{"id":27092,"date":"2026-09-02T12:48:49","date_gmt":"2026-09-02T07:18:49","guid":{"rendered":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/?p=27092"},"modified":"2026-09-02T12:48:49","modified_gmt":"2026-09-02T07:18:49","slug":"%e0%a4%b9%e0%a4%b0%e0%a4%ac%e0%a4%a8%e0%a5%8d%e0%a4%b8-%e0%a4%aa%e0%a4%b9%e0%a5%87%e0%a4%b2%e0%a4%bf%e0%a4%af%e0%a4%be%e0%a4%81","status":"publish","type":"post","link":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/%e0%a4%b9%e0%a4%b0%e0%a4%ac%e0%a4%a8%e0%a5%8d%e0%a4%b8-%e0%a4%aa%e0%a4%b9%e0%a5%87%e0%a4%b2%e0%a4%bf%e0%a4%af%e0%a4%be%e0%a4%81\/","title":{"rendered":"\u0939\u0930\u092c\u0928\u094d\u200d\u0938 \u092a\u0939\u0947\u0932\u093f\u092f\u093e\u0901"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u0915\u094b\u0932\u093f\u0928\u094d\u0938 \u0936\u092c\u094d\u0926\u0915\u094b\u0936 \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u092a\u0939\u0947\u0932\u0940 \u0915\u093e \u092e\u0924\u0932\u092c \u0939\u0948\u2013 &#8220;\u092e\u0928\u094b\u0930\u091c\u0902\u0928 \u0915\u0947 \u0932\u093f\u090f \u0928\u093f\u0930\u094d\u092e\u093f\u0924 \u0910\u0938\u093e \u0915\u094b\u0908 \u092d\u0940 \u0916\u093f\u0932\u094c\u0928\u093e, \u0938\u092e\u0938\u094d\u092f\u093e \u092f\u093e \u0905\u0928\u094d\u092f \u092f\u0941\u0915\u094d\u0924\u093f \u091c\u094b \u0915\u094c\u0936\u0932 \u092f\u093e \u0927\u0948\u0930\u094d\u092f\u092a\u0942\u0930\u094d\u0935\u0915 \u092a\u094d\u0930\u092f\u093e\u0938 \u0926\u094d\u0935\u093e\u0930\u093e \u0939\u0932 \u0915\u0940 \u091c\u093e\u0928\u0947 \u0935\u093e\u0932\u0940 \u0915\u0920\u093f\u0928\u093e\u0907\u092f\u094b\u0902 \u0915\u094b \u092a\u094d\u0930\u0938\u094d\u200d\u0924\u0941\u0924 \u0915\u0930\u0924\u0940 \u0939\u094b\u0964\u2019\u2019 \u0905\u0927\u093f\u0915\u093e\u0902\u0936 \u092a\u0939\u0947\u0932\u093f\u092f\u093e\u0901 \u090f\u0915 \u092a\u0947\u091a\u0940\u0926\u093e \u0938\u092e\u0938\u094d\u200d\u092f\u093e \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948\u0902 \u091c\u093f\u0928\u094d\u0939\u0947\u0902 \u0906\u0938\u093e\u0928\u0940 \u0938\u0947 \u0939\u0932 \u0928\u0939\u0940\u0902 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0938\u093e\u0925 \u0939\u0940 \u0907\u0928\u094d\u200d\u0939\u0947\u0902 \u0907\u0938 \u0924\u0930\u0939 \u0921\u093f\u091c\u093c\u093e\u0907\u0928 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u092f\u0939 \u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u0914\u0930 \u0906\u0915\u0930\u094d\u0937\u0915 \u0939\u094b\u0902, \u0924\u093e\u0915\u093f \u092a\u0939\u0947\u0932\u0940 \u0939\u0932 \u0915\u0930\u0928\u0947 \u0935\u093e\u0932\u093e \u0938\u092e\u093e\u0927\u093e\u0928 \u0915\u093e \u092a\u0924\u093e \u0932\u0917\u093e\u0928\u0947 \u092e\u0947\u0902 \u0938\u092e\u092f \u0914\u0930 \u090a\u0930\u094d\u091c\u093e \u0915\u093e \u0928\u093f\u0935\u0947\u0936 \u0915\u0930\u0947\u0964 \u0917\u0923\u093f\u0924\u0940\u092f \u092a\u0939\u0947\u0932\u093f\u092f\u093e\u0901 \u092c\u091a\u094d\u200d\u091a\u094b\u0902 \u0915\u094b \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0938\u092e\u0943\u0926\u094d\u0927 \u0917\u0923\u093f\u0924\u0940\u092f \u0905\u0928\u094d\u0935\u0947\u0937\u0923 \u0914\u0930 \u0924\u093e\u0930\u094d\u0915\u093f\u0915 \u0924\u0930\u094d\u0915\u094b\u0902 (logical reasoning) \u092e\u0947\u0902 \u0938\u0902\u0932\u0917\u094d\u0928 \u0915\u0930 \u0938\u0915\u0924\u0940 \u0939\u0948\u0902 (\u090f\u0935\u0930\u0947\u0921, 2001)\u0964 \u0907\u0938 \u0932\u0947\u0916 \u092e\u0947\u0902 \u0939\u092e \u090f\u0915 \u091c\u093e\u092a\u093e\u0928\u0940 \u092a\u0939\u0947\u0932\u0940 \u2018\u0915\u0947\u0928\u0915\u0947\u0928\u2019 (\u091c\u093f\u0938\u0947 \u0939\u092e\u0928\u0947 \u0939\u0930\u092c\u0928\u094d\u0938 \u092a\u0939\u0947\u0932\u0940 \u0928\u093e\u092e \u0926\u093f\u092f\u093e \u0939\u0948) \u0915\u0947 \u0935\u093f\u0938\u094d\u200d\u0924\u093e\u0930 \u0914\u0930 \u0935\u093f\u0935\u093f\u0927\u0924\u093e\u0913\u0902 \u0915\u093e \u0935\u0930\u094d\u0923\u0928 \u0915\u0930\u0947\u0902\u0917\u0947 \u0914\u0930 \u092b\u093f\u0930 \u0907\u0928 \u092a\u0939\u0947\u0932\u093f\u092f\u094b\u0902 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u092c\u091a\u094d\u200d\u091a\u094b\u0902 \u0915\u0940 \u092a\u094d\u0930\u0924\u093f\u0915\u094d\u0930\u093f\u092f\u093e\u0913\u0902 \u092a\u0930 \u091a\u0930\u094d\u091a\u093e \u0915\u0930\u0947\u0902\u0917\u0947\u0964<\/p>\n\n\n\n<p><p><a href=\"http:\/\/www.kenkenpuzzle.com\/\" target=\"_blank\" rel=\"noreferrer noopener\" data-mce-href=\"http:\/\/www.kenkenpuzzle.com\/\">\u0915\u0947\u0928\u0915\u0947\u0928 \u092a\u0939\u0947\u0932\u093f\u092f\u094b\u0902<\/a> \u0915\u093e \u0906\u0935\u093f\u0937\u094d\u0915\u093e\u0930 \u090f\u0915 \u091c\u093e\u092a\u093e\u0928\u0940 \u0936\u093f\u0915\u094d\u0937\u0915 <b><i>\u0924\u0947\u0924\u094d\u0938\u0941\u092f\u093e \u092e\u093f\u092f\u093e\u092e\u094b\u091f\u094b<\/i><\/b> \u0926\u094d\u0935\u093e\u0930\u093e \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0925\u093e\u0964 \u0907\u0928 \u092a\u0939\u0947\u0932\u093f\u092f\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0909\u0928\u094d\u0939\u094b\u0902\u0928\u0947 \u0905\u092a\u0928\u0947 \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u093f\u092f\u094b\u0902 \u0915\u0947 \u0938\u0940\u0916\u0928\u0947 \u0915\u0947 \u0909\u092a\u0915\u0930\u0923 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0915\u093f\u092f\u093e \u0925\u093e\u0964 \u0915\u0947\u0928\u0915\u0947\u0928 \u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u0948 \u091a\u0924\u0941\u0930\u093e\u0908 \u0914\u0930 \u0907\u0938\u0940 \u0924\u0930\u094d\u095b \u092a\u0930 \u0939\u0930\u092c\u0928\u094d\u0938 \u092a\u0939\u0947\u0932\u0940 \u2018\u0939\u0930 \u092c\u0928\u094d\u0926\u093e \u0938\u092e\u091d\u0926\u093e\u0930\u2019 (\u0938\u094d\u0925\u093e\u0928\u0940\u092f \u0939\u0930\u093f\u092f\u093e\u0923\u0935\u0940 \u092d\u093e\u0937\u093e \u092e\u0947\u0902 \u092a\u094d\u0930\u092f\u0941\u0915\u094d\u0924 \u0939\u094b\u0928\u0947 \u0935\u093e\u0932\u093e \u0935\u093e\u0915\u094d\u092f\u093e\u0902\u0936) \u0915\u093e \u0938\u0902\u0915\u094d\u0937\u093f\u092a\u094d\u0924 \u0928\u093e\u092e \u0939\u0948, \u091c\u093f\u0938\u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u0948 \u0915\u093f \u0939\u0930 \u0915\u094b\u0908 \u0915\u0941\u091b \u092d\u0940 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0915\u094d\u0937\u092e\u0924\u093e \u0930\u0916\u0924\u093e \u0939\u0948\u0964<\/p><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u0915\u0947\u0928\u0915\u0947\u0928 \u092a\u0939\u0947\u0932\u0940 \u0938\u0947 \u0936\u0941\u0930\u0941\u0906\u0924 \u0915\u0930\u0928\u093e<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u0907\u0928 \u092a\u0939\u0947\u0932\u093f\u092f\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 \u0916\u0947\u0932\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f 3 \u00d7 3 \u092f\u093e 4 \u00d7 4 \u092f\u093e 5 \u00d7 5&#8230;.. \u0906\u0915\u093e\u0930 \u0915\u0940 \u090f\u0915 \u0917\u094d\u0930\u093f\u0921 \u0932\u0947\u0902\u0964<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"164\" height=\"164\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-fig1.png\" alt=\"harbans-fig1\" class=\"wp-image-27496\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-fig1.png 164w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-fig1-150x150.png?crop=1 150w\" sizes=\"auto, (max-width: 164px) 100vw, 164px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u0907\u0938 \u092a\u0939\u0947\u0932\u0940 \u0915\u093e \u0932\u0915\u094d\u0937\u094d\u092f \u0939\u094b\u0917\u093e \u092a\u0942\u0930\u0940 \u0917\u094d\u0930\u093f\u0921 \u0915\u094b \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0938\u0947 \u092d\u0930\u0928\u093e \u0914\u0930 \u092f\u0939 \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u0930\u0928\u093e \u0915\u093f \u0915\u093f\u0938\u0940 \u092d\u0940 \u092a\u0902\u0915\u094d\u0924\u093f \u092f\u093e \u0938\u094d\u0924\u092e\u094d\u092d \u092e\u0947\u0902 \u0915\u094b\u0908 \u092d\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0926\u094b\u0939\u0930\u093e\u0908 \u0928 \u091c\u093e\u090f\u0964 3\u00d73 \u0915\u0940 \u0907\u0938 \u0917\u094d\u0930\u093f\u0921 \u092e\u0947\u0902 \u0939\u092e \u0915\u0947\u0935\u0932 \u0924\u0940\u0928 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 1, 2 \u0935 3 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0917\u0947\u0964 4 \u00d7 4 \u0915\u0940 \u0917\u094d\u0930\u093f\u0921 \u0935\u093e\u0932\u0940 \u092a\u0939\u0947\u0932\u0940 \u092e\u0947\u0902 \u0939\u092e 1, 2, 3 \u0935 4 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0917\u0947; 5\u00d75 \u0915\u0940 \u0917\u094d\u0930\u093f\u0921 \u092e\u0947\u0902 \u0938\u0902\u0916\u094d\u092f\u093e 1, 2, 3, 4 \u0935 5 \u0915\u093e \u0914\u0930 \u0907\u0938\u0940 \u0924\u0930\u0939 \u092f\u0939 \u0906\u0917\u0947 \u092d\u0940 \u091c\u093e\u0930\u0940 \u0930\u0939\u0947\u0917\u093e\u0964 \u092e\u094b\u091f\u0940 \u0930\u0947\u0916\u093e \u0938\u0947 \u092c\u0928\u0947 \u0915\u094d\u0937\u0947\u0924\u094d\u0930 \u0915\u094b \u092a\u093f\u0902\u091c\u0930\u093e (\u0938\u092e\u0942\u0939 \u092c\u0949\u0915\u094d\u0938) \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0938\u092e\u0942\u0939 \u092c\u0949\u0915\u094d\u0938 \u0915\u0947 \u0936\u0940\u0930\u094d\u0937 \u092c\u093e\u090f\u0901 \u0915\u094b\u0928\u0947 \u092e\u0947\u0902 \u090f\u0915 \u2018\u0932\u0915\u094d\u0937\u094d\u092f \u0938\u0902\u0916\u094d\u092f\u093e\u2019 \u0914\u0930 \u090f\u0915 \u0917\u0923\u093f\u0924\u0940\u092f \u0938\u0902\u0915\u094d\u0930\u093f\u092f\u093e \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u0906\u092a\u0915\u0947 \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u093f\u0902\u091c\u0930\u0947 \u0915\u0947 \u0935\u0930\u094d\u0917\u094b\u0902 \u092e\u0947\u0902 \u0926\u0930\u094d\u091c \u0915\u0940 \u0917\u0908 \u0938\u0902\u0916\u094d\u200d\u092f\u093e\u090f\u0901 (\u0915\u093f\u0938\u0940 \u092d\u0940 \u0915\u094d\u0930\u092e \u092e\u0947\u0902) \u0910\u0938\u0940 \u0939\u094b\u0928\u0940 \u091a\u093e\u0939\u093f\u090f \u0915\u093f \u0938\u0942\u091a\u093f\u0924 \u0938\u0902\u0915\u094d\u0930\u093f\u092f\u093e (+, -, \u00d7 \u092f\u093e \u00f7) \u0915\u0947 \u0938\u093e\u0925 \u0909\u0928\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0932\u0915\u094d\u0937\u094d\u092f \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0947\u0964 \u090f\u0915 \u0935\u0930\u094d\u0917 \u0935\u093e\u0932\u0947 \u092a\u093f\u0902\u091c\u0930\u0947 \u0915\u094b \u2018\u092b\u094d\u0930\u0940\u092c\u0940\u2019 (single box) \u0928\u093e\u092e \u0926\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964 \u092b\u094d\u0930\u0940\u092c\u0940 \u092e\u0947\u0902 \u0909\u0938\u0940 \u0938\u0902\u0916\u094d\u200d\u092f\u093e \u0915\u094b \u092d\u0930\u0947\u0902 \u091c\u094b \u092c\u0949\u0915\u094d\u0938 \u092e\u0947\u0902 \u0926\u0940 \u0917\u0908 \u0939\u0948\u0964 \u092f\u093e\u0926 \u0930\u0916\u0947\u0902! \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u090f\u0915 \u0939\u0940 \u092a\u0902\u0915\u094d\u0924\u093f \u092f\u093e \u0938\u094d\u0924\u092e\u094d\u092d \u0915\u0947 \u092d\u0940\u0924\u0930 \u0926\u094b\u0939\u0930\u093e\u092f\u093e \u0928\u0939\u0940\u0902 \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u091c\u0948\u0938\u0947 \u0915\u093f \u2018\u0938\u0941\u0921\u094b\u0915\u0942\u2019 \u092e\u0947\u0902 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/p>\n\n\n\n<p><p>\u0936\u0941\u0930\u0941\u0906\u0924 \u092e\u0947\u0902, \u0939\u092e \u090a\u092a\u0930 \u0926\u093f\u0916\u093e\u0908 \u0917\u0908 3 \u00d7 3 \u0915\u0940 \u0917\u094d\u0930\u093f\u0921 \u0932\u0947\u0924\u0947 \u0939\u0948\u0902\u0964 \u092a\u0939\u0932\u0947 \u092a\u093f\u0902\u091c\u0930\u0947 \u092e\u0947\u0902, \u0909\u092a\u092f\u094b\u0917 \u0915\u0940 \u091c\u093e\u0928\u0947 \u0935\u093e\u0932\u0940 \u0917\u0923\u093f\u0924\u0940\u092f \u0938\u0902\u0915\u094d\u0930\u093f\u092f\u093e <strong>\u091c\u094b\u0921\u093c<\/strong> \u0939\u0948 \u0914\u0930 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u093e \u092f\u094b\u0917\u092b\u0932 5 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964 \u091a\u0942\u0901\u0915\u093f \u0907\u0938 \u0938\u092e\u0942\u0939 \u092c\u0949\u0915\u094d\u0938 \u092e\u0947\u0902 2 \u0935\u0930\u094d\u0917 \u0939\u0948\u0902, \u0907\u0938\u0932\u093f\u090f \u092f\u0939\u093e\u0901 \u0926\u094b \u0938\u092e\u094d\u092d\u093e\u0935\u0928\u093e\u090f\u0901 \u0939\u0948\u0902 2 \u0914\u0930 3, \u091c\u093f\u0928\u094d\u0939\u0947\u0902 \u0915\u093f\u0938\u0940 \u092d\u0940 \u0915\u094d\u0930\u092e \u092e\u0947\u0902 \u0930\u0916\u093e \u091c\u093e \u0938\u0915\u0924\u093e (3 + 2 \u092f\u093e 2 + 3 = 5)\u0964<\/p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"511\" height=\"301\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-fig2-1.png\" alt=\"harbans-fig2\" class=\"wp-image-27448\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-fig2-1.png 511w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-fig2-1-343x202.png 343w\" sizes=\"auto, (max-width: 511px) 100vw, 511px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\u0924\u094b, \u0936\u0941\u0930\u0942 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902<\/h2>\n\n\n\n<ol class=\"wp-block-list mb-0\">\n<li class=\"mb-0\">\u092b\u094d\u0930\u0940\u092c\u0940 (single box) \u092e\u0947\u0902 3 \u0926\u0930\u094d\u091c \u0915\u0930\u0947\u0902\u0964 \u090f\u0915\u0932 \u0935\u0930\u094d\u0917 \u0938\u0947 \u0936\u0941\u0930\u0942 \u0915\u0930\u0928\u093e \u0939\u092e\u0947\u0936\u093e \u0938\u092c\u0938\u0947 \u0905\u091a\u094d\u091b\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/li>\n<\/ol>\n\n\n\n<p class=\"has-text-align-left mb-0 has-custom-css wp-custom-css-bbc56ef3 wp-block-paragraph\">\u091a\u0930\u0923 1<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"158\" height=\"159\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-step1.png\" alt=\"harbans-step1\" class=\"wp-image-27502\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-step1.png 158w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-step1-150x150.png?crop=1 150w\" sizes=\"auto, (max-width: 158px) 100vw, 158px\" \/><\/figure>\n\n\n\n<ol start=\"2\" class=\"wp-block-list mb-0\">\n<li class=\"mb-0\">4 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0928\u093f\u091a\u0932\u0947-\u092c\u093e\u090f\u0901 \u0938\u092e\u0942\u0939 \u092c\u0949\u0915\u094d\u0938 \u0915\u0947 \u0928\u0940\u091a\u0947 \u0935\u093e\u0932\u0947 \u0935\u0930\u094d\u0917 \u092e\u0947\u0902 1 \u0914\u0930 \u090a\u092a\u0930 \u0935\u093e\u0932\u0947 \u0935\u0930\u094d\u0917 \u092e\u0947\u0902 3 \u092d\u0930\u093e \u091c\u093e\u0928\u093e \u091a\u093e\u0939\u093f\u090f \u0915\u094d\u200d\u092f\u094b\u0902\u0915\u093f 3 \u092a\u0939\u0932\u0947 \u0938\u0947 \u0939\u0940 \u0905\u0928\u094d\u0924\u093f\u092e \u092a\u0902\u0915\u094d\u0924\u093f \u092e\u0947\u0902 \u092d\u0930\u093e \u0939\u0941\u0906 \u0939\u0948, \u091c\u0948\u0938\u093e \u0915\u093f \u091a\u093f\u0924\u094d\u0930 \u092e\u0947\u0902 \u0926\u093f\u0916\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964<\/li>\n<\/ol>\n\n\n\n<p class=\"mb-0 has-custom-css wp-custom-css-eff47ea4 wp-block-paragraph\">\u091a\u0930\u0923 2<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"163\" height=\"165\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-step2.png\" alt=\"harbans-step2\" class=\"wp-image-27439\"\/><\/figure>\n\n\n\n<ol start=\"3\" class=\"wp-block-list mb-0\">\n<li class=\"mb-0\">\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092a\u0902\u0915\u094d\u0924\u093f \u0914\u0930 \u0938\u094d\u0924\u092e\u094d\u092d \u092e\u0947\u0902 1, 2 \u0914\u0930 3 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964 \u0928\u093f\u091a\u0932\u0940 \u092a\u0902\u0915\u094d\u0924\u093f \u092e\u0947\u0902 1 \u0914\u0930 3 \u092a\u0939\u0932\u0947 \u0938\u0947 \u0939\u0940 \u0939\u0948\u0902, \u0907\u0938\u0932\u093f\u090f \u0928\u093f\u091a\u0932\u0940 \u092a\u0902\u0915\u094d\u0924\u093f \u0915\u0947 \u092c\u0940\u091a \u0935\u093e\u0932\u0947 \u0935\u0930\u094d\u0917 \u0914\u0930 \u0936\u0940\u0930\u094d\u0937 \u092c\u093e\u090f\u0901 \u0935\u0930\u094d\u0917 \u092e\u0947\u0902 \u092d\u0930\u0947 \u091c\u093e\u0928\u093e \u0935\u093e\u0932\u093e \u090f\u0915\u092e\u093e\u0924\u094d\u0930 \u0935\u093f\u0915\u0932\u094d\u092a 2 \u0939\u0948\u0964 \u092b\u093f\u0930 \u0936\u0940\u0930\u094d\u0937 \u092a\u0902\u0915\u094d\u0924\u093f \u0915\u0947 \u092c\u0940\u091a \u0935\u093e\u0932\u0947 \u0935\u0930\u094d\u0917 \u092e\u0947\u0902 3 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f \u0914\u0930 \u0907\u0938\u0915\u0947 \u0938\u093e\u0925 \u0939\u0940 \u0936\u0940\u0930\u094d\u0937 \u092a\u093f\u0902\u091c\u0930\u093e \u092a\u0942\u0930\u093e \u092d\u0930 \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/li>\n<\/ol>\n\n\n\n<p class=\"mb-0 has-custom-css wp-custom-css-21089160 wp-block-paragraph\">\u091a\u0930\u0923 3<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"165\" height=\"168\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-step3.jpg\" alt=\"harbans-step3\" class=\"wp-image-27442\"\/><\/figure>\n\n\n\n<ol start=\"4\" class=\"wp-block-list mb-0\">\n<li class=\"mb-0\">\u0905\u092c \u0939\u092e \u0907\u0938\u0940 \u0924\u0930\u094d\u0915 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0926\u093e\u0908\u0902 \u0913\u0930 \u0915\u0947 \u0938\u094d\u200d\u0924\u092e\u094d\u200d\u092d \u0915\u0947 \u092a\u0939\u0932\u0947 \u0914\u0930 \u0926\u0942\u0938\u0930\u0947 \u0935\u0930\u094d\u0917\u094b\u0902 \u092e\u0947\u0902 1 \u0914\u0930 2 \u092d\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/li>\n<\/ol>\n\n\n\n<p class=\"mb-0 has-custom-css wp-custom-css-5bde3b4e wp-block-paragraph\">\u091a\u0930\u0923 4<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"165\" height=\"166\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-step4.jpg\" alt=\"harbans-step4\" class=\"wp-image-27445\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-step4.jpg 165w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-step4-150x150.jpg?crop=1 150w\" sizes=\"auto, (max-width: 165px) 100vw, 165px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\u0906\u0907\u090f \u0905\u092c \u0939\u092e \u0939\u0930\u092c\u0928\u094d\u0938 \u092a\u0939\u0947\u0932\u0940 \u092a\u0930 \u091a\u0932\u0924\u0947 \u0939\u0948\u0902<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u0915\u0947\u0928\u0915\u0947\u0928 \u092a\u0939\u0947\u0932\u0940 \u0915\u093e \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0939\u092e \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 (\u0915\u094d\u0930\u092e\u093e\u0917\u0924 \u092f\u093e \u0905\u0915\u094d\u0930\u092e\u093e\u0917\u0924) \u0915\u0947 \u090f\u0915 \u092f\u093e\u0926\u0943\u091a\u094d\u091b\u093f\u0915 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0914\u0930 \u0909\u0928 \u092a\u0930 \u0938\u0902\u0915\u094d\u0930\u093f\u092f\u093e\u0913\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 3\u00d73 \u0915\u0940 \u092a\u0939\u0947\u0932\u0940 \u092e\u0947\u0902 \u0906\u092a 0, 1, 2 \u092f\u093e 1, 2, 3 \u092f\u093e 10, 20, 30 \u092f\u093e \u0924\u0940\u0928 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915\u094b\u0902\/\u0905\u092d\u093e\u091c\u094d\u200d\u092f \u0938\u0902\u0916\u094d\u200d\u092f\u093e\u0913\u0902\/\u0938\u092e \u0938\u0902\u0916\u094d\u200d\u092f\u093e\u0913\u0902\/\u0935\u093f\u0937\u092e \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u092f\u0939 \u0938\u0902\u0916\u094d\u200d\u092f\u093e\u090f\u0901 \u0938\u092e\u093e\u0928 \u0926\u0942\u0930\u0940 \u092a\u0930 (these need not be equally spaced) \u0939\u094b\u0902 \u092f\u0939 \u091c\u093c\u0930\u0942\u0930\u0940 \u0928\u0939\u0940\u0902 \u0939\u0948\u0964 \u0907\u0938\u0940 \u0924\u0930\u0939 4\u00d74 \u0915\u0940 \u092a\u0939\u0947\u0932\u0940 \u0915\u0947 \u0932\u093f\u090f \u0939\u092e \u0915\u093f\u0928\u094d\u0939\u0940\u0902 \u092d\u0940 \u091a\u093e\u0930 \u0930\u0947\u0902\u0921\u092e \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u093e \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0932\u0947 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u0914\u0930 \u0907\u0938\u0940 \u0924\u0930\u0939 \u092f\u0939 \u0906\u0917\u0947 \u092d\u0940 \u091c\u093e\u0930\u0940 \u0930\u0939\u0947\u0917\u093e\u0964 \u0939\u092e \u0915\u0941\u091b \u0909\u0926\u093e\u0939\u0930\u0923\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0907\u0938\u0947 \u0938\u094d\u092a\u0937\u094d\u091f \u0915\u0930\u0947\u0902\u0917\u0947\u0964<\/p>\n\n\n\n<p><p><strong>\u0909\u0926\u093e\u0939\u0930\u0923 1<\/strong><\/p><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">3\u00d73 \u0915\u0940 \u0907\u0938 \u092a\u0939\u0947\u0932\u0940 \u092e\u0947\u0902 \u0939\u092e \u0938\u0902\u0916\u094d\u092f\u093e 10, 20, 30 \u0914\u0930 \u091c\u094b\u0921\u093c \u0914\u0930 \u0918\u091f\u093e\u0935 \u0915\u0940 \u0938\u0902\u0915\u094d\u0930\u093f\u092f\u093e\u0913\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0917\u0947\u0964 \u090f\u0915\u0932 \u0935\u0930\u094d\u0917 \u092e\u0947\u0902 \u0938\u0902\u0916\u094d\u200d\u092f\u093e 30 \u092d\u0930\u0947\u0902\u0964<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u090f\u0915\u0932 \u0935\u0930\u094d\u0917 \u0938\u0947 \u0936\u0941\u0930\u0942 \u0915\u0930\u0928\u093e \u0939\u092e\u0947\u0936\u093e \u0938\u092c\u0938\u0947 \u0905\u091a\u094d\u091b\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"181\" height=\"195\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-illustration1.1.png\" alt=\"harbans-illustration1.1\" class=\"wp-image-27463\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u092b\u093f\u0930 \u0915\u0947\u0928\u0915\u0947\u0928 \u092a\u0939\u0947\u0932\u0940 \u0915\u0947 \u091c\u0948\u0938\u0947 \u0928\u093f\u092f\u092e\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f \u0939\u092e \u0932\u0915\u094d\u0937\u094d\u092f \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0926\u0940 \u0917\u0908 \u0938\u0902\u0915\u094d\u0930\u093f\u092f\u093e \u0915\u0947 \u0938\u093e\u0925 10, 20 \u0914\u0930 30 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0917\u094d\u0930\u093f\u0921 \u0915\u094b \u092d\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"180\" height=\"196\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-illustration1.2.png\" alt=\"harbans-illustration1.2\" class=\"wp-image-27466\"\/><\/figure>\n\n\n\n<p><p><strong>\u0909\u0926\u093e\u0939\u0930\u0923 2<\/strong><\/p><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1 \u0938\u0947 5 \u0924\u0915 \u0915\u0940 \u0915\u093f\u0928\u094d\u0939\u0940\u0902 \u0924\u0940\u0928 \u0915\u094d\u0930\u092e\u093e\u0917\u0924 \u0938\u0902\u0916\u094d\u200d\u092f\u093e\u0913\u0902 (consecutive numbers) \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902 (\u0938\u094b\u091a\u0947\u0902 \u0914\u0930 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u091a\u0941\u0928\u0947\u0902)\u0964<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"177\" height=\"193\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-illustration2.png\" alt=\"harbans-illustration2\" class=\"wp-image-27469\"\/><\/figure>\n\n\n\n<p><p><strong>\u0909\u0926\u093e\u0939\u0930\u0923 3<\/strong><\/p><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1 \u0938\u0947 15 \u0924\u0915 \u0915\u0940 \u0924\u0940\u0928 \u0915\u094d\u0930\u092e\u093e\u0917\u0924 \u0938\u092e \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0964<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"368\" height=\"194\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-illustration3.png\" alt=\"harbans-illustration3\" class=\"wp-image-27472\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-illustration3.png 368w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-illustration3-360x190.png 360w\" sizes=\"auto, (max-width: 368px) 100vw, 368px\" \/><\/figure>\n\n\n\n<p><strong>\u0909\u0926\u093e\u0939\u0930\u0923 4<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1 \u0938\u0947 10 \u0924\u0915 \u0915\u0940 \u0915\u093f\u0928\u094d\u0939\u0940\u0902 3 \u0905\u092d\u093e\u091c\u094d\u200d\u092f \u0938\u0902\u0916\u094d\u200d\u092f\u093e\u0913\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0964<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"180\" height=\"194\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-illustration4.png\" alt=\"harbans-illustration4\" class=\"wp-image-27475\"\/><\/figure>\n\n\n\n<p><strong>\u0909\u0926\u093e\u0939\u0930\u0923 5<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">-5 \u0914\u0930 5 \u0915\u0947 \u092c\u0940\u091a \u0915\u0947 3 \u0915\u094d\u0930\u092e\u093e\u0917\u0924 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0964<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"176\" height=\"191\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-illustration5.png\" alt=\"harbans-illustration5\" class=\"wp-image-27478\"\/><\/figure>\n\n\n\n<p><strong>\u0909\u0926\u093e\u0939\u0930\u0923 6<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">3 \u092d\u093f\u0928\u094d\u200d\u0928\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902 : 1\/1, 1\/2, 1\/3<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-illustration6.png\" alt=\"harbans-illustration6\" class=\"wp-image-27481\"\/><\/figure>\n\n\n\n<p><strong>\u0909\u0926\u093e\u0939\u0930\u0923 7<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">3 \u092d\u093f\u0928\u094d\u200d\u0928\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902 : 1\/1, 1\/2, 1\/3<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"178\" height=\"194\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-illustration7.png\" alt=\"harbans-illustration7\" class=\"wp-image-27484\"\/><\/figure>\n\n\n\n<p><strong>\u0909\u0926\u093e\u0939\u0930\u0923 8<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(i) \u0909\u092a\u092f\u094b\u0917 \u0915\u0940 \u091c\u093e\u0928\u0947 \u0935\u093e\u0932\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u091a\u0941\u0928\u0947\u0902 \u0914\u0930 \u0909\u0928\u094d\u0939\u0947\u0902 \\(x\\), \\(y\\) \u0914\u0930 \\(z\\) \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092e\u093e\u0928\u0947\u0902; \u092f\u0939\u093e\u0901 \u0938\u0902\u0915\u094d\u0930\u093f\u092f\u093e\u0913\u0902 \u0915\u094b \u092a\u0940\u0932\u0947 \u0930\u0902\u0917 \u0938\u0947 \u0939\u093e\u0907\u0932\u093e\u0907\u091f \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948 \u0914\u0930 \u092a\u0930\u093f\u0923\u093e\u092e \u0915\u094b \u0907\u0928\u0938\u0947 \u092a\u0939\u0932\u0947 \u0932\u093f\u0916\u093e \u0917\u092f\u093e \u0939\u0948\u0964 (ii) -5 \u0938\u0947 5 \u0924\u0915 \u0915\u0947 3 \u0915\u094d\u0930\u092e\u093e\u0917\u0924 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0964<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"175\" height=\"191\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-illustration8.png\" alt=\"harbans-illustration8\" class=\"wp-image-27487\"\/><\/figure>\n\n\n\n<p><strong>\u0909\u0926\u093e\u0939\u0930\u0923 9<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0909\u0928 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u093e \u091a\u092f\u0928 \u0915\u0930\u0947\u0902 \u091c\u093f\u0928\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0907\u0938 \u092a\u0939\u0947\u0932\u0940 \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"178\" height=\"196\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-illustration9.png\" alt=\"harbans-illustration9\" class=\"wp-image-27490\"\/><\/figure>\n\n\n\n<p><\/p><p><strong>\u0909\u0926\u093e\u0939\u0930\u0923 10<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1\/\\(x\\), \\(x\\), \\(x\\)<sup>2<\/sup> \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0964<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"176\" height=\"192\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-illustration10.png\" alt=\"harbans-illustration10\" class=\"wp-image-27493\"\/><\/figure>\n\n\n\n<p><p>\u092f\u0939\u093e\u0901 \u0939\u092e \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0915\u0948\u0938\u0947 \u0939\u0930\u092c\u0928\u094d\u0938 \u092a\u0939\u0947\u0932\u093f\u092f\u093e\u0901 \u0915\u0947\u0928\u0915\u0947\u0928 \u092a\u0939\u0947\u0932\u093f\u092f\u094b\u0902 \u0938\u0947 \u0905\u0932\u0917 \u0939\u0948\u0902\u0964 \u0939\u0930\u092c\u0928\u094d\u0938 \u092a\u0939\u0947\u0932\u093f\u092f\u094b\u0902 \u092e\u0947\u0902 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0938\u0902\u0915\u094d\u0930\u093f\u092f\u093e\u0913\u0902 \u0915\u0947 \u0938\u093e\u0925 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0947 \u0938\u0902\u0916\u094d\u092f\u093e \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u091c\u0948\u0938\u0947 \u0915\u093f 10 \u0915\u0947 \u0917\u0941\u0923\u091c, \u0938\u092e \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901, \u0935\u093f\u0937\u092e \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901, \u0926\u0936\u092e\u0932\u0935, \u092d\u093f\u0928\u094d\u200d\u0928, \u092a\u0942\u0930\u094d\u0923 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901, \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915, \u091a\u0930 \u0907\u0924\u094d\u092f\u093e\u0926\u093f\u0964 \u0907\u0938\u0915\u0947 \u0905\u0932\u093e\u0935\u093e \u0906\u0938\u093e\u0928 \u092d\u093e\u0937\u093e \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u2018\u092a\u093f\u0902\u091c\u0930\u093e\u2019 \u0928\u093e\u092e \u0915\u094b \u2018\u0938\u092e\u0942\u0939 \u092c\u0949\u0915\u094d\u0938\u2019 \u0914\u0930 \u2018\u092b\u094d\u0930\u0940\u092c\u0940\u2019 \u0915\u094b \u2018\u090f\u0915\u0932 \u092c\u0949\u0915\u094d\u0938\u2019 \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u094d\u0930\u0924\u093f\u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964 \u0915\u094b\u0908 \u092d\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u093f\u0938\u0940 \u092d\u0940 \u092a\u0902\u0915\u094d\u0924\u093f \u092f\u093e \u0938\u094d\u200d\u0924\u092e\u094d\u092d \u092e\u0947\u0902 \u0926\u094b\u0939\u0930\u093e\u0908 \u0928\u0939\u0940\u0902 \u091c\u093e\u090f\u0917\u0940, \u092f\u0939 \u0928\u093f\u092f\u092e <em>\u0939\u0930\u092c\u0928\u094d\u0938 \u092a\u0939\u0947\u0932\u093f\u092f\u094b\u0902<\/em> \u0914\u0930 <em>\u0915\u0947\u0928\u0915\u0947\u0928<\/em> \u092a\u0939\u0947\u0932\u093f\u092f\u094b\u0902 \u0926\u094b\u0928\u094b\u0902 \u092e\u0947\u0902 \u0938\u092e\u093e\u0928 \u0939\u0948 \u0914\u0930 \u092a\u094d\u0930\u0924\u0940\u0915\u093e\u0924\u094d\u092e\u0915 \u0928\u093f\u0930\u0942\u092a\u0923 \u092d\u0940 \u0938\u092e\u093e\u0928 \u0939\u0948, \u092f\u093e\u0928\u0940 \u0932\u0915\u094d\u0937\u094d\u092f \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b \u0938\u0902\u0915\u094d\u0930\u093f\u092f\u093e \u0915\u0947 \u0938\u093e\u0925 \u092c\u0949\u0915\u094d\u0938 \u0915\u0947 \u0936\u0940\u0930\u094d\u0937 \u092a\u0930 \u0932\u093f\u0916\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0915\u0947 \u0905\u0932\u093e\u0935\u093e, \u0916\u093c\u093e\u0928\u094b\u0902 (cells) \u0915\u0940 \u0905\u0932\u0917-\u0905\u0932\u0917 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0932\u093f\u090f \u0939\u092e \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0947 \u092a\u093f\u0902\u091c\u0930\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u0928\u0940\u091a\u0947 \u0915\u0941\u091b \u092a\u0939\u0947\u0932\u093f\u092f\u094b\u0902 \u0915\u0947 \u0909\u0926\u093e\u0939\u0930\u0923 \u0926\u093f\u0916\u093e\u090f \u0917\u090f \u0939\u0948\u0902 \u091c\u093f\u0928\u092e\u0947\u0902 \u0926\u094b \u0938\u0947 \u0905\u0927\u093f\u0915 \u0916\u093c\u093e\u0928\u094b\u0902 \u0935\u093e\u0932\u0947 \u092a\u093f\u0902\u091c\u0930\u0947 \u0939\u0948\u0902\u0964<\/p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"176\" height=\"402\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-fig-3.png\" alt=\"harbans-fig-3\" class=\"wp-image-27451\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-fig-3.png 176w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-fig-3-158x360.png 158w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-fig-3-88x202.png 88w\" sizes=\"auto, (max-width: 176px) 100vw, 176px\" \/><\/figure>\n\n\n\n<p><p><strong>\u0938\u092d\u0940 \u0909\u092e\u094d\u0930 \u0915\u0947 \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u093f\u092f\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 \u0907\u0938\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0907\u0938 \u092a\u0939\u0947\u0932\u0940 \u0915\u0947 \u091b\u093f\u092a\u0947 \u0939\u0941\u090f \u092a\u0948\u091f\u0930\u094d\u0928\u094b\u0902 \u0914\u0930 \u0938\u092e\u094d\u092d\u093e\u0935\u0928\u093e\u0913\u0902 \u0915\u0940 \u092a\u0921\u093c\u0924\u093e\u0932 \u0915\u0930\u0928\u093e<\/strong><\/p><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u091c\u092c \u0939\u092e \u092a\u0939\u0947\u0932\u093f\u092f\u094b\u0902 \u0915\u0940 \u092a\u0921\u093c\u0924\u093e\u0932 \u0915\u0930 \u0930\u0939\u0947 \u0925\u0947, \u0924\u092c \u0907\u0928 \u092a\u0939\u0947\u0932\u093f\u092f\u094b\u0902 \u0915\u094b \u092c\u0928\u093e\u0928\u0947 \u0914\u0930 \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0926\u094c\u0930\u093e\u0928 \u0915\u0908 \u092a\u0948\u091f\u0930\u094d\u0928 \u0939\u092e\u093e\u0930\u0947 \u0938\u093e\u092e\u0928\u0947 \u0906\u090f\u0964 \u0939\u092e\u0928\u0947 \u092e\u0939\u0938\u0942\u0938 \u0915\u093f\u092f\u093e \u0915\u093f \u0907\u0938 \u0924\u0930\u0939 \u0915\u0940 \u092a\u0939\u0947\u0932\u093f\u092f\u093e\u0901 \u0932\u094b \u092b\u094d\u0932\u094b\u0930 \u0939\u093e\u0908 \u0938\u0940\u0932\u093f\u0902\u0917 \u091f\u0949\u0938\u094d\u200d\u0915 (\u092f\u093e\u0928\u0940 \u0915\u093f \u0907\u0928\u092e\u0947\u0902 \u0915\u0920\u093f\u0928\u093e\u0908 \u0915\u093e \u0938\u094d\u0924\u0930 \u092c\u0922\u093c\u0924\u093e \u091a\u0932\u093e \u091c\u093e\u0924\u093e \u0939\u0948) \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0915\u093e\u092e \u0915\u0930\u0924\u0940 \u0939\u0948\u0902 \u0914\u0930 \u092c\u091a\u094d\u200d\u091a\u094b\u0902 \u0915\u0947 \u0915\u092e\u094d\u092a\u094d\u092f\u0942\u091f\u0947\u0936\u0928\u0932 \u091a\u093f\u0928\u094d\u0924\u0928 \u0915\u094c\u0936\u0932 \u0915\u094b \u092d\u0940 \u092c\u0922\u093c\u093e\u0935\u093e \u0926\u0947\u0924\u0940 \u0939\u0948\u0902\u0964 \u0905\u092a\u0928\u0947 \u0915\u0925\u0928 \u0915\u093e \u0938\u092e\u0930\u094d\u0925\u0928 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0939\u092e 3 \u00d7 3 \u0915\u0940 \u0917\u094d\u0930\u093f\u0921 \u092e\u0947\u0902 \u0926\u0947\u0916\u0947 \u0917\u090f \u092a\u0948\u091f\u0930\u094d\u0928 \u0914\u0930 3 \u00d7 3 \u0915\u0940 \u0917\u094d\u0930\u093f\u0921 \u0935\u093e\u0932\u0940 \u092a\u0939\u0947\u0932\u0940 \u092c\u0928\u093e\u0928\u0947 \u0915\u0940 \u0938\u092e\u094d\u092d\u093e\u0935\u0928\u093e\u0913\u0902 \u0915\u094b \u0938\u094d\u092a\u0937\u094d\u091f \u0915\u0930\u0947\u0902\u0917\u0947\u0964 \u0906\u0907\u090f \u0939\u092e 3 \u00d7 3 \u0917\u094d\u0930\u093f\u0921 \u092e\u0947\u0902 3 \u0938\u0902\u0916\u094d\u200d\u092f\u093e\u0913\u0902 0, 1 \u0935 2 \u0915\u094b \u092d\u0930\u0928\u0947 \u0915\u093e \u090f\u0915 \u0909\u0926\u093e\u0939\u0930\u0923 \u0932\u0947\u0902\u0964 \u0939\u092e \u0907\u0938 \u092c\u093e\u0924 \u0915\u093e \u0905\u0935\u0932\u094b\u0915\u0928 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0915\u094d\u0930\u092e\u091a\u092f (permutation) \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0917\u0923\u0928\u093e \u092d\u0940 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0938\u092e\u094d\u092d\u093e\u0935\u093f\u0924 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b \u092d\u0930\u0947 \u091c\u093e\u0928\u0947 \u0915\u0947 \u0915\u0941\u0932 12 \u0924\u0930\u0940\u0915\u093c\u0947 \u0939\u0948\u0902\u0964<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"554\" height=\"464\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/possibilitiesfig-4.png\" alt=\"possibilitiesfig 4\" class=\"wp-image-27509\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/possibilitiesfig-4.png 554w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/possibilitiesfig-4-430x360.png 430w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/possibilitiesfig-4-241x202.png 241w\" sizes=\"auto, (max-width: 554px) 100vw, 554px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u0939\u092e \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u092a\u0939\u0932\u0947 \u0935\u0930\u094d\u0917 \u0915\u094b 3 \u0938\u092e\u094d\u092d\u093e\u0935\u093f\u0924 \u0924\u0930\u0940\u0915\u093c\u094b\u0902 \u0938\u0947 \u092d\u0930\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u0926\u0942\u0938\u0930\u0947 \u0914\u0930 \u091a\u094c\u0925\u0947 \u0935\u0930\u094d\u0917\u094b\u0902 \u0915\u094b 2 \u0938\u092e\u094d\u092d\u093e\u0935\u093f\u0924 \u0924\u0930\u0940\u0915\u093c\u094b\u0902 \u0938\u0947 \u092d\u0930\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u092c\u093e\u0915\u093c\u0940 \u0935\u0930\u094d\u0917\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0915\u0947\u0935\u0932 \u090f\u0915 \u0939\u0940 \u0935\u093f\u0915\u0932\u094d\u092a \u092c\u091a\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0932\u093f\u090f, \u0938\u092e\u094d\u092d\u093e\u0935\u0928\u093e\u0913\u0902 \u0915\u0940 \u0915\u0941\u0932 \u0938\u0902\u0916\u094d\u092f\u093e 3 \u00d7 2 \u00d7 2 = 12 \u0939\u0948\u0964<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"177\" height=\"185\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-fig-5.png\" alt=\"harbans-fig-5\" class=\"wp-image-27499\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u092a\u093f\u0902\u091c\u0930\u094b\u0902 \u0914\u0930 \u0938\u0902\u0915\u094d\u0930\u093f\u092f\u093e\u0913\u0902 \u0915\u094b \u092c\u0926\u0932 \u0915\u0930\u0915\u0947 \u0938\u093f\u0930\u094d\u092b\u093c \u090f\u0915 \u0939\u0940 \u0917\u094d\u0930\u093f\u0921 \u0938\u0947 \u092a\u094d\u0930\u091a\u0941\u0930 \u092e\u093e\u0924\u094d\u0930\u093e \u092e\u0947\u0902 \u092a\u0939\u0947\u0932\u093f\u092f\u093e\u0901 \u092c\u0928\u093e\u0908 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948\u0902\u0964 \u091c\u092c \u092f\u0939 \u092a\u0939\u0947\u0932\u093f\u092f\u093e\u0901 \u0905\u0932\u0917-\u0905\u0932\u0917 \u0915\u0915\u094d\u0937\u093e\u0913\u0902 \u0915\u0947 \u092c\u091a\u094d\u200d\u091a\u094b\u0902 \u0915\u094b \u0926\u0940 \u0917\u0908\u0902, \u0924\u094b \u0939\u092e\u0928\u0947 \u092a\u093e\u092f\u093e \u0915\u093f \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u0940 \u0910\u0938\u0940 \u092a\u0939\u0947\u0932\u093f\u092f\u093e\u0901 \u092c\u0928\u093e\u0928\u0947 \u0914\u0930 \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0905\u0932\u0917-\u0905\u0932\u0917 \u0924\u0930\u0940\u0915\u093c\u0947 \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0925\u0947\u0964 \u0924\u0940\u0938\u0930\u0940 \u0914\u0930 \u091a\u094c\u0925\u0940 \u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0915\u0908 \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u093f\u092f\u094b\u0902 \u0928\u0947 \u092a\u0939\u0947\u0932\u0940 \u092c\u0928\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0932\u0915\u094d\u0937\u094d\u092f \u0938\u0902\u0916\u094d\u092f\u093e \u0932\u093f\u0916\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u2018\u0905\u0928\u0941\u092e\u093e\u0928 \u0914\u0930 \u0924\u094d\u0930\u0941\u091f\u093f\u2019 \u0915\u0940 \u0930\u0923\u0928\u0940\u0924\u093f \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u0914\u0930 \u0907\u0938\u0947 \u0939\u0932 \u0915\u0930\u0924\u0947 \u0938\u092e\u092f \u0905\u092a\u0928\u0940 \u0924\u094d\u0930\u0941\u091f\u093f\u092f\u094b\u0902 \u0915\u094b \u0920\u0940\u0915 \u0915\u093f\u092f\u093e\u0964 \u092a\u0939\u0947\u0932\u0940 \u092c\u0928\u093e\u0928\u0947 \u0915\u093e \u090f\u0915 \u0914\u0930 \u0924\u0930\u0940\u0915\u093c\u093e \u091c\u093f\u0938\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0924\u0940\u0938\u0930\u0940 \u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0926\u094b \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u093f\u092f\u094b\u0902 \u0928\u0947 \u0915\u093f\u092f\u093e, \u0935\u0939 \u0925\u093e \u2018\u0938\u092e\u093e\u0927\u093e\u0928 \u0938\u0947 \u092a\u0939\u0947\u0932\u0940 \u092c\u0928\u093e\u0928\u0947 \u0915\u0940 \u0930\u0923\u0928\u0940\u0924\u093f\u2019, \u092f\u093e\u0928\u0940 \u0909\u0928\u094d\u0939\u094b\u0902\u0928\u0947 \u0932\u0915\u094d\u0937\u094d\u092f \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0914\u0930 \u0909\u092a\u092f\u094b\u0917 \u0915\u0940 \u0917\u0908 \u0938\u0902\u0915\u094d\u0930\u093f\u092f\u093e\u0913\u0902 \u0924\u0915 \u092a\u0939\u0941\u0901\u091a\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0938\u092e\u093e\u0927\u093e\u0928 \u0938\u0947 \u0936\u0941\u0930\u0941\u0906\u0924 \u0915\u0940 (\u0932\u0947\u0915\u093f\u0928 \u0907\u0938\u0947 \u0905\u092a\u0928\u0940 \u092a\u0939\u0947\u0932\u0940 \u0936\u0940\u091f \u092e\u0947\u0902 \u0928\u0939\u0940\u0902 \u0932\u093f\u0916\u093e)\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \u0909\u0928\u094d\u0939\u094b\u0902\u0928\u0947 3 \u00d7 3 \u0915\u0940 \u0917\u094d\u0930\u093f\u0921 \u0915\u0940 \u092a\u0939\u0932\u0940 \u092a\u0902\u0915\u094d\u0924\u093f \u092e\u0947\u0902 1, 2, 3 \u0915\u094b \u0930\u0916\u0928\u0947 \u0915\u093e \u092b\u093c\u0948\u0938\u0932\u093e \u0915\u093f\u092f\u093e \u0914\u0930 \u092b\u093f\u0930 \u0932\u0915\u094d\u0937\u094d\u092f \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0947 \u0924\u094c\u0930 \u092a\u0930 1 \u0915\u094b \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f 3 \u092e\u0947\u0902 \u0938\u0947 2 \u0915\u094b \u0918\u091f\u093e \u0926\u093f\u092f\u093e\u0964 \u0907\u0938 \u0924\u0930\u0939 \u0909\u0928\u094d\u0939\u094b\u0902\u0928\u0947 \u0932\u0915\u094d\u0937\u094d\u092f \u0938\u0902\u0916\u094d\u092f\u093e 1 \u0914\u0930 \u0938\u0902\u0915\u094d\u0930\u093f\u092f\u093e \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u2018\u0918\u091f\u093e\u0928\u093e\u2019 \u0915\u0947 \u0938\u093e\u0925 2 \u0916\u093c\u093e\u0928\u094b\u0902 \u0935\u093e\u0932\u0947 \u090f\u0915 \u092a\u093f\u0902\u091c\u0930\u0947 \u0915\u093e \u0928\u093f\u0930\u094d\u092e\u093e\u0923 \u0915\u093f\u092f\u093e\u0964 \u0907\u0938 \u0924\u0930\u0939 \u0915\u0947 \u0905\u0935\u0938\u0930\u094b\u0902 \u0928\u0947 \u0909\u0928\u094d\u0939\u0947\u0902 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923\u093e\u0924\u094d\u092e\u0915 \u0914\u0930 \u0924\u093e\u0930\u094d\u0915\u093f\u0915 \u0930\u0942\u092a \u0938\u0947 \u0938\u094b\u091a\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092a\u094d\u0930\u0947\u0930\u093f\u0924 \u0915\u093f\u092f\u093e, \u091c\u094b \u0915\u093f \u092e\u0939\u0924\u094d\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0917\u0923\u093f\u0924\u0940\u092f \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e\u090f\u0901 \u0939\u0948\u0902\u0964 \u0907\u0938\u0915\u0947 \u0905\u0932\u093e\u0935\u093e, \u092a\u0939\u0947\u0932\u0940 \u092c\u0928\u093e\u0924\u0947 \u0938\u092e\u092f \u092f\u0939 \u0926\u0947\u0916\u093e \u0917\u092f\u093e \u0915\u093f \u0938\u093f\u0930\u094d\u092b\u093c \u090f\u0915 \u092a\u0939\u0947\u0932\u0940 \u0932\u0947\u0915\u0930 \u0939\u092e \u092a\u094d\u0930\u091a\u0941\u0930 \u092e\u093e\u0924\u094d\u0930\u093e \u092e\u0947\u0902 \u0907\u0938\u0915\u0947 \u0915\u0908 \u092d\u093f\u0928\u094d\u0928 \u0930\u0942\u092a \u092c\u0928\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n\n\n\n<p><p>\u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0915\u093f \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u090f\u0915 \u092a\u0939\u0947\u0932\u0940 \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 0, 1, 2 \u0938\u0902\u0916\u094d\u200d\u092f\u093e\u0913\u0902 \u0915\u094b \u092d\u0930\u0928\u093e \u0939\u0948 \u0914\u0930 \u0939\u092e 0, 1, 2 \u0915\u0947 \u092c\u091c\u093e\u092f 10, 20, 30 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u090f\u0915 \u0914\u0930 \u092a\u0939\u0947\u0932\u0940 \u092c\u0928\u093e\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902\u0964 \u092a\u0939\u0932\u0940 \u0932\u0915\u094d\u0937\u094d\u092f \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b \u0927\u094d\u200d\u092f\u093e\u0928-\u0938\u0947 \u0926\u0947\u0916\u0947\u0902, \u092f\u0939 1 \u0914\u0930 2 \u092f\u093e\u0928\u0940 \u0915\u093f \u0926\u0942\u0938\u0930\u0940 \u0914\u0930 \u0924\u0940\u0938\u0930\u0940 \u0938\u0902\u0916\u094d\u200d\u092f\u093e \u0915\u093e \u092f\u094b\u0917\u092b\u0932 \u0939\u0948\u0964 \u0907\u0938\u0932\u093f\u090f, \u0939\u092e 3<sup>+<\/sup> \u0915\u094b 50<sup>+<\/sup> \u0938\u0947 \u092c\u0926\u0932 \u0926\u0947\u0902\u0917\u0947 \u0915\u094d\u092f\u094b\u0902\u0915\u093f 50 \u0926\u0942\u0938\u0930\u0940 \u0914\u0930 \u0924\u0940\u0938\u0930\u0940 \u0938\u0902\u0916\u094d\u200d\u092f\u093e \u0915\u093e \u092f\u094b\u0917\u092b\u0932 \u0939\u0948\u0964 \u0907\u0938\u0940 \u0924\u0930\u0939, 1 \u0915\u094b 1 + 0, \u092f\u093e\u0928\u0940 \u0915\u093f \u092a\u0939\u0932\u0940 \u0914\u0930 \u0926\u0942\u0938\u0930\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u091c\u094b\u0921\u093c\u0915\u0930 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0932\u093f\u090f 1 \u0915\u094b 30, \u092f\u093e\u0928\u0940 \u0915\u093f 10 \u0914\u0930 20 \u0915\u0947 \u092f\u094b\u0917\u092b\u0932 \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u094d\u0930\u0924\u093f\u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u090f\u0917\u093e, \u091c\u0948\u0938\u093e \u0915\u093f \u0928\u0940\u091a\u0947 \u0926\u093f\u0916\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964<\/p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"177\" height=\"194\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-fig-6.png\" alt=\"harbans-fig-6\" class=\"wp-image-27457\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u0924\u094b, \u0939\u092e\u093e\u0930\u0940 \u0928\u0908 \u092a\u0939\u0947\u0932\u0940 \u0939\u094b\u0917\u0940\u2013<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"176\" height=\"193\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/08\/harbans-fig-7.png\" alt=\"harbans-fig-7\" class=\"wp-image-27460\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u0907\u0938 \u0924\u0930\u0939 \u0939\u092e \u0917\u094d\u0930\u093f\u0921 \u092e\u0947\u0902 \u092d\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u0928\u094d\u200d\u0939\u0940\u0902 \u092d\u0940 \u0924\u0940\u0928 \u0938\u0902\u0916\u094d\u200d\u092f\u093e\u0913\u0902 (\u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915, \u092d\u093f\u0928\u094d\u200d\u0928 \u0906\u0926\u093f) \u0915\u094b \u0932\u0947 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u092b\u093f\u0930 \u0909\u092a\u0930\u094b\u0915\u094d\u0924 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0932\u0915\u094d\u0937\u094d\u092f \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u092c\u0926\u0932 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u0906\u092a \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u090a\u092a\u0930 \u0926\u093f\u090f \u0917\u090f \u0938\u092d\u0940 \u0909\u0926\u093e\u0939\u0930\u0923 (1 \u0938\u0947 10) \u0915\u0947\u0935\u0932 \u090f\u0915 \u092a\u0939\u0947\u0932\u0940 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u092c\u0928\u093e\u090f \u0917\u090f \u0939\u0948\u0902\u0964 \u0907\u0928\u092e\u0947\u0902 \u092a\u093f\u0902\u091c\u0930\u094b\u0902 \u0915\u094b \u0938\u092e\u093e\u0928 \u0930\u0916\u0924\u0947 \u0939\u0941\u090f \u0932\u0915\u094d\u0937\u094d\u092f \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u092c\u0926\u0932 \u0926\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0907\u0938\u0915\u0947 \u0905\u0932\u093e\u0935\u093e 3 \u00d7 3 \u0915\u0940 \u0917\u094d\u0930\u093f\u0921 \u092e\u0947\u0902 \u0939\u092e \u0935\u093f\u0915\u0930\u094d\u0923 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u092e\u0947\u0902 \u092a\u0948\u091f\u0930\u094d\u0928 \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u090f\u0915 \u092c\u093e\u0930 \u092f\u0939 \u092a\u0948\u091f\u0930\u094d\u0928 \u0938\u092e\u091d \u0906 \u091c\u093e\u090f\u0901, \u0924\u094b \u092a\u0939\u0947\u0932\u0940 \u0915\u094b \u0915\u092e-\u0938\u0947-\u0915\u092e \u091a\u0930\u0923\u094b\u0902 \u092e\u0947\u0902 \u0939\u0932 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/p>\n\n\n\n<p><p><strong>\u092c\u091a\u094d\u200d\u091a\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0916\u094b\u091c-\u092c\u0940\u0928<\/strong><\/p><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0907\u0928 \u092a\u0939\u0947\u0932\u093f\u092f\u094b\u0902 \u0915\u094b \u0906\u0938\u093e\u0928\u0940 \u0938\u0947 \u0938\u094d\u0915\u0942\u0932 \u0915\u0940 \u092a\u093e\u0920\u094d\u092f\u091a\u0930\u094d\u092f\u093e \u092e\u0947\u0902 \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u092a\u094d\u0930\u093e\u0925\u092e\u093f\u0915 \u0938\u0947 \u0909\u091a\u094d\u091a\u0924\u0930 \u092e\u093e\u0927\u094d\u092f\u092e\u093f\u0915 \u0915\u0915\u094d\u0937\u093e\u0913\u0902 \u0924\u0915 \u0926\u0940 \u0917\u0908 \u0905\u0927\u093f\u0915\u093e\u0902\u0936 \u0938\u094d\u0915\u0942\u0932\u0940 \u0917\u0923\u093f\u0924 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0915\u0947 \u0932\u093f\u090f \u0907\u0938 \u0924\u0930\u0939 \u0915\u0940 \u092a\u0939\u0947\u0932\u093f\u092f\u093e\u0901 \u092c\u0928\u093e\u0908 \u091c\u093e 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\u0915\u0930\u0928\u093e \u0939\u092e\u0947\u0936\u093e \u0938\u092e\u094d\u092d\u0935 \u0939\u0948?<\/li>\n\n\n\n<li>\u0915\u094d\u092f\u093e \u0915\u093f\u0938\u0940 \u092a\u0939\u0947\u0932\u0940 \u0915\u093e \u0915\u0947\u0935\u0932 \u090f\u0915 \u0939\u0940 \u0938\u092e\u093e\u0927\u093e\u0928 \u0939\u094b\u0924\u093e \u0939\u0948 \u092f\u093e \u090f\u0915 \u0938\u0947 \u0905\u0927\u093f\u0915 \u0938\u092e\u093e\u0927\u093e\u0928 \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902?<\/li>\n\n\n\n<li><p>4 \u00d7 4 \u0915\u0940 \u090f\u0915 \u0917\u094d\u0930\u093f\u0921 \u092e\u0947\u0902 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u092d\u0930\u0928\u0947 \u0915\u0947 \u0924\u0930\u0940\u0915\u093c\u094b\u0902 \u0915\u0940 \u0938\u092e\u094d\u092d\u093e\u0935\u093f\u0924 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094d\u092f\u093e \u0939\u0948? \u0915\u094d\u092f\u093e \u0939\u092e <em>n \u00d7 n<\/em> \u0915\u0940 \u0917\u094d\u0930\u093f\u0921 \u092e\u0947\u0902 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u092d\u0930\u0928\u0947 \u0915\u0947 \u0924\u0930\u0940\u0915\u093c\u094b\u0902 \u0915\u0940 \u0938\u092e\u094d\u092d\u093e\u0935\u093f\u0924 \u0938\u0902\u0916\u094d\u092f\u093e \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0940\u0915\u0930\u0923 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902?<\/p><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u0915\u094b\u0932\u093f\u0928\u094d\u0938 \u0936\u092c\u094d\u0926\u0915\u094b\u0936 \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u092a\u0939\u0947\u0932\u0940 \u0915\u093e \u092e\u0924\u0932\u092c \u0939\u0948\u2013 &#8220;\u092e\u0928\u094b\u0930\u091c\u0902\u0928 \u0915\u0947 \u0932\u093f\u090f \u0928\u093f\u0930\u094d\u092e\u093f\u0924 \u0910\u0938\u093e \u0915\u094b\u0908 \u092d\u0940 \u0916\u093f\u0932\u094c\u0928\u093e, \u0938\u092e\u0938\u094d\u092f\u093e \u092f\u093e \u0905\u0928\u094d\u092f \u092f\u0941\u0915\u094d\u0924\u093f \u091c\u094b \u0915\u094c\u0936\u0932 \u092f\u093e \u0927\u0948\u0930\u094d\u092f\u092a\u0942\u0930\u094d\u0935\u0915 \u092a\u094d\u0930\u092f\u093e\u0938 \u0926\u094d\u0935\u093e\u0930\u093e \u0939\u0932 \u0915\u0940 \u091c\u093e\u0928\u0947 \u0935\u093e\u0932\u0940 \u0915\u0920\u093f\u0928\u093e\u0907\u092f\u094b\u0902 \u0915\u094b \u092a\u094d\u0930\u0938\u094d\u200d\u0924\u0941\u0924 \u0915\u0930\u0924\u0940 \u0939\u094b\u0964\u2019\u2019 \u0905\u0927\u093f\u0915\u093e\u0902\u0936 \u092a\u0939\u0947\u0932\u093f\u092f\u093e\u0901 \u090f\u0915 \u092a\u0947\u091a\u0940\u0926\u093e \u0938\u092e\u0938\u094d\u200d\u092f\u093e \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948\u0902 \u091c\u093f\u0928\u094d\u0939\u0947\u0902 \u0906\u0938\u093e\u0928\u0940 \u0938\u0947 \u0939\u0932 \u0928\u0939\u0940\u0902 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0938\u093e\u0925 \u0939\u0940 \u0907\u0928\u094d\u200d\u0939\u0947\u0902 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