{"id":935,"date":"2026-10-05T02:42:41","date_gmt":"2026-10-05T02:42:41","guid":{"rendered":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/?p=935"},"modified":"2026-10-05T02:54:52","modified_gmt":"2026-10-05T02:54:52","slug":"2-%e0%a4%b0%e0%a5%88%e0%a4%96%e0%a4%bf%e0%a4%95-%e0%a4%ac%e0%a4%b9%e0%a5%81%e0%a4%aa%e0%a4%a6%e0%a5%8b%e0%a4%82-%e0%a4%95%e0%a4%be-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%9a%e0%a4%af-introduction-to-l","status":"publish","type":"post","link":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/2026\/10\/05\/2-%e0%a4%b0%e0%a5%88%e0%a4%96%e0%a4%bf%e0%a4%95-%e0%a4%ac%e0%a4%b9%e0%a5%81%e0%a4%aa%e0%a4%a6%e0%a5%8b%e0%a4%82-%e0%a4%95%e0%a4%be-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%9a%e0%a4%af-introduction-to-l\/","title":{"rendered":"*2* | \u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092a\u0930\u093f\u091a\u092f | Introduction to Linear Polynomials"},"content":{"rendered":"<div id=\"pl-935\"  class=\"panel-layout\" ><div id=\"pg-935-0\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-935-0-0\"  class=\"panel-grid-cell\" ><div id=\"panel-935-0-0-0\" 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-CH2-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;\">Ch2 - \u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926 - \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=\"ch2g-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 - \u092c\u0939\u0941\u092a\u0926 \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\u091a\u092f - \u092c\u0939\u0941\u092a\u0926 \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948? - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u092c\u0939\u0941\u092a\u0926 \u092e\u0924\u0932\u092c \u092c\u0939\u0941\u0924 \u092a\u0926 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 \u092a\u0926 \u092e\u0924\u0932\u092c \u0939\u093f\u0938\u094d\u0938\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u091c\u0948\u0938\u0947 2x+3 \u092e\u0947\u0902 \u0926\u094b \u092a\u0926 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 2x \u090f\u0915 \u092a\u0926 \u0914\u0930 3 \u0926\u0942\u0938\u0930\u093e \u092a\u0926\u0964 x \u091a\u0930 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u091a\u0930 \u092e\u0924\u0932\u092c \u092c\u0926\u0932\u0928\u0947 \u0935\u093e\u0932\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964 2 \u0914\u0930 3 \u0905\u091a\u0930 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 \u0905\u091a\u0930 \u092e\u0924\u0932\u092c \u0928\u0939\u0940\u0902 \u092c\u0926\u0932\u0924\u0947 \u0939\u0948\u0902\u0964 \u092c\u0939\u0941\u092a\u0926 \u092e\u0947\u0902 x \u0915\u0940 \u0918\u093e\u0924 \u092a\u0942\u0930\u094d\u0923 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 1,2,3 \u0939\u094b \u0938\u0915\u0924\u0940 \u0939\u0948\u0964 \u090b\u0923 \u092f\u093e \u092d\u093f\u0928\u094d\u0928 \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u092f\u0939\u0940 \u092c\u0939\u0941\u092a\u0926 \u0915\u0940 \u092a\u0939\u091a\u093e\u0928 \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;\">\u092c\u0939\u0941\u092a\u0926 = \u091a\u0930 + \u0905\u091a\u0930 + \u0918\u093e\u0924<\/span><br><span>\u091c\u0948\u0938\u0947 2x+3 , x\u00b2+5x+6 , 4x\u00b3-2x+1<\/span><\/div><div style=\"background:#e3f2fd;border-left:4px solid #1565c0;padding:6px 10px;font-weight:bold;margin-top:8px;\">\u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926 \u0915\u094d\u092f\u093e? - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u091c\u093f\u0938\u092e\u0947\u0902 x \u0915\u0940 \u0938\u092c\u0938\u0947 \u092c\u0921\u093c\u0940 \u0918\u093e\u0924 1 \u0939\u094b \u0935\u0939 \u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0930\u0948\u0916\u093f\u0915 \u092e\u0924\u0932\u092c \u0938\u0940\u0927\u0940 \u0930\u0947\u0916\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0915\u093e \u0917\u094d\u0930\u093e\u092b \u0938\u0940\u0927\u0940 \u0930\u0947\u0916\u093e \u092c\u0928\u0924\u093e \u0939\u0948\u0964 \u0921\u093f\u0917\u094d\u0930\u0940 1 \u0939\u094b\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;\">\u0930\u0948\u0916\u093f\u0915 : ax + b , a\u22600 , \u0918\u093e\u0924=1<\/div><div>\u091c\u0948\u0938\u0947 2x+3 , x-5 , -3x+7<\/div><div>\u090f\u0915 \u091a\u0930 \u090f\u0915 \u0918\u093e\u0924 = \u0930\u0948\u0916\u093f\u0915<\/div><\/div><\/div><\/div>\n\n<div id=\"ch2g-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 - \u0921\u093f\u0917\u094d\u0930\u0940 \u0914\u0930 \u092a\u094d\u0930\u0915\u093e\u0930<\/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;\">\u0921\u093f\u0917\u094d\u0930\u0940 \u0915\u094d\u092f\u093e? - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u092c\u0939\u0941\u092a\u0926 \u092e\u0947\u0902 x \u0915\u0940 \u0938\u092c\u0938\u0947 \u092c\u0921\u093c\u0940 \u0918\u093e\u0924 \u0915\u094b \u0921\u093f\u0917\u094d\u0930\u0940 \u0915\u0939\u0924\u0947 \u0939\u0948\u0902\u0964 \u0921\u093f\u0917\u094d\u0930\u0940 \u0938\u0947 \u092a\u094d\u0930\u0915\u093e\u0930 \u0924\u092f \u0939\u094b\u0924\u093e \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:15px;font-weight:bold;\">\u0905\u091a\u0930 : 5 => \u0921\u093f\u0917\u094d\u0930\u0940 0<\/div><div style=\"font-size:15px;font-weight:bold;color:#d32f2f;\">\u0930\u0948\u0916\u093f\u0915 : 2x+3 => \u0921\u093f\u0917\u094d\u0930\u0940 1<\/div><div style=\"font-size:15px;font-weight:bold;\">\u0926\u094d\u0935\u093f\u0918\u093e\u0924 : x\u00b2+2x+1 => \u0921\u093f\u0917\u094d\u0930\u0940 2<\/div><div style=\"font-size:15px;font-weight:bold;\">\u0924\u094d\u0930\u093f\u0918\u093e\u0924 : x\u00b3+3x => \u0921\u093f\u0917\u094d\u0930\u0940 3<\/div><\/div>\u0930\u0948\u0916\u093f\u0915 \u0915\u0940 \u0921\u093f\u0917\u094d\u0930\u0940 \u0939\u092e\u0947\u0936\u093e 1 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u092f\u0939\u0940 \u0907\u0938\u0915\u0940 \u092a\u0939\u091a\u093e\u0928 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964<div style=\"background:#e8f5e9;border-left:4px solid #2e7d32;padding:6px 10px;font-weight:bold;margin-top:8px;\">\u092a\u0926\u094b\u0902 \u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930 \u092a\u094d\u0930\u0915\u093e\u0930 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u090f\u0915 \u092a\u0926 \u0935\u093e\u0932\u093e \u090f\u0915\u092a\u0926\u0940\u092f \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u091c\u0948\u0938\u0947 5x\u0964 \u0926\u094b \u092a\u0926 \u0935\u093e\u0932\u093e \u0926\u094d\u0935\u093f\u092a\u0926\u0940\u092f \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u091c\u0948\u0938\u0947 2x+3\u0964 \u0924\u0940\u0928 \u092a\u0926 \u0935\u093e\u0932\u093e \u0924\u094d\u0930\u093f\u092a\u0926\u0940\u092f \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u091c\u0948\u0938\u0947 x\u00b2+2x+3\u0964 \u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926 \u0905\u0927\u093f\u0915\u0924\u0930 \u0926\u094d\u0935\u093f\u092a\u0926\u0940\u092f \u0939\u094b\u0924\u093e \u0939\u0948\u0964 ax+b \u092e\u0947\u0902 \u0926\u094b \u092a\u0926 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 \u0915\u092d\u0940 \u0915\u092d\u0940 \u090f\u0915\u092a\u0926\u0940\u092f \u092d\u0940 \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u091c\u0948\u0938\u0947 ax\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;\">\u090f\u0915\u092a\u0926\u0940 1 \u092a\u0926 : 5x , \u0926\u094d\u0935\u093f\u092a\u0926\u0940 2 \u092a\u0926 : ax+b , \u0924\u094d\u0930\u093f\u092a\u0926\u0940 3 \u092a\u0926 : ax\u00b2+bx+c<\/span><\/div><\/div><\/div>\n\n<div id=\"ch2g-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 - \u0936\u0942\u0928\u094d\u092f\u0915 \u0914\u0930 \u0917\u094d\u0930\u093e\u092b<\/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;\">\u0936\u0942\u0928\u094d\u092f\u0915 \u0915\u094d\u092f\u093e? - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u092c\u0939\u0941\u092a\u0926 \u0915\u093e \u092e\u093e\u0928 \u0936\u0942\u0928\u094d\u092f \u0915\u0930\u0928\u0947 \u0935\u093e\u0932\u093e x \u0936\u0942\u0928\u094d\u092f\u0915 \u0915\u0939\u0932\u093e\u0924\u093e \u0939\u0948\u0964 \u0930\u0948\u0916\u093f\u0915 \u092e\u0947\u0902 \u090f\u0915 \u0939\u0940 \u0936\u0942\u0928\u094d\u092f\u0915 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0921\u093f\u0917\u094d\u0930\u0940 1 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u091c\u093f\u0924\u0928\u0940 \u0921\u093f\u0917\u094d\u0930\u0940 \u0909\u0924\u0928\u0947 \u0936\u0942\u0928\u094d\u092f\u0915 \u0939\u094b\u0924\u0947 \u0939\u0948\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;\">ax+b=0 => x = -b\/a \u0936\u0942\u0928\u094d\u092f\u0915<\/div><div style=\"font-size:14px;\">2x+3=0 => x=-3\/2 \u0936\u0942\u0928\u094d\u092f\u0915<\/div><div style=\"font-size:14px;\">x-5=0 => x=5 \u0936\u0942\u0928\u094d\u092f\u0915<\/div><div style=\"font-size:13px;margin-top:4px;background:#fff;padding:3px 8px;border-radius:5px;\">\u0930\u0948\u0916\u093f\u0915 \u0915\u093e 1 \u0939\u0940 \u0936\u0942\u0928\u094d\u092f\u0915 \u0939\u094b\u0924\u093e \u0939\u0948<\/div><\/div>\u0936\u0942\u0928\u094d\u092f\u0915 \u092e\u0924\u0932\u092c \u0917\u094d\u0930\u093e\u092b x-\u0905\u0915\u094d\u0937 \u0915\u094b \u091c\u0939\u093e\u0901 \u0915\u093e\u091f\u0924\u093e \u0939\u0948 \u0935\u0939 \u092c\u093f\u0902\u0926\u0941 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<div style=\"background:#e3f2fd;border-left:4px solid #1565c0;padding:6px 10px;font-weight:bold;margin-top:8px;\">\u0917\u094d\u0930\u093e\u092b \u0915\u094d\u092f\u093e? - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926 y=ax+b \u0915\u093e \u0917\u094d\u0930\u093e\u092b \u0938\u0940\u0927\u0940 \u0930\u0947\u0916\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u092f\u0939 x-\u0905\u0915\u094d\u0937 \u0915\u094b \u090f\u0915 \u092c\u093e\u0930 \u0915\u093e\u091f\u0924\u093e \u0939\u0948\u0964 \u0915\u093e\u091f\u0928\u0947 \u0935\u093e\u0932\u093e \u092c\u093f\u0902\u0926\u0941 (-b\/a,0) \u0939\u094b\u0924\u093e \u0939\u0948\u0964 y-\u0905\u0915\u094d\u0937 \u0915\u094b (0,b) \u092a\u0930 \u0915\u093e\u091f\u0924\u093e \u0939\u0948\u0964 \u0922\u093e\u0932 a \u0939\u094b\u0924\u093e \u0939\u0948\u0964 a \u0927\u0928 \u0924\u094b \u090a\u092a\u0930 \u091c\u093e\u0924\u0940 \u0939\u0948\u0964 a \u090b\u0923 \u0924\u094b \u0928\u0940\u091a\u0947 \u091c\u093e\u0924\u0940 \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;\">y=ax+b \u0930\u0947\u0916\u093e , x-\u0905\u0915\u094d\u0937 \u092a\u0930 (-b\/a,0) , y \u092a\u0930 (0,b)<\/span><br><span>\u0922\u093e\u0932 = a<\/span><\/div><\/div><\/div>\n\n<div id=\"ch2g-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>\u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926 \u0930\u094b\u091c\u093c\u092e\u0930\u094d\u0930\u093e \u092e\u0947\u0902 \u0932\u0917\u0924\u093e \u0939\u0948\u0964 \u0926\u0941\u0915\u093e\u0928 \u092e\u0947\u0902 \u0932\u093e\u092d \u0939\u093e\u0928\u093f ax+b \u0938\u0947 \u0928\u093f\u0915\u0932\u0924\u093e \u0939\u0948\u0964 \u092e\u094b\u092c\u093e\u0907\u0932 \u092c\u093f\u0932 b + a*x \u0938\u0947 \u092c\u0928\u0924\u093e \u0939\u0948\u0964 \u091f\u0948\u0915\u094d\u0938\u0940 \u0915\u093f\u0930\u093e\u092f\u093e b + a*km \u0938\u0947 \u092c\u0928\u0924\u093e \u0939\u0948\u0964 \u0917\u0924\u093f \u0926\u0942\u0930\u0940 \u092e\u0947\u0902 s=vt+b \u0930\u0948\u0916\u093f\u0915 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u092e\u0936\u0940\u0928 \u0915\u094b y=ax+b \u0915\u094b\u0921 \u0938\u0947 \u091a\u0932\u093e\u0924\u0947 \u0939\u0948\u0902\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;\">\u092c\u093f\u0932 = b + a*x , \u0915\u093f\u0930\u093e\u092f\u093e = b + a*km<\/span><br><span>\u0938\u092c \u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926 ax+b<\/span><\/div><div style=\"background:#e0f2f1;border-left:4px solid #009688;padding:6px 10px;font-weight:bold;margin-top:8px;\">Trick \u092f\u093e\u0926 - \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;\">\u0930\u0942\u092a : ax+b , a\u22600<\/div><div style=\"font-size:15px;font-weight:bold;color:#d32f2f;\">\u0921\u093f\u0917\u094d\u0930\u0940=1 , \u0936\u0942\u0928\u094d\u092f\u0915=1 , \u0936\u0942\u0928\u094d\u092f\u0915=-b\/a<\/div><div style=\"font-size:15px;font-weight:bold;\">\u0917\u094d\u0930\u093e\u092b=\u0938\u0940\u0927\u0940 \u0930\u0947\u0916\u093e , x \u092a\u0930 (-b\/a,0)<\/div><div style=\"font-size:15px;font-weight:bold;\">y \u092a\u0930 (0,b) , \u0922\u093e\u0932=a<\/div><div style=\"font-size:13px;margin-top:4px;background:#fff;padding:3px;border-radius:5px;\">\u092c\u0939\u0941\u092a\u0926 \u092e\u0947\u0902 \u0918\u093e\u0924 \u092a\u0942\u0930\u094d\u0923 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u094b\u0924\u0940 \u0939\u0948<\/div><\/div>\u092f\u0939\u0940 \u0905\u0917\u094d\u0928\u093f\u0935\u0940\u0930 \u092e\u0947\u0902 \u092a\u0915\u094d\u0915\u093e \u092a\u0942\u091b\u0924\u093e \u0939\u0948\u0964 \u0936\u0942\u0928\u094d\u092f\u0915 -b\/a \u0938\u092c\u0938\u0947 \u091c\u094d\u092f\u093e\u0926\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=\"ch2gp\" 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=\"ch2gi\" 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=\"ch2gn\" 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('ch2g-'+i);\nif(el)el.style.display=(i===n?'block':'none');\n}\ndocument.getElementById('ch2gi').textContent=n+' \/ '+t;\nc=n;\n}\ndocument.getElementById('ch2gn').onclick=function(){var n=c+1;if(n>t)n=1;s(n);};\ndocument.getElementById('ch2gp').onclick=function(){var n=c-1;if(n<1)n=t;s(n);};\n})();\n<\/script><\/div><\/div><\/div><\/div><div id=\"pg-935-1\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-935-1-0\"  class=\"panel-grid-cell\" ><div id=\"panel-935-1-0-0\" 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-CH2-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;\">Ch2 - \u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926 - \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=\"ch2g2-1\" 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 - \u092c\u0939\u0941\u092a\u0926 \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \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 - \u092c\u0939\u0941\u092a\u0926 \u0915\u094d\u092f\u093e \u0928\u0939\u0940\u0902? - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u092c\u0939\u0941\u092a\u0926 \u092e\u0947\u0902 \u091a\u0930 \u0915\u0940 \u0918\u093e\u0924 \u092a\u0942\u0930\u094d\u0923 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u094b\u0928\u0940 \u091a\u093e\u0939\u093f\u090f\u0964 0,1,2,3 \u0939\u094b \u0938\u0915\u0924\u0940 \u0939\u0948\u0964 \u090b\u0923 \u0928\u0939\u0940\u0902 \u0939\u094b \u0938\u0915\u0924\u0940\u0964 \u092d\u093f\u0928\u094d\u0928 \u0928\u0939\u0940\u0902 \u0939\u094b \u0938\u0915\u0924\u0940\u0964 1\/x = x\u207b\u00b9 \u0928\u0939\u0940\u0902 \u0939\u0948 \u092c\u0939\u0941\u092a\u0926\u0964 \u221ax = x\u00b9\/\u00b2 \u0928\u0939\u0940\u0902 \u0939\u0948 \u092c\u0939\u0941\u092a\u0926\u0964<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;\">\u092c\u0939\u0941\u092a\u0926 \u0939\u0948 : x\u00b2+2x+3 , 5x , 7<\/div><div style=\"font-size:15px;font-weight:bold;color:#d32f2f;\">\u092c\u0939\u0941\u092a\u0926 \u0928\u0939\u0940\u0902 : 1\/x , \u221ax , x\u207b\u00b2+3<\/div><div style=\"font-size:13px;\">\u0918\u093e\u0924 \u090b\u0923 \u092f\u093e \u092d\u093f\u0928\u094d\u0928 \u0928\u0939\u0940\u0902 \u0939\u094b\u0928\u0940 \u091a\u093e\u0939\u093f\u090f<\/div><\/div><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 - \u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926 \u0930\u0942\u092a - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926 \u090f\u0915 \u091a\u0930 \u092e\u0947\u0902 ax+b \u0930\u0942\u092a \u0939\u094b\u0924\u093e \u0939\u0948\u0964 a\u22600 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964 a=0 \u0924\u094b \u0905\u091a\u0930 \u092c\u0928 \u091c\u093e\u0924\u093e \u0939\u0948\u0964 a \u0917\u0941\u0923\u093e\u0902\u0915 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 b \u0905\u091a\u0930 \u092a\u0926 \u0939\u094b\u0924\u093e \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;\">p(x)=ax+b , a\u22600<\/div><div>\u0921\u093f\u0917\u094d\u0930\u0940=1 , \u092e\u093e\u0928\u0915 \u0930\u0942\u092a<\/div><div>\u091c\u0948\u0938\u0947 2x+3 \u092e\u0947\u0902 a=2 b=3<\/div><div>x-5 \u092e\u0947\u0902 a=1 b=-5<\/div><\/div>a \u0936\u0942\u0928\u094d\u092f \u0928\u0939\u0940\u0902 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964 \u0935\u0939\u0940 \u0936\u0930\u094d\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964<\/div><\/div>\n\n<div id=\"ch2g2-2\" 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 - \u0921\u093f\u0917\u094d\u0930\u0940 \u0914\u0930 \u0936\u0942\u0928\u094d\u092f\u0915 \u092b\u0949\u0930\u094d\u092e\u0942\u0932\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:#e3f2fd;border-left:4px solid #1565c0;padding:6px 10px;font-weight:bold;\">\u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 3 - \u0921\u093f\u0917\u094d\u0930\u0940 \u0914\u0930 \u0936\u0942\u0928\u094d\u092f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u0921\u093f\u0917\u094d\u0930\u0940 \u091c\u093f\u0924\u0928\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948 \u0936\u0942\u0928\u094d\u092f\u0915 \u0909\u0924\u0928\u0947 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 \u0930\u0948\u0916\u093f\u0915 \u0915\u0940 \u0921\u093f\u0917\u094d\u0930\u0940 1 \u0907\u0938\u0932\u093f\u090f 1 \u0936\u0942\u0928\u094d\u092f\u0915\u0964 \u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u0915\u0947 2 \u0936\u0942\u0928\u094d\u092f\u0915\u0964 \u0924\u094d\u0930\u093f\u0918\u093e\u0924 \u0915\u0947 3 \u0936\u0942\u0928\u094d\u092f\u0915\u0964<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;\">\u0921\u093f\u0917\u094d\u0930\u0940 = \u0936\u0942\u0928\u094d\u092f\u0915\u094b\u0902 \u0915\u0940 \u0905\u0927\u093f\u0915\u0924\u092e \u0938\u0902\u0916\u094d\u092f\u093e<\/div><div style=\"font-size:15px;font-weight:bold;color:#d32f2f;\">\u0930\u0948\u0916\u093f\u0915 \u0921\u093f\u0917\u094d\u0930\u09401 => 1 \u0936\u0942\u0928\u094d\u092f\u0915<\/div><div>\u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u0921\u093f\u0917\u094d\u0930\u09402 => 2 \u0936\u0942\u0928\u094d\u092f\u0915<\/div><div>\u0924\u094d\u0930\u093f\u0918\u093e\u0924 \u0921\u093f\u0917\u094d\u0930\u09403 => 3 \u0936\u0942\u0928\u094d\u092f\u0915<\/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 - \u0936\u0942\u0928\u094d\u092f\u0915 \u092b\u0949\u0930\u094d\u092e\u0942\u0932\u093e - \u0939\u0947\u0921\u093f\u0902\u0917 - Most Important<\/div>\u0930\u0948\u0916\u093f\u0915 p(x)=ax+b \u0915\u093e \u0936\u0942\u0928\u094d\u092f\u0915 \u0935\u0939 x \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u0939\u093e\u0901 p(x)=0 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 ax+b=0 => x=-b\/a\u0964 \u092f\u0939\u0940 \u092b\u0949\u0930\u094d\u092e\u0942\u0932\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0938\u092c\u0938\u0947 \u091c\u094d\u092f\u093e\u0926\u093e \u092a\u0942\u091b\u0924\u093e \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;\">\u0936\u0942\u0928\u094d\u092f\u0915 = -b\/a<\/div><div style=\"font-size:14px;\">p(x)=2x+3 => -3\/2<\/div><div style=\"font-size:14px;\">p(x)=x-5 => -(-5)\/1=5<\/div><div style=\"font-size:14px;\">p(x)=3x+6 => -6\/3=-2<\/div><div style=\"font-size:13px;margin-top:4px;background:#fff;padding:3px 8px;border-radius:5px;\">a= x \u0915\u093e \u0917\u0941\u0923\u093e\u0902\u0915 , b= \u0905\u091a\u0930<\/div><\/div><\/div><\/div>\n\n<div id=\"ch2g2-3\" 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 - \u0917\u094d\u0930\u093e\u092b \u0914\u0930 \u0917\u0941\u0923\u0928\u0916\u0902\u0921<\/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 - \u0917\u094d\u0930\u093e\u092b \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>y=ax+b \u0915\u093e \u0917\u094d\u0930\u093e\u092b \u0938\u0940\u0927\u0940 \u0930\u0947\u0916\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u092f\u0939 x-\u0905\u0915\u094d\u0937 \u0915\u094b (-b\/a,0) \u092a\u0930 \u0915\u093e\u091f\u0924\u093e \u0939\u0948\u0964 y-\u0905\u0915\u094d\u0937 \u0915\u094b (0,b) \u092a\u0930 \u0915\u093e\u091f\u0924\u093e \u0939\u0948\u0964 a \u0922\u093e\u0932 \u0939\u094b\u0924\u093e \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:16px;font-weight:bold;\">y=ax+b => \u0930\u0947\u0916\u093e<\/div><div>x-\u0905\u0915\u094d\u0937 \u0915\u091f\u093e\u0928 : (-b\/a,0)<\/div><div>y-\u0905\u0915\u094d\u0937 \u0915\u091f\u093e\u0928 : (0,b)<\/div><div>\u0922\u093e\u0932 m = a<\/div><div>a>0 \u090a\u092a\u0930 , a<0 \u0928\u0940\u091a\u0947<\/div><\/div>\u0930\u0948\u0916\u093f\u0915 \u0915\u093e \u0917\u094d\u0930\u093e\u092b \u0939\u092e\u0947\u0936\u093e \u0930\u0947\u0916\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0935\u0915\u094d\u0930 \u0928\u0939\u0940\u0902 \u092c\u0928\u0924\u093e\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 - \u0917\u0941\u0923\u0928\u0916\u0902\u0921 \u092a\u094d\u0930\u092e\u0947\u092f - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u092f\u0926\u093f x=c \u0936\u0942\u0928\u094d\u092f\u0915 \u0939\u0948 \u0924\u094b (x-c) \u0917\u0941\u0923\u0928\u0916\u0902\u0921 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0930\u0948\u0916\u093f\u0915 \u092e\u0947\u0902 \u090f\u0915 \u0917\u0941\u0923\u0928\u0916\u0902\u0921 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<div style=\"background:#e0f2f1;border:3px solid #009688;padding:8px;border-radius:8px;text-align:center;margin:6px 0;\"><div style=\"font-size:15px;font-weight:bold;\">\u092f\u0926\u093f p(c)=0 \u0924\u094b (x-c) \u0917\u0941\u0923\u0928\u0916\u0902\u0921<\/div><div>p(x)=x-5 \u0936\u0942\u0928\u094d\u092f\u0915 5 => (x-5) \u0917\u0941\u0923\u0928\u0916\u0902\u0921<\/div><div>p(x)=2x+3 \u0936\u0942\u0928\u094d\u092f\u0915 -3\/2 => (x+3\/2)<\/div><div>\u092f\u093e (2x+3) \u0917\u0941\u0923\u0928\u0916\u0902\u0921<\/div><\/div>\u0930\u0948\u0916\u093f\u0915 \u092e\u0947\u0902 p(x)=a(x-\u0936\u0942\u0928\u094d\u092f\u0915) \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/div><\/div>\n\n<div id=\"ch2g2-4\" 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 - \u0938\u092d\u0940 \u092b\u0949\u0930\u094d\u092e\u0942\u0932\u0947 \u090f\u0915 \u0938\u093e\u0925 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;\">\u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 7 - \u092e\u093e\u0928 \u0928\u093f\u0915\u093e\u0932\u0928\u093e - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>p(x)=ax+b \u092e\u0947\u0902 x=c \u0930\u0916\u0928\u0947 \u092a\u0930 \u092e\u093e\u0928 ac+b \u0906\u0924\u093e \u0939\u0948\u0964 \u092f\u0939\u0940 \u092c\u0939\u0941\u092a\u0926 \u0915\u093e \u092e\u093e\u0928 \u0939\u094b\u0924\u093e \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:16px;font-weight:bold;\">p(c)=a*c + b<\/div><div>p(x)=2x+3 p(2)=7 , p(0)=3 , p(-1)=1<\/div><div>p(x)=x-5 p(5)=0 \u0936\u0942\u0928\u094d\u092f\u0915<\/div><\/div><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:10px;border-radius:10px;text-align:center;margin:6px 0;\"><div style=\"font-size:16px;font-weight:bold;\">\u0930\u0942\u092a : p(x)=ax+b , a\u22600<\/div><div style=\"font-size:16px;font-weight:bold;color:#d32f2f;\">\u0921\u093f\u0917\u094d\u0930\u0940=1 , \u0936\u0942\u0928\u094d\u092f\u0915=1<\/div><div style=\"font-size:18px;font-weight:bold;color:#1565c0;\">\u0936\u0942\u0928\u094d\u092f\u0915 = -b\/a<\/div><div style=\"font-size:15px;\">x-\u0905\u0915\u094d\u0937 : (-b\/a,0) , y : (0,b)<\/div><div style=\"font-size:15px;\">p(c)=ac+b , \u0922\u093e\u0932=a<\/div><div style=\"font-size:15px;\">\u0917\u0941\u0923\u0928\u0916\u0902\u0921 : a(x-\u0936\u0942\u0928\u094d\u092f\u0915)<\/div><div style=\"font-size:13px;margin-top:4px;background:#fff;padding:3px;border-radius:5px;\">\u092c\u0939\u0941\u092a\u0926 \u0936\u0930\u094d\u0924 : \u0918\u093e\u0924 \u092a\u0942\u0930\u094d\u0923 \u0938\u0902\u0916\u094d\u092f\u093e \u22650<\/div><\/div>\u092f\u0939\u0940 \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 \u0936\u0942\u0928\u094d\u092f\u0915 -b\/a \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=\"ch2g2p\" 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=\"ch2g2i\" 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=\"ch2g2n\" 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('ch2g2-'+i);\nif(el)el.style.display=(i===n?'block':'none');\n}\ndocument.getElementById('ch2g2i').textContent=n+' \/ '+t;\nc=n;\n}\ndocument.getElementById('ch2g2n').onclick=function(){var n=c+1;if(n>t)n=1;s(n);};\ndocument.getElementById('ch2g2p').onclick=function(){var n=c-1;if(n<1)n=t;s(n);};\n})();\n<\/script><\/div><\/div><\/div><\/div><div id=\"pg-935-2\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-935-2-0\"  class=\"panel-grid-cell\" ><div id=\"panel-935-2-0-0\" 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-CH2-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;\">Ch2 - \u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926 - \u092d\u093e\u0917 3\/4 - \u0905\u092d\u094d\u092f\u093e\u0938 \u092a\u0942\u0930\u093e Detail<\/span><\/div>\n\n<div style=\"padding:10px 12px;\">\n<div id=\"ch2g3-1\" 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 2.1 - \u092c\u0939\u0941\u092a\u0926 \u092a\u0939\u091a\u093e\u0928 - Detail<\/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 - \u0915\u094c\u0928 \u092c\u0939\u0941\u092a\u0926 \u0939\u0948 \u0915\u094c\u0928 \u0928\u0939\u0940\u0902 - \u092a\u0942\u0930\u093e Detail - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q1. \u092c\u0924\u093e\u0913 \u092c\u0939\u0941\u092a\u0926 \u0939\u0948 \u092f\u093e \u0928\u0939\u0940\u0902? \u0915\u093e\u0930\u0923 \u0938\u0939\u093f\u0924\u0964<\/b><br><br><b>(i) 4x\u00b2+3x+7<\/b><br>\u0939\u0932: \u0939\u0948\u0964 \u0918\u093e\u0924 2 \u092a\u0942\u0930\u094d\u0923 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948\u0964 \u091a\u0930 x \u0939\u0948\u0964 \u0917\u0941\u0923\u093e\u0902\u0915 4,3,7 \u0905\u091a\u0930 \u0939\u0948\u0902\u0964 \u0921\u093f\u0917\u094d\u0930\u0940 2 \u0939\u0948\u0964 \u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u092c\u0939\u0941\u092a\u0926 \u0939\u0948\u0964<br><br><b>(ii) y\u00b2+\u221a2<\/b><br>\u0939\u0932: \u0939\u0948\u0964 \u0918\u093e\u0924 2 \u092a\u0942\u0930\u094d\u0923 \u0939\u0948\u0964 \u221a2 \u0905\u091a\u0930 \u0939\u0948\u0964 \u0918\u093e\u0924 \u092a\u0942\u0930\u094d\u0923 \u0939\u0948 \u0907\u0938\u0932\u093f\u090f \u092c\u0939\u0941\u092a\u0926 \u0939\u0948\u0964<br><br><b>(iii) 3\u221at + t\u221a2<\/b><br>\u0939\u0932: \u0928\u0939\u0940\u0902 \u0939\u0948\u0964 \u221at = t\u00b9\/\u00b2 \u0918\u093e\u0924 1\/2 \u092d\u093f\u0928\u094d\u0928 \u0939\u0948\u0964 \u092c\u0939\u0941\u092a\u0926 \u092e\u0947\u0902 \u0918\u093e\u0924 \u092d\u093f\u0928\u094d\u0928 \u0928\u0939\u0940\u0902 \u0939\u094b\u0928\u0940 \u091a\u093e\u0939\u093f\u090f\u0964<br><br><b>(iv) y + 2\/y<\/b><br>\u0939\u0932: \u0928\u0939\u0940\u0902 \u0939\u0948\u0964 2\/y = 2y\u207b\u00b9 \u0918\u093e\u0924 -1 \u090b\u0923 \u0939\u0948\u0964 \u090b\u0923 \u0918\u093e\u0924 \u0928\u0939\u0940\u0902 \u0939\u094b\u0928\u0940 \u091a\u093e\u0939\u093f\u090f\u0964<br><br><b>(v) x\u00b9\u2070+y\u00b3+t\u2075\u2070<\/b><br>\u0939\u0932: \u0939\u0948\u0964 \u0918\u093e\u0924 10,3,50 \u092a\u0942\u0930\u094d\u0923 \u0939\u0948\u0902\u0964 \u0924\u0940\u0928 \u091a\u0930 \u0935\u093e\u0932\u093e \u092c\u0939\u0941\u092a\u0926 \u0939\u0948\u0964 \u0921\u093f\u0917\u094d\u0930\u0940 50 \u0938\u092c\u0938\u0947 \u092c\u0921\u093c\u0940\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;\">Rule : \u0918\u093e\u0924 \u092a\u0942\u0930\u094d\u0923 \u0938\u0902\u0916\u094d\u092f\u093e 0,1,2... \u0939\u094b\u0928\u0940 \u091a\u093e\u0939\u093f\u090f<\/span><br><span>\u090b\u0923 \u092f\u093e \u092d\u093f\u0928\u094d\u0928 \u0928\u0939\u0940\u0902<\/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 - \u0921\u093f\u0917\u094d\u0930\u0940 \u0914\u0930 \u092a\u094d\u0930\u0915\u093e\u0930 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q2. \u0921\u093f\u0917\u094d\u0930\u0940 \u092c\u0924\u093e\u0913\u0964<\/b><br>(i) 2x-3 \u0930\u0948\u0916\u093f\u0915 \u0921\u093f\u0917\u094d\u0930\u09401<br>(ii) 5 \u0905\u091a\u0930 \u0921\u093f\u0917\u094d\u0930\u09400<br>(iii) x\u00b3+2x\u00b2+3x+1 \u0924\u094d\u0930\u093f\u0918\u093e\u0924 \u0921\u093f\u0917\u094d\u0930\u09403<br>(iv) 7x\u00b3 \u0921\u093f\u0917\u094d\u0930\u09403 \u090f\u0915\u092a\u0926\u0940\u092f<\/div><\/div>\n\n<div id=\"ch2g3-2\" 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 2.2 - \u092e\u093e\u0928 \u0928\u093f\u0915\u093e\u0932\u0928\u093e - Detail<\/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 - \u092c\u0939\u0941\u092a\u0926 \u0915\u093e \u092e\u093e\u0928 - \u092a\u0942\u0930\u093e Detail - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q3. p(x)=5x-4x\u00b2+3 \u092a\u0930 \u092e\u093e\u0928 \u0928\u093f\u0915\u093e\u0932\u094b\u0964<\/b><br><br><b>(i) p(0)<\/b><br>\u0939\u0932: x=0 \u0930\u0916\u094b\u0964 p(0)=5*0-4*0\u00b2+3=0-0+3=3\u0964<br>Detail: 0 \u0930\u0916\u0928\u0947 \u092a\u0930 \u0905\u091a\u0930 \u0939\u0940 \u092c\u091a\u0924\u093e \u0939\u0948\u0964 p(0)=3\u0964<br><br><b>(ii) p(-1)<\/b><br>\u0939\u0932: x=-1 \u0930\u0916\u094b\u0964 p(-1)=5*(-1)-4*(-1)\u00b2+3= -5-4*1+3= -5-4+3= -6\u0964<br>Detail: (-1)\u00b2=1 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u090b\u0923 \u0915\u093e \u0935\u0930\u094d\u0917 \u0927\u0928\u0964 -5-4=-9+3=-6\u0964<br><br><b>(iii) p(2)<\/b><br>\u0939\u0932: x=2 \u0930\u0916\u094b\u0964 p(2)=5*2-4*4+3=10-16+3= -3\u0964<br>Detail: 4*4=16\u0964 10+3=13-16=-3\u0964<br><br><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 - \u0930\u0948\u0916\u093f\u0915 p(x)=2x+3 \u092a\u0930 \u092e\u093e\u0928 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q4. p(x)=2x+3 \u092a\u0930 p(0),p(1),p(-3\/2)<\/b><br><br>p(0)=2*0+3=3\u0964<br>p(1)=2*1+3=5\u0964<br>p(-3\/2)=2*(-3\/2)+3= -3+3=0\u0964<br>Detail: p(-3\/2)=0 \u0907\u0938\u0932\u093f\u090f -3\/2 \u0936\u0942\u0928\u094d\u092f\u0915 \u0939\u0948\u0964 \u0936\u0942\u0928\u094d\u092f\u0915 \u092a\u0930 \u092e\u093e\u0928 \u0936\u0942\u0928\u094d\u092f \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u092f\u0939\u0940 \u092a\u0939\u091a\u093e\u0928 \u0939\u0948\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;\">p(c)=0 => c \u0936\u0942\u0928\u094d\u092f\u0915 \u0939\u094b\u0924\u093e \u0939\u0948<\/span><br><span>p(-3\/2)=0 => -3\/2 \u0936\u0942\u0928\u094d\u092f\u0915<\/span><\/div><\/div><\/div>\n\n<div id=\"ch2g3-3\" 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 2.3 - \u0936\u0942\u0928\u094d\u092f\u0915 \u0928\u093f\u0915\u093e\u0932\u0928\u093e - Detail<\/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 - \u0936\u0942\u0928\u094d\u092f\u0915 \u0928\u093f\u0915\u093e\u0932\u094b - \u092a\u0942\u0930\u093e Detail - \u0939\u0947\u0921\u093f\u0902\u0917 - Most Important<\/div><b>Q5. \u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926 \u0915\u0947 \u0936\u0942\u0928\u094d\u092f\u0915 \u0928\u093f\u0915\u093e\u0932\u094b\u0964<\/b><br><br><b>(i) p(x)=x+5<\/b><br>\u0939\u0932: p(x)=0 \u0915\u0930\u094b\u0964 x+5=0 => x=-5\u0964<br>Detail: ax+b=0 => x=-b\/a\u0964 \u092f\u0939\u093e\u0901 a=1 b=5 => -5\/1=-5\u0964 \u0936\u0942\u0928\u094d\u092f\u0915 -5\u0964<br><br><b>(ii) p(x)=x-5<\/b><br>\u0939\u0932: x-5=0 => x=5\u0964<br>Detail: a=1 b=-5 => -(-5)\/1=5\u0964 \u0936\u0942\u0928\u094d\u092f\u0915 5\u0964<br><br><b>(iii) p(x)=2x+5<\/b><br>\u0939\u0932: 2x+5=0 => 2x=-5 => x=-5\/2\u0964<br>Detail: a=2 b=5 => -5\/2\u0964 \u0936\u0942\u0928\u094d\u092f\u0915 -5\/2\u0964<br><br><b>(iv) p(x)=3x-2<\/b><br>\u0939\u0932: 3x-2=0 => 3x=2 => x=2\/3\u0964<br>Detail: a=3 b=-2 => -(-2)\/3=2\/3\u0964<br><br><b>(v) p(x)=3x<\/b><br>\u0939\u0932: 3x=0 => x=0\u0964<br>Detail: a=3 b=0 => -0\/3=0\u0964 \u0936\u0942\u0928\u094d\u092f\u0915 0\u0964<br><br><b>(vi) p(x)=ax+b , a\u22600<\/b><br>\u0939\u0932: ax+b=0 => x=-b\/a\u0964 \u092f\u0939\u0940 \u0938\u0942\u0924\u094d\u0930 \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;\">\u0936\u0942\u0928\u094d\u092f\u0915 = -b\/a<\/div><div>2x+5=-5\/2 , 3x-2=2\/3 , x+5=-5<\/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 - \u0936\u0942\u0928\u094d\u092f\u0915 \u0938\u0924\u094d\u092f\u093e\u092a\u0928 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q6. \u091c\u093e\u0901\u091a\u094b -5 \u0914\u0930 2 \u0936\u0942\u0928\u094d\u092f\u0915 \u0939\u0948\u0902 \u0915\u094d\u092f\u093e p(x)=2x+10 \u0914\u0930 x-2 \u092a\u0930?<\/b><br>p(x)=2x+10 p(-5)=2*(-5)+10=0 => -5 \u0936\u0942\u0928\u094d\u092f\u0915 \u0939\u0948\u0964<br>p(x)=x-2 p(2)=0 => 2 \u0936\u0942\u0928\u094d\u092f\u0915 \u0939\u0948\u0964 Detail \u092e\u0947\u0902 \u092e\u093e\u0928 \u0930\u0916\u0915\u0930 \u091c\u093e\u0901\u091a\u094b\u0964<\/div><\/div>\n\n<div id=\"ch2g3-4\" 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 2.4 - \u0917\u094d\u0930\u093e\u092b \u0914\u0930 \u092a\u0942\u0930\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 - Detail<\/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 - \u0917\u094d\u0930\u093e\u092b \u0914\u0930 \u0915\u091f\u093e\u0928 - \u092a\u0942\u0930\u093e Detail - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q7. y=2x+3 \u0915\u093e x \u0914\u0930 y \u0905\u0915\u094d\u0937 \u0915\u091f\u093e\u0928\u0964<\/b><br>\u0939\u0932: x-\u0905\u0915\u094d\u0937 \u092a\u0930 y=0 => 0=2x+3 => x=-3\/2 => \u092c\u093f\u0902\u0926\u0941 (-3\/2,0)\u0964<br>y-\u0905\u0915\u094d\u0937 \u092a\u0930 x=0 => y=0+3=3 => \u092c\u093f\u0902\u0926\u0941 (0,3)\u0964<br>Detail: \u0917\u094d\u0930\u093e\u092b \u0930\u0947\u0916\u093e \u0939\u094b\u0924\u0940 \u0939\u0948 \u091c\u094b \u0907\u0928 \u0926\u094b \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0938\u0947 \u091c\u093e\u0924\u0940 \u0939\u0948\u0964 \u0922\u093e\u0932 a=2 \u0927\u0928 \u0939\u0948 \u0907\u0938\u0932\u093f\u090f \u090a\u092a\u0930 \u091c\u093e\u0924\u0940 \u0939\u0948\u0964<br><br><b>Q8. y=x-5 \u0915\u093e \u0936\u0942\u0928\u094d\u092f\u0915 \u0914\u0930 \u0917\u094d\u0930\u093e\u092b\u0964<\/b><br>\u0939\u0932: \u0936\u0942\u0928\u094d\u092f\u0915 x=5\u0964 x \u0915\u091f\u093e\u0928 (5,0) y \u0915\u091f\u093e\u0928 (0,-5)\u0964<br>Detail: p(5)=0 \u0917\u094d\u0930\u093e\u092b x \u0915\u094b 5 \u092a\u0930 \u0915\u093e\u091f\u0924\u093e \u0939\u0948\u0964<br><br><div style=\"background:#e8f5e9;border-left:4px solid #2e7d32;padding:6px 10px;font-weight:bold;margin-top:8px;\">\u092a\u094d\u0930\u0936\u094d\u0928 8 - \u092a\u0942\u0930\u0947 \u092a\u093e\u0920 \u092e\u093f\u0936\u094d\u0930\u093f\u0924 - \u0939\u0947\u0921\u093f\u0902\u0917 - \u0915\u094b\u0908 \u0928\u0939\u0940\u0902 \u091b\u0942\u091f\u093e<\/div><b>Q9. p(x)=5x-4x\u00b2+3 \u0915\u093e p(0),p(-1),p(2) \u0939\u092e\u0928\u0947 \u0915\u093f\u092f\u093e\u0964<\/b><br><b>Q10. p(y)=y\u00b2-y+1 p(0)=1 p(1)=1 p(2)=3\u0964<\/b><br>Detail: y=0 =>0-0+1=1\u0964 y=1=>1-1+1=1\u0964 y=2=>4-2+1=3\u0964<br><br><b>Q11. \u0938\u0924\u094d\u092f\u093e\u092a\u093f\u0924 \u0915\u0930\u094b x=-1\/\u221a3 \u0914\u0930 2\/\u221a3 \u0936\u0942\u0928\u094d\u092f\u0915 \u0939\u0948\u0902 3x\u00b2-5x?<\/b><br>Detail: 3*(1\/3)-5*(-1\/\u221a3) \u0928\u0939\u0940\u0902 \u0936\u0942\u0928\u094d\u092f\u0964 \u0917\u0923\u0928\u093e Detail \u092e\u0947\u0902\u0964 \u0930\u0948\u0916\u093f\u0915 \u0928\u0939\u0940\u0902 \u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u0939\u0948\u0964<br><br><b>Q12. \u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926 \u092c\u0928\u093e\u0913 \u091c\u093f\u0938\u0915\u093e \u0936\u0942\u0928\u094d\u092f\u0915 -3 \u0939\u094b\u0964<\/b><br>\u0939\u0932: \u0936\u0942\u0928\u094d\u092f\u0915 -3 => (x-(-3))=(x+3) \u0917\u0941\u0923\u0928\u0916\u0902\u0921\u0964 p(x)=x+3 \u092f\u093e 2x+6 \u092f\u093e a(x+3)\u0964<br>Detail: p(x)=a(x-\u0936\u0942\u0928\u094d\u092f\u0915) = a(x+3)\u0964 a=1 \u0924\u094b x+3\u0964 a=2 \u0924\u094b 2x+6\u0964 \u0905\u0928\u0902\u0924 \u092c\u0939\u0941\u092a\u0926 \u092c\u0928 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<div style=\"background:#fff9c4;border:3px solid #fbc02d;padding:8px;border-radius:10px;text-align:center;margin:6px 0;\"><div style=\"font-weight:bold;\">\u092c\u0928\u093e\u0928\u093e : \u0936\u0942\u0928\u094d\u092f\u0915 c => p(x)=a(x-c)<\/div><div>\u0936\u0942\u0928\u094d\u092f\u0915 -3 => p(x)=x+3 , 2x+6 , 3x+9...<\/div><div>\u0936\u0942\u0928\u094d\u092f\u0915 5 => p(x)=x-5 , 2x-10...<\/div><\/div><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 Detail - \u0915\u094b\u0908 Shortcut \u0928\u0939\u0940\u0902 - \u0930\u094b\u091f\u0940 \u092a\u0915\u094d\u0915\u0940 \u0906\u092a\u0915\u0947 \u0938\u093e\u0925!<\/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=\"ch2g3p\" 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=\"ch2g3i\" 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=\"ch2g3n\" 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('ch2g3-'+i);\nif(el)el.style.display=(i===n?'block':'none');\n}\ndocument.getElementById('ch2g3i').textContent=n+' \/ '+t;\nc=n;\n}\ndocument.getElementById('ch2g3n').onclick=function(){var n=c+1;if(n>t)n=1;s(n);};\ndocument.getElementById('ch2g3p').onclick=function(){var n=c-1;if(n<1)n=t;s(n);};\n})();\n<\/script><\/div><\/div><\/div><\/div><div id=\"pg-935-3\"  class=\"panel-grid panel-no-style\" ><div id=\"pgc-935-3-0\"  class=\"panel-grid-cell\" ><div id=\"panel-935-3-0-0\" 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-CH2-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;\">Ch2 - \u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926 - \u092d\u093e\u0917 4\/4 - MCQ \u0905\u0917\u094d\u0928\u093f\u0935\u0940\u0930 Special<\/span><\/div>\n\n<div style=\"padding:10px 12px;\">\n<div id=\"ch2g4-1\" 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 - \u092c\u0939\u0941\u092a\u0926 \u092a\u0939\u091a\u093e\u0928 - \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: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 - \u092c\u0939\u0941\u092a\u0926 \u0939\u0948 \u092f\u093e \u0928\u0939\u0940\u0902 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q1. \u0915\u094c\u0928 \u092c\u0939\u0941\u092a\u0926 \u0939\u0948?<\/b><br>A) x\u00b2+\u221ax B) 1\/x+2 C) x\u00b2+3x+2 D) x\u207b\u00b2+5<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans C) x\u00b2+3x+2 \u0918\u093e\u0924 \u092a\u0942\u0930\u094d\u0923 2,1,0<\/span><br>Detail: A \u221ax=x\u00b9\/\u00b2 \u092d\u093f\u0928\u094d\u0928 \u0928\u0939\u0940\u0902 B 1\/x=x\u207b\u00b9 \u090b\u0923 \u0928\u0939\u0940\u0902 D x\u207b\u00b2 \u090b\u0923 \u0928\u0939\u0940\u0902<br><br><b>Q2. \u0915\u094c\u0928 \u092c\u0939\u0941\u092a\u0926 \u0928\u0939\u0940\u0902 \u0939\u0948?<\/b><br>A) 5 B) 2x+3 C) y+2\/y D) x\u00b9\u2070<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans C) y+2\/y = y+2y\u207b\u00b9 \u0918\u093e\u0924 -1<\/span><br><br><b>Q3. 3\u221at + t\u221a2 \u092c\u0939\u0941\u092a\u0926 \u0915\u094d\u092f\u094b\u0902 \u0928\u0939\u0940\u0902?<\/b><br>A) \u221at = t\u00b9\/\u00b2 \u092d\u093f\u0928\u094d\u0928 B) \u221a2 \u0915\u093e\u0930\u0923 C) \u0926\u094b\u0928\u094b\u0902 D) \u0939\u0948<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans A) \u221at \u0918\u093e\u0924 1\/2 \u092d\u093f\u0928\u094d\u0928<\/span><br><br><b>Q4. \u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926 \u0915\u094c\u0928?<\/b><br>A) x\u00b2+1 B) 2x+3 C) x\u00b3 D) 5<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans B) 2x+3 \u0918\u093e\u09241<\/span><br><br><div style=\"background:#e3f2fd;border-left:4px solid #1565c0;padding:6px 10px;font-weight:bold;margin-top:8px;\">MCQ - \u0921\u093f\u0917\u094d\u0930\u0940 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q5. 2x+3 \u0915\u0940 \u0921\u093f\u0917\u094d\u0930\u0940?<\/b><br>A) 0 B) 1 C) 2 D) 3<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans B) 1 \u0930\u0948\u0916\u093f\u0915<\/span><br><br><b>Q6. \u0905\u091a\u0930 \u092c\u0939\u0941\u092a\u0926 7 \u0915\u0940 \u0921\u093f\u0917\u094d\u0930\u0940?<\/b><br>A) 0 B) 1 C) 7 D) \u0928\u0939\u0940\u0902<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans A) 0<\/span><br><br><b>Q7. x\u00b3+2x\u00b2+x \u0921\u093f\u0917\u094d\u0930\u0940?<\/b><br>A) 1 B) 2 C) 3 D) 0<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans C) 3 \u0924\u094d\u0930\u093f\u0918\u093e\u0924<\/span><br><br><b>Q8. p(x)=ax+b a\u22600 \u0915\u094d\u092f\u094b\u0902?<\/b><br>A) a=0 \u0924\u094b \u0905\u091a\u0930 B) a=0 \u0924\u094b \u0930\u0948\u0916\u093f\u0915 \u0928\u0939\u0940\u0902 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) a=0 \u0924\u094b bx \u0905\u091a\u0930 \u0921\u093f\u0917\u094d\u0930\u09400<\/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;\">Rule : \u0918\u093e\u0924 \u092a\u0942\u0930\u094d\u0923 \u22650 , \u0930\u0948\u0916\u093f\u0915 ax+b a\u22600 \u0921\u093f\u0917\u094d\u0930\u09401<\/span><\/div><\/div><\/div>\n\n<div id=\"ch2g4-2\" 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 - \u092e\u093e\u0928 \u0914\u0930 \u0936\u0942\u0928\u094d\u092f\u0915 - \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: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 - \u092e\u093e\u0928 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q9. p(x)=5x-4x\u00b2+3 p(0)=?<\/b><br>A) 0 B) 3 C) 5 D) -4<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans B) 3 Detail: 0-0+3<\/span><br><br><b>Q10. p(x)=5x-4x\u00b2+3 p(-1)=?<\/b><br>A) -6 B) 6 C) 3 D) -2<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans A) -6 Detail: -5-4+3=-6<\/span><br><br><b>Q11. p(x)=2x+3 p(-3\/2)=?<\/b><br>A) 0 B) 3 C) -3 D) 5<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans A) 0 \u0907\u0938\u0932\u093f\u090f -3\/2 \u0936\u0942\u0928\u094d\u092f\u0915<\/span><br><br><b>Q12. p(x)=x-5 p(5)=?<\/b><br>A) 0 B) 5 C) -5 D) 10<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans A) 0 Detail: 5-5=0 \u0936\u0942\u0928\u094d\u092f\u0915<\/span><br><br><div style=\"background:#ffebee;border-left:4px solid #d32f2f;padding:6px 10px;font-weight:bold;margin-top:8px;\">MCQ - \u0936\u0942\u0928\u094d\u092f\u0915 - Most Important \u0905\u0917\u094d\u0928\u093f\u0935\u0940\u0930 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q13. p(x)=x+5 \u0936\u0942\u0928\u094d\u092f\u0915?<\/b><br>A) 5 B) -5 C) 0 D) 1<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans B) -5 Detail: x+5=0 => -5<\/span><br><br><b>Q14. p(x)=2x+5 \u0936\u0942\u0928\u094d\u092f\u0915?<\/b><br>A) 5\/2 B) -5\/2 C) 2\/5 D) -2\/5<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans B) -5\/2 Detail: -b\/a=-5\/2<\/span><br><br><b>Q15. p(x)=3x-2 \u0936\u0942\u0928\u094d\u092f\u0915?<\/b><br>A) 2\/3 B) -2\/3 C) 3\/2 D) -3\/2<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans A) 2\/3 Detail: -(-2)\/3<\/span><br><br><b>Q16. ax+b \u0936\u0942\u0928\u094d\u092f\u0915?<\/b><br>A) b\/a B) -b\/a C) a\/b D) -a\/b<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans B) -b\/a \u0905\u0917\u094d\u0928\u093f\u0935\u0940\u0930 \u092e\u0947\u0902 \u0938\u092c\u0938\u0947 \u091c\u094d\u092f\u093e\u0926\u093e \u092a\u0942\u091b\u0924\u093e \u0939\u0948<\/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;\">\u0936\u0942\u0928\u094d\u092f\u0915 = -b\/a \u0938\u092c\u0938\u0947 Important<\/span><\/div><\/div><\/div>\n\n<div id=\"ch2g4-3\" 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 - \u0917\u094d\u0930\u093e\u092b \u0914\u0930 \u0917\u0941\u0923\u0928\u0916\u0902\u0921<\/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 - \u0917\u094d\u0930\u093e\u092b - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q17. y=ax+b \u0917\u094d\u0930\u093e\u092b?<\/b><br>A) \u0935\u0915\u094d\u0930 B) \u0938\u0940\u0927\u0940 \u0930\u0947\u0916\u093e C) \u0917\u094b\u0932\u093e D) \u092a\u0930\u0935\u0932\u092f<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans B) \u0938\u0940\u0927\u0940 \u0930\u0947\u0916\u093e \u0930\u0948\u0916\u093f\u0915<\/span><br><br><b>Q18. y=2x+3 x-\u0905\u0915\u094d\u0937 \u0915\u091f\u093e\u0928?<\/b><br>A) (0,3) B) (-3\/2,0) C) (3\/2,0) D) (0,-3\/2)<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans B) (-3\/2,0) Detail: y=0 => x=-3\/2<\/span><br><br><b>Q19. y=2x+3 y-\u0905\u0915\u094d\u0937 \u0915\u091f\u093e\u0928?<\/b><br>A) (0,3) B) (3,0) C) (-3\/2,0) D) (0,0)<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans A) (0,3) Detail: x=0 => y=3<\/span><br><br><b>Q20. y=x-5 x \u0915\u091f\u093e\u0928?<\/b><br>A) (5,0) B) (0,5) C) (0,-5) D) (-5,0)<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans A) (5,0) \u0936\u0942\u0928\u094d\u092f\u0915 5<\/span><br><br><div style=\"background:#e0f2f1;border-left:4px solid #009688;padding:6px 10px;font-weight:bold;margin-top:8px;\">MCQ - \u0917\u0941\u0923\u0928\u0916\u0902\u0921 \u0914\u0930 \u092c\u0928\u093e\u0928\u093e - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q21. p(c)=0 \u0924\u094b \u0917\u0941\u0923\u0928\u0916\u0902\u0921?<\/b><br>A) (x+c) B) (x-c) C) x D) c<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans B) (x-c)<\/span><br><br><b>Q22. \u0936\u0942\u0928\u094d\u092f\u0915 5 \u0935\u093e\u0932\u093e \u092c\u0939\u0941\u092a\u0926?<\/b><br>A) x+5 B) x-5 C) 2x+5 D) 3x<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans B) x-5 Detail: (x-5)=0 =>5<\/span><br><br><b>Q23. \u0936\u0942\u0928\u094d\u092f\u0915 -3 \u0935\u093e\u0932\u093e \u092c\u0939\u0941\u092a\u0926?<\/b><br>A) x-3 B) x+3 C) x+5 D) x<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans B) x+3 Detail: (x+3)=0 =>-3<\/span><br><br><b>Q24. \u0936\u0942\u0928\u094d\u092f\u0915 -3 \u0935\u093e\u0932\u0947 \u0915\u093f\u0924\u0928\u0947 \u092c\u0939\u0941\u092a\u0926?<\/b><br>A) 1 B) 2 C) \u0905\u0928\u0902\u0924 D) 0<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans C) \u0905\u0928\u0902\u0924 a(x+3) a\u22600<\/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;\">x (-b\/a,0) y (0,b) \u0922\u093e\u0932 a \u0917\u0941\u0923\u0928\u0916\u0902\u0921 (x-c)<\/span><\/div><\/div><\/div>\n\n<div id=\"ch2g4-4\" 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 - \u0905\u0917\u094d\u0928\u093f\u0935\u0940\u0930 Special Final<\/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 - \u0905\u0917\u094d\u0928\u093f\u0935\u0940\u0930 Special - \u0939\u0947\u0921\u093f\u0902\u0917<\/div><b>Q25. \u0930\u0948\u0916\u093f\u0915 \u0915\u0947 \u0915\u093f\u0924\u0928\u0947 \u0936\u0942\u0928\u094d\u092f\u0915?<\/b><br>A) 0 B) 1 C) 2 D) \u0905\u0928\u0902\u0924<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans B) 1 \u0921\u093f\u0917\u094d\u0930\u09401<\/span><br><br><b>Q26. \u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u0915\u0947 \u0915\u093f\u0924\u0928\u0947 \u0936\u0942\u0928\u094d\u092f\u0915 max?<\/b><br>A) 1 B) 2 C) 3 D) 0<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans B) 2 \u0921\u093f\u0917\u094d\u0930\u09402<\/span><br><br><b>Q27. p(x)=3x \u0936\u0942\u0928\u094d\u092f\u0915?<\/b><br>A) 0 B) 3 C) -3 D) 1<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans A) 0 Detail: 3x=0 =>0<\/span><br><br><b>Q28. p(x)=x+2x\u00b2+3 \u0915\u094c\u0928 \u0938\u093e?<\/b><br>A) \u0930\u0948\u0916\u093f\u0915 B) \u0926\u094d\u0935\u093f\u0918\u093e\u0924 C) \u0924\u094d\u0930\u093f\u0918\u093e\u0924 D) \u0905\u091a\u0930<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans B) \u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u0921\u093f\u0917\u094d\u0930\u09402<\/span><br><br><b>Q29. \u092c\u093f\u0932 = 50+10x \u0915\u094c\u0928 \u0938\u093e \u092c\u0939\u0941\u092a\u0926?<\/b><br>A) \u0930\u0948\u0916\u093f\u0915 B) \u0926\u094d\u0935\u093f\u0918\u093e\u0924 C) \u0905\u091a\u0930 D) \u0928\u0939\u0940\u0902<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans A) \u0930\u0948\u0916\u093f\u0915 ax+b 10x+50<\/span><br><br><b>Q30. y= -2x+5 \u0922\u093e\u0932?<\/b><br>A) -2 B) 5 C) 2 D) -5<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans A) -2 Detail: y=ax+b a \u0922\u093e\u0932<\/span><br><br><b>Q31. a>0 \u0924\u094b \u0930\u0947\u0916\u093e?<\/b><br>A) \u090a\u092a\u0930 \u091c\u093e\u0924\u0940 B) \u0928\u0940\u091a\u0947 C) \u0938\u0940\u0927\u0940 D) \u0917\u094b\u0932\u093e<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans A) \u090a\u092a\u0930 \u091c\u093e\u0924\u0940 \u0927\u0928 \u0922\u093e\u0932<\/span><br><br><b>Q32. \u0930\u0948\u0916\u093f\u0915 \u0915\u093e \u092e\u093e\u0928\u0915 \u0930\u0942\u092a?<\/b><br>A) ax\u00b2+bx+c B) ax+b a\u22600 C) x\u00b3 D) a<br><span style=\"background:#e8f5e9;padding:2px 8px;border-radius:5px;font-weight:bold;\">Ans B) ax+b a\u22600<\/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 \u0905\u0917\u094d\u0928\u093f\u0935\u0940\u0930 Trick - Ch2 \u092a\u0942\u0930\u093e<\/div><div>\u0930\u0942\u092a ax+b a\u22600 \u0921\u093f\u0917\u094d\u0930\u09401 \u0936\u0942\u0928\u094d\u092f\u09151<\/div><div>\u0936\u0942\u0928\u094d\u092f\u0915 = -b\/a \u0938\u092c\u0938\u0947 \u091c\u094d\u092f\u093e\u0926\u093e \u092a\u0942\u091b\u0924\u093e<\/div><div>x (-b\/a,0) y (0,b) \u0922\u093e\u0932 a \u0917\u094d\u0930\u093e\u092b \u0930\u0947\u0916\u093e<\/div><div>p(c)=a(x-c) \u0905\u0928\u0902\u0924 \u092c\u0939\u0941\u092a\u0926<\/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=\"ch2g4p\" 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=\"ch2g4i\" 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=\"ch2g4n\" 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('ch2g4-'+i);\nif(el)el.style.display=(i===n?'block':'none');\n}\ndocument.getElementById('ch2g4i').textContent=n+' \/ '+t;\nc=n;\n}\ndocument.getElementById('ch2g4n').onclick=function(){var n=c+1;if(n>t)n=1;s(n);};\ndocument.getElementById('ch2g4p').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>Ch2 &#8211; \u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926 &#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; \u092c\u0939\u0941\u092a\u0926 \u0915\u094d\u092f\u093e?\u092a\u0930\u093f\u091a\u092f &#8211; \u092c\u0939\u0941\u092a\u0926 \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948? &#8211; \u0939\u0947\u0921\u093f\u0902\u0917\u092c\u0939\u0941\u092a\u0926 \u092e\u0924\u0932\u092c \u092c\u0939\u0941\u0924 \u092a\u0926 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 \u092a\u0926 \u092e\u0924\u0932\u092c \u0939\u093f\u0938\u094d\u0938\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u091c\u0948\u0938\u0947 2x+3 \u092e\u0947\u0902 \u0926\u094b \u092a\u0926 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 2x \u090f\u0915 \u092a\u0926 \u0914\u0930 3 \u0926\u0942\u0938\u0930\u093e \u092a\u0926\u0964 x \u091a\u0930 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u091a\u0930 [&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-935","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; *2* | \u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092a\u0930\u093f\u091a\u092f | Introduction to Linear Polynomials &#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. Complete online learning portal by Pargai Defence &amp; Academic.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/2026\/10\/05\/2-\u0930\u0948\u0916\u093f\u0915-\u092c\u0939\u0941\u092a\u0926\u094b\u0902-\u0915\u093e-\u092a\u0930\u093f\u091a\u092f-introduction-to-l\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Mathematics &#187; *2* | \u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092a\u0930\u093f\u091a\u092f | Introduction to Linear Polynomials &#187; Class-9th - Agniveer Foundation Hub | Pargai Defence &amp; Academic.\" \/>\n<meta property=\"og:description\" content=\"Class 9 Online Classes in Bageshwar with NCERT Textbook based study material, chapter-wise learning, MCQs, assignments and Agniveer Foundation. Complete online learning portal by Pargai Defence &amp; Academic.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/2026\/10\/05\/2-\u0930\u0948\u0916\u093f\u0915-\u092c\u0939\u0941\u092a\u0926\u094b\u0902-\u0915\u093e-\u092a\u0930\u093f\u091a\u092f-introduction-to-l\/\" \/>\n<meta property=\"og:site_name\" content=\"Class-9th - Agniveer Foundation Hub | Pargai Defence &amp; Academic.\" \/>\n<meta property=\"article:published_time\" content=\"2026-10-05T02:42:41+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-10-05T02:54:52+00:00\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"10 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/2026\\\/10\\\/05\\\/2-%e0%a4%b0%e0%a5%88%e0%a4%96%e0%a4%bf%e0%a4%95-%e0%a4%ac%e0%a4%b9%e0%a5%81%e0%a4%aa%e0%a4%a6%e0%a5%8b%e0%a4%82-%e0%a4%95%e0%a4%be-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%9a%e0%a4%af-introduction-to-l\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/2026\\\/10\\\/05\\\/2-%e0%a4%b0%e0%a5%88%e0%a4%96%e0%a4%bf%e0%a4%95-%e0%a4%ac%e0%a4%b9%e0%a5%81%e0%a4%aa%e0%a4%a6%e0%a5%8b%e0%a4%82-%e0%a4%95%e0%a4%be-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%9a%e0%a4%af-introduction-to-l\\\/\"},\"author\":{\"name\":\"admin\",\"@id\":\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/#\\\/schema\\\/person\\\/d4ecf71bc91964603da3f31c3b5d0715\"},\"headline\":\"*2* | \u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092a\u0930\u093f\u091a\u092f | Introduction to Linear Polynomials\",\"datePublished\":\"2026-10-05T02:42:41+00:00\",\"dateModified\":\"2026-10-05T02:54:52+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/2026\\\/10\\\/05\\\/2-%e0%a4%b0%e0%a5%88%e0%a4%96%e0%a4%bf%e0%a4%95-%e0%a4%ac%e0%a4%b9%e0%a5%81%e0%a4%aa%e0%a4%a6%e0%a5%8b%e0%a4%82-%e0%a4%95%e0%a4%be-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%9a%e0%a4%af-introduction-to-l\\\/\"},\"wordCount\":40,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/#organization\"},\"articleSection\":[\"Mathematics\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/2026\\\/10\\\/05\\\/2-%e0%a4%b0%e0%a5%88%e0%a4%96%e0%a4%bf%e0%a4%95-%e0%a4%ac%e0%a4%b9%e0%a5%81%e0%a4%aa%e0%a4%a6%e0%a5%8b%e0%a4%82-%e0%a4%95%e0%a4%be-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%9a%e0%a4%af-introduction-to-l\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/2026\\\/10\\\/05\\\/2-%e0%a4%b0%e0%a5%88%e0%a4%96%e0%a4%bf%e0%a4%95-%e0%a4%ac%e0%a4%b9%e0%a5%81%e0%a4%aa%e0%a4%a6%e0%a5%8b%e0%a4%82-%e0%a4%95%e0%a4%be-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%9a%e0%a4%af-introduction-to-l\\\/\",\"url\":\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/2026\\\/10\\\/05\\\/2-%e0%a4%b0%e0%a5%88%e0%a4%96%e0%a4%bf%e0%a4%95-%e0%a4%ac%e0%a4%b9%e0%a5%81%e0%a4%aa%e0%a4%a6%e0%a5%8b%e0%a4%82-%e0%a4%95%e0%a4%be-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%9a%e0%a4%af-introduction-to-l\\\/\",\"name\":\"Mathematics &#187; *2* | \u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092a\u0930\u093f\u091a\u092f | Introduction to Linear Polynomials &#187; Class-9th - Agniveer Foundation Hub | Pargai Defence &amp; Academic.\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/#website\"},\"datePublished\":\"2026-10-05T02:42:41+00:00\",\"dateModified\":\"2026-10-05T02:54:52+00:00\",\"description\":\"Class 9 Online Classes in Bageshwar with NCERT Textbook based study material, chapter-wise learning, MCQs, assignments and Agniveer Foundation. Complete online learning portal by Pargai Defence & Academic.\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/2026\\\/10\\\/05\\\/2-%e0%a4%b0%e0%a5%88%e0%a4%96%e0%a4%bf%e0%a4%95-%e0%a4%ac%e0%a4%b9%e0%a5%81%e0%a4%aa%e0%a4%a6%e0%a5%8b%e0%a4%82-%e0%a4%95%e0%a4%be-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%9a%e0%a4%af-introduction-to-l\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/2026\\\/10\\\/05\\\/2-%e0%a4%b0%e0%a5%88%e0%a4%96%e0%a4%bf%e0%a4%95-%e0%a4%ac%e0%a4%b9%e0%a5%81%e0%a4%aa%e0%a4%a6%e0%a5%8b%e0%a4%82-%e0%a4%95%e0%a4%be-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%9a%e0%a4%af-introduction-to-l\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/2026\\\/10\\\/05\\\/2-%e0%a4%b0%e0%a5%88%e0%a4%96%e0%a4%bf%e0%a4%95-%e0%a4%ac%e0%a4%b9%e0%a5%81%e0%a4%aa%e0%a4%a6%e0%a5%8b%e0%a4%82-%e0%a4%95%e0%a4%be-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%9a%e0%a4%af-introduction-to-l\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"*2* | \u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092a\u0930\u093f\u091a\u092f | Introduction to Linear Polynomials\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/#website\",\"url\":\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/\",\"name\":\"Class-6th - Agniveer Foundation | Pargai Defence & Academic.\",\"description\":\"Class 9th Online Classes in Bageshwar with NCERT Textbook based study material, chapter-wise learning,  MCQs, assignments and Agniveer Foundation. Complete online learning portal by Pargai Defence &amp; Academic.\",\"publisher\":{\"@id\":\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/#organization\"},\"alternateName\":\"Agniveer Foundation Class-6th\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/#organization\",\"name\":\"Pargai Defence & Academic.\",\"alternateName\":\"Pargai Institute of Defence Studies.\",\"url\":\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/wp-content\\\/uploads\\\/2026\\\/07\\\/cropped-channels4_profile.jpg\",\"contentUrl\":\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/wp-content\\\/uploads\\\/2026\\\/07\\\/cropped-channels4_profile.jpg\",\"width\":512,\"height\":512,\"caption\":\"Pargai Defence & Academic.\"},\"image\":{\"@id\":\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/#\\\/schema\\\/logo\\\/image\\\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/#\\\/schema\\\/person\\\/d4ecf71bc91964603da3f31c3b5d0715\",\"name\":\"admin\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/d74d2ed3f17c48067bcb3273bb8f4de11563c441bc3d2855fbb8e5aea27f629f?s=96&d=mm&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/d74d2ed3f17c48067bcb3273bb8f4de11563c441bc3d2855fbb8e5aea27f629f?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/d74d2ed3f17c48067bcb3273bb8f4de11563c441bc3d2855fbb8e5aea27f629f?s=96&d=mm&r=g\",\"caption\":\"admin\"},\"sameAs\":[\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\"],\"url\":\"https:\\\/\\\/academic.pargaidefenceacademy.in\\\/Class-9th\\\/author\\\/admin\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Mathematics &#187; *2* | \u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092a\u0930\u093f\u091a\u092f | Introduction to Linear Polynomials &#187; Class-9th - Agniveer Foundation Hub | Pargai Defence &amp; Academic.","description":"Class 9 Online Classes in Bageshwar with NCERT Textbook based study material, chapter-wise learning, MCQs, assignments and Agniveer Foundation. Complete online learning portal by Pargai Defence & Academic.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/2026\/10\/05\/2-\u0930\u0948\u0916\u093f\u0915-\u092c\u0939\u0941\u092a\u0926\u094b\u0902-\u0915\u093e-\u092a\u0930\u093f\u091a\u092f-introduction-to-l\/","og_locale":"en_US","og_type":"article","og_title":"Mathematics &#187; *2* | \u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092a\u0930\u093f\u091a\u092f | Introduction to Linear Polynomials &#187; Class-9th - Agniveer Foundation Hub | Pargai Defence &amp; Academic.","og_description":"Class 9 Online Classes in Bageshwar with NCERT Textbook based study material, chapter-wise learning, MCQs, assignments and Agniveer Foundation. Complete online learning portal by Pargai Defence & Academic.","og_url":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/2026\/10\/05\/2-\u0930\u0948\u0916\u093f\u0915-\u092c\u0939\u0941\u092a\u0926\u094b\u0902-\u0915\u093e-\u092a\u0930\u093f\u091a\u092f-introduction-to-l\/","og_site_name":"Class-9th - Agniveer Foundation Hub | Pargai Defence &amp; Academic.","article_published_time":"2026-10-05T02:42:41+00:00","article_modified_time":"2026-10-05T02:54:52+00:00","author":"admin","twitter_card":"summary_large_image","twitter_misc":{"Written by":"admin","Est. reading time":"10 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/2026\/10\/05\/2-%e0%a4%b0%e0%a5%88%e0%a4%96%e0%a4%bf%e0%a4%95-%e0%a4%ac%e0%a4%b9%e0%a5%81%e0%a4%aa%e0%a4%a6%e0%a5%8b%e0%a4%82-%e0%a4%95%e0%a4%be-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%9a%e0%a4%af-introduction-to-l\/#article","isPartOf":{"@id":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/2026\/10\/05\/2-%e0%a4%b0%e0%a5%88%e0%a4%96%e0%a4%bf%e0%a4%95-%e0%a4%ac%e0%a4%b9%e0%a5%81%e0%a4%aa%e0%a4%a6%e0%a5%8b%e0%a4%82-%e0%a4%95%e0%a4%be-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%9a%e0%a4%af-introduction-to-l\/"},"author":{"name":"admin","@id":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/#\/schema\/person\/d4ecf71bc91964603da3f31c3b5d0715"},"headline":"*2* | \u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092a\u0930\u093f\u091a\u092f | Introduction to Linear Polynomials","datePublished":"2026-10-05T02:42:41+00:00","dateModified":"2026-10-05T02:54:52+00:00","mainEntityOfPage":{"@id":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/2026\/10\/05\/2-%e0%a4%b0%e0%a5%88%e0%a4%96%e0%a4%bf%e0%a4%95-%e0%a4%ac%e0%a4%b9%e0%a5%81%e0%a4%aa%e0%a4%a6%e0%a5%8b%e0%a4%82-%e0%a4%95%e0%a4%be-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%9a%e0%a4%af-introduction-to-l\/"},"wordCount":40,"commentCount":0,"publisher":{"@id":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/#organization"},"articleSection":["Mathematics"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/2026\/10\/05\/2-%e0%a4%b0%e0%a5%88%e0%a4%96%e0%a4%bf%e0%a4%95-%e0%a4%ac%e0%a4%b9%e0%a5%81%e0%a4%aa%e0%a4%a6%e0%a5%8b%e0%a4%82-%e0%a4%95%e0%a4%be-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%9a%e0%a4%af-introduction-to-l\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/2026\/10\/05\/2-%e0%a4%b0%e0%a5%88%e0%a4%96%e0%a4%bf%e0%a4%95-%e0%a4%ac%e0%a4%b9%e0%a5%81%e0%a4%aa%e0%a4%a6%e0%a5%8b%e0%a4%82-%e0%a4%95%e0%a4%be-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%9a%e0%a4%af-introduction-to-l\/","url":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/2026\/10\/05\/2-%e0%a4%b0%e0%a5%88%e0%a4%96%e0%a4%bf%e0%a4%95-%e0%a4%ac%e0%a4%b9%e0%a5%81%e0%a4%aa%e0%a4%a6%e0%a5%8b%e0%a4%82-%e0%a4%95%e0%a4%be-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%9a%e0%a4%af-introduction-to-l\/","name":"Mathematics &#187; *2* | \u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092a\u0930\u093f\u091a\u092f | Introduction to Linear Polynomials &#187; Class-9th - Agniveer Foundation Hub | Pargai Defence &amp; Academic.","isPartOf":{"@id":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/#website"},"datePublished":"2026-10-05T02:42:41+00:00","dateModified":"2026-10-05T02:54:52+00:00","description":"Class 9 Online Classes in Bageshwar with NCERT Textbook based study material, chapter-wise learning, MCQs, assignments and Agniveer Foundation. Complete online learning portal by Pargai Defence & Academic.","breadcrumb":{"@id":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/2026\/10\/05\/2-%e0%a4%b0%e0%a5%88%e0%a4%96%e0%a4%bf%e0%a4%95-%e0%a4%ac%e0%a4%b9%e0%a5%81%e0%a4%aa%e0%a4%a6%e0%a5%8b%e0%a4%82-%e0%a4%95%e0%a4%be-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%9a%e0%a4%af-introduction-to-l\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/2026\/10\/05\/2-%e0%a4%b0%e0%a5%88%e0%a4%96%e0%a4%bf%e0%a4%95-%e0%a4%ac%e0%a4%b9%e0%a5%81%e0%a4%aa%e0%a4%a6%e0%a5%8b%e0%a4%82-%e0%a4%95%e0%a4%be-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%9a%e0%a4%af-introduction-to-l\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/2026\/10\/05\/2-%e0%a4%b0%e0%a5%88%e0%a4%96%e0%a4%bf%e0%a4%95-%e0%a4%ac%e0%a4%b9%e0%a5%81%e0%a4%aa%e0%a4%a6%e0%a5%8b%e0%a4%82-%e0%a4%95%e0%a4%be-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%9a%e0%a4%af-introduction-to-l\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/"},{"@type":"ListItem","position":2,"name":"*2* | \u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092a\u0930\u093f\u091a\u092f | Introduction to Linear Polynomials"}]},{"@type":"WebSite","@id":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/#website","url":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/","name":"Class-6th - Agniveer Foundation | Pargai Defence & Academic.","description":"Class 9th Online Classes in Bageshwar with NCERT Textbook based study material, chapter-wise learning,  MCQs, assignments and Agniveer Foundation. Complete online learning portal by Pargai Defence &amp; Academic.","publisher":{"@id":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/#organization"},"alternateName":"Agniveer Foundation Class-6th","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/#organization","name":"Pargai Defence & Academic.","alternateName":"Pargai Institute of Defence Studies.","url":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/#\/schema\/logo\/image\/","url":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/wp-content\/uploads\/2026\/07\/cropped-channels4_profile.jpg","contentUrl":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/wp-content\/uploads\/2026\/07\/cropped-channels4_profile.jpg","width":512,"height":512,"caption":"Pargai Defence & Academic."},"image":{"@id":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/#\/schema\/person\/d4ecf71bc91964603da3f31c3b5d0715","name":"admin","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/secure.gravatar.com\/avatar\/d74d2ed3f17c48067bcb3273bb8f4de11563c441bc3d2855fbb8e5aea27f629f?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/d74d2ed3f17c48067bcb3273bb8f4de11563c441bc3d2855fbb8e5aea27f629f?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/d74d2ed3f17c48067bcb3273bb8f4de11563c441bc3d2855fbb8e5aea27f629f?s=96&d=mm&r=g","caption":"admin"},"sameAs":["https:\/\/academic.pargaidefenceacademy.in\/Class-9th"],"url":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/author\/admin\/"}]}},"_links":{"self":[{"href":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/wp-json\/wp\/v2\/posts\/935","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/wp-json\/wp\/v2\/comments?post=935"}],"version-history":[{"count":5,"href":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/wp-json\/wp\/v2\/posts\/935\/revisions"}],"predecessor-version":[{"id":940,"href":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/wp-json\/wp\/v2\/posts\/935\/revisions\/940"}],"wp:attachment":[{"href":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/wp-json\/wp\/v2\/media?parent=935"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/wp-json\/wp\/v2\/categories?post=935"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/wp-json\/wp\/v2\/tags?post=935"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}