{"id":11841,"date":"2024-09-01T12:57:00","date_gmt":"2024-09-01T07:27:00","guid":{"rendered":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/%e0%a4%b5%e0%a4%b0%e0%a5%8d%e0%a4%97%e0%a4%ae%e0%a5%82%e0%a4%b2-%e0%a4%95%e0%a5%87-%e0%a4%b8%e0%a4%b5%e0%a4%be%e0%a4%b2-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%be%e0%a4%ae%e0%a4%be%e0%a4%a8%e0%a5%8d\/"},"modified":"2026-05-18T09:42:49","modified_gmt":"2026-05-18T04:12:49","slug":"%e0%a4%b5%e0%a4%b0%e0%a5%8d%e0%a4%97%e0%a4%ae%e0%a5%82%e0%a4%b2-%e0%a4%95%e0%a5%87-%e0%a4%b8%e0%a4%b5%e0%a4%be%e0%a4%b2-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%be%e0%a4%ae%e0%a4%be%e0%a4%a8%e0%a5%8d","status":"publish","type":"post","link":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/%e0%a4%b5%e0%a4%b0%e0%a5%8d%e0%a4%97%e0%a4%ae%e0%a5%82%e0%a4%b2-%e0%a4%95%e0%a5%87-%e0%a4%b8%e0%a4%b5%e0%a4%be%e0%a4%b2-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%be%e0%a4%ae%e0%a4%be%e0%a4%a8%e0%a5%8d\/","title":{"rendered":"\u0935\u0930\u094d\u0917\u092e\u0942\u0932 \u0915\u0947 \u0938\u0935\u093e\u0932 \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0940\u0915\u0930\u0923"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u091b\u0924\u094d\u0924\u0940\u0938\u0917\u0922\u093c \u0915\u0947 \u0927\u092e\u0924\u0930\u0940 \u092e\u0947\u0902 \u0938\u094d\u0925\u093f\u0924 \u0905\u095b\u0940\u092e \u092a\u094d\u0930\u0947\u092e\u091c\u0940 \u0938\u094d\u0915\u0942\u0932 \u092e\u0947\u0902, \u092e\u0948\u0902\u0928\u0947 \u0915\u0915\u094d\u0937\u093e-8 \u0915\u0940 \u0917\u0923\u093f\u0924 \u0915\u0940 \u0915\u0915\u094d\u0937\u093e \u0926\u0947\u0916\u0940, \u091c\u0939\u093e\u0901 \u0936\u093f\u0915\u094d\u0937\u0915 \u0928\u0947 \u0935\u0930\u094d\u0917\u092e\u0942\u0932 \u0938\u093f\u0916\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0928\u090f \u0924\u0930\u0940\u0958\u0947 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u0925\u093e\u0964 \u0909\u0928\u094d\u0939\u094b\u0902\u0928\u0947 \u0935\u0930\u094d\u0917\u092e\u0942\u0932 \u0915\u0947 \u0938\u0935\u093e\u0932 \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u091a\u093f\u0924\u094d\u0930\u093e\u0924\u094d\u092e\u0915 \u0935\u093f\u0927\u093f \u0905\u092a\u0928\u093e\u0908 \u0925\u0940, \u091c\u094b \u092a\u093e\u0930\u092e\u094d\u092a\u0930\u093f\u0915 \u0924\u0930\u0940\u0958\u094b\u0902 \u0938\u0947 \u092d\u093f\u0928\u094d\u0928 \u0925\u0940\u0964 \u0907\u0938 \u0932\u0947\u0916 \u092e\u0947\u0902, \u092e\u0948\u0902 \u0907\u0938 \u091a\u093f\u0924\u094d\u0930\u093e\u0924\u094d\u092e\u0915 \u0924\u0930\u0940\u0958\u0947 \u0914\u0930 \u092a\u093e\u0930\u092e\u094d\u092a\u0930\u093f\u0915 \u0935\u093f\u0927\u093f \u0915\u0947 \u092c\u0940\u091a \u090f\u0915 \u0938\u092e\u094d\u092c\u0928\u094d\u0927 \u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u093e \u092a\u094d\u0930\u092f\u093e\u0938 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f, \u0907\u0938 \u0935\u093f\u0927\u093f \u0915\u094b \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0940\u0915\u0943\u0924 \u0915\u0930\u0928\u0947 \u0915\u093e \u092a\u094d\u0930\u092f\u093e\u0938 \u0915\u0930 \u0930\u0939\u0940 \u0939\u0942\u0901\u0964  <\/p>\n\n<p class=\"wp-block-paragraph\">\u0936\u093f\u0915\u094d\u0937\u0915 \u0928\u0947 \u092a\u093e\u0920 \u0915\u0940 \u0936\u0941\u0930\u0941\u0906\u0924 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0935\u093e\u0932 \u0938\u0947 \u0915\u0940 :<\/p>\n\n<p class=\"wp-block-paragraph\"><strong>\u092e\u0948\u0902\u0928\u0947 1000 \u092a\u094c\u0927\u0947 \u0959\u0930\u0940\u0926\u0947 \u0939\u0948\u0902\u0964 \u0905\u092c \u0909\u0928\u094d\u0939\u0947\u0902 \u0906\u092f\u0924\u093e\u0915\u093e\u0930 \u091c\u092e\u093e\u0935\u091f \u092e\u0947\u0902 \u0907\u0938 \u0924\u0930\u0939 \u0932\u0917\u093e\u0928\u093e \u0939\u0948 \u0915\u093f \u092a\u0902\u0915\u094d\u0924\u093f\u092f\u094b\u0902 \u0914\u0930 \u0938\u094d\u0924\u092e\u094d\u092d\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0964 \u092f\u0926\u093f \u092e\u0941\u091d\u0947 \u0910\u0938\u093e \u0915\u0930\u0928\u093e \u0939\u094b, \u0924\u094b \u0909\u0915\u094d\u200d\u0924 \u0936\u0930\u094d\u0924 \u0915\u094b \u092a\u0942\u0930\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092e\u0941\u091d\u0947 \u0914\u0930 \u0915\u093f\u0924\u0928\u0947 \u092a\u094c\u0927\u094b\u0902 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u094b\u0917\u0940? <\/strong><\/p>\n\n<p class=\"wp-block-paragraph\">\u0906\u0907\u090f \u0926\u0947\u0916\u0947\u0902 \u0915\u093f \u0939\u092e \u0907\u0938 \u0938\u0935\u093e\u0932 \u0915\u094b \u092a\u093e\u0930\u092e\u094d\u092a\u0930\u093f\u0915 \u0924\u0930\u0940\u0958\u0947 \u0938\u0947 \u0915\u0948\u0938\u0947 \u0939\u0932 \u0915\u0930\u0924\u0947\u0964 \u0907\u0938 \u0938\u0935\u093e\u0932 \u0938\u0947 \u0938\u0902\u0915\u0947\u0924 \u092e\u093f\u0932\u0924\u093e \u0939\u0948 \u0915\u093f \u0939\u092e\u0947\u0902 \u0938\u092c\u0938\u0947 \u092c\u0921\u093c\u0940 3-\u0905\u0902\u0915\u0940\u092f \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0947 \u092c\u093e\u0926 \u0935\u093e\u0932\u0940 \u0905\u0917\u0932\u0940 \u0935\u0930\u094d\u0917 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u093e \u092a\u0924\u093e \u0932\u0917\u093e\u0928\u093e \u0939\u0948\u0964 \u092a\u0902\u0915\u094d\u0924\u093f\u092f\u094b\u0902 \u0914\u0930 \u0938\u094d\u0924\u092e\u094d\u092d\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0938\u092e\u093e\u0928 \u0939\u094b\u0928\u093e \u092f\u0939 \u0926\u0930\u094d\u0936\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0939\u092e \u0935\u0930\u094d\u0917 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u092c\u093e\u0924 \u0915\u0930 \u0930\u0939\u0947 \u0939\u0948\u0902\u0964 \u092a\u0930 \u0938\u092c\u0938\u0947 \u092c\u0921\u093c\u0940 3-\u0905\u0902\u0915\u0940\u092f \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094d\u092f\u094b\u0902? \u091c\u092c \u0907\u0938 \u0938\u0935\u093e\u0932 \u0915\u094b \u0926\u0940\u0930\u094d\u0918 (\u0932\u092e\u094d\u092c\u0940) \u0935\u093f\u092d\u093e\u091c\u0928 \u0935\u093f\u0927\u093f \u0938\u0947 \u0939\u0932 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0939\u092e \u092a\u093e\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0907\u0938\u0915\u093e \u0909\u0924\u094d\u0924\u0930 1000 \u0938\u0947 \u0915\u092e \u0938\u092c\u0938\u0947 \u092c\u0921\u093c\u0940 \u092a\u0942\u0930\u094d\u0923 \u0935\u0930\u094d\u0917 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u093e \u0935\u0930\u094d\u0917\u092e\u0942\u0932 \u0939\u094b\u0917\u093e, \u091c\u094b \u0938\u092c\u0938\u0947 \u092c\u0921\u093c\u093e 3-\u0905\u0902\u0915\u0940\u092f \u092a\u0942\u0930\u094d\u0923 \u0935\u0930\u094d\u0917 \u0939\u094b\u0917\u093e\u0964 \u0907\u0938 \u0938\u0935\u093e\u0932 \u0915\u0947 \u0924\u0930\u094d\u0915 \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930, \u0939\u092e\u0947\u0902 \u0938\u092c\u0938\u0947 \u092c\u095c\u0940 3-\u0905\u0902\u0915\u0940\u092f \u0935\u0930\u094d\u0917 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0947 \u092c\u093e\u0926 \u0915\u0940 \u0905\u0917\u0932\u0940 \u0935\u0930\u094d\u0917 \u0938\u0902\u0916\u094d\u092f\u093e \u0916\u094b\u091c\u0928\u0940 \u0939\u0948, \u091c\u094b \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 4-\u0905\u0902\u0915\u0940\u092f \u0935\u0930\u094d\u0917 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u094b\u0917\u0940\u0964 \u092f\u0926\u093f \u0907\u0938 \u0938\u0902\u0916\u094d\u092f\u093e \u092e\u0947\u0902 \u0938\u0947 1000 \u0918\u091f\u093e \u0926\u093f\u092f\u093e \u091c\u093e\u090f, \u0924\u094b \u0939\u092e\u0947\u0902 \u0906\u0935\u0936\u094d\u092f\u0915 \u092a\u094c\u0927\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u092e\u093f\u0932 \u091c\u093e\u090f\u0917\u0940\u0964      <\/p>\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/Generalising-figure-1.jpg\" alt=\"&#x938;&#x93E;&#x92E;&#x93E;&#x928;&#x94D;&#x92F;&#x940;&#x915;&#x930;&#x923; &#x91A;&#x93F;&#x924;&#x94D;&#x930;-1\" class=\"wp-image-15918\" style=\"width:277px;height:auto\"\/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-1<\/figcaption><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<p class=\"wp-block-paragraph\">\u091a\u093f\u0924\u094d\u0930-1 \u092e\u0947\u0902 1000 \u0915\u093e \u0935\u0930\u094d\u0917\u092e\u0942\u0932 \u092a\u0924\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0926\u0940\u0930\u094d\u0918 (\u0932\u092e\u094d\u092c\u0940) \u0935\u093f\u092d\u093e\u091c\u0928 \u0935\u093f\u0927\u093f \u0926\u093f\u0916\u093e\u0908 \u0917\u0908 \u0939\u0948\u0964 \u092f\u0939\u093e\u0901 \u092f\u0926\u093f \u0939\u092e 32 \u0915\u093e \u0935\u0930\u094d\u0917 \u0932\u0947\u0902 \u0914\u0930 \u0909\u0938\u092e\u0947\u0902 \u0938\u0947 1000 \u0918\u091f\u093e\u090f\u0901 \u0924\u094b \u0939\u092e\u0947\u0902 \u0909\u0924\u094d\u0924\u0930 \u092e\u093f\u0932 \u091c\u093e\u090f\u0917\u093e\u0964 <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\mathbf{32^2 &#8211; 1000 = 24}\\) \u0907\u0938\u0932\u093f\u090f, \u0909\u0924\u094d\u0924\u0930 \\(\\mathbf{24}\\) \u0939\u094b\u0917\u093e\u0964<\/p>\n<\/div>\n<\/div>\n\n<p class=\"wp-block-paragraph\">\u0905\u092c, \u0939\u092e 1000 \u0915\u094b \\(N\\) \u0914\u0930 31 \u0915\u094b \\(m\\) \u092e\u093e\u0928\u0915\u0930 \u0907\u0938 \u0935\u093f\u0927\u093f \u0915\u094b \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0940\u0915\u0943\u0924 \u0915\u0930\u0928\u0947 \u0915\u093e \u092a\u094d\u0930\u092f\u093e\u0938 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u0924\u092c \u0907\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u094b \\((m+1)^{2} &#8211; N\\)= \u0906\u0935\u0936\u094d\u092f\u0915 \u092a\u094c\u0927\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0932\u093f\u0916\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0902 \u0915\u093f \u092f\u0939\u093e\u0901 \u0926\u0940\u0930\u094d\u0918 (\u0932\u092e\u094d\u092c\u0940) \u0935\u093f\u092d\u093e\u091c\u0928 \u0935\u093f\u0927\u093f \u0915\u0947 \u092c\u093e\u0926 \u0926\u094b 2-\u0905\u0902\u0915\u0940\u092f \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u093e \u0917\u0941\u0923\u093e \u0915\u0930\u0928\u093e \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/p>\n\n<p class=\"wp-block-paragraph\">\u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0907\u0938 \u0938\u0935\u093e\u0932 \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u0947 \u0938\u0947 \u092a\u0939\u0932\u0947, \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u093f\u092f\u094b\u0902 \u0915\u094b \u0938\u092c\u0938\u0947 \u092c\u095c\u0940 \u092f\u093e \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 3 \u092f\u093e 4-\u0905\u0902\u0915\u0940\u092f \u0935\u0930\u094d\u0917 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0940 \u092a\u0939\u091a\u093e\u0928 \u0915\u0930\u0928\u0947 \u091c\u0948\u0938\u0947 \u0938\u0935\u093e\u0932\u094b\u0902 \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u093e \u092a\u0930\u094d\u092f\u093e\u092a\u094d\u0924 \u0905\u092d\u094d\u092f\u093e\u0938 \u0915\u0930\u093e\u092f\u093e \u0917\u092f\u093e \u0925\u093e\u0964 \u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0905\u0927\u093f\u0915\u093e\u0902\u0936 \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u093f\u092f\u094b\u0902 \u0928\u0947 \u0907\u0938 \u0938\u0935\u093e\u0932 \u0915\u094b \u0935\u0930\u094d\u0917\u092e\u0942\u0932 \u0928\u093f\u0915\u093e\u0932\u0928\u0947 \u0915\u0940 \u0926\u0940\u0930\u094d\u0918 (\u0932\u092e\u094d\u092c\u0940) \u0935\u093f\u092d\u093e\u091c\u0928 \u0935\u093f\u0927\u093f \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u093e \u092a\u094d\u0930\u092f\u093e\u0938 \u0915\u093f\u092f\u093e \u0914\u0930 \u0909\u0928\u092e\u0947\u0902 \u0938\u0947 \u0915\u0941\u091b \u0907\u0938\u0947 \u0939\u0932 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0938\u092b\u0932 \u092d\u0940 \u0930\u0939\u0947\u0964 <\/p>\n\n<p class=\"wp-block-paragraph\">\u0939\u093e\u0932\u093e\u0901\u0915\u093f, \u0936\u093f\u0915\u094d\u0937\u0915 \u0928\u0947 \u0907\u0938\u0947 \u0938\u092e\u091d\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0920\u0940\u0915 \u0907\u0938 \u0924\u0930\u0940\u0958\u0947 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0924\u094b \u0928\u0939\u0940\u0902 \u0915\u093f\u092f\u093e, \u091c\u093f\u0938\u092e\u0947\u0902 \u0938\u092c\u0938\u0947 \u092c\u0921\u093c\u0940 3-\u0905\u0902\u0915\u0940\u092f \u0935\u0930\u094d\u0917 \u0938\u0902\u0916\u094d\u092f\u093e \u0914\u0930 \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 4-\u0905\u0902\u0915\u0940\u092f \u0935\u0930\u094d\u0917 \u0938\u0902\u0916\u094d\u092f\u093e \u0936\u093e\u092e\u093f\u0932 \u0939\u094b\u0964<\/p>\n\n<p class=\"wp-block-paragraph\">\u0907\u0938\u0915\u0940 \u092c\u091c\u093e\u092f, \u0909\u0928\u094d\u0939\u094b\u0902\u0928\u0947 \u091a\u093f\u0924\u094d\u0930-2 \u0915\u0947 \u0938\u092e\u093e\u0928 \u090f\u0915 \u0906\u0930\u0947\u0916 \u092c\u0928\u093e\u092f\u093e \u0914\u0930 \u0915\u0939\u093e \u0915\u093f 1000 \u092a\u094c\u0927\u094b\u0902 \u0915\u094b \u091c\u092e\u093e\u0915\u0930 \u0915\u0947\u0935\u0932 31 \u0917\u0941\u0923\u093e 31 \u0915\u093e \u090f\u0915 \u0935\u0930\u094d\u0917 \u092c\u0928\u093e\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u0914\u0930 \u091c\u093f\u0938\u092e\u0947\u0902 \u0938\u0947 \u0915\u0941\u091b \u092a\u094c\u0927\u0947 \u092c\u091a \u091c\u093e\u090f\u0901\u0917\u0947, \u091c\u094b \u0936\u0947\u0937\u092b\u0932 \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0902\u0917\u0947\u0964 \u091c\u093f\u0928\u094d\u0939\u0947\u0902 \u0926\u094b\u0928\u094b\u0902 \u092d\u0941\u091c\u093e\u0913\u0902 \u092a\u0930 \u0914\u0930 \u091c\u092e\u093e\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0938\u0947 \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u093f\u092f\u094b\u0902 \u0915\u094b 32 \u0915\u093e \u0935\u0930\u094d\u0917 \u092a\u0924\u093e \u0915\u0930\u0928\u0947 \u0915\u093e \u0938\u0902\u0915\u0947\u0924 \u092e\u093f\u0932\u0947\u0917\u093e \u091c\u094b \u0915\u093f \u092a\u094c\u0927\u094b\u0902 \u0915\u0940 \u0915\u0941\u0932 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u094b\u0917\u0940 \u0914\u0930 \u0907\u0938\u092e\u0947\u0902 \u0938\u0947 1000 \u0918\u091f\u093e\u0928\u0947 \u092a\u0930 \u0959\u0930\u0940\u0926\u0947 \u091c\u093e\u0928\u0947 \u0935\u093e\u0932\u0947 \u092a\u094c\u0927\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u092e\u093f\u0932 \u091c\u093e\u090f\u0917\u0940\u0964 \u0905\u092c \u0907\u0938 \u091a\u093f\u0924\u094d\u0930\u093e\u0924\u094d\u092e\u0915 \u0924\u0930\u0940\u0958\u0947 \u0915\u094b \u0907\u0938 \u0938\u0935\u093e\u0932 \u0915\u093e \u0909\u0924\u094d\u0924\u0930 \u0916\u094b\u091c\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092c\u0922\u093c\u093e\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u091c\u093f\u0938\u0938\u0947 \u0939\u092e\u0947\u0902 32 \u0915\u093e \u0935\u0930\u094d\u0917 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0928\u0939\u0940\u0902 \u0939\u094b\u0917\u0940\u0964  <\/p>\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"743\" height=\"736\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/Generalising-figure-2.jpg\" alt=\"&#x938;&#x93E;&#x92E;&#x93E;&#x928;&#x94D;&#x92F;&#x940;&#x915;&#x930;&#x923; &#x91A;&#x93F;&#x924;&#x94D;&#x930;-2\" class=\"wp-image-15408\" style=\"object-fit:cover\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/Generalising-figure-2.jpg 743w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/Generalising-figure-2-363x360.jpg 363w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/Generalising-figure-2-727x720.jpg 727w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/Generalising-figure-2-204x202.jpg 204w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/Generalising-figure-2-150x150.jpg 150w\" sizes=\"auto, (max-width: 743px) 100vw, 743px\" \/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-2<\/figcaption><\/figure>\n\n<p class=\"wp-block-paragraph\">\u092e\u093e\u0928\u093e \u0915\u093f \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u092a\u094c\u0927\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \\(N\\) \u0939\u0948, \u091c\u094b \u0915\u093f \u090f\u0915 \u092a\u0942\u0930\u094d\u0923 \u0935\u0930\u094d\u0917 \u0928\u0939\u0940\u0902 \u0939\u0948 \u0914\u0930 \\(N\\) \u0938\u0947 \u091b\u094b\u091f\u093e \u0938\u092c\u0938\u0947 \u092c\u0921\u093c\u093e \u092a\u0942\u0930\u094d\u0923 \u0935\u0930\u094d\u0917 \\(m^{2}\\) \u0939\u0948\u0964 \u0905\u092c m \u0917\u0941\u0923\u093e m \u0915\u0947 \u0935\u0930\u094d\u0917 \u092e\u0947\u0902 \u092a\u094c\u0927\u094b\u0902 \u0915\u094b \u091c\u092e\u093e\u0928\u0947 \u0915\u0947 \u092c\u093e\u0926, \u0936\u0947\u0937 \u092a\u094c\u0927\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \\(N &#8211; m^{2}\\) \u0939\u094b\u0917\u0940\u0964 \u092f\u093e\u0926 \u0915\u0930\u0947\u0902 \u0915\u093f \u092a\u093f\u091b\u0932\u0947 \u0938\u0935\u093e\u0932 \u092e\u0947\u0902 \u092f\u0939 \u0915\u0948\u0938\u0947 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0925\u093e, \\(1000 &#8211; 31^{2} = 39\\), \u091c\u094b \u0915\u093f \u0926\u0940\u0930\u094d\u0918 (\u0932\u092e\u094d\u092c\u0940) \u0935\u093f\u092d\u093e\u091c\u0928 \u0935\u093f\u0927\u093f \u092e\u0947\u0902 \u0936\u0947\u0937\u092b\u0932 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u0941\u0906 \u0925\u093e\u0964<\/p>\n\n<p class=\"wp-block-paragraph\">\u0905\u092c \u0907\u0928 \u092c\u091a\u0947 \u0939\u0941\u090f \u092a\u094c\u0927\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 m \u092a\u094c\u0927\u0947 \u0915\u093f\u0938\u0940 \u090f\u0915 \u092d\u0941\u091c\u093e \u092a\u0930 \u091c\u092e\u093e\u090f \u091c\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930, \u0907\u0928\u094d\u0939\u0947\u0902 \u091c\u092e\u093e\u0928\u0947 \u0915\u0947 \u092c\u093e\u0926 \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u0905\u092c \\((N-m^{2} 2 )-m\\) \u092a\u094c\u0927\u0947 \u092c\u091a\u0947 \u0930\u0939\u0947\u0902\u0917\u0947\u0964 \u092f\u093e\u0928\u0940, \u092a\u093f\u091b\u0932\u0947 \u0938\u0935\u093e\u0932 \u092e\u0947\u0902 \\((1000 -31^{2})-31=39-31=8\\) \u092a\u094c\u0927\u0947 \u092c\u091a\u0947 \u0925\u0947\u0964 \u092f\u093e\u0926 \u0915\u0940\u091c\u093f\u090f \u0915\u093f \u0935\u0930\u094d\u0917 \u0915\u0940 \u0926\u0942\u0938\u0930\u0940 \u092d\u0941\u091c\u093e \u092a\u0930 \\(39-31=8\\) \u092a\u094c\u0927\u0947 \u0932\u0917\u093e\u090f \u0917\u090f \u0925\u0947\u0964 \u091a\u093f\u0924\u094d\u0930-3 \u0926\u0947\u0916\u0947\u0902\u0964   <\/p>\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"639\" height=\"732\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/Generalising-figure3.jpg\" alt=\"&#x938;&#x93E;&#x92E;&#x93E;&#x928;&#x94D;&#x92F;&#x940;&#x915;&#x930;&#x923; &#x91A;&#x93F;&#x924;&#x94D;&#x930;-3\" class=\"wp-image-15412\" style=\"object-fit:cover\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/Generalising-figure3.jpg 639w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/Generalising-figure3-314x360.jpg 314w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/Generalising-figure3-629x720.jpg 629w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/Generalising-figure3-176x202.jpg 176w\" sizes=\"auto, (max-width: 639px) 100vw, 639px\" \/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-3<\/figcaption><\/figure>\n\n<p class=\"wp-block-paragraph\">\u0932\u0947\u0915\u093f\u0928 \u0927\u094d\u092f\u093e\u0928 \u0926\u0940\u091c\u093f\u090f \u0915\u093f \u0926\u0942\u0938\u0930\u0940 \u092d\u0941\u091c\u093e \u092a\u0930 \u0915\u0941\u0932 \u092e\u093f\u0932\u093e\u0915\u0930 \\(m+1\\) \u0907\u0915\u093e\u0907\u092f\u093e\u0901 \u0939\u0948\u0902\u0964 \u0907\u0938\u0932\u093f\u090f \u0939\u092e\u0947\u0902 \\((m + 1) &#8211; [(N &#8211; m^{2}) &#8211; m]\\) \u092a\u094c\u0927\u0947 \u0959\u0930\u0940\u0926\u0928\u0947 \u0915\u0940 \u095b\u0930\u0942\u0930\u0924 \u0939\u0948\u0964 \u092a\u093f\u091b\u0932\u0947 \u0909\u0926\u093e\u0939\u0930\u0923 \u092e\u0947\u0902 \u0939\u092e\u0928\u0947 \u0926\u0947\u0916\u093e \u0915\u093f, \u0939\u092e\u0947\u0902 \\((31+1) \u2013 8 = 24\\) \u092a\u094c\u0927\u0947 \u0959\u0930\u0940\u0926\u0928\u0947 \u0939\u094b\u0902\u0917\u0947\u0964<\/p>\n\n<p class=\"wp-block-paragraph\">\u0939\u093e\u0932\u093e\u0901\u0915\u093f, \u0905\u0917\u0930 \u0939\u092e \\(1000\\) \u0915\u0940 \u092c\u091c\u093e\u092f \\(990\\) \u092a\u094c\u0927\u094b\u0902 \u0938\u0947 \u0936\u0941\u0930\u0942 \u0915\u0930\u0924\u0947, \u0924\u094b \u0939\u092e\u093e\u0930\u093e \u092f\u0939 \u0924\u0930\u094d\u0915 \u0915\u093e\u092e \u0928\u0939\u0940\u0902 \u0915\u0930\u0947\u0917\u093e\u0964 \u0910\u0938\u093e \u0907\u0938\u0932\u093f\u090f \u0939\u0948 \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0924\u092c \\((N-m^{2}) \u2013 m &lt; m\\)\u092d\u0941\u091c\u093e\u0913\u0902 \u092e\u0947\u0902 \u0938\u0947 \u0915\u093f\u0938\u0940 \u090f\u0915 \u0915\u094b \u092a\u0942\u0930\u093e \u0928\u0939\u0940\u0902 \u092d\u0930 \u0938\u0915\u0947\u0902\u0917\u0947\u0964 \u0907\u0938\u0947 \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092a\u094c\u0927\u094b\u0902 \u0915\u094b \u092a\u0939\u0932\u0947 \u090f\u0915 \u0939\u0940 \u092d\u0941\u091c\u093e \u092a\u0930 \u0932\u0917\u093e\u0928\u0947 \u0915\u0940 \u092c\u091c\u093e\u092f, \u0939\u092e \u0926\u094b\u0928\u094b\u0902 \u092d\u0941\u091c\u093e\u0913\u0902 \u092a\u0930 \u090f\u0915-\u090f\u0915 \u0915\u0930\u0915\u0947 \u092a\u094c\u0927\u0947 \u0932\u0917\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 (\u091a\u093f\u0924\u094d\u0930-4 \u0926\u0947\u0916\u0947\u0902)\u0964   <\/p>\n\n<p class=\"wp-block-paragraph\">\u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0930\u0942\u092a \u0938\u0947, \u0907\u0938\u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u0948 \u0915\u093f \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u0935\u0930\u094d\u0917 \u0915\u0940 \u0926\u094b\u0928\u094b\u0902 \u092d\u0941\u091c\u093e\u0913\u0902 \u092a\u0930 \\(m+m +1=2 m +1\\) \u0938\u094d\u0925\u093e\u0928 (\u0938\u094d\u0932\u0949\u091f) \u0939\u0948\u0902\u0964 \u092f\u0926\u093f \u0939\u092e \u0936\u0947\u0937 \\(N-m^{2} \\) \u092a\u094c\u0927\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0907\u0928 \u0938\u094d\u0925\u093e\u0928\u094b\u0902 \u0915\u094b \u092d\u0930\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0959\u0930\u0940\u0926\u0947 \u091c\u093e\u0928\u0947 \u0935\u093e\u0932\u0947 \u0906\u0935\u0936\u094d\u092f\u0915 \u092a\u094c\u0927\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \\(2m+1-N-m ^{2}\\) \u0939\u094b\u0928\u0940 \u091a\u093e\u0939\u093f\u090f\u0964  <br\/><\/p>\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"609\" height=\"670\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/Generalising-figure4.jpg\" alt=\"&#x938;&#x93E;&#x92E;&#x93E;&#x928;&#x94D;&#x92F;&#x940;&#x915;&#x930;&#x923; &#x91A;&#x93F;&#x924;&#x94D;&#x930;-4\" class=\"wp-image-15415\" style=\"object-fit:cover\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/Generalising-figure4.jpg 609w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/Generalising-figure4-327x360.jpg 327w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/Generalising-figure4-184x202.jpg 184w\" sizes=\"auto, (max-width: 609px) 100vw, 609px\" \/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-4<\/figcaption><\/figure>\n\n<p class=\"wp-block-paragraph\">\u092f\u0939\u093e\u0901 \u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0928\u0947 \u092f\u094b\u0917\u094d\u092f \u0939\u0948 \u0915\u093f \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u093f\u092f\u094b\u0902 \u0915\u094b \u0915\u0947\u0935\u0932 \u091c\u094b\u0921\u093c \u0914\u0930 \u0918\u091f\u093e\u0928\u093e \u0939\u094b\u0924\u093e \u0939\u0948, \u0928 \u0915\u093f \u0917\u0941\u0923\u093e \u0915\u0930\u0928\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u091a\u0942\u0901\u0915\u093f \u091c\u094b\u0921\u093c \u0914\u0930 \u0918\u091f\u093e\u0928\u093e, \u0917\u0941\u0923\u093e \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u092e\u0947\u0902 \u0938\u0930\u0932 \u0938\u0902\u0915\u094d\u0930\u093f\u092f\u093e\u090f\u0901 \u0939\u0948\u0902, \u0907\u0938\u0932\u093f\u090f \u095a\u0932\u0924\u093f\u092f\u094b\u0902 \u0915\u0940 \u0938\u092e\u094d\u092d\u093e\u0935\u0928\u093e \u0915\u092e \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u0907\u0938\u0915\u0947 \u0938\u093e\u0925 \u0939\u0940, \u092f\u0939 \u0935\u093f\u0927\u093f \u0909\u0928\u094d\u0939\u0947\u0902 \u091a\u093f\u0924\u094d\u0930 \u0930\u0942\u092a \u0938\u0947 \u0938\u0924\u094d\u092f\u093e\u092a\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u093e \u0905\u0935\u0938\u0930 \u092d\u0940 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u0940 \u0939\u0948 \u0915\u093f \\((m+1 )^ {2} -N\\) \u0914\u0930 \\(2m+1-(N-m^{2})\\) \u0938\u092e\u093e\u0928 \u0939\u0948\u0902\u0964  <\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u091b\u0924\u094d\u0924\u0940\u0938\u0917\u0922\u093c \u0915\u0947 \u0927\u092e\u0924\u0930\u0940 \u092e\u0947\u0902 \u0938\u094d\u0925\u093f\u0924 \u0905\u095b\u0940\u092e \u092a\u094d\u0930\u0947\u092e\u091c\u0940 \u0938\u094d\u0915\u0942\u0932 \u092e\u0947\u0902, \u092e\u0948\u0902\u0928\u0947 \u0915\u0915\u094d\u0937\u093e-8 \u0915\u0940 \u0917\u0923\u093f\u0924 \u0915\u0940 \u0915\u0915\u094d\u0937\u093e \u0926\u0947\u0916\u0940, \u091c\u0939\u093e\u0901 \u0936\u093f\u0915\u094d\u0937\u0915 \u0928\u0947 \u0935\u0930\u094d\u0917\u092e\u0942\u0932 \u0938\u093f\u0916\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0928\u090f \u0924\u0930\u0940\u0958\u0947 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u0925\u093e\u0964 \u0909\u0928\u094d\u0939\u094b\u0902\u0928\u0947 \u0935\u0930\u094d\u0917\u092e\u0942\u0932 \u0915\u0947 \u0938\u0935\u093e\u0932 \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u091a\u093f\u0924\u094d\u0930\u093e\u0924\u094d\u092e\u0915 \u0935\u093f\u0927\u093f \u0905\u092a\u0928\u093e\u0908 \u0925\u0940, \u091c\u094b \u092a\u093e\u0930\u092e\u094d\u092a\u0930\u093f\u0915 \u0924\u0930\u0940\u0958\u094b\u0902 \u0938\u0947 \u092d\u093f\u0928\u094d\u0928 \u0925\u0940\u0964 \u0907\u0938 \u0932\u0947\u0916 \u092e\u0947\u0902, \u092e\u0948\u0902 \u0907\u0938 [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":28266,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_wpcom_ai_launchpad_first_post":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[239],"tags":[263,602,581,561],"stage-class":[1008],"magazine_category":[287],"class_list":["post-11841","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category---hi","tag-263","tag-602","tag-581","tag-561","stage-class-middle-class-6-8-hi","magazine_category--20--2024"],"acf":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/Generalising-a-Square-Root-thumbnail.png","_links":{"self":[{"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/posts\/11841","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/comments?post=11841"}],"version-history":[{"count":1,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/posts\/11841\/revisions"}],"predecessor-version":[{"id":23776,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/posts\/11841\/revisions\/23776"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/media\/28266"}],"wp:attachment":[{"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/media?parent=11841"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/categories?post=11841"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/tags?post=11841"},{"taxonomy":"stage-class","embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/stage-class?post=11841"},{"taxonomy":"magazine_category","embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/magazine_category?post=11841"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}