{"id":2270,"date":"2022-03-20T08:10:17","date_gmt":"2022-03-20T08:10:17","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=2270"},"modified":"2022-03-22T14:28:26","modified_gmt":"2022-03-22T14:28:26","slug":"bank-jobs-%e0%a6%b8%e0%a6%b0%e0%a6%b2-%e0%a6%b8%e0%a6%ae%e0%a7%80%e0%a6%95%e0%a6%b0%e0%a6%a3-%e0%a6%b8%e0%a6%b9%e0%a6%b8%e0%a6%ae%e0%a7%80%e0%a6%95%e0%a6%b0%e0%a6%a3%e0%a7%87%e0%a6%b0","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/bank-jobs-%e0%a6%b8%e0%a6%b0%e0%a6%b2-%e0%a6%b8%e0%a6%ae%e0%a7%80%e0%a6%95%e0%a6%b0%e0%a6%a3-%e0%a6%b8%e0%a6%b9%e0%a6%b8%e0%a6%ae%e0%a7%80%e0%a6%95%e0%a6%b0%e0%a6%a3%e0%a7%87%e0%a6%b0\/","title":{"rendered":"Bank Jobs | \u09b8\u09b0\u09b2 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3, \u09b8\u09c2\u099a\u0995 \u0993 \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae"},"content":{"rendered":"\r\n<h2><strong>\u09b8\u09b0\u09b2 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/strong><\/h2>\r\n\r\n\r\n\r\n<p>\u09af\u09c7 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7 \u098f\u0995 \u0998\u09be\u09a4 \u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u098f\u0995\u099f\u09bf \u09ae\u09be\u09a4\u09cd\u09b0 \u0985\u099c\u09cd\u099e\u09be\u09a4 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09aa\u09cd\u09b0\u09a4\u09c0\u0995 \u09a5\u09be\u0995\u09c7 \u09a4\u09be\u0995\u09c7 \u09b8\u09b0\u09b2 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09ac\u09b2\u09c7\u0964 \u09af\u09c7\u09ae\u09a8: 2(5x \u2013 14) = 21\u00a0<\/p>\r\n\r\n\r\n\r\n<h3><strong>\u0989\u09aa\u0995\u09be\u09b0\u09c0 \u0995\u09cc\u09b6\u09b2<\/strong>\u00a0<\/h3>\r\n\r\n\r\n\r\n<p>\u09e7\u0964 \u09b8\u0982\u0996\u09cd\u09af\u09be \u09a7\u09b0\u09be\u09b0 \u09b8\u09ae\u09af\u09bc \u099b\u09cb\u099f \u09b8\u0982\u0996\u09cd\u09af\u09be \u09ac\u09be x \u09a7\u09b0\u09c7 \u09ae\u09cd\u09af\u09be\u09a5 \u0995\u09b0\u09c1\u09a8\u0964\u00a0<\/p>\r\n\r\n\r\n\r\n<p>\u09af\u09c7\u09ae\u09a8: \u0995\u09cb\u09a8\u09cb \u098f\u0995\u099f\u09bf \u09b8\u0982\u0996\u09cd\u09af\u09be \u0985\u09aa\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u09e9 \u0997\u09c1\u09a3\u0964 \u09aa\u09cd\u09b0\u09a5\u09ae \u09b8\u0982\u0996\u09cd\u09af\u09be\u099f\u09bf \u09ec \u09a7\u09b0\u09b2\u09c7 \u09aa\u09b0\u09c7\u09b0\u099f\u09bf \u09e8 \u09a7\u09b0\u09c1\u09a8 \u0995\u09bf\u0982\u09ac\u09be \u09aa\u09cd\u09b0\u09a5\u09ae \u09b8\u0982\u0996\u09cd\u09af\u09be\u099f\u09bf 3x \u09a7\u09b0\u09b2\u09c7 \u09aa\u09b0\u09c7\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be\u099f\u09bf x \u09a7\u09b0\u09c1\u09a8\u0964\u00a0\u00a0<\/p>\r\n\r\n\r\n\r\n<p>\u09e8\u0964 \u09af\u09a5\u09be\u09b8\u09ae\u09cd\u09ad\u09ac \u09ad\u0997\u09cd\u09a8\u09be\u0982\u09b6 \u098f\u09a1\u09bc\u09bf\u09af\u09bc\u09c7 \u099a\u09b2\u09c1\u09a8\u0964\u00a0<\/p>\r\n\r\n\r\n\r\n<p>\u09af\u09c7\u09ae\u09a8: \u098f\u0995\u099f\u09bf \u09b8\u0982\u0996\u09cd\u09af\u09be \u0986\u09b0\u09c7\u0995\u099f\u09bf \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u0985\u09b0\u09cd\u09a7\u09c7\u0995\u0964 \u098f\u0996\u09be\u09a8\u09c7 \u09ac\u09a1\u09bc \u09b8\u0982\u0996\u09cd\u09af\u09be\u0995\u09c7 x \u098f\u09ac\u0982 \u099b\u09cb\u099f \u09b8\u0982\u0996\u09cd\u09af\u09be\u0995\u09c7 x\/2 \u09a8\u09be \u09a7\u09b0\u09c7 \u09ac\u09a1\u09bc \u09b8\u0982\u0996\u09cd\u09af\u09be\u0995\u09c7 2x \u0993 \u099b\u09cb\u099f \u09b8\u0982\u0996\u09cd\u09af\u09be\u0995\u09c7 x \u09a7\u09b0\u09c1\u09a8\u0964\u00a0<\/p>\r\n\r\n\r\n\r\n<p>\u09e9\u0964 \u098f\u0995\u099f\u09bf \u0997\u09be\u09a3\u09bf\u09a4\u09bf\u0995 \u09b8\u09ae\u09b8\u09cd\u09af\u09be\u0995\u09c7 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09ac\u09be\u09a8\u09be\u09a4\u09c7 \u09b8\u09ac \u09b8\u09ae\u09af\u09bc \u09a6\u09c1\u0987 \u09aa\u09be\u09b6\u09c7\u09b0 \u09ae\u09be\u09a8 \u09b8\u09ae\u09be\u09a8 \u09ac\u09be\u09a8\u09be\u09a8\u0964\u00a0\u00a0\u00a0<\/p>\r\n\r\n\r\n\r\n<p><strong>\u09b8\u09ae\u09b8\u09cd\u09af\u09be \u09e7.<\/strong> x \u098f\u09b0 \u09ae\u09be\u09a8 \u0995\u09a4 \u09b9\u09b2\u09c7 a(x-a) = b(x-b) \u09b9\u09ac\u09c7?\u00a0<\/p>\r\n\r\n\r\n\r\n<ul>\r\n<li>1\u00a0<\/li>\r\n<li>a \u2013 b\u00a0<\/li>\r\n<li>b \u2013 a\u00a0<\/li>\r\n<li>a + b <strong>\u00a0<\/strong><\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p><strong>\u09b8\u09ae\u09be\u09a7\u09be\u09a8:<\/strong><\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\">\r\n<pre>ax \u2013 a^2 = bx \u2013 b^2 \\\\\r\n\\Rightarrow ax \u2013 bx = a^2 \u2013 b^2 \\\\\r\n\\Rightarrow x (a \u2013 b) = (a+b) (a-b) \\\\\r\n\\therefore x = (a+b) <\/pre>\r\n<\/div>\r\n\r\n\r\n\r\n<p><strong>\u09b8\u09ae\u09b8\u09cd\u09af\u09be \u09e8.<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{x}{3}+1=\\frac{x}{4}+1<\/span> \u09a4\u09ac\u09c7 x \u098f\u09b0 \u09ae\u09be\u09a8 \u0995\u09a4?\u00a0<\/p>\r\n\r\n\r\n\r\n<ul>\r\n<li>3\u00a0<\/li>\r\n<li>2<\/li>\r\n<li>1<\/li>\r\n<li>0<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p><strong>\u09b8\u09ae\u09be\u09a7\u09be\u09a8:<\/strong><\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\">\r\n<pre>\\frac{x}{3} + 1= \\frac{x}{4} + 1\\\\\r\n \\Rightarrow \\frac{x}{3} = \\frac{x}{4} +1 -1\\\\\r\n \\Rightarrow \\frac{x}{3} = \\frac{x}{4}\\\\\r\n \\Rightarrow \\frac{x}{3} \u2013 \\frac{x}{4} = 0\\\\\r\n \\Rightarrow \\frac{(4x \u2013 3x)}{12} = 0\\\\\r\n\\therefore x=0 <\/pre>\r\n<\/div>\r\n\r\n\r\n\r\n<p><strong>\u09b8\u09ae\u09b8\u09cd\u09af\u09be \u09e9\u0964<\/strong> \u09a6\u09c1\u0987 \u0985\u0999\u09cd\u0995 \u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u098f\u0995\u099f\u09bf \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u09a6\u09b6\u0995 \u09b8\u09cd\u09a5\u09be\u09a8\u09c0\u09af\u09bc \u0985\u0999\u09cd\u0995 \u098f\u0995\u0995 \u09b8\u09cd\u09a5\u09be\u09a8\u09c0\u09af\u09bc \u0985\u0999\u09cd\u0995 \u09a5\u09c7\u0995\u09c7 \u09eb \u09ac\u09a1\u09bc\u0964 \u09b8\u0982\u0996\u09cd\u09af\u09be\u099f\u09bf \u09a5\u09c7\u0995\u09c7 \u0985\u0982\u0995\u09a6\u09cd\u09ac\u09af\u09bc\u09c7\u09b0 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf\u09b0 \u09eb \u0997\u09c1\u09a3 \u09ac\u09bf\u09af\u09bc\u09cb\u0997 \u0995\u09b0\u09b2\u09c7 \u0985\u0982\u0995\u09a6\u09cd\u09ac\u09af\u09bc \u09b8\u09cd\u09a5\u09be\u09a8 \u09ac\u09bf\u09a8\u09bf\u09ae\u09af\u09bc \u0995\u09b0\u09c7\u0964 \u09b8\u0982\u0996\u09cd\u09af\u09be\u099f\u09bf \u0995\u09a4?<\/p>\r\n\r\n\r\n\r\n<ul>\r\n<li>61\u00a0<\/li>\r\n<li>94<\/li>\r\n<li>72<\/li>\r\n<li>83\u00a0<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p><strong>\u09b8\u09ae\u09be\u09a7\u09be\u09a8:<\/strong> \u09a7\u09b0\u09bf \u098f\u0995\u0995 \u09b8\u09cd\u09a5\u09be\u09a8\u09c0\u09af\u09bc \u09b8\u0982\u0996\u09cd\u09af\u09be x\u00a0<\/p>\r\n\r\n\r\n\r\n<p>\u09a6\u09b6\u0995 \u09b8\u09cd\u09a5\u09be\u09a8\u09c0\u09af\u09bc \u09b8\u0982\u0996\u09cd\u09af\u09be x+5\u00a0<\/p>\r\n\r\n\r\n\r\n<p>\u09b8\u0982\u0996\u09cd\u09af\u09be\u099f\u09bf 10(x+5) + x = 11x + 50\u00a0<\/p>\r\n\r\n\r\n\r\n<p>\u0985\u0982\u0995\u09a6\u09cd\u09ac\u09af\u09bc\u09c7\u09b0 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf\u09b0 \u09eb \u0997\u09c1\u09a3 = 5(x+x+5) = 5(2x+5)\u00a0<\/p>\r\n\r\n\r\n\r\n<p>\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8\u09ae\u09a4\u09c7, <span class=\"katex-eq\" data-katex-display=\"false\">11x +50 - 5(2x+5)= 10x + (x+5)<\/span><\/p>\r\n\r\n\r\n\r\n<span class=\"katex-eq\" data-katex-display=\"false\">\\Rightarrow 10x = 20<\/span>\r\n\r\n\r\n\r\n<span class=\"katex-eq\" data-katex-display=\"false\">\\Rightarrow x=2<\/span>\r\n\r\n\r\n\r\n<span class=\"katex-eq\" data-katex-display=\"false\">\\Rightarrow x+5=7<\/span>\r\n\r\n\r\n\r\n<p>\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09b8\u0982\u0996\u09cd\u09af\u09be\u099f\u09bf \u09ed\u09e8\u00a0<\/p>\r\n\r\n\r\n\r\n<p><strong>\u09b8\u09ae\u09b8\u09cd\u09af\u09be \u09ea\u0964<\/strong> \u098f\u0995\u099f\u09bf \u09b8\u0982\u0996\u09cd\u09af\u09be \u0985\u09aa\u09b0 \u098f\u0995\u099f\u09bf \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 2\/3 \u0997\u09c1\u09a3\u0964 \u09b8\u0982\u0996\u09cd\u09af\u09be \u09a6\u09c1\u099f\u09bf\u09b0 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf \u09e7\u09e6\u09e6 \u09b9\u09b2\u09c7 \u09ac\u09a1\u09bc \u09b8\u0982\u0996\u09cd\u09af\u09be\u099f\u09bf\u09b0 \u09ae\u09be\u09a8 \u0995\u09a4?\u00a0<\/p>\r\n\r\n\r\n\r\n<ul>\r\n<li>55\u00a0<\/li>\r\n<li>70<\/li>\r\n<li>65<\/li>\r\n<li>60<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p><strong>\u09b8\u09ae\u09be\u09a7\u09be\u09a8:<\/strong> \u09ac\u09a1\u09bc \u09b8\u0982\u0996\u09cd\u09af\u09be\u099f\u09bf 3x \u098f\u09ac\u0982 \u099b\u09cb\u099f \u09b8\u0982\u0996\u09cd\u09af\u09be\u099f\u09bf 2x.\u00a0<\/p>\r\n\r\n\r\n\r\n<p>\u09b8\u09ae\u09b7\u09cd\u099f\u09bf 5x=100.\u00a0<\/p>\r\n\r\n\r\n\r\n<p>\u09a4\u09be\u09b9\u09b2\u09c7 x= 100\/5=20.\u00a0<\/p>\r\n\r\n\r\n\r\n<p>\u09a4\u09be\u09b9\u09b2\u09c7 \u09ac\u09a1\u09bc \u09b8\u0982\u0996\u09cd\u09af\u09be\u099f\u09bf 20 * 3 = 60\u00a0<\/p>\r\n\r\n\r\n\r\n<h2><strong><strong>\u09a6\u09cd\u09ac\u09bf\u0998\u09be\u09a4 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3<\/strong><\/strong><\/h2>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\">\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, <span class=\"katex-eq\" data-katex-display=\"false\">ax^2+bx+c=0<\/span> \u098f\u0995\u099f\u09bf \u098f\u0995 \u099a\u09b2\u0995 \u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u09a6\u09cd\u09ac\u09bf\u0998\u09be\u09a4 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0964 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf \u09b8\u09ae\u09be\u09a7\u09be\u09a8 \u0995\u09b0\u09b2\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u098f\u09b0 \u09a6\u09c1\u0987\u099f\u09bf \u09ae\u09be\u09a8 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc\u0964<\/span><\/p>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">x= -b \\pm \\frac{\\sqrt{(b^2 - 4ac)}}{2a} <\/span><\/span><\/p>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">b^2-4ac<\/span> \u0995\u09c7 \u09a6\u09cd\u09ac\u09bf\u0998\u09be\u09a4 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 <strong>\u09a8\u09bf\u09b6\u09cd\u099a\u09be\u09af\u09bc\u0995<\/strong> \u09ac\u09b2\u09c7\u0964 \u0995\u09be\u09b0\u09a3 \u098f\u099f\u09bf <\/span><b>\u09ae\u09c2\u09b2\u09a6\u09cd\u09ac\u09df\u09c7\u09b0<\/b><span style=\"font-weight: 400;\"> \u09aa\u09cd\u09b0\u0995\u09c3\u09a4\u09bf \u0993 \u09a7\u09b0\u09a3 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09c7\u0964<\/span><\/p>\r\n\r\n\r\n\r\n<h2><strong>\u09a8\u09bf\u09b6\u09cd\u099a\u09be\u09af\u09bc\u0995\u09c7\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be \u09ad\u09c7\u09a6\u09c7 \u09a6\u09cd\u09ac\u09bf\u0998\u09be\u09a4 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 \u09ae\u09c2\u09b2\u09a6\u09cd\u09ac\u09df\u09c7\u09b0 \u09aa\u09cd\u09b0\u0995\u09c3\u09a4\u09bf \u0993 \u09a7\u09b0\u09a8<\/strong><\/h2>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\">\u0995) b\u00b2- 4ac &gt; 0 \u098f\u09ac\u0982 \u09aa\u09c2\u09b0\u09cd\u09a3\u09ac\u09b0\u09cd\u0997 \u09b9\u09b2\u09c7 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf\u09b0 \u09ae\u09c2\u09b2\u09a6\u09cd\u09ac\u09df <strong>\u09ac\u09be\u09b8\u09cd\u09a4\u09ac, \u0985\u09b8\u09ae\u09be\u09a8 \u0993 \u09ae\u09c2\u09b2\u09a6<\/strong> \u09b9\u09ac\u09c7\u00a0<\/span><\/p>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\">\u0996) b\u00b2- 4ac &gt; 0 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u09aa\u09c2\u09b0\u09cd\u09a3\u09ac\u09b0\u09cd\u0997 \u09a8\u09be \u09b9\u09b2\u09c7 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf\u09b0 \u09ae\u09c2\u09b2\u09a6\u09cd\u09ac\u09df <strong>\u09ac\u09be\u09b8\u09cd\u09a4\u09ac, \u0985\u09b8\u09ae\u09be\u09a8 \u0993 \u0985\u09ae\u09c2\u09b2\u09a6<\/strong> \u09b9\u09ac\u09c7\u0964<\/span><\/p>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\">\u0997) b\u00b2- 4ac = 0 \u09b9\u09b2\u09c7 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf\u09b0 \u09ae\u09c2\u09b2\u09a6\u09cd\u09ac\u09af\u09bc <strong>\u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u0993 \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09b8\u09ae\u09be\u09a8<\/strong> \u09b9\u09ac\u09c7; \u098f\u09ac\u0982\u00a0<\/span><\/p>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\">\u0998) b\u00b2- 4ac &lt; 0 \u09b9\u09b2\u09c7 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf \u0995\u09cb\u09a8\u09cb \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u09ae\u09c2\u09b2 \u09a8\u09c7\u0987\u0964<\/span><\/p>\r\n\r\n\r\n\r\n<ul>\r\n<li><strong>If <span class=\"katex-eq\" data-katex-display=\"false\">x=1+\\sqrt{2}<\/span> and <span class=\"katex-eq\" data-katex-display=\"false\">y=1-\\sqrt{2}<\/span>, find the value of <span class=\"katex-eq\" data-katex-display=\"false\">(x^2+y^2)<\/span>.<\/strong><\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p><strong>Ans:\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\">\r\n<pre>x^2 + y^2 = (x+y)^2  - 2xy \\\\\r\n= ((1+\u221a2) + (1- \u221a2))^2  - 2(1+\u221a2)(1- \u221a2)\\\\\r\n= 2^2 - 2(1 - 2) \\\\\r\n= 4 + 2 = 6 <\/pre>\r\n<\/div>\r\n\r\n\r\n\r\n<ul>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><strong>If a + b+ c = 12, a + b = 4, and a + c = 7, what is the value of a\u00b2?<\/strong><\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p><strong>Ans: <\/strong><\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\">\r\n<pre>a+b+c = 12 , a+b=4 \\\\\r\nSo,\\; c = 12 - 4= 8 \\\\\r\nif, \\; c=4 \\;then, \\\\\r\na+c =7\\\\\r\nSo,\\; a= 7 - 8 = -1 \\\\\r\n\\therefore a^2 = 1 <\/pre>\r\n<\/div>\r\n\r\n\r\n\r\n<ul>\r\n<li><strong>If the value of <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{x}{z}<\/span> is 1 more than <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{y}{z}<\/span>, then y =?<\/strong><\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p><strong>Ans:\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\">\r\n<pre> \\frac{x}{z} -1 = \\frac{y}{z} \\\\\r\n\\Rightarrow \\frac{x}{z} - \\frac{y}{z} = 1\\\\\r\n \\Rightarrow \\frac{(x-y)}{z} = 1 \\\\\r\n\\Rightarrow x-y=z\\\\\r\n\\therefore y=x-z<\/pre>\r\n<\/div>\r\n\r\n\r\n\r\n<ul>\r\n<li><strong>\u09af\u09a6\u09bf <span class=\"katex-eq\" data-katex-display=\"false\">x(2x+1)=0<\/span> \u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">(x+12)(2x-3)=0<\/span> \u09b9\u09af\u09bc, \u09a4\u09be \u09b9\u09b2\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u098f\u09b0 \u09ae\u09be\u09a8 \u0995\u09a4 \u09b9\u09ac\u09c7?<\/strong><\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\"><strong>Ans:<\/strong>\u00a0<\/span><\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\">\r\n<pre>x(2x + 1) = 0\\\\\r\n\\Rightarrow 2x^2 + x = 0 \\\\\r\n\\Rightarrow 2x+1 = 0 (\u0989\u09ad\u09df\\; \u09aa\u0995\u09cd\u09b7\u09c7\\; x \\;\u09a6\u09cd\u09ac\u09be\u09b0\u09be\\; \u09ad\u09be\u0997\\; \u0995\u09b0\u09c7)\\\\\r\n\\therefore  x = -\\frac{1}{2}\\\\\r\n\u098f\u0996\u09a8,\\; ( x+12) (2x-3) = 0\\\\\r\nx+12 = 0 \\;\u09b9\u09b2\u09c7,\\\\\r\n x=-12\\\\\r\n(2x-3)= 0 \\;\u09b9\u09b2\u09c7,\\\\\r\n2x=3\\\\\r\n\\therefore x=\\frac{3}{2}<\/pre>\r\n<\/div>\r\n\r\n\r\n\r\n<h2><strong>\u09b8\u09b0\u09b2 \u09b8\u09b9\u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u00a0\u00a0<\/strong><\/h2>\r\n\r\n\r\n\r\n<p>\u09b8\u09b0\u09b2 \u09b8\u09b9\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09ac\u09b2\u09a4\u09c7 \u09a6\u09c1\u0987 \u099a\u09b2\u0995\u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0995\u09c7 \u09ac\u09cb\u099d\u09be\u09af\u09bc, \u09af\u0996\u09a8 \u09a4\u09be\u09a6\u09c7\u09b0 \u098f\u0995\u09a4\u09cd\u09b0\u09c7 \u0989\u09aa\u09b8\u09cd\u09a5\u09be\u09aa\u09a8 \u0995\u09b0\u09be \u09b9\u09af\u09bc \u098f\u09ac\u0982 \u099a\u09b2\u0995 \u09a6\u09c1\u0987\u099f\u09bf \u098f\u0995\u0987 \u09ac\u09c8\u09b6\u09bf\u09b7\u09cd\u099f\u09cd\u09af\u09c7\u09b0 \u09b9\u09af\u09bc\u0964\u00a0\u0986\u09ac\u09be\u09b0 \u098f\u09b0\u09c2\u09aa \u09a6\u09c1\u0987\u099f\u09bf \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0995\u09c7 \u098f\u0995\u09a4\u09cd\u09b0\u09c7 \u09b8\u09b0\u09b2 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u099c\u09cb\u099f\u0993 \u09ac\u09b2\u09c7\u0964<\/p>\r\n\r\n\r\n\r\n<p>\u09b8\u09b0\u09b2 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b8\u09be\u09a7\u09be\u09b0\u09a3\u09a4 \u09a6\u09c1\u099f\u09bf \u09aa\u09a6\u09cd\u09a7\u09a4\u09bf \u09a5\u09c7\u0995\u09c7 \u09ac\u09c7\u09b6\u09bf \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u0986\u09b8\u09c7\u0964\u00a0<\/p>\r\n\r\n\r\n\r\n<p>\u09e7\u0964 \u09aa\u09cd\u09b0\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u09a8 \u09aa\u09a6\u09cd\u09a7\u09a4\u09bf<\/p>\r\n\r\n\r\n\r\n<p>\u09e8\u0964 \u0985\u09aa\u09a8\u09af\u09bc\u09a8 \u09aa\u09a6\u09cd\u09a7\u09a4\u09bf<\/p>\r\n\r\n\r\n\r\n<p><strong>\u09aa\u09cd\u09b0\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u09a8 \u09aa\u09a6\u09cd\u09a7\u09a4\u09bf:<\/strong> \u098f\u0995\u099f\u09bf \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a5\u09c7\u0995\u09c7 \u098f\u0995\u099f\u09bf \u099a\u09b2\u0995\u09c7\u09b0 \u09ae\u09be\u09a8 \u0985\u09aa\u09b0 \u099a\u09b2\u0995\u09c7\u09b0 \u09ae\u09be\u09a7\u09cd\u09af\u09ae\u09c7 \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09c7 \u09aa\u09cd\u09b0\u09be\u09aa\u09cd\u09a4 \u09ae\u09be\u09a8 \u0985\u09aa\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7 \u09ac\u09b8\u09be\u09b2\u09c7 \u098f\u0995 \u099a\u09b2\u0995 \u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc\u0964 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf \u09b8\u09ae\u09be\u09a7\u09be\u09a8\u09c7\u09b0 \u09ae\u09be\u09a7\u09cd\u09af\u09ae\u09c7 \u099a\u09b2\u0995\u099f\u09bf\u09b0 \u09ae\u09be\u09a8 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc\u0964\u00a0<\/p>\r\n\r\n\r\n\r\n<p><strong>\u0985\u09aa\u09a8\u09af\u09bc\u09a8 \u09aa\u09a6\u09cd\u09a7\u09a4\u09bf<\/strong>: \u098f\u0995\u099f\u09bf \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0995\u09c7 \u09ac\u09be \u0989\u09ad\u09af\u09bc \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0995\u09c7 \u098f\u09b0\u09c2\u09aa \u09b8\u0982\u0996\u09cd\u09af\u09be \u09a6\u09bf\u09af\u09bc\u09c7 \u0997\u09c1\u09a3 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7 \u09af\u09c7\u09a8 \u0997\u09c1\u09a3\u09a8\u09c7\u09b0 \u09aa\u09b0 \u0989\u09ad\u09af\u09bc \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u098f\u0995\u099f\u09bf \u099a\u09b2\u0995\u09c7\u09b0 \u09b8\u09b9\u0997\u09c7\u09b0 \u09aa\u09b0\u09ae\u09ae\u09be\u09a8 \u09b8\u09ae\u09be\u09a8 \u09b9\u09af\u09bc\u0964 \u098f\u09b0\u09aa\u09b0 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u099c\u09a8\u09ae\u09a4 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0995\u09c7 \u09af\u09cb\u0997 \u09ac\u09be \u09ac\u09bf\u09af\u09bc\u09cb\u0997 \u0995\u09b0\u09b2\u09c7 \u09b8\u09b9\u0997 \u09b8\u09ae\u09be\u09a8\u0995\u09c3\u09a4 \u099a\u09b2\u0995\u099f\u09bf \u0985\u09aa\u09a8\u09c0\u09a4 \u09ac\u09be \u0985\u09aa\u09b8\u09be\u09b0\u09bf\u09a4 \u09b9\u09af\u09bc\u0964\u00a0<\/p>\r\n\r\n\r\n\r\n<p><strong>\u09b8\u09ae\u09b8\u09cd\u09af\u09be \u09ed\u0964<\/strong> \u09af\u09a6\u09bf x + 5y = 16 \u098f\u09ac\u0982 x = -3y \u09b9\u09af\u09bc \u09a4\u09ac\u09c7 y = \u0995\u09a4?<\/p>\r\n\r\n\r\n\r\n<ul>\r\n<li>-24<\/li>\r\n<li>2<\/li>\r\n<li>8<\/li>\r\n<li>-2<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p><strong>\u09b8\u09ae\u09be\u09a7\u09be\u09a8:<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">-3y+5y=16\\\\ \\Rightarrow 2y=16\\\\ \\therefore y=8<\/span><\/p>\r\n\r\n\r\n\r\n<h2><b>\u09b8\u09c2\u099a\u0995<\/b><\/h2>\r\n\r\n\r\n\r\n<ul>\r\n<li><span style=\"font-weight: 400;\">\u09b8\u09be\u09a7\u09be\u09b0\u09a3\u09a4 \u09b8\u09c2\u099a\u0995\u0995\u09c7 power \u09ac\u09be \u09b6\u0995\u09cd\u09a4\u09bf \u09ac\u09b2\u09be \u09b9\u09df\u0964 \u09af\u09c7\u09ae\u09a8: <span class=\"katex-eq\" data-katex-display=\"false\">a^n<\/span> \u098f n \u09b9\u09b2\u09cb a \u098f\u09b0 \u09b8\u09c2\u099a\u0995 \u098f\u09ac\u0982 \u098f\u0996\u09be\u09a8\u09c7 a \u09b9\u099a\u09cd\u099b\u09c7 \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf\u0964 <\/span><\/li>\r\n<li>\u09a6\u09c1\u099f\u09bf \u09b0\u09be\u09b6\u09bf \u0997\u09c1\u09a3 \u0986\u0995\u09be\u09b0\u09c7 \u09a5\u09be\u0995\u09b2\u09c7 \u098f\u09ac\u0982 \u09a4\u09be\u09a6\u09c7\u09b0 \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf \u098f\u0995\u0987 \u09b9\u09b2\u09c7 \u09a4\u09be\u09a6\u09c7\u09b0 power \u09ac\u09be \u09b6\u0995\u09cd\u09a4\u09bf\u09b0 \u09af\u09cb\u0997 \u09b9\u09df\u0964<\/li>\r\n<li>\u09b8\u09c2\u099a\u0995\u09c7\u09b0 \u09ae\u09be\u09a7\u09cd\u09af\u09ae\u09c7 \u09ac\u09dc \u09b8\u0982\u0996\u09cd\u09af\u09be\u0997\u09c1\u09b2\u09cb\u0995\u09c7 \u09b8\u09b9\u099c\u09c7 \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09be \u09af\u09be\u09df\u0964<\/li>\r\n<li>\u0986\u09ac\u09be\u09b0 \u09b8\u09c2\u099a\u0995\u09c7\u09b0 \u09ae\u09be\u09a7\u09cd\u09af\u09ae\u09c7\u0987 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u09ac\u09c8\u099c\u09cd\u099e\u09be\u09a8\u09bf\u0995 \u09b0\u09c1\u09aa \u09ac\u09be \u0986\u09a6\u09b0\u09cd\u09b6 \u09b0\u09c2\u09aa \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09be \u09af\u09be\u09df\u0964<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\">\u0995\u09cb\u09a8\u09cb \u098f\u0995\u099f\u09bf \u09b0\u09be\u09b6\u09bf\u09a4\u09c7 \u098f\u0995\u0987 \u0989\u09ce\u09aa\u09be\u09a6\u0995 \u09af\u09a4 \u09ac\u09be\u09b0 \u0997\u09c1\u09a3 \u0986\u0995\u09be\u09b0\u09c7 \u09a5\u09be\u0995\u09c7, \u09b8\u09c7\u0987 \u09b8\u0982\u0996\u09cd\u09af\u09be\u0995\u09c7 \u0989\u09ce\u09aa\u09be\u09a6\u0995\u099f\u09bf\u09b0 \u09b8\u09c2\u099a\u0995 \u098f\u09ac\u0982 \u0989\u09ce\u09aa\u09be\u09a6\u0995\u099f\u09bf\u0995\u09c7 <strong>\u09ad\u09bf\u09a4\u09cd\u09a4\u09bf<\/strong> \u09ac\u09b2\u09be \u09b9\u09df\u0964 \u09af\u09c7\u09ae\u09a8: <span class=\"katex-eq\" data-katex-display=\"false\">2\\times 2\\times 2\\times 2=2^4<\/span><\/span><\/p>\r\n\r\n\r\n\r\n<ul>\r\n<li><span style=\"font-weight: 400;\">\u098f\u0995\u0987 \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf\u09b0 \u0995\u09a4\u0995\u0997\u09c1\u09b2\u09cb \u09b0\u09be\u09b6\u09bf \u09ac\u09be \u09b8\u0982\u0996\u09cd\u09af\u09be \u0997\u09c1\u09a3 \u0986\u0995\u09be\u09b0\u09c7 \u09a5\u09be\u0995\u09b2\u09c7 \u09b8\u09ac\u0997\u09c1\u09b2\u09cb \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf \u09a5\u09c7\u0995\u09c7 \u098f\u0995\u099f\u09bf \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf <\/span>\u09a8\u09bf\u09a4\u09c7 \u09b9\u09ac\u09c7 <span style=\"font-weight: 400;\">\u098f\u09ac\u0982 \u098f\u0987 \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf\u09b0 \u09b8\u09c2\u099a\u0995 \u09b9\u09ac\u09c7 \u09b0\u09be\u09b6\u09bf\u0997\u09c1\u09b2\u09cb\u09b0 power \u098f\u09b0 \u09af\u09cb\u0997\u09ab\u09b2\u0964 \u09af\u09c7\u09ae\u09a8: <span class=\"katex-eq\" data-katex-display=\"false\">a^2 \\times a^3 \\times a^5=a^{(2+3+5)}=a^{10}<\/span><\/span><\/li>\r\n<li>\u098f\u0987 \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf\u09b0 \u0995\u09a4\u0995\u0997\u09c1\u09b2\u09cb \u09b0\u09be\u09b6\u09bf \u09ac\u09be \u09b8\u0982\u0996\u09cd\u09af\u09be \u09ad\u09be\u0997 \u0986\u0995\u09be\u09b0\u09c7 \u09a5\u09be\u0995\u09b2\u09c7 \u09b8\u09ac\u0997\u09c1\u09b2\u09cb \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf \u09a5\u09c7\u0995\u09c7 \u098f\u0995\u099f\u09bf \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf \u09a8\u09bf\u09a4\u09c7 \u09b9\u09ac\u09c7 \u098f\u09ac\u0982 \u098f\u0987 \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf\u09b0 \u09b8\u09c2\u099a\u0995 \u09b9\u09ac\u09c7 \u09aa\u09cd\u09b0\u09a5\u09ae \u09b0\u09be\u09b6\u09bf\u09b0 power \u09a5\u09c7\u0995\u09c7 \u09aa\u09b0\u09c7\u09b0 \u09b0\u09be\u09b6\u09bf\u0997\u09c1\u09b2\u09cb\u09b0 power \u098f\u09b0 \u09ac\u09bf\u09df\u09cb\u0997\u09ab\u09b2\u0964 \u09af\u09c7\u09ae\u09a8: <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{a^5}{a^3}=a^{5-3}=a^2<\/span><\/li>\r\n<li>\u09ad\u09bf\u09a4\u09cd\u09a4\u09bf \u09ad\u09bf\u09a8\u09cd\u09a8 \u09ad\u09bf\u09a8\u09cd\u09a8 \u09b9\u09b2\u09c7 \u098f\u09ac\u0982 \u09b8\u09c2\u099a\u0995 \u09af\u09a6\u09bf \u098f\u0995\u0987 \u09b9\u09df \u09a4\u09be\u09b9\u09b2\u09c7 \u09b8\u09ac\u0997\u09c1\u09b2\u09cb \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf\u09b0 \u0997\u09c1\u09a3\u09ab\u09b2\u09c7\u09b0 \u0990 \u098f\u0995\u0987 power \u09b9\u09ac\u09c7\u0964<\/li>\r\n<li>\u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf\u09b0 \u09b8\u09c2\u099a\u0995 \u09ac\u09be power \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u09b9\u09b2\u09c7 \u0990 \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf\u0995\u09c7 1 \u098f\u09b0 \u09a8\u09bf\u099a\u09c7 \u09b2\u09bf\u0996\u09a4\u09c7 \u09b9\u09df \u098f\u09ac\u0982 power \u09b9\u09df \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995\u0964 \u09af\u09c7\u09ae\u09a8: <span class=\"katex-eq\" data-katex-display=\"false\">a^{-2}=\\frac{1}{a^2}<\/span><\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<h3><b>\u09b8\u09c2\u099a\u0995\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0<\/b><\/h3>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\">\u09b8\u09c2\u09a4\u09cd\u09b0-\u09e7 (\u0997\u09c1\u09a3\u09c7\u09b0): <span class=\"katex-eq\" data-katex-display=\"false\">a^m \\times a^n=a^{m+n}<\/span><\/span><\/p>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\">\u09b8\u09c2\u09a4\u09cd\u09b0-\u09e8 (\u09ad\u09be\u0997\u09c7\u09b0): <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{a^m}{a^n}=a^{m-n}<\/span><\/span><\/p>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\">\u09b8\u09c2\u09a4\u09cd\u09b0-\u09e9 (\u0997\u09c1\u09a3\u09c7\u09b0 \u0998\u09be\u09a4): <span class=\"katex-eq\" data-katex-display=\"false\">(ab)^n=a^n \\times b^n<\/span><\/span><\/p>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\">\u09b8\u09c2\u09a4\u09cd\u09b0-\u09ea (\u09ad\u09be\u0997\u09c7\u09b0 \u0998\u09be\u09a4): <span class=\"katex-eq\" data-katex-display=\"false\">(\\frac{a}{b})^n = \\frac{a^n}{b^n}<\/span><\/span><\/p>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\">\u09b8\u09c2\u09a4\u09cd\u09b0-\u09eb (\u0998\u09be\u09a4\u09c7\u09b0 \u0998\u09be\u09a4): <span class=\"katex-eq\" data-katex-display=\"false\">(a^m)^n=a^{mn}<\/span><\/span><\/p>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\">\u09b8\u09c2\u09a4\u09cd\u09b0-\u09ec: <span class=\"katex-eq\" data-katex-display=\"false\">a^0=1<\/span><\/span><\/p>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\">\u09b8\u09c2\u09a4\u09cd\u09b0-\u09ed: <span class=\"katex-eq\" data-katex-display=\"false\">a^{-1}=\\frac{1}{a}<\/span><\/span><\/p>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\">\u09b8\u09c2\u09a4\u09cd\u09b0-\u09ee: <span class=\"katex-eq\" data-katex-display=\"false\">a^{-n}=\\frac{1}{a^n}<\/span><\/span><\/p>\r\n\r\n\r\n\r\n<p><span style=\"font-weight: 400;\">\u09b8\u09c2\u09a4\u09cd\u09b0 \u09ef: <span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{a}=a^{\\frac{1}{2}}<\/span><\/span><\/p>\r\n\r\n\r\n\r\n<h2><strong>\u09b8\u09c2\u099a\u0995 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3<\/strong><\/h2>\r\n\r\n\r\n\r\n<p>\u098f \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7 \u0985\u099c\u09cd\u099e\u09be\u09a4 \u099a\u09b2\u0995 \u09b8\u09c2\u099a\u0995\u09b0\u09c2\u09aa\u09c7 \u09a5\u09be\u0995\u09c7\u0964\u00a0\u09af\u09c7\u09ae\u09a8: ?<strong><sup>?<\/sup><\/strong>= ?;\u00a0 ??<strong><sup>?<\/sup><\/strong>=?^(?+?) \u0987\u09a4\u09cd\u09af\u09be\u09a6\u09bf\u0964<\/p>\r\n\r\n\r\n\r\n<p><strong>\u09b8\u09ae\u09b8\u09cd\u09af\u09be-\u09e6\u09eb:\u00a0 3(27<\/strong><strong><sup>?<\/sup><\/strong><strong>) = 9<\/strong><strong><sup>(?+4)<\/sup><\/strong><strong>\u00a0 \u098f\u09b0 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 \u0995\u09b0\u0964\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\">\r\n<pre>3(3^{3x}) = 3^{2(x+4)}\\\\\r\n\\Rightarrow 3^{1+3x}=2(x+4)\\\\\r\n\\Rightarrow 3x+1=2(x+4)\\\\\r\n\\Rightarrow 3x-2x=4-1\\\\\r\n\\therefore x=3<\/pre>\r\n<\/div>\r\n\r\n\r\n\r\n<p><strong>\u09b8\u09ae\u09b8\u09cd\u09af\u09be \u09ec\u0964 <\/strong>\u00a0<span class=\"katex-eq\" data-katex-display=\"false\">x^2+px+6=0<\/span> \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 \u09ae\u09c2\u09b2\u09a6\u09cd\u09ac\u09af\u09bc \u09b8\u09ae\u09be\u09a8 \u098f\u09ac\u0982 p&gt;0 \u09a4\u09ac\u09c7 p \u098f\u09b0 \u09ae\u09be\u09a8 \u0995\u09a4?\u00a0\u00a0\u00a0<\/p>\r\n\r\n\r\n\r\n<ul>\r\n<li>\u221a48\u00a0\u00a0<\/li>\r\n<li>0<\/li>\r\n<li>\u221a6\u00a0<\/li>\r\n<li>\u221a24 <strong>\u00a0<\/strong><\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p><strong>\u09b8\u09ae\u09be\u09a7\u09be\u09a8:<\/strong><\/p>\r\n\r\n\r\n\r\n<p>\u09af\u09a6\u09bf, b<strong><sup>2<\/sup><\/strong> \u2013 4ac = 0 \u09b9\u09af\u09bc \u09a4\u09ac\u09c7 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 \u09ae\u09c2\u09b2\u09a6\u09cd\u09ac\u09af\u09bc \u09b8\u09ae\u09be\u09a8 \u09b9\u09ac\u09c7, \u09a4\u09be\u0987 \u098f\u0996\u09be\u09a8\u09c7, a=1, b=p, c=6 \u09a4\u09be\u09b9\u09b2\u09c7,\u00a0<\/p>\r\n\r\n\r\n\r\n<span class=\"katex-eq\" data-katex-display=\"false\">p^2-4.1.6=0\\\\ \\Rightarrow p^2=24\\\\ \\therefore p=\\sqrt{24}<\/span>\r\n\r\n\r\n\r\n<h2><b>\u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae\u00a0<\/b><\/h2>\r\n\r\n\r\n\r\n<ul>\r\n<li><span style=\"font-weight: 400;\">\u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae (Logarithm) \u09ac\u09cd\u09af\u09ac\u09b9\u09be\u09b0 \u0995\u09b0\u09be \u09b9\u09df \u09b8\u09c2\u099a\u0995\u09c0\u09df \u09b0\u09be\u09b6\u09bf\u09b0 \u09ae\u09be\u09a8 \u09ac\u09c7\u09b0 \u0995\u09b0\u09be\u09b0 \u099c\u09a8\u09cd\u09af\u0964 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae\u0995\u09c7 \u09b8\u0982\u0995\u09cd\u09b7\u09c7\u09aa\u09c7 \u09b2\u0997 (log) \u09ac\u09b2\u09be \u09b9\u09df\u0964 <\/span><\/li>\r\n<li>\u09ac\u09dc \u09ac\u09dc \u09b0\u09be\u09b6\u09bf\u09b0 \u0997\u09c1\u09a3, \u09ad\u09be\u0997 \u0987\u09a4\u09cd\u09af\u09be\u09a6\u09bf \u09b8\u0982\u0995\u09cd\u09b7\u09c7\u09aa\u09c7 \u09b8\u09b9\u099c\u09c7 \u0995\u09b0\u09a4\u09c7 \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae \u09ac\u09cd\u09af\u09ac\u09b9\u09be\u09b0 \u0995\u09b0\u09be \u09b9\u09df\u0964 \u09af\u09c7\u09ae\u09a8: \u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf, {3^2} = 9, \u098f\u0987 \u0997\u09be\u09a3\u09bf\u09a4\u09bf\u0995 \u0989\u0995\u09cd\u09a4\u09bf\u099f\u09bf\u0995\u09c7 \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u09b2\u09bf\u0996\u09be \u09b9\u09df log <b>3<\/b> 9 = 2 \u098f\u0996\u09be\u09a8\u09c7 3 \u09b9\u099a\u09cd\u099b\u09c7 \u09b2\u0997\u09c7\u09b0 \u09ac\u09c7\u09b8\u0964<\/li>\r\n<li>\u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae \u09b9\u09b2\u09cb <strong>\u09b8\u09c2\u099a\u0995\u09c7\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09aa\u09cd\u09b0\u0995\u09cd\u09b0\u09bf\u09df\u09be<\/strong>\u0964<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<h3><b>\u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09c0\u00a0\u00a0<\/b><\/h3>\r\n\r\n\r\n\r\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\">\r\n<pre>\u09b8\u09c2\u09a4\u09cd\u09b0-\u09e7\\; (\u09b6\u09c2\u09a3\u09cd\u09af\\; \u0993\\; \u098f\u0995\\; \u09b2\u0997): a &gt; 0 \\;\u098f\u09ac\u0982\\; a \u2260 1 \\;\u09b9\u09b2\u09c7,\\; \\log_a 1= 0,\\; \\log_a a= 1\\\\\r\n\u09b8\u09c2\u09a4\u09cd\u09b0-\u09e8\\; (\u0997\u09c1\u09a3\u09ab\u09b2\u09c7\u09b0\\; \u09b2\u0997): \\log_a (MN) = \\log_a M + \\log_a N\\\\\r\n\u09b8\u09c2\u09a4\u09cd\u09b0-\u09e9\\; (\u09ad\u09be\u0997\u09c7\u09b0\\; \u09b8\u09c2\u09a4\u09cd\u09b0): \\log_a (\\frac{M}{N}) = \\log_a M - \\log_a N\\\\\r\n\u09b8\u09c2\u09a4\u09cd\u09b0-\u09ea\\; (\u0998\u09be\u09a4\u09c7\u09b0\\; \u09b2\u0997): \\log_a {M^r} = r \\log_a M <\/pre>\r\n<\/div>\r\n\r\n\r\n\r\n<ul>\r\n<li><strong>If <span class=\"katex-eq\" data-katex-display=\"false\">a^x=b, b^y=c, c^z=a<\/span> then the value of xyz =?\u00a0<\/strong><\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p><strong>Ans: <\/strong><\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\">\r\n<pre>a^x=b  \u2192 (i)\\\\\r\nb^y=c  \u2192 (ii)\\\\\r\nc^z=a  \u2192 (iii)\\\\\r\nUsing\\; (i)\\; and\\; (ii),\\; we\\; can\\; write\\\\\r\na^{xy}=c  \u2192 (iv)\\\\\r\nUsing\\; (iii)\\; and\\; (iv),\\; we\\; get\\; \\\\\r\na^{xyz}=a^1  [Since,\\;  a^1=a ]\\\\\r\n\\therefore  xyz=1<\/pre>\r\n<\/div>\r\n\r\n\r\n\r\n<ul>\r\n<li><strong>If <span class=\"katex-eq\" data-katex-display=\"false\">\\Big(\\frac{a}{b} \\Big)^{(x-1)}=\\Big(\\frac{b}{a} \\Big)^{(x-3)}<\/span> then what is the value of x?\u00a0<\/strong><\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p><strong>Ans: <\/strong><\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\">\r\n<pre>\\Big(\\frac{a}{b}\\Big)^{(x-1)} = \\Big(\\frac{a}{b}\\Big)^{-(x-3)}\\\\\r\n Then,\\; x-1 = - (x-3)\\\\\r\n \\Rightarrow x-1 = 3 - x \\\\\r\n\\Rightarrow 2x = 4 \\\\\r\n\\therefore x=2<\/pre>\r\n<\/div>\r\n\r\n\r\n\r\n<ul>\r\n<li><strong><span class=\"katex-eq\" data-katex-display=\"false\">2^{n-1}+2^{n+1}=320<\/span> \u09b9\u09b2\u09c7 n \u098f\u09b0 \u09ae\u09be\u09a8 \u0995\u09a4?\u00a0<\/strong><\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p><strong>Ans:\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\">\r\n<pre>2 ^n (2^{-1} +2^1 )= 320\\\\\r\n\\Rightarrow 2^n \\Big( \\frac{1}{2} + 2\\Big) = 320\\\\\r\n\\Rightarrow 2^n \\Big( \\frac{5}{2}\\Big)=320\\\\\r\n\\Rightarrow 2^n = 320\\times \\frac{2}{5}\\\\\r\n\\Rightarrow 2^n=642\\\\\r\n\\Rightarrow 2^n=128\\\\\r\n\\Rightarrow 2^n=2^7\\\\\r\n\\therefore n=7<\/pre>\r\n<\/div>\r\n\r\n\r\n\r\n<ul>\r\n<li><strong> <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{\\log 36}{\\log 6}<\/span>\u00a0<\/strong><\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p><strong>Ans:\u00a0<\/strong><\/p>\r\n\r\n\r\n\r\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\">\r\n<pre>\\frac{\\log 6^2}{\\log 6}\\\\\r\n\\Rightarrow \\frac{2\\log 6}{\\log 6}=2<\/pre>\r\n<\/div>\r\n","protected":false},"excerpt":{"rendered":"<p>\u09b8\u09b0\u09b2 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09af\u09c7 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7 \u098f\u0995 \u0998\u09be\u09a4 \u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u098f\u0995\u099f\u09bf \u09ae\u09be\u09a4\u09cd\u09b0 \u0985\u099c\u09cd\u099e\u09be\u09a4 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09aa\u09cd\u09b0\u09a4\u09c0\u0995 \u09a5\u09be\u0995\u09c7 \u09a4\u09be\u0995\u09c7 \u09b8\u09b0\u09b2 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09ac\u09b2\u09c7\u0964 \u09af\u09c7\u09ae\u09a8: 2(5x \u2013 14) = 21\u00a0 \u0989\u09aa\u0995\u09be\u09b0\u09c0 \u0995\u09cc\u09b6\u09b2\u00a0 \u09e7\u0964 \u09b8\u0982\u0996\u09cd\u09af\u09be \u09a7\u09b0\u09be\u09b0 \u09b8\u09ae\u09af\u09bc \u099b\u09cb\u099f \u09b8\u0982\u0996\u09cd\u09af\u09be \u09ac\u09be x \u09a7\u09b0\u09c7 \u09ae\u09cd\u09af\u09be\u09a5 \u0995\u09b0\u09c1\u09a8\u0964\u00a0 \u09af\u09c7\u09ae\u09a8: \u0995\u09cb\u09a8\u09cb \u098f\u0995\u099f\u09bf \u09b8\u0982\u0996\u09cd\u09af\u09be<\/p>\n<p> <a 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