q7. (4,-3) \u0915\u093f\u0938\u092e\u0947\u0902?<\/b><br>A) I B) II C) III D) IV<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans D) IV (+,-)<\/span><br><br><b>Q8. (2,2) \u0915\u093f\u0938\u092e\u0947\u0902?<\/b><br>A) I B) II C) III D) IV<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans A) I (+,+)<\/span><div style=\"background:#fff9c4;border:2px solid #fbc02d;padding:6px;border-radius:8px;text-align:center;margin:6px 0;\"><span style=\"font-weight:bold;\">Trick : I (+,+) II (-,+) III (-,-) IV (+,-)<\/span><\/div><\/div><\/div>\n\n<div id=\"ch1g4-2\" 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 - MCQ 9-16 - \u0926\u0942\u0930\u0940 \u092b\u0949\u0930\u094d\u092e\u0942\u0932\u0947<\/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;\">MCQ - \u0905\u0915\u094d\u0937 \u0938\u0947 \u0926\u0942\u0930\u0940 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q9. (3,4) \u0915\u0940 x-\u0905\u0915\u094d\u0937 \u0938\u0947 \u0926\u0942\u0930\u0940?<\/b><br>A) 3 B) 4 C) 5 D) 0<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans B) 4 |y|=4<\/span><br><br><b>Q10. (3,4) \u0915\u0940 y-\u0905\u0915\u094d\u0937 \u0938\u0947 \u0926\u0942\u0930\u0940?<\/b><br>A) 3 B) 4 C) 5 D) 7<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans A) 3 |x|=3<\/span><br><br><b>Q11. (-5,12) \u0915\u0940 x-\u0905\u0915\u094d\u0937 \u0938\u0947 \u0926\u0942\u0930\u0940?<\/b><br>A) 5 B) 12 C) 13 D) -12<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans B) 12 \u0926\u0942\u0930\u0940 \u0927\u0928 \u0939\u094b\u0924\u0940 \u0939\u0948<\/span><br><br><div style=\"background:#ffebee;border-left:4px solid #d32f2f;padding:6px 10px;font-weight:bold;margin-top:8px;\">MCQ - \u092e\u0942\u0932 \u0938\u0947 \u0926\u0942\u0930\u0940 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q12. (3,4) \u0915\u0940 \u092e\u0942\u0932 \u0938\u0947 \u0926\u0942\u0930\u0940?<\/b><br>A) 3 B) 4 C) 5 D) 7<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans C) 5 \u221a(9+16)<\/span><br><br><b>Q13. (6,8) \u0915\u0940 \u092e\u0942\u0932 \u0938\u0947 \u0926\u0942\u0930\u0940?<\/b><br>A) 6 B) 8 C) 10 D) 14<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans C) 10<\/span><br><br><b>Q14. (5,12) \u0915\u0940 \u092e\u0942\u0932 \u0938\u0947?<\/b><br>A) 12 B) 13 C) 17 D) 10<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans B) 13 \u091f\u094d\u0930\u093f\u092a\u0932\u0947\u091f 5-12-13<\/span><br><br><b>Q15. (-3,4) \u0915\u0940 \u092e\u0942\u0932 \u0938\u0947?<\/b><br>A) 3 B) 4 C) 5 D) 1<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans C) 5 \u0935\u0930\u094d\u0917 \u0927\u0928<\/span><br><br><b>Q16. (0,0) \u0915\u0940 (3,4) \u0938\u0947 \u0926\u0942\u0930\u0940?<\/b><br>A) 3 B) 4 C) 5 D) 0<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans C) 5<\/span><div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:6px;border-radius:8px;text-align:center;margin:6px 0;\"><span style=\"font-weight:bold;\">OP=\u221a(x\u00b2+y\u00b2) \u0926\u0942\u0930\u0940 \u0939\u092e\u0947\u0936\u093e \u0927\u0928<\/span><\/div><\/div><\/div>\n\n<div id=\"ch1g4-3\" 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 - MCQ 17-24 - \u0926\u094b \u092c\u093f\u0902\u0926\u0941 \u0926\u0942\u0930\u0940 \u0928\u093f\u0930\u094d\u0926\u0947\u0936<\/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;\">MCQ - \u0926\u094b \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0926\u0942\u0930\u0940 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q17. A(2,3) B(5,7) \u0926\u0942\u0930\u0940?<\/b><br>A) 3 B) 4 C) 5 D) 6<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans C) 5 \u221a[(3)\u00b2+(4)\u00b2]<\/span><br><br><b>Q18. A(1,1) B(4,5) \u0926\u0942\u0930\u0940?<\/b><br>A) 3 B) 4 C) 5 D) 25<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans C) 5<\/span><br><br><b>Q19. \u0926\u094b \u092c\u093f\u0902\u0926\u0941 (0,0)(6,8) \u0926\u0942\u0930\u0940?<\/b><br>A) 6 B) 8 C) 10 D) 14<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans C) 10<\/span><br><br><div style=\"background:#e0f2f1;border-left:4px solid #009688;padding:6px 10px;font-weight:bold;margin-top:8px;\">MCQ - \u0928\u093f\u0930\u094d\u0926\u0947\u0936 \u0394x \u0394y - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q20. (2,3) \u0938\u0947 (5,7) \u091c\u093e\u0928\u0947 \u092e\u0947\u0902 \u0394x?<\/b><br>A) 2 B) 3 C) 5 D) 7<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans B) 3 x2-x1<\/span><br><br><b>Q21. (2,3) \u0938\u0947 (5,7) \u092e\u0947\u0902 \u0394y?<\/b><br>A) 2 B) 3 C) 4 D) 7<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans C) 4<\/span><br><br><b>Q22. \u0930\u094b\u092c\u094b\u091f (0,0) \u0938\u0947 (10,0) \u0394x \u0394y?<\/b><br>A) (10,0) B) (0,10) C) (10,10) D) (0,0)<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans A) (10,0) \u0938\u093f\u0930\u094d\u092b x<\/span><br><br><b>Q23. \u092a\u094d\u0930\u093f\u0902\u091f\u0930 (1,1) \u0938\u0947 (1,6) \u0394x \u0394y?<\/b><br>A) (0,5) B) (5,0) C) (5,5) D) (1,5)<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans A) (0,5) \u0938\u093f\u0930\u094d\u092b y<\/span><br><br><b>Q24. AB \u0926\u0942\u0930\u0940 \u092b\u0949\u0930\u094d\u092e\u0942\u0932\u093e?<\/b><br>A) (x2-x1)+(y2-y1) B) \u221a[(x2-x1)\u00b2+(y2-y1)\u00b2] C) x2+x1 D) y2+y1<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans B) \u221a[(x2-x1)\u00b2+(y2-y1)\u00b2]<\/span><div style=\"background:#fff9c4;border:2px solid #fbc02d;padding:6px;border-radius:8px;text-align:center;margin:6px 0;\"><span style=\"font-weight:bold;\">\u0394x=x2-x1 \u0394y=y2-y1 move(\u0394x,\u0394y)<\/span><\/div><\/div><\/div>\n\n<div id=\"ch1g4-4\" 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 - MCQ 25-32 - \u092e\u0927\u094d\u092f \u0914\u0930 \u0905\u0917\u094d\u0928\u093f\u0935\u0940\u0930 Special<\/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;\">MCQ - \u092e\u0927\u094d\u092f \u092c\u093f\u0902\u0926\u0941 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q25. (2,4) (6,8) \u092e\u0927\u094d\u092f?<\/b><br>A) (4,6) B) (2,4) C) (8,12) D) (3,5)<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans A) (4,6) \u0914\u0938\u0924<\/span><br><br><b>Q26. (0,0)(10,10) \u092e\u0927\u094d\u092f?<\/b><br>A) (0,0) B) (10,10) C) (5,5) D) (20,20)<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans C) (5,5)<\/span><br><br><b>Q27. \u092e\u0927\u094d\u092f \u092b\u0949\u0930\u094d\u092e\u0942\u0932\u093e?<\/b><br>A) (x1+x2, y1+y2) B) [(x1+x2)\/2,(y1+y2)\/2] C) (x2-x1) D) \u221a<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans B) \u0914\u0938\u0924 \/2<\/span><br><br><div style=\"background:#ffebee;border-left:4px solid #d32f2f;padding:6px 10px;font-weight:bold;margin-top:8px;\">MCQ - \u0905\u0917\u094d\u0928\u093f\u0935\u0940\u0930 Special - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q28. GPS \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948?<\/b><br>A) (x,y) B) (\u0905\u0915\u094d\u0937\u093e\u0902\u0936,\u0926\u0947\u0936\u093e\u0902\u0924\u0930) C) \u0926\u094b\u0928\u094b\u0902 D) \u0915\u094b\u0908 \u0928\u0939\u0940\u0902<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans C) \u0926\u094b\u0928\u094b\u0902 (x,y) \u0939\u0940<\/span><br><br><b>Q29. CNC \u092e\u0936\u0940\u0928 \u0915\u093f\u0938\u0938\u0947 \u091a\u0932\u0924\u0940 \u0939\u0948?<\/b><br>A) (x,y) \u0928\u093f\u0930\u094d\u0926\u0947\u0936 B) \u092c\u094b\u0932\u0928\u0947 \u0938\u0947 C) \u0939\u093e\u0925 \u0938\u0947 D) \u0915\u094b\u0908 \u0928\u0939\u0940\u0902<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans A) (x,y) \u0928\u093f\u0930\u094d\u0926\u0947\u0936<\/span><br><br><b>Q30. \u092c\u093f\u0902\u0926\u0941 ( -6,8) \u092e\u0942\u0932 \u0938\u0947 \u0926\u0942\u0930\u0940?<\/b><br>A) 6 B) 8 C) 10 D) 14<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans C) 10 \u221a36+64<\/span><br><br><b>Q31. \u0915\u094c\u0928 \u0938\u093e \u091a\u0924\u0941\u0930\u094d\u0925\u093e\u0902\u0936 \u092e\u0947\u0902 x \u0927\u0928 y \u090b\u0923?<\/b><br>A) I B) II C) III D) IV<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans D) IV (+,-)<\/span><br><br><b>Q32. x-\u0905\u0915\u094d\u0937 \u0915\u093e \u0938\u092e\u0940\u0915\u0930\u0923?<\/b><br>A) y=0 B) x=0 C) x=y D) x+y=0<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans A) y=0<\/span><div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:8px;border-radius:10px;text-align:center;margin:6px 0;\"><div style=\"font-weight:bold;font-size:15px;\">Final Trick - Ch1 \u092a\u0942\u0930\u093e<\/div><div>O=(0,0) , x=0 y-\u0905\u0915\u094d\u0937 , y=0 x-\u0905\u0915\u094d\u0937<\/div><div>I (+,+) II (-,+) III (-,-) IV (+,-)<\/div><div>OP=\u221a(x\u00b2+y\u00b2) , AB=\u221a[(x2-x1)\u00b2+(y2-y1)\u00b2]<\/div><div>Mid=[(x1+x2)\/2,(y1+y2)\/2]<\/div><\/div><\/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=\"ch1g4p\" 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=\"ch1g4i\" 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=\"ch1g4n\" 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('ch1g4-'+i);\nif(el)el.style.display=(i===n?'block':'none');\n}\ndocument.getElementById('ch1g4i').textContent=n+' \/ '+t;\nc=n;\n}\ndocument.getElementById('ch1g4n').onclick=function(){var n=c+1;if(n>t)n=1;s(n);};\ndocument.getElementById('ch1g4p').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>Ch1 &#8211; \u092f\u0902\u0924\u094d\u0930 \u0915\u094b \u0928\u093f\u0930\u094d\u0926\u0947\u0936 &#8211; \u092d\u093e\u0917 1\/4 &#8211; \u092a\u0930\u093f\u091a\u092f \u0927\u093e\u0930\u093e \u092a\u094d\u0930\u0935\u093e\u0939 \ud83d\udd34 \u092d\u093e\u0917 1\/4 &#8211; \u092a\u0930\u093f\u091a\u092f &#8211; \u092f\u0902\u0924\u094d\u0930 \u0915\u094d\u092f\u093e?\u092a\u093e\u0920 \u092a\u0930\u093f\u091a\u092f &#8211; \u092f\u0902\u0924\u094d\u0930 \u0915\u094b \u0915\u0948\u0938\u0947 \u092c\u0924\u093e\u090f\u0901? &#8211; \u0939\u0947\u0921\u093f\u0902\u0917\u0938\u094b\u091a\u094b \u0930\u094b\u092c\u094b\u091f \u0915\u094b \u091a\u0932\u093e\u0928\u093e \u0939\u0948\u0964 \u092c\u094b\u0932\u094b \u0906\u0917\u0947 \u091a\u0932\u0964 \u0915\u093f\u0924\u0928\u093e \u0906\u0917\u0947? \u0930\u094b\u092c\u094b\u091f \u0938\u092e\u091d\u0947\u0917\u093e \u0928\u0939\u0940\u0902\u0964 \u0938\u0902\u0916\u094d\u092f\u093e \u092c\u0924\u093e\u0928\u0940 \u092a\u0921\u093c\u0947\u0917\u0940\u0964 5 \u0915\u0926\u092e \u0906\u0917\u0947 \u091a\u0932\u0964 \u0924\u092c \u0938\u092e\u091d\u0947\u0917\u093e\u0964 \u092f\u0939\u0940 \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u092e\u0936\u0940\u0928 \u0915\u094b [&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-929","post","type-post","status-publish","format-standard","hentry","category-mathematics"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Mathematics &#187; *1* | \u092f\u0902\u0924\u094d\u0930 \u0915\u094b \u092a\u094d\u0930\u0947\u0930\u093f\u0924 \u0915\u0930\u0928\u093e \u2014 \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 | Instructing a Machine \u2014 Use of Coordinates &#187; Class-9th - Agniveer Foundation Hub | Pargai Defence &amp; Academic.<\/title>\n<meta name=\"description\" content=\"Class 9 Online Classes in Bageshwar with NCERT Textbook based study material, chapter-wise learning, MCQs, assignments and Agniveer Foundation. 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