{"id":28033,"date":"2026-09-06T22:12:40","date_gmt":"2026-09-06T16:42:40","guid":{"rendered":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/?p=28033"},"modified":"2026-09-06T22:12:40","modified_gmt":"2026-09-06T16:42:40","slug":"%e0%a4%aa%e0%a5%82%e0%a4%b0%e0%a5%8d%e0%a4%a3%e0%a4%be%e0%a4%82%e0%a4%95-%e0%a4%b0%e0%a4%82%e0%a4%97%e0%a5%80%e0%a4%a8-%e0%a4%95%e0%a4%be%e0%a4%89%e0%a4%82%e0%a4%9f%e0%a4%b0%e0%a5%8b%e0%a4%82","status":"publish","type":"post","link":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/%e0%a4%aa%e0%a5%82%e0%a4%b0%e0%a5%8d%e0%a4%a3%e0%a4%be%e0%a4%82%e0%a4%95-%e0%a4%b0%e0%a4%82%e0%a4%97%e0%a5%80%e0%a4%a8-%e0%a4%95%e0%a4%be%e0%a4%89%e0%a4%82%e0%a4%9f%e0%a4%b0%e0%a5%8b%e0%a4%82\/","title":{"rendered":"\u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 : \u0930\u0902\u0917\u0940\u0928 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 \u0938\u0902\u0916\u094d\u092f\u093e \u0930\u0947\u0916\u093e \u0915\u093e \u0935\u093f\u0938\u094d\u0924\u093e\u0930"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u0915\u0941\u091b \u0906\u092f\u0924\u093e\u0915\u093e\u0930 \u092c\u093f\u0928\u094d\u200d\u0926\u0941 \u0935\u093e\u0932\u0940 \u0936\u0940\u091f (rectangular dot sheets), \u0926\u094b \u0935\u093f\u092a\u0930\u0940\u0924 \u0930\u0902\u0917\u094b\u0902 \u0915\u0947 \u0938\u094d\u0915\u0947\u091a-\u092a\u0947\u0928 (\u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \u0932\u093e\u0932 \u0914\u0930 \u0939\u0930\u093e), \u090f\u0915 \u0938\u094d\u0915\u0947\u0932 \u0914\u0930 \u090f\u0915 \u092a\u0947\u0902\u0938\u093f\u0932 \u0932\u0947\u0902\u0964 \u0938\u092c\u0938\u0947 \u092a\u0939\u0932\u0947 \u090a\u092a\u0930 \u0938\u0947 \u0926\u0942\u0938\u0930\u0947 \u0928\u092e\u094d\u200d\u092c\u0930 \u0915\u0940 \u0930\u0947\u0916\u093e \u0915\u0947 \u092c\u093f\u0928\u094d\u200d\u0926\u0941\u0913\u0902 \u0915\u094b \u0906\u092a\u0938 \u092e\u0947\u0902 \u091c\u094b\u095c\u0947\u0902\u0964 \u092b\u093f\u0930 \u092f\u0939\u0940 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e 5\u0935\u0940\u0902, 8\u0935\u0940\u0902, 11\u0935\u0940\u0902, \u2026 \u0930\u0947\u0916\u093e\u0913\u0902 \u0915\u0947 \u0932\u093f\u090f \u092d\u0940 \u0926\u094b\u0939\u0930\u093e\u090f\u0901, \u0924\u093e\u0915\u093f \u092c\u093f\u0928\u094d\u200d\u0926\u0941\u0913\u0902 \u0915\u0940 \u0939\u0930 2 \u0930\u0947\u0916\u093e\u0913\u0902 \u0915\u0947 \u092c\u093e\u0926 \u092c\u093f\u0928\u094d\u200d\u0926\u0941\u0913\u0902 \u0915\u094b \u091c\u094b\u0921\u093c\u0928\u0947 \u0935\u093e\u0932\u0940 \u090f\u0915 \u0930\u0947\u0916\u093e \u092e\u094c\u091c\u0942\u0926 \u0939\u094b\u0964 \u0905\u092c \u092c\u0940\u091a \u092e\u0947\u0902 \u0915\u093f\u0938\u0940 \u090f\u0915 \u092c\u093f\u0928\u094d\u200d\u0926\u0941 \u0915\u094b \u091a\u0941\u0928\u0947\u0902 \u0914\u0930 \u0909\u0938 \u092a\u0930 &#8216;0&#8217; (\u0936\u0942\u0928\u094d\u092f) \u0915\u093e \u0932\u0947\u092c\u0932 \u0932\u0917\u093e\u090f\u0901\u0964 \u092b\u093f\u0930 \u0909\u0938\u0915\u0947 \u0926\u093e\u0908\u0902 \u0913\u0930 \u0915\u0947 \u092c\u093f\u0928\u094d\u200d\u0926\u0941\u0913\u0902 \u092a\u0930 \u0915\u094d\u0930\u092e\u093f\u0915 \u0930\u0942\u092a \u0938\u0947 1, 2, 3 \u0906\u0926\u093f \u0915\u093e \u0932\u0947\u092c\u0932 \u0932\u0917\u093e\u090f\u0901\u0964 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0930\u0947\u0916\u093e (horizontal line) \u092a\u0930 \u0907\u0938\u0940 \u0924\u0930\u0939 \u0932\u0947\u092c\u0932 \u0932\u0917\u093e\u090f\u0901\u0964 \u092f\u0939 \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u0930\u0947\u0902 \u0915\u093f \u0938\u092d\u0940 \u0936\u0942\u0928\u094d\u092f (zeros) \u090f\u0915 \u0939\u0940 \u0938\u0940\u0927\u0940 \u0932\u092e\u094d\u200d\u092c\u0935\u0924 \u0930\u0947\u0916\u093e (vertical line) \u092e\u0947\u0902 \u0939\u094b\u0902 (<b>\u091a\u093f\u0924\u094d\u0930-1<\/b>)\u0964<\/p>\n\n\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:70%\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/Integers-fig-1-hin.jpg\" alt=\"\" class=\"wp-image-27666\"\/><figcaption class=\"wp-element-caption\"><strong>\u091a\u093f\u0924\u094d\u0930-1<\/strong><\/figcaption><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:32%\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"628\" height=\"720\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure2.jpg\" alt=\"\" class=\"wp-image-27669\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure2.jpg 628w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure2-314x360.jpg 314w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure2-176x202.jpg 176w\" sizes=\"auto, (max-width: 628px) 100vw, 628px\" \/><figcaption class=\"wp-element-caption\"><strong>\u091a\u093f\u0924\u094d\u0930-2<\/strong><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<ol start=\"1\" class=\"wp-block-list mb-1\">\n<li class=\"has-custom-css wp-custom-css-e70f57ec\"><strong>\u092a\u0930\u0935\u0930\u094d\u0924\u0940 (Successors) \u0914\u0930 \u092a\u0942\u0930\u094d\u0935\u0935\u0930\u094d\u0924\u0940 (Predecessors)<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-a nested-list\">\n<li>2 \u0914\u0930 5 \u0915\u0947 \u092c\u0940\u091a \u0915\u0940 \u0915\u094b\u0908 \u092d\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u091a\u0941\u0928\u0947\u0902\u0964 \u0909\u0938\u0938\u0947 \u0938\u092e\u094d\u200d\u092c\u0928\u094d\u0927\u093f\u0924 \u092c\u093f\u0928\u094d\u200d\u0926\u0941 \u092a\u0930 \u0917\u094b\u0932\u093e \u092c\u0928\u093e\u090f\u0901\u0964 \u091c\u0948\u0938\u093e \u0915\u093f \u0926\u093f\u0916\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948 (<b>\u091a\u093f\u0924\u094d\u0930-2<\/b> &#8211; \u092f\u0939\u093e\u0901 \u091a\u0941\u0928\u0940 \u0917\u0908 \u0938\u0902\u0916\u094d\u092f\u093e 3 \u0939\u0948), \u0938\u092e\u093e\u0928 \u0926\u0942\u0930\u0940 \u092a\u0930 \u0909\u0924\u0928\u0947 \u0939\u0940 \u0915\u093e\u0909\u0902\u091f\u0930 \u092c\u0928\u093e\u090f\u0901 \u091c\u093f\u0924\u0928\u0940 \u0935\u0939 \u0938\u0902\u0916\u094d\u092f\u093e \u0926\u0930\u094d\u0936\u093e\u0924\u0940 \u0939\u0948\u0964<\/li>\n\n\n\n<li>\u0905\u0917\u0932\u0940 \u0930\u0947\u0916\u093e \u092e\u0947\u0902, \u0905\u092a\u0928\u0940 \u091a\u0941\u0928\u0940 \u0939\u0941\u0908 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u093e \u092a\u0930\u0935\u0930\u094d\u0924\u0940 (successor) \u092c\u0928\u093e\u090f\u0901 \u0914\u0930 \u0909\u0938\u0938\u0947 \u0938\u092e\u094d\u200d\u092c\u0928\u094d\u0927\u093f\u0924 \u092c\u093f\u0928\u094d\u200d\u0926\u0941 \u092a\u0930 \u0917\u094b\u0932\u093e \u0932\u0917\u093e\u090f\u0901\u0964<\/li>\n\n\n\n<li>\u0909\u0938\u0938\u0947 \u0905\u0917\u0932\u0940 \u0930\u0947\u0916\u093e \u092e\u0947\u0902, \u0905\u092a\u0928\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u093e \u092a\u0942\u0930\u094d\u0935\u0935\u0930\u094d\u0924\u0940 (predecessor) \u092c\u0928\u093e\u090f\u0901 \u0914\u0930 \u0909\u0938\u0938\u0947 \u0938\u092e\u094d\u200d\u092c\u0928\u094d\u0927\u093f\u0924 \u092c\u093f\u0928\u094d\u200d\u0926\u0941 \u092a\u0930 \u0917\u094b\u0932\u093e \u0932\u0917\u093e\u090f\u0901\u0964<\/li>\n\n\n\n<li>1 \u0915\u093e \u092a\u0942\u0930\u094d\u0935\u0935\u0930\u094d\u0924\u0940 \u092c\u0928\u093e\u090f\u0901\u0964 \u0906\u092a\u0928\u0947 \u0915\u093f\u0924\u0928\u0947 \u0915\u093e\u0909\u0902\u091f\u0930 \u092c\u0928\u093e\u090f? \u0914\u0930 \u0915\u094d\u092f\u094b\u0902?<\/li>\n\n\n\n<li>0 (\u0936\u0942\u0928\u094d\u092f) \u0915\u093e \u092a\u0942\u0930\u094d\u0935\u0935\u0930\u094d\u0924\u0940 \u0915\u094d\u092f\u093e \u0939\u094b\u0917\u093e? \u0939\u092e \u0907\u0938\u0947 \u0915\u0939\u093e\u0901 \u0914\u0930 \u0915\u0948\u0938\u0947 \u092c\u0928\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902?<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u092a\u0942\u0930\u094d\u0935\u0935\u0930\u094d\u0924\u0940 \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e \u090f\u0915 \u0915\u093c\u0926\u092e ________ (\u0926\u093e\u090f\u0901\/\u092c\u093e\u090f\u0901) \u091a\u0932\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n\n\n\n<i><p class=\"ui-comments\" style=\"line-height:175% !important; background-color:#fdf7e5 !important;\">0 (\u0936\u0942\u0928\u094d\u092f) \u0915\u0947 \u092a\u0942\u0930\u094d\u0935\u0935\u0930\u094d\u0924\u0940 (predecessor) \u0938\u0947 \u0938\u092e\u094d\u200d\u092c\u0928\u094d\u0927\u093f\u0924 \u092c\u093f\u0928\u094d\u200d\u0926\u0941 \u0915\u094b \u0916\u094b\u091c\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e \u0938\u0902\u0916\u094d\u092f\u093e \u0930\u0947\u0916\u093e \u0915\u093e \u092c\u093e\u0908\u0902 \u0913\u0930 \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u091a\u0942\u0901\u0915\u093f \u092f\u0939 \u0936\u0942\u0928\u094d\u092f \u0938\u0947 \u090f\u0915 \u0907\u0915\u093e\u0908 (one unit) \u0915\u0940 \u0926\u0942\u0930\u0940 \u092a\u0930 \u0939\u0948, \u0907\u0938\u0932\u093f\u090f \u0939\u092e\u0947\u0902 \u0907\u0938\u0947 1 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0905\u0902\u0915\u093f\u0924 \u0915\u0930\u0928\u093e \u091a\u093e\u0939\u093f\u090f, \u0932\u0947\u0915\u093f\u0928 \u091a\u0942\u0901\u0915\u093f \u092f\u0939 \u092c\u093e\u0908\u0902 \u0913\u0930 \u0939\u0948, \u0907\u0938\u0932\u093f\u090f \u0939\u092e \u0907\u0938\u0947 \u0926\u093e\u0908\u0902 \u0913\u0930 \u0935\u093e\u0932\u0947 1 \u0938\u0947 \u0905\u0932\u0917 \u0926\u093f\u0916\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u201c-1\u201d \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0905\u0902\u0915\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u092a\u0939\u0932\u0947 \u0915\u0940 \u0924\u0930\u0939 \u0939\u0940, \u0939\u092e \u092f\u0939\u093e\u0901 \u090f\u0915 \u0915\u093e\u0909\u0902\u091f\u0930 \u092c\u0928\u093e\u0924\u0947 \u0939\u0948\u0902, \u0932\u0947\u0915\u093f\u0928 \u091a\u0942\u0901\u0915\u093f \u092f\u0939 \u092c\u093e\u0908\u0902 \u0913\u0930 \u0915\u0940 \u0917\u0924\u093f (\u092e\u0942\u0935\u092e\u0947\u0902\u091f) \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0924\u093e \u0939\u0948, \u0907\u0938\u0932\u093f\u090f \u0939\u092e \u0926\u0942\u0938\u0930\u0947 \u0930\u0902\u0917 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0907\u0938\u0947 \u0938\u0902\u0916\u094d\u092f\u093e \u0930\u0947\u0916\u093e \u0915\u0947 \u0928\u0940\u091a\u0947 \u092c\u0928\u093e\u0924\u0947 \u0939\u0948\u0902 (<b>\u091a\u093f\u0924\u094d\u0930-3<\/b>)\u0964 \u0939\u092e \u0907\u0938 \u0926\u0942\u0938\u0930\u0947 \u0930\u0902\u0917 \u0915\u0947 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u094b <b>\u090b\u0923\u093e\u0924\u094d\u092e\u0915 (negative)<\/b> \u0915\u0939\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u092a\u0939\u0932\u0947 \u0930\u0902\u0917 \u0915\u0947 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u094b <b>\u0927\u0928\u093e\u0924\u094d\u092e\u0915 (positive)<\/b>\u0964 \u0907\u0938\u0940 \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930,  <span style=\"color: #068006;\"> \u0936\u0942\u0928\u094d\u092f \u0915\u0947 \u0926\u093e\u0908\u0902 \u0913\u0930 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u0927\u0928\u093e\u0924\u094d\u092e\u0915 (positive) <\/span> \u0914\u0930 <span style=\"color: #FF0000;\"> \u0907\u0938\u0915\u0947 \u092c\u093e\u0908\u0902 \u0913\u0930 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u090b\u0923\u093e\u0924\u094d\u092e\u0915 (negative)<\/span> \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p><\/i>\n\n\n\n<ol start=\"2\" class=\"wp-block-list mb-1\">\n<li class=\"has-custom-css wp-custom-css-358345ec\"><strong>\u092a\u0942\u0930\u094d\u0935\u0935\u0930\u094d\u0924\u0940 \u0915\u0947 \u0938\u093e\u0925 \u0928\u0908 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-a nested-list\">\n<li>-1 \u0915\u093e \u092a\u0942\u0930\u094d\u0935\u0935\u0930\u094d\u0924\u0940 (predecessor) \u092c\u0928\u093e\u090f\u0901\u0964 \u0907\u0938\u0940 \u092a\u0948\u091f\u0930\u094d\u0928 (\u092a\u094d\u0930\u093e\u0930\u0942\u092a) \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f, \u0939\u092e \u0907\u0938 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b \u0915\u0948\u0938\u0947 \u0932\u093f\u0916\u0947\u0902\u0917\u0947?<\/li>\n\n\n\n<li>\u0905\u092c, \u0938\u0902\u0916\u094d\u092f\u093e \u0930\u0947\u0916\u093e \u0915\u0947 \u0909\u0938 \u0939\u093f\u0938\u094d\u0938\u0947 \u0915\u094b \u0924\u0926\u0928\u0941\u0938\u093e\u0930 \u0905\u0902\u0915\u093f\u0924 \u0915\u0930\u0947\u0902 \u091c\u094b 0 \u0915\u0947 \u092c\u093e\u0908\u0902 \u0913\u0930 \u0939\u0948, \u091c\u0948\u0938\u0947 \u0915\u093f -2, -3, -4, \u0906\u0926\u093f\u0964<\/li>\n\n\n\n<li>-4 \u092c\u0928\u093e\u090f\u0901\u0964 \u0906\u092a\u0928\u0947 0 \u0915\u0947 ________ (\u092c\u093e\u090f\u0901\/\u0926\u093e\u090f\u0901) \u0913\u0930 \u0930\u0947\u0916\u093e \u0915\u0947 ________ (\u090a\u092a\u0930\/\u0928\u0940\u091a\u0947) \u0915\u093f\u0924\u0928\u0947 ________ (\u0932\u093e\u0932\/\u0939\u0930\u0947) \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e?<\/li>\n<\/ul>\n\n\n\n<i><p class=\"ui-comments\" style=\"line-height:175% !important; background-color:#fdf7e5 !important;\">\u0915\u093f\u0938\u0940 \u092d\u0940 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u093e \u092a\u0942\u0930\u094d\u0935\u0935\u0930\u094d\u0924\u0940 \u092c\u0928\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u091c\u0948\u0938\u0947 \u0939\u0940 \u0939\u092e \u090f\u0915 \u0915\u093c\u0926\u092e \u092c\u093e\u090f\u0901 \u0916\u093f\u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u0939\u092e\u0947\u0902 \u090f\u0915 <span style=\"color: #FF0000;\">\u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930<\/span> \u091c\u094b\u0921\u093c\u0928\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/p><\/i>\n\n\n\n<p class=\"mb-1 wp-block-paragraph\"><em><strong>\u092f\u0939 \u0915\u0930\u0915\u0947 \u0926\u0947\u0916\u0947\u0902 :<\/strong><\/em><\/p>\n\n\n\n<ol start=\"1\" style=\"list-style-type:upper-roman\" class=\"wp-block-list\">\n<li>-3 \u0915\u093e \u092a\u0942\u0930\u094d\u0935\u0935\u0930\u094d\u0924\u0940 \u092c\u0928\u093e\u090f\u0901\u0964<\/li>\n\n\n\n<li>-19 \u0915\u093e \u092a\u0942\u0930\u094d\u0935\u0935\u0930\u094d\u0924\u0940 ________ \u0939\u0948\u0964 \u0907\u0938\u0947 ________ (18\/20) ________ (\u0932\u093e\u0932\/\u0939\u0930\u0947) \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 \u0926\u093f\u0916\u093e\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u092f\u0939 -19 \u0915\u0947 ________ (\u092c\u093e\u090f\u0901\/\u0926\u093e\u090f\u0901) \u0913\u0930 \u0938\u094d\u0925\u093f\u0924 \u0939\u0948\u0964<\/li>\n<\/ol>\n\n\n\n<p class=\"mb-1 wp-block-paragraph\"><em><strong>\u0938\u094b\u091a\u0947\u0902 :<\/strong><\/em><\/p>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-a is-uppercase\">\n<li>\u0915\u094c\u0928-\u0938\u093e \u0936\u0939\u0930 \u0905\u0927\u093f\u0915 \u0920\u0923\u094d\u200d\u0921\u093e \u0939\u0948? -7\u00b0C \u0924\u093e\u092a\u092e\u093e\u0928 \u0935\u093e\u0932\u093e \u0936\u093f\u092e\u0932\u093e \u092f\u093e -8\u00b0C \u0924\u093e\u092a\u092e\u093e\u0928 \u0935\u093e\u0932\u093e \u0932\u0947\u0939?<\/li>\n\n\n\n<li>\u092f\u0926\u093f \u0938\u092e\u0941\u0926\u094d\u0930 \u0915\u093e \u0938\u094d\u0924\u0930 0 \u092e\u0940\u091f\u0930 \u092a\u0930 \u0939\u0948, \u0914\u0930 5 \u092e\u0940\u091f\u0930 \u090a\u0901\u091a\u0947 \u0916\u092e\u094d\u200d\u092d\u0947 \u0915\u094b 5 \u0926\u094d\u0935\u093e\u0930\u093e \u0926\u093f\u0916\u093e\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0924\u094b 5 \u092e\u0940\u091f\u0930 \u0917\u0939\u0930\u0947 \u0917\u0921\u094d\u0922\u0947 \u0915\u094b ________ \u0926\u094d\u0935\u093e\u0930\u093e \u0926\u093f\u0916\u093e\u092f\u093e \u091c\u093e\u090f\u0917\u093e\u0964 \u0915\u094d\u092f\u093e -6 \u092e\u0940\u091f\u0930, 5 \u092e\u0940\u091f\u0930 \u0917\u0939\u0930\u0947 \u0917\u0921\u094d\u0922\u0947 \u0938\u0947 \u092d\u0940 \u0905\u0927\u093f\u0915 \u0917\u0939\u0930\u0947 \u0917\u0921\u094d\u0922\u0947 \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0924\u093e \u0939\u0948?<\/li>\n\n\n\n<li>300 \u20b9 \u0915\u0947 \u0915\u0930\u094d\u091c\u093c \u0935\u093e\u0932\u0940 \u0924\u093f\u0924\u093f\u0930, 200 \u20b9 \u0915\u0947 \u0915\u0930\u094d\u091c\u093c \u0935\u093e\u0932\u0947 \u091f\u093f\u0902\u0915\u0942 \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u092e\u0947\u0902 ________ (\u0905\u0927\u093f\u0915 \u0905\u092e\u0940\u0930\/\u0905\u0927\u093f\u0915 \u0917\u093c\u0930\u0940\u092c) \u0939\u0948\u0964<\/li>\n<\/ul>\n\n\n\n<ol start=\"3\" class=\"wp-block-list mb-1\">\n<li class=\"has-custom-css wp-custom-css-cb78f9c8\"><strong>\u092a\u0930\u0935\u0930\u094d\u0924\u0940 -1 \u0915\u093e<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"mb-1 wp-block-paragraph\">\u092a\u0930\u0935\u0930\u094d\u0924\u0940 \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e \u090f\u0915 \u0915\u093c\u0926\u092e ________ (\u0926\u093e\u090f\u0901\/\u092c\u093e\u090f\u0901) \u091a\u0932\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n\n\n\n<ul class=\"list-type-alpha start-a\">\r\n  <li>\u0924\u094b, \u0915\u094c\u0928-\u0938\u0940 \u0938\u0902\u0916\u094d\u092f\u093e -1 \u0915\u0940 \u092a\u0930\u0935\u0930\u094d\u0924\u0940 (successor) \u0939\u0948?<\/li>\r\n  <li>-1 \u0915\u0947 \u092a\u0930\u0935\u0930\u094d\u0924\u0940 \u0915\u094b \u0926\u093f\u0916\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u0924\u0928\u0947 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 (\u0914\u0930 \u0915\u093f\u0938 \u0930\u0902\u0917 \u0915\u0947) \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948?<\/li>\r\n  <li>\u092a\u0930\u0935\u0930\u094d\u0924\u0940 \u0915\u0947 \u0932\u093f\u090f (\u0914\u0930 \u0907\u0938\u0932\u093f\u090f \u0926\u093e\u0908\u0902 \u0913\u0930 \u0915\u093c\u0926\u092e \u092c\u0922\u093c\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f), \u0939\u092e\u0928\u0947 \u0939\u092e\u0947\u0936\u093e \u090f\u0915 <span style=\"color: #00af00;\">\u0927\u0928\u093e\u0924\u094d\u092e\u0915<\/span> \u0915\u093e\u0909\u0902\u091f\u0930 \u091c\u094b\u0921\u093c\u093e \u0939\u0948\u0964 \u091c\u092c \u0939\u092e \u092f\u0939\u093e\u0901 \u0910\u0938\u093e \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0939\u092e\u0947\u0902 \u090f\u0915 ________ (\u0932\u093e\u0932 \u0915\u093e\u0909\u0902\u091f\u0930\/\u0939\u0930\u093e \u0915\u093e\u0909\u0902\u091f\u0930\/\u0932\u093e\u0932-\u0939\u0930\u093e \u091c\u094b\u0921\u093c\u093e) \u092e\u093f\u0932\u0924\u093e \u0939\u0948?\r\n  <\/li>\r\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"260\" height=\"720\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure3-1.png\" alt=\"\" class=\"wp-image-27859\" style=\"aspect-ratio:0.36113146709658506;width:149px;height:auto\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure3-1.png 260w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure3-1-130x360.png 130w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure3-1-73x202.png 73w\" sizes=\"auto, (max-width: 260px) 100vw, 260px\" \/><figcaption class=\"wp-element-caption\"><strong>\u091a\u093f\u0924\u094d\u0930-3<\/strong><\/figcaption><\/figure>\n<\/div>\n\n\n<i><p class=\"ui-comments\" style=\"line-height:175% !important; background-color:#fdf7e5 !important;\">\u092f\u0939 \u0927\u0928\u093e\u0924\u094d\u092e\u0915-\u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u093e \u091c\u094b\u0921\u093c\u093e \u0936\u0942\u0928\u094d\u092f \u0915\u0947 \u0938\u092e\u0924\u0941\u0932\u094d\u200d\u092f \u0939\u094b\u0924\u093e \u0939\u0948 <b>(\u091a\u093f\u0924\u094d\u0930-3)<\/b> \u0964 \u0907\u0938\u0932\u093f\u090f, \u0905\u092c \u0938\u0947 \u0939\u092e \u0910\u0938\u0947 \u091c\u094b\u0921\u093c\u0947 \u0915\u094b &#8216;\u0936\u0942\u0928\u094d\u092f \u091c\u094b\u0921\u093c\u093e&#8217; (zero pair) \u0915\u0939\u0947\u0902\u0917\u0947\u0964 \u091a\u0942\u0901\u0915\u093f \u092f\u0947 \u0936\u0942\u0928\u094d\u092f \u0915\u0947 \u0938\u092e\u0924\u0941\u0932\u094d\u200d\u092f \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u0907\u0938\u0932\u093f\u090f \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e\u0928\u0941\u0938\u093e\u0930 \u0907\u0928\u094d\u0939\u0947\u0902 \u0939\u091f\u093e\u092f\u093e (\u092f\u093e \u091c\u094b\u0921\u093c\u093e) \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/p><\/i>\n\n\n\n<p class=\"mb-1 wp-block-paragraph\"><em><strong>\u092f\u0939 \u0915\u0930\u0915\u0947 \u0926\u0947\u0916\u0947\u0902 :<\/strong><\/em><\/p>\n\n\n\n<ol start=\"3\" style=\"list-style-type:upper-roman\" class=\"wp-block-list\">\n<li>0 = _____ + _____ = _____ + _____ = _____ + _____ <br> (\u0928\u094b\u091f : \u092f\u0939\u093e\u0901 \u0936\u0942\u0928\u094d\u092f \u0915\u094b \u0905\u0932\u0917-\u0905\u0932\u0917 &#8216;\u0936\u0942\u0928\u094d\u092f \u091c\u094b\u0921\u093c\u094b\u0902&#8217; \u092f\u093e \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u092f\u094b\u0917 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0926\u0930\u094d\u0936\u093e\u0928\u093e \u0939\u0948\u0964)<\/li>\n<\/ol>\n\n\n\n<ol start=\"4\" class=\"wp-block-list mb-1\">\n<li class=\"has-custom-css wp-custom-css-55b98c7c\"><strong>\u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u091c\u094b\u0921\u093c\u0928\u093e<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"mb-1 wp-block-paragraph\">\u091c\u092c \u0939\u092e \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u091c\u094b\u0921\u093c\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0939\u092e \u090f\u0915 \u0928\u0939\u0940\u0902, \u092c\u0932\u094d\u0915\u093f \u0915\u0908 \u0915\u093c\u0926\u092e ________ (\u0926\u093e\u090f\u0901\/\u092c\u093e\u090f\u0901) \u091a\u0932\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(\u0915) 4 \u092e\u0947\u0902 3 \u091c\u094b\u095c\u0947\u0902      (\u0916) -5 \u092e\u0947\u0902 2 \u091c\u094b\u095c\u0947\u0902       (\u0917) -3 \u092e\u0947\u0902 5 \u091c\u094b\u095c\u0947\u0902<\/p>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-a nested-list\">\n<li>4 + 3 : 4 \u0915\u0947 ________ (\u092c\u093e\u090f\u0901\/\u0926\u093e\u090f\u0901) \u0913\u0930 ________ \u0915\u093c\u0926\u092e \u091a\u0932\u0947\u0902, \u0914\u0930 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0915\u093c\u0926\u092e \u092a\u0930 1 ________ (\u0932\u093e\u0932\/\u0939\u0930\u093e) \u0915\u093e\u0909\u0902\u091f\u0930 \u091c\u094b\u0921\u093c\u0947\u0902\u0964<\/li>\n\n\n\n<li>(-5) + 2 : -5 \u0915\u0947 ________ (\u092c\u093e\u090f\u0901\/\u0926\u093e\u090f\u0901) \u0913\u0930 ________ \u0915\u093c\u0926\u092e \u091a\u0932\u0947\u0902, \u0914\u0930 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0915\u093c\u0926\u092e \u092a\u0930 1 ________ (\u0932\u093e\u0932\/\u0939\u0930\u093e) \u0915\u093e\u0909\u0902\u091f\u0930 \u091c\u094b\u0921\u093c\u0947\u0902\u0964<\/li>\n\n\n\n<li>(-3) + 5 : -3 \u0915\u0947 ________ (\u092c\u093e\u090f\u0901\/\u0926\u093e\u090f\u0901) \u0913\u0930 ________ \u0915\u093c\u0926\u092e \u091a\u0932\u0947\u0902, \u0914\u0930 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0915\u093c\u0926\u092e \u092a\u0930 1 ________ (\u0932\u093e\u0932\/\u0939\u0930\u093e) \u0915\u093e\u0909\u0902\u091f\u0930 \u091c\u094b\u0921\u093c\u0947\u0902\u0964<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-thumbnail\"><img loading=\"lazy\" decoding=\"async\" width=\"360\" height=\"150\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure4-360x150.jpg\" alt=\"\" class=\"wp-image-27727\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure4-360x150.jpg 360w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure4-640x267.jpg 640w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure4-1280x533.jpg 1280w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure4-768x320.jpg 768w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure4-1536x640.jpg 1536w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure4-1200x500.jpg 1200w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure4.jpg 1728w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><figcaption class=\"wp-element-caption\"><strong>\u091a\u093f\u0924\u094d\u0930-4<\/strong><\/figcaption><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">\u0906\u092a\u0928\u0947 \u0924\u0940\u0928\u094b\u0902 \u0938\u0935\u093e\u0932\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0939\u0940 \u0930\u0923\u0928\u0940\u0924\u093f \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e\u0964 \u0915\u094d\u092f\u093e \u0906\u092a\u0915\u094b \u0915\u093f\u0938\u0940 \u0938\u0935\u093e\u0932 \u092e\u0947\u0902 \u0936\u0942\u0928\u094d\u092f \u091c\u094b\u0921\u093c\u093e \u092e\u093f\u0932\u093e?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0915\u094d\u092f\u093e \u090f\u0915 \u0939\u0930\u093e \u0915\u093e\u0909\u0902\u091f\u0930 \u091c\u094b\u0921\u093c\u0928\u093e, \u090f\u0915 \u0932\u093e\u0932 \u0915\u093e\u0909\u0902\u091f\u0930 \u0915\u094b \u0939\u091f\u093e\u0928\u0947 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u0940 \u0939\u0948? \u091c\u092c \u0938\u092e\u094d\u200d\u092d\u0935 \u0939\u094b, \u0924\u092c \u092f\u0939\u0940 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0915\u0930\u0915\u0947 \u0907\u0928\u094d\u0939\u0940\u0902 \u0938\u0935\u093e\u0932\u094b\u0902 \u0915\u094b \u0926\u094b\u092c\u093e\u0930\u093e \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u093e \u092a\u094d\u0930\u092f\u093e\u0938 \u0915\u0930\u0947\u0902\u0964 \u0915\u094d\u092f\u093e \u0906\u092a\u0915\u094b \u0935\u0939\u0940 \u0909\u0924\u094d\u0924\u0930 \u092e\u093f\u0932\u0924\u0947 \u0939\u0948\u0902?<\/p>\n\n\n\n<i><div class=\"ui-comments\" style=\"line-height:175% !important; background-color:#fdf7e5 !important; margin-bottom:2rem !important;\">\n  <p style=\"margin-bottom:0.5rem !important;\">\u0924\u094b, \u0915\u093f\u0938\u0940 <span style=\"color:#FF0000;\">\u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e<\/span> \u0915\u094b \u091c\u094b\u0921\u093c\u0928\u0947 \u0915\u093e \u0905\u0930\u094d\u0925 \u0915\u093f\u0938\u0915\u0947 \u0938\u092e\u0924\u0941\u0932\u094d\u092f \u0939\u0948 :<\/p>\n  \n  <ol style=\"list-style-type: lower-roman; margin-bottom: 0rem !important;\">\n    <li><span style=\"color:#FF0000;\">\u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902<\/span> \u0915\u094b \u091c\u094b\u0921\u093c\u0928\u0947 (\u0914\u0930 \u092f\u0926\u093f \u0915\u094b\u0908 \u0936\u0942\u0928\u094d\u092f \u091c\u094b\u0921\u093c\u093e \u092c\u0928\u0947, \u0924\u094b \u0909\u0938\u0947 \u0939\u091f\u093e\u0928\u0947) <b>\u0905\u0925\u0935\u093e<\/b>\n    <\/li>\n    <li><span style=\"color:#068006;\">\u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902<\/span> \u0915\u094b \u0939\u091f\u093e\u0928\u0947\u0964\n    <\/li>\n  <\/ol>\n<\/div><\/i>\n\n\n\n<p class=\"mb-1 wp-block-paragraph\"><em><strong>\u092f\u0939 \u0915\u0930\u0915\u0947 \u0926\u0947\u0916\u0947\u0902 :<\/strong><\/em><\/p>\n\n\n\n<ol start=\"4\" style=\"list-style-type:lower-roman\" class=\"wp-block-list\">\n<li>(-5) + 5 = ____<\/li>\n\n\n\n<li>(-8) + ____ = 0<\/li>\n\n\n\n<li>____ + 4 = 0<\/li>\n<\/ol>\n\n\n\n<p class=\"mb-1 wp-block-paragraph\"><em><strong>\u0938\u094b\u091a\u0947\u0902 :<\/strong><\/em><\/p>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-d is-uppercase mb-1\">\n<li>\u0924\u093f\u0924\u093f\u0930 \u0915\u094b \u091c\u0928\u094d\u092e\u0926\u093f\u0928 \u0915\u0947 \u0909\u092a\u0939\u093e\u0930 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 100 \u20b9 \u092e\u093f\u0932\u0947\u0964 \u0909\u0938\u0928\u0947 \u0907\u0938\u0938\u0947 \u0905\u092a\u0928\u0947 300 \u20b9 \u0915\u0947 \u0915\u0930\u094d\u091c\u093c \u0915\u093e \u0915\u0941\u091b \u0939\u093f\u0938\u094d\u0938\u093e \u091a\u0941\u0915\u093e \u0926\u093f\u092f\u093e\u0964<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-a nested-list  mb-1\">\n<li>\u0905\u092c \u0915\u093f\u0924\u0928\u093e \u0915\u0930\u094d\u091c\u093c \u092c\u091a\u093e \u0939\u0948?<\/li>\n\n\n\n<li>\u0924\u094b, \u0915\u093f\u0924\u0928\u093e \u0915\u0930\u094d\u091c\u093c \u091a\u0941\u0915\u093e\u092f\u093e \u0917\u092f\u093e, \u092f\u093e\u0928\u0940 \u0918\u091f\u093e\u092f\u093e (subtracted) \u0917\u092f\u093e?<\/li>\n\n\n\n<li>\u092f\u0926\u093f \u092e\u0942\u0932 \u0915\u0930\u094d\u091c\u093c 300 \u20b9 \u0915\u094b -3 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0932\u093f\u0916\u093e \u091c\u093e\u090f, \u0924\u094b \u0909\u092a\u0939\u093e\u0930 ________ (1\/-1) \u0939\u0948 \u0914\u0930 \u092c\u091a\u093e \u0939\u0941\u0906 \u0915\u0930\u094d\u091c\u093c ________ \u0939\u0948\u0964<\/li>\n\n\n\n<li>\u092c\u091a\u093e \u0939\u0941\u0906 \u0915\u0930\u094d\u091c\u093c = \u092e\u0942\u0932 \u0915\u0930\u094d\u091c\u093c + \u0909\u092a\u0939\u093e\u0930 = \u092e\u0942\u0932 \u0915\u0930\u094d\u091c\u093c \u2013 \u091a\u0941\u0915\u093e\u092f\u093e \u0917\u092f\u093e \u0915\u0930\u094d\u091c\u093c, \u092f\u093e\u0928\u0940 _______ = (-3) + _______ = (-3) \u2013 _______<\/li>\n\n\n\n<li>\u0939\u094b\u0924\u093e \u092f\u0926\u093f \u0909\u092a\u0939\u093e\u0930 500 \u20b9 \u0915\u093e \u0939\u094b\u0924\u093e?<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-e is-uppercase mb-1\">\n<li>\u091f\u093f\u0928\u091f\u093f\u0928 \u092a\u0930 200 \u20b9 \u0915\u093e \u0915\u0930\u094d\u091c\u093c \u0925\u093e \u0932\u0947\u0915\u093f\u0928 \u0909\u0938\u0928\u0947 600 \u20b9 \u0915\u093e \u092e\u0941\u0928\u093e\u092b\u093c\u093e (\u0932\u093e\u092d) \u0915\u092e\u093e\u092f\u093e\u0964<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-a nested-list\">\n<li>\u092e\u0941\u0928\u093e\u092b\u093c\u093e \u0915\u092e\u093e\u0928\u0947 \u0915\u0947 \u092c\u093e\u0926 \u091f\u093f\u0928\u091f\u093f\u0928 \u0915\u0947 \u092a\u093e\u0938 \u0915\u0941\u0932 \u0915\u093f\u0924\u0928\u0940 \u0930\u0915\u092e \u0925\u0940?<\/li>\n\n\n\n<li>\u092f\u0926\u093f 200 \u20b9 \u0915\u0947 \u0915\u0930\u094d\u091c\u093c \u0915\u094b -2 \u0932\u093f\u0916\u093e \u091c\u093e\u090f, \u0924\u094b 600 \u20b9 \u0915\u093e \u092e\u0941\u0928\u093e\u092b\u093c\u093e ________ (6\/-6) \u0939\u094b\u0917\u093e \u0914\u0930 \u092e\u0941\u0928\u093e\u092b\u093c\u0947 \u0915\u0947 \u092c\u093e\u0926 \u091f\u093f\u0928\u091f\u093f\u0928 \u0915\u0947 \u092a\u093e\u0938 \u092c\u091a\u0940 \u0930\u0915\u092e ________ \u0939\u094b\u0917\u0940\u0964<\/li>\n\n\n\n<li>\u0924\u094b, (-2) + _______ = _______<\/li>\n<\/ul>\n\n\n\n<ol start=\"5\" class=\"wp-block-list mb-1\">\n<li class=\"has-custom-css wp-custom-css-fcf2e53a\"><strong>\u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u0918\u091f\u093e\u0928\u093e<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"mb-1 wp-block-paragraph\">\u091c\u092c \u0939\u092e \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u0918\u091f\u093e\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0939\u092e \u090f\u0915 \u0928\u0939\u0940\u0902, \u092c\u0932\u094d\u0915\u093f \u0915\u0908 \u0915\u093c\u0926\u092e ____________ (\u0926\u093e\u0908\u0902\/\u092c\u093e\u0908\u0902) \u0913\u0930 \u091a\u0932\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0906\u092a ____________ (\u0932\u093e\u0932\/\u0939\u0930\u0947) \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u094b \u0939\u091f\u093e\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n\n\n\n<p class=\"mb-1 wp-block-paragraph\">(\u0915) 6 \u092e\u0947\u0902 \u0938\u0947 2 \u0918\u091f\u093e\u090f\u0901         (\u0916) -2 \u092e\u0947\u0902 \u0938\u0947 3 \u0918\u091f\u093e\u090f\u0901            (\u0917) 3 \u092e\u0947\u0902 \u0938\u0947 5 \u0918\u091f\u093e\u090f\u0901<\/p>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-a mb-1\">\n<li>6 \u2013 2 : 6 \u0915\u0947 ____________ (\u092c\u093e\u0908\u0902\/\u0926\u093e\u0908\u0902) \u0913\u0930 _______ \u0915\u093c\u0926\u092e \u091a\u0932\u0947\u0902, \u0939\u0930 \u0915\u093c\u0926\u092e \u092a\u0930 1 \u0915\u093e\u0909\u0902\u091f\u0930 \u0939\u091f\u093e\u0924\u0947 \u091c\u093e\u090f\u0901\u0964<\/li>\n\n\n\n<li>(-2) \u2013 3 : -2 \u0915\u0947 ____________ (\u092c\u093e\u0908\u0902\/\u0926\u093e\u0908\u0902) \u0913\u0930_______ \u0915\u093c\u0926\u092e \u091a\u0932\u0947\u0902, \u0939\u0930 \u0915\u093c\u0926\u092e \u092a\u0930 1 \u0915\u093e\u0909\u0902\u091f\u0930 \u0939\u091f\u093e\u0924\u0947 \u091c\u093e\u090f\u0901\u0964<br>\u091c\u092c \u0906\u092a\u0915\u0947 \u092a\u093e\u0938 \u0915\u093e\u0909\u0902\u091f\u0930 \u0916\u093c\u0924\u094d\u092e \u0939\u094b \u0917\u090f \u0924\u094b \u0906\u092a\u0928\u0947 \u0915\u094d\u092f\u093e \u0915\u093f\u092f\u093e?<\/li>\n\n\n\n<li>3 \u2013 5 : 3 \u0915\u0947 ____________ (\u092c\u093e\u0908\u0902\/\u0926\u093e\u0908\u0902) \u0913\u0930  _______ \u0915\u093c\u0926\u092e \u091a\u0932\u0947\u0902, \u0939\u0930 \u0915\u093c\u0926\u092e \u092a\u0930 1 \u0915\u093e\u0909\u0902\u091f\u0930 \u0939\u091f\u093e\u0924\u0947 \u091c\u093e\u090f\u0901\u0964<br>\u091c\u092c \u0906\u092a\u0915\u0947 \u092a\u093e\u0938 \u0915\u093e\u0909\u0902\u091f\u0930 \u0916\u093c\u0924\u094d\u092e \u0939\u094b \u0917\u090f \u0924\u094b \u0906\u092a\u0928\u0947 \u0915\u094d\u092f\u093e \u0915\u093f\u092f\u093e? \u0906\u0907\u0921\u093f\u092f\u093e \u0915\u0947 \u0932\u093f\u090f <b>\u091a\u093f\u0924\u094d\u0930-5<\/b> \u0926\u0947\u0916\u0947\u0902\u0964<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0906\u092a\u0928\u0947 \u0924\u0940\u0928\u094b\u0902 \u0938\u0935\u093e\u0932\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0939\u0940 \u0930\u0923\u0928\u0940\u0924\u093f \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e\u0964 \u0915\u094d\u092f\u093e \u0906\u092a\u0928\u0947 \u092a\u093e\u092f\u093e \u0915\u093f \u090f\u0915 \u0939\u0930\u0947 \u0915\u093e\u0909\u0902\u091f\u0930 \u0915\u094b \u0939\u091f\u093e\u0928\u093e, \u090f\u0915 \u0932\u093e\u0932 \u0915\u093e\u0909\u0902\u091f\u0930 \u0915\u094b \u091c\u094b\u0921\u093c\u0928\u0947 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u0940 \u0939\u0948? \u091c\u092c \u0906\u092a \u0915\u0930 \u0938\u0915\u0947\u0902, \u0924\u094b \u0910\u0938\u093e \u0915\u0930\u0915\u0947 \u0907\u0928\u094d\u0939\u0940\u0902 \u0938\u0935\u093e\u0932\u094b\u0902 \u0915\u094b \u092b\u093f\u0930 \u0938\u0947 \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u093e \u092a\u094d\u0930\u092f\u093e\u0938 \u0915\u0930\u0947\u0902\u0964 \u0915\u094d\u092f\u093e \u0906\u092a\u0915\u094b \u0935\u0939\u0940 \u0909\u0924\u094d\u0924\u0930 \u092e\u093f\u0932\u0924\u0947 \u0939\u0948\u0902?<\/p>\n\n\n\n<i><div class=\"ui-comments\" style=\"line-height:175% !important; background-color:#fdf7e5 !important; margin-bottom:2rem !important;\">\n  <p style=\"margin-bottom:0.5rem !important;\">\u0924\u094b, \u090f\u0915  <span style=\"color:#068006;\">\u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e<\/span> \u0915\u094b \u0918\u091f\u093e\u0928\u093e \u0907\u0938\u0915\u0947 \u0938\u092e\u0924\u0941\u0932\u094d\u092f \u0939\u0948 :<\/p>\n  \n  <ol style=\"list-style-type: lower-roman; margin-bottom: 0rem !important;\">\n    <li><span style=\"color:#068006;\">\u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902<\/span> \u0915\u094b <b>\u0939\u091f\u093e\u0928\u093e<\/b> (\u0914\u0930 \u092f\u0926\u093f \u0915\u094b\u0908 \u0936\u0942\u0928\u094d\u092f-\u091c\u094b\u0921\u093c\u0947 \u0939\u094b\u0902 \u0924\u094b \u0909\u0928\u094d\u0939\u0947\u0902 \u0939\u091f\u093e\u0928\u093e) <b>\u0905\u0925\u0935\u093e<\/b><\/li>\n    <li><span style=\"color:#FF0000;\">\u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902<\/span> \u0915\u094b \u091c\u094b\u0921\u093c\u0928\u093e\n    <\/li>\n<\/ol>\n<p style=\"margin-bottom: 0rem !important;\">\u0915\u094d\u092f\u093e \u0906\u092a\u0928\u0947 \u0936\u0942\u0928\u094d\u092f-\u091c\u094b\u0921\u093c\u093e (zero-pair) \u0930\u0923\u0928\u0940\u0924\u093f \u0915\u093e \u092a\u094d\u0930\u092f\u093e\u0938 \u0915\u093f\u092f\u093e? \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948 \u092f\u0926\u093f \u0939\u092e \u0924\u092c \u0924\u0915 \u0936\u0942\u0928\u094d\u092f-\u091c\u094b\u0921\u093c\u0947 \u091c\u094b\u0921\u093c\u0924\u0947 \u091c\u093e\u090f\u0901 \u091c\u092c \u0924\u0915 \u0915\u093f \u092a\u0930\u094d\u092f\u093e\u092a\u094d\u0924 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930 \u0928 \u0939\u094b \u091c\u093e\u090f\u0901 \u0914\u0930 \u092b\u093f\u0930 \u0909\u0928\u094d\u0939\u0947\u0902 \u0939\u091f\u093e \u0926\u0947\u0902?<\/p>\n<\/div><\/i>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-medium\"><img loading=\"lazy\" decoding=\"async\" width=\"552\" height=\"360\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure5-552x360.jpg\" alt=\"\" class=\"wp-image-27762\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure5-552x360.jpg 552w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure5-309x202.jpg 309w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure5-768x501.jpg 768w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure5.jpg 1103w\" sizes=\"auto, (max-width: 552px) 100vw, 552px\" \/><figcaption class=\"wp-element-caption\"><strong>\u091a\u093f\u0924\u094d\u0930-5<\/strong><\/figcaption><\/figure>\n<\/div>\n\n\n<p class=\"mb-1 wp-block-paragraph\"><em><strong>\u092f\u0939 \u0915\u0930\u0915\u0947 \u0926\u0947\u0916\u0947\u0902 :<\/strong><\/em><\/p>\n\n\n\n<ol start=\"7\" style=\"list-style-type:upper-roman\" class=\"wp-block-list mb-1\">\n<li><strong>(-5) \u2013 7:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-a nested-list mb-1\">\n<li>\u0915\u094d\u092f\u093e \u0906\u092a \u0907\u0938\u0915\u0947 \u0932\u093f\u090f \u0938\u0902\u0916\u094d\u092f\u093e \u0930\u0947\u0916\u093e \u092a\u0930 0 \u0924\u0915 \u092a\u0939\u0941\u0901\u091a\u0924\u0947 \u0939\u0948\u0902\/\u092f\u093e 0 \u0915\u094b \u092a\u093e\u0930 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902?<\/li>\n\n\n\n<li>\u0906\u092a\u0915\u094b \u0915\u093f\u0924\u0928\u0947 \u0936\u0942\u0928\u094d\u092f-\u091c\u094b\u0921\u093c\u0947 (zero pairs) \u091c\u094b\u0921\u093c\u0928\u0947 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u0948?<\/li>\n\n\n\n<li>\u0907\u0938\u0947 \u090f\u0915 \u092c\u093e\u0930 \u092e\u0947\u0902 \u090f\u0915 \u0915\u093c\u0926\u092e \u0915\u0930\u0915\u0947 \u0906\u091c\u093c\u092e\u093e\u090f\u0901\u0964 \u0906\u092a \u0915\u093f\u0924\u0928\u0947 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930 \u091c\u094b\u0921\u093c\u0924\u0947 \u0939\u0948\u0902?<\/li>\n\n\n\n<li>\u0906\u092a \u0907\u0928 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u094b \u0915\u093f\u0938 \u0938\u0902\u0916\u094d\u092f\u093e \u092e\u0947\u0902 \u091c\u094b\u0921\u093c\u0924\u0947 \u0939\u0948\u0902?<\/li>\n\n\n\n<li>\u0924\u094b, _______ \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u094b _______ \u092e\u0947\u0902 \u091c\u094b\u0921\u093c\u0928\u093e _______ + (- _______) \u0939\u0948\u0964 \u092f\u0939 (-5) \u2013 7 \u0938\u0947 \u0915\u093f\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u092e\u094d\u200d\u092c\u0928\u094d\u0927\u093f\u0924 \u0939\u0948?<\/li>\n\n\n\n<li>\u0936\u0942\u0928\u094d\u092f-\u091c\u094b\u0921\u093c\u094b\u0902 (zero pairs) \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0914\u0930 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0906\u092a\u0938 \u092e\u0947\u0902 \u0915\u093f\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u092e\u094d\u200d\u092c\u0928\u094d\u0927\u093f\u0924 \u0939\u0948\u0902?<\/li>\n<\/ul>\n\n\n\n<ol start=\"8\" style=\"list-style-type:upper-roman\" class=\"wp-block-list mb-1\">\n<li><strong>10 \u2013 14:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-a nested-list mb-1\">\n<li>\u0915\u094d\u092f\u093e \u0906\u092a \u0907\u0938\u0915\u0947 \u0932\u093f\u090f \u0938\u0902\u0916\u094d\u092f\u093e \u0930\u0947\u0916\u093e \u092a\u0930 0 \u0924\u0915 \u092a\u0939\u0941\u0901\u091a\u0924\u0947 \u0939\u0948\u0902\/\u092f\u093e 0 \u0915\u094b \u092a\u093e\u0930 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902?<\/li>\n\n\n\n<li>\u0906\u092a\u0915\u094b \u0915\u093f\u0924\u0928\u0947 \u0936\u0942\u0928\u094d\u092f-\u091c\u094b\u0921\u093c\u0947 \u091c\u094b\u0921\u093c\u0928\u0947 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u0948?<\/li>\n\n\n\n<li>\u0907\u0938\u0947 \u090f\u0915 \u092c\u093e\u0930 \u092e\u0947\u0902 \u090f\u0915 \u0915\u093c\u0926\u092e \u0915\u0930\u0915\u0947 \u0906\u091c\u093c\u092e\u093e\u090f\u0901\u0964 \u0906\u092a \u0915\u093f\u0924\u0928\u0947 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930 \u091c\u094b\u0921\u093c\u0924\u0947 \u0939\u0948\u0902?<\/li>\n\n\n\n<li>\u0906\u092a \u0907\u0928 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u094b \u0915\u093f\u0938 \u0938\u0902\u0916\u094d\u092f\u093e \u092e\u0947\u0902 \u091c\u094b\u0921\u093c\u0924\u0947 \u0939\u0948\u0902?<\/li>\n\n\n\n<li>\u0924\u094b, _______ \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u094b _______ \u092e\u0947\u0902 \u091c\u094b\u0921\u093c\u0928\u093e _______ + (- _______) \u0939\u0948\u0964 \u092f\u0939 10 \u2013 14 \u0938\u0947 \u0915\u093f\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u092e\u094d\u200d\u092c\u0928\u094d\u0927\u093f\u0924 \u0939\u0948?<\/li>\n\n\n\n<li>\u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0914\u0930 \u0936\u0942\u0928\u094d\u092f-\u091c\u094b\u0921\u093c\u094b\u0902 \u0915\u0940 \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u0938\u0902\u0916\u094d\u092f\u093e \u0906\u092a\u0938 \u092e\u0947\u0902 \u0915\u093f\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u092e\u094d\u200d\u092c\u0928\u094d\u0927\u093f\u0924 \u0939\u0948\u0902?<\/li>\n<\/ul>\n\n\n\n<ol start=\"6\" class=\"wp-block-list mb-1\">\n<li class=\"has-custom-css wp-custom-css-ce7a3319\"><strong>\u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u091c\u094b\u0921\u093c\u0928\u093e<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"mb-1 wp-block-paragraph\">\u091c\u092c \u0939\u092e \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u091c\u094b\u0921\u093c\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0939\u092e \u090f\u0915 \u0928\u0939\u0940\u0902, \u092c\u0932\u094d\u0915\u093f \u0915\u0908 \u0915\u093c\u0926\u092e ____________ (\u0926\u093e\u0908\u0902\/\u092c\u093e\u0908\u0902) \u0913\u0930 \u091a\u0932\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n\n\n\n<p class=\"mb-1 wp-block-paragraph\">(\u0915) -5 \u092e\u0947\u0902 -2 \u091c\u094b\u0921\u093c\u0947\u0902     (\u0916) 4 \u092e\u0947\u0902 -3 \u091c\u094b\u0921\u093c\u0947\u0902       (\u0917) 3 \u092e\u0947\u0902 -5 \u091c\u094b\u0921\u093c\u0947\u0902<\/p>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-a nested-list mb-1\">\n<li>(-5) + (-2) : -5 \u0915\u0947 ____________ (\u092c\u093e\u0908\u0902\/\u0926\u093e\u0908\u0902) \u0913\u0930_______ \u0915\u093c\u0926\u092e \u091a\u0932\u0947\u0902, \u0939\u0930 \u0915\u093c\u0926\u092e \u092a\u0930 1 ____________ (\u0932\u093e\u0932\/\u0939\u0930\u0947) \u0915\u093e\u0909\u0902\u091f\u0930 \u091c\u094b\u0921\u093c\u0924\u0947 \u091c\u093e\u090f\u0901\u0964<\/li>\n\n\n\n<li>4 + (-3) : 4 \u0915\u0947 ____________ (\u092c\u093e\u0908\u0902\/\u0926\u093e\u0908\u0902) \u0913\u0930 _______ \u0915\u093c\u0926\u092e \u091a\u0932\u0947\u0902, \u0939\u0930 \u0915\u093c\u0926\u092e \u092a\u0930 1 ____________ (\u0932\u093e\u0932\/\u0939\u0930\u0947) \u0915\u093e\u0909\u0902\u091f\u0930 \u091c\u094b\u0921\u093c\u0924\u0947 \u091c\u093e\u090f\u0901\u0964<\/li>\n\n\n\n<li>3 + (-5) : 3 \u0915\u0947 ____________ (\u092c\u093e\u0908\u0902\/\u0926\u093e\u0908\u0902) \u0913\u0930  _______ \u0915\u093c\u0926\u092e \u091a\u0932\u0947\u0902, \u0939\u0930 \u0915\u093c\u0926\u092e \u092a\u0930 1 ____________ (\u0932\u093e\u0932\/\u0939\u0930\u0947) \u0915\u093e\u0909\u0902\u091f\u0930 \u091c\u094b\u0921\u093c\u0924\u0947 \u091c\u093e\u090f\u0901\u0964<\/li>\n<\/ul>\n\n\n\n<p class=\"mb-1 wp-block-paragraph\">\u0915\u094d\u092f\u093e \u0906\u092a\u0915\u094b \u0915\u093f\u0938\u0940 \u092d\u0940 \u0938\u0935\u093e\u0932 \u0915\u0947 \u0932\u093f\u090f \u0936\u0942\u0928\u094d\u092f-\u091c\u094b\u0921\u093c\u093e \u092e\u093f\u0932\u093e?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0915\u094d\u092f\u093e \u090f\u0915 \u0932\u093e\u0932 \u0915\u093e\u0909\u0902\u091f\u0930 \u091c\u094b\u0921\u093c\u0928\u093e, \u090f\u0915 \u0939\u0930\u0947 \u0915\u093e\u0909\u0902\u091f\u0930 \u0915\u094b \u0939\u091f\u093e\u0928\u0947 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u0940 \u0939\u0948?<\/p>\n\n\n\n<div class=\"wp-block-group is-vertical is-content-justification-center is-layout-flex wp-container-core-group-is-layout-524f8de7 wp-block-group-is-layout-flex\">\n<figure class=\"wp-block-image size-thumbnail\"><img loading=\"lazy\" decoding=\"async\" width=\"360\" height=\"107\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure6-360x107.jpg\" alt=\"\" class=\"wp-image-27785\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure6-360x107.jpg 360w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure6-640x191.jpg 640w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure6-768x229.jpg 768w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure6.jpg 1200w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><figcaption class=\"wp-element-caption\"><strong>\u091a\u093f\u0924\u094d\u0930-6<\/strong><\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-thumbnail\"><img loading=\"lazy\" decoding=\"async\" width=\"360\" height=\"112\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure7-1-360x112.png\" alt=\"\" class=\"wp-image-28002\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure7-1-360x112.png 360w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure7-1-640x199.png 640w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure7-1-768x239.png 768w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure7-1.png 1200w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-thumbnail\"><img loading=\"lazy\" decoding=\"async\" width=\"360\" height=\"125\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure7-2-1-360x125.png\" alt=\"\" class=\"wp-image-28007\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure7-2-1-360x125.png 360w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure7-2-1-640x221.png 640w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure7-2-1-768x266.png 768w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure7-2-1.png 1200w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><figcaption class=\"wp-element-caption\"><strong>\u091a\u093f\u0924\u094d\u0930-7<\/strong><\/figcaption><\/figure>\n<\/div>\n\n\n\n<i><div class=\"ui-comments\" style=\"line-height:175% !important; background-color:#fdf7e5 !important; margin-bottom: 2rem;\">\n  <p style=\"margin-bottom:0.5rem !important;\">\u0915\u0926\u092e\u094b\u0902 \u0915\u0940 \u0926\u093f\u0936\u093e \u090a\u092a\u0930 \u0926\u093f\u090f \u0917\u090f \u092c\u093f\u0928\u094d\u0926\u0941 2 \u0938\u0947 \u0906\u0924\u0940 \u0939\u0948 \u092f\u0926\u093f \u0939\u092e \u092f\u0939 \u092e\u093e\u0928\u0947\u0902 \u0915\u093f 3 \u0915\u094b \u091c\u094b\u0921\u093c\u0928\u093e, -1 \u0915\u094b \u0924\u0940\u0928 \u092c\u093e\u0930 \u091c\u094b\u0921\u093c\u0928\u0947 \u091c\u0948\u0938\u093e \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0947 \u0926\u0947\u0916\u0928\u0947 \u0915\u093e \u090f\u0915 \u0914\u0930 \u0924\u0930\u0940\u0915\u093c\u093e \u092f\u0939 \u0939\u094b\u0917\u093e \u0915\u093f \u092f\u0939 3 \u0915\u094b \u091c\u094b\u0921\u093c\u0928\u0947 \u0938\u0947 \u0905\u0932\u0917 \u0939\u0948\u0964 \u0907\u0938\u0932\u093f\u090f, \u092f\u0939 \u0909\u0938\u0940 \u0926\u093f\u0936\u093e \u092e\u0947\u0902 \u0915\u093c\u0926\u092e \u092c\u0922\u093c\u093e\u0928\u093e \u0928\u0939\u0940\u0902 \u0939\u094b \u0938\u0915\u0924\u093e \u091c\u0948\u0938\u093e \u0915\u093f \u090f\u0915 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b \u091c\u094b\u0921\u093c\u0924\u0947 \u0938\u092e\u092f \u0939\u094b\u0924\u093e \u0939\u0948! \u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0902 \u0915\u093f \u092f\u0926\u093f \u0939\u092e \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930 \u091c\u094b\u0921\u093c\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u092a\u0930\u093f\u0923\u093e\u092e\u0940 \u0936\u0942\u0928\u094d\u092f-\u091c\u094b\u0921\u093c\u094b\u0902 \u0915\u094b \u0939\u091f\u093e \u0926\u093f\u092f\u093e \u091c\u093e\u0928\u093e \u091a\u093e\u0939\u093f\u090f <b>(\u091a\u093f\u0924\u094d\u0930-6)<\/b> \u0964 \u0938\u0935\u093e\u0932 (\u0917) \u0915\u0947 \u0932\u093f\u090f \u0906\u092a \u0915\u093f\u0928 \u0905\u0932\u0917-\u0905\u0932\u0917 \u0930\u0923\u0928\u0940\u0924\u093f\u092f\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902? \u0915\u094d\u092f\u093e \u0906\u092a\u0915\u094b \u0935\u0939\u0940 \u092a\u0930\u093f\u0923\u093e\u092e \u092e\u093f\u0932\u0924\u093e \u0939\u0948 \u091c\u094b \u090f\u0915 \u092c\u093e\u0930 \u092e\u0947\u0902 \u090f\u0915 \u0915\u093c\u0926\u092e \u0906\u0917\u0947 \u092c\u0922\u093c\u0928\u0947 \u0938\u0947 \u092e\u093f\u0932\u0924\u093e \u0939\u0948? <b>(\u091a\u093f\u0924\u094d\u0930-7)<\/b> \u0924\u094b, \u090f\u0915 <span style=\"color:#FF0000;\"> \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e<\/span> \u0915\u094b \u091c\u094b\u0921\u093c\u0928\u093e \u0907\u0938\u0915\u0947 \u0938\u092e\u0924\u0941\u0932\u094d\u092f (\u092c\u0930\u093e\u092c\u0930) \u0939\u0948 :<\/p>\n  \n  <ol style=\"list-style-type: lower-roman; margin-bottom: 0rem !important;\">\n    <li><span style=\"color:#FF0000;\">\u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902<\/span> \u0915\u094b ______________ (\u091c\u094b\u0921\u093c\u0928\u093e\/\u0939\u091f\u093e\u0928\u093e)<\/li>\n    <li><span style=\"color:#068006;\">\u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902<\/span> \u0915\u094b ______________ (\u091c\u094b\u0921\u093c\u0928\u093e\/\u0939\u091f\u093e\u0928\u093e) \u0915\u094d\u092f\u093e \u092f\u0939 \u0935\u0948\u0938\u093e \u0939\u0940 \u0939\u0948 \u091c\u0948\u0938\u093e \u0939\u092e \u092a\u0939\u0932\u0947 \u0939\u0940 \u0915\u0941\u091b \u0915\u0930 \u091a\u0941\u0915\u0947 \u0939\u0948\u0902?\n    <\/li>\n<\/ol>\n<p style=\"margin-bottom: 0rem !important;\">\u0924\u094b, \u090f\u0915 <span style=\"color:#068006;\">\u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e<\/span> \u0915\u094b \u091c\u094b\u0921\u093c\u0928\u093e, \u090f\u0915<span style=\"color:#068006;\"> \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e<\/span> \u0915\u094b ______________ (\u091c\u094b\u0921\u093c\u0928\u0947\/\u0918\u091f\u093e\u0928\u0947) \u0915\u0947 \u0938\u092e\u0924\u0941\u0932\u094d\u092f \u0939\u0948\u0964\n<br>\u092f\u0947 \u0926\u094b\u0928\u094b\u0902 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u0906\u092a\u0938 \u092e\u0947\u0902 \u0915\u093f\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u092e\u094d\u092c\u0928\u094d\u0927\u093f\u0924 \u0939\u0948?<sup>1<\/sup><\/p>\n<\/div><\/i>\n\n\n\n<p class=\"mb-1 wp-block-paragraph\"><em><strong>\u092f\u0939 \u0915\u0930\u0915\u0947 \u0926\u0947\u0916\u0947\u0902 :<\/strong><\/em><\/p>\n\n\n\n<ol start=\"9\" style=\"list-style-type:upper-roman\" class=\"wp-block-list\">\n<li>7 + (-7) = ___<\/li>\n\n\n\n<li>3 + ___ = 0<\/li>\n\n\n\n<li>____ + (-6) = 0<\/li>\n<\/ol>\n\n\n\n<p class=\"mb-1 wp-block-paragraph\"><em><strong>\u0938\u094b\u091a\u0947\u0902 :<\/strong><\/em><\/p>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-f is-uppercase mb-1\">\n<li>\u091f\u093f\u0902\u0915\u0942 \u092a\u0930 \u20b9200 \u0915\u093e \u0915\u0930\u094d\u091c\u093c (debt) \u0925\u093e \u0914\u0930 \u0909\u0938\u0947 \u20b9500 \u0914\u0930 \u0909\u0927\u093e\u0930 \u0932\u0947\u0928\u0947 \u092a\u0921\u093c\u0947\u0964<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-a nested-list mb-1\">\n<li>\u0905\u092c \u0915\u0941\u0932 \u0915\u093f\u0924\u0928\u093e \u0915\u0930\u094d\u091c\u093c \u0939\u094b \u0917\u092f\u093e \u0939\u0948?<\/li>\n\n\n\n<li>\u092f\u0926\u093f \u20b9200 \u0915\u0947 \u0915\u0930\u094d\u091c\u093c \u0915\u094b -2 \u092e\u093e\u0928\u093e \u091c\u093e\u090f, \u0924\u094b \u0928\u092f\u093e \u0915\u0930\u094d\u091c\u093c \u0914\u0930 \u0915\u0941\u0932 \u0915\u0930\u094d\u091c\u093c \u0915\u094d\u092f\u093e \u0939\u094b\u0902\u0917\u0947?<\/li>\n\n\n\n<li>\u0924\u094b, (-2) + _______ = _______ = (-2) \u2013 _______<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-g is-uppercase mb-1\">\n<li>\u091f\u093f\u0928\u091f\u093f\u0928 \u0915\u0947 \u092a\u093e\u0938 \u20b9400 \u0925\u0947 \u0914\u0930 \u0909\u0938\u0947 \u20b9100 \u0915\u093e \u0928\u0941\u0915\u093c\u0938\u093e\u0928 (loss) \u0939\u0941\u0906\u0964<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-a nested-list mb-1\">\n<li>If  \u20b9400 \u0915\u094b 4 \u092e\u093e\u0928\u093e \u091c\u093e\u090f, \u0924\u094b \u20b9100 \u0915\u093e \u0928\u0941\u0915\u093c\u0938\u093e\u0928 ___ (1\/-1).<\/li>\n\n\n\n<li>\u0915\u093c\u0938\u093e\u0928 \u0915\u0947 \u092c\u093e\u0926 \u091f\u093f\u0928\u091f\u093f\u0928 \u0915\u0947 \u092a\u093e\u0938 \u0915\u093f\u0924\u0928\u0947 \u20b9 \u092c\u091a\u0947? \u0914\u0930 _______ \u20b9 \u0915\u093e \u0928\u0941\u0915\u093c\u0938\u093e\u0928 _______ \u0939\u0948\u0964<\/li>\n\n\n\n<li>\u0924\u094b, 4 + _______ = _______<\/li>\n\n\n\n<li>\u092f\u0926\u093f \u0928\u0941\u0915\u093c\u0938\u093e\u0928 \u20b9900 \u0915\u093e \u0939\u094b\u0924\u093e, \u0924\u094b \u091f\u093f\u0928\u091f\u093f\u0928 \u0915\u0947 \u092a\u093e\u0938 \u0915\u094d\u092f\u093e \u092c\u091a\u0924\u093e?<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-h is-uppercase mb-1\">\n<li>\u091f\u0941\u0932\u0941 \u0915\u0947 \u092a\u093e\u0938 \u092d\u0940 \u20b9400 \u0925\u0947 \u0914\u0930 \u0909\u0938\u0928\u0947 \u20b9100 \u0916\u0930\u094d\u091a \u0915\u093f\u090f\u0964<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-a nested-list\">\n<li>\u0907\u0938\u0940 \u0938\u0902\u0915\u0947\u0924-\u092a\u0926\u094d\u0927\u0924\u093f (notation) \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f, \u0915\u094d\u092f\u093e \u092f\u0939 4 \u2013 1 = _______ \u0939\u0948?<\/li>\n\n\n\n<li>\u0924\u094b, \u0915\u094d\u092f\u093e 4 + (-1) = 4 \u2013 1 \u0939\u0948?<\/li>\n\n\n\n<li>\u092f\u0926\u093f \u091f\u0941\u0932\u0941 \u0915\u094b \u20b9900 \u0916\u0930\u094d\u091a \u0915\u0930\u0928\u0947 \u092a\u0921\u093c\u0924\u0947, \u0924\u094b \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e?<\/li>\n\n\n\n<li>\u092f\u0926\u093f \u091f\u093f\u0928\u091f\u093f\u0928 \u0915\u094b \u20b9900 \u0915\u093e \u0928\u0941\u0915\u093c\u0938\u093e\u0928 \u0939\u094b\u0924\u093e \u0914\u0930 \u091f\u0941\u0932\u0941 \u0915\u094b \u20b9900 \u0916\u0930\u094d\u091a \u0915\u0930\u0928\u0947 \u092a\u0921\u093c\u0924\u0947, \u0924\u094b \u0915\u094c\u0928 \u0905\u0927\u093f\u0915 \u0917\u093c\u0930\u0940\u092c \u0939\u094b\u0924\u093e?<\/li>\n<\/ul>\n\n\n\n<ol start=\"7\" class=\"wp-block-list mb-1\">\n<li class=\"has-custom-css wp-custom-css-8361c2c4\"><strong>\u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915\u094b\u0902 \u0915\u093e \u092f\u094b\u0917<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u092f\u094b\u0917 (\u091c\u094b\u0921\u093c) \u0915\u0947 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u091c\u094b\u0921\u093c\u094b\u0902 (pairs) \u092a\u0930 \u0935\u093f\u091a\u093e\u0930 \u0915\u0930\u0947\u0902 : 5 + (-1) \u0914\u0930 (-1) + 5 (\u091a\u093f\u0924\u094d\u0930-8 ) \u0914\u0930 \u0938\u093e\u0925 \u0939\u0940 2 + (-5) \u0924\u0925\u093e (-5) + 2 (\u091a\u093f\u0924\u094d\u0930-9)\u0964 \u0906\u092a \u0915\u094d\u092f\u093e \u0926\u0947\u0916\u0924\u0947 \u0939\u0948\u0902?<\/p>\n\n\n\n<div class=\"wp-block-group is-vertical is-content-justification-center is-layout-flex wp-container-core-group-is-layout-20d0575b wp-block-group-is-layout-flex\">\n<figure class=\"wp-block-image size-medium\"><img loading=\"lazy\" decoding=\"async\" width=\"512\" height=\"360\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure8-512x360.jpg\" alt=\"\" class=\"wp-image-27804\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure8-512x360.jpg 512w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure8-1025x720.jpg 1025w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure8-288x202.jpg 288w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure8-768x540.jpg 768w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure8.jpg 1200w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><figcaption class=\"wp-element-caption\"><strong>\u091a\u093f\u0924\u094d\u0930-8<\/strong><\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-medium\"><img loading=\"lazy\" decoding=\"async\" width=\"571\" height=\"360\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure9-571x360.jpg\" alt=\"\" class=\"wp-image-27807\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure9-571x360.jpg 571w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure9-1143x720.jpg 1143w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure9-321x202.jpg 321w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure9-768x484.jpg 768w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure9.jpg 1200w\" sizes=\"auto, (max-width: 571px) 100vw, 571px\" \/><figcaption class=\"wp-element-caption\"><strong>\u091a\u093f\u0924\u094d\u0930-9<\/strong><\/figcaption><\/figure>\n<\/div>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-a nested-list mb-1\">\n<li><b>\u091a\u093f\u0924\u094d\u0930-8<\/b> \u0915\u0947 \u0926\u094b\u0928\u094b\u0902 \u091a\u093f\u0924\u094d\u0930 \u0906\u092a\u0938 \u092e\u0947\u0902 \u0915\u093f\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u092e\u094d\u200d\u092c\u0928\u094d\u0927\u093f\u0924 \u0939\u0948\u0902? \u0915\u094d\u092f\u093e \u0906\u092a \u0928\u0940\u091a\u0947 \u0935\u093e\u0932\u093e \u091a\u093f\u0924\u094d\u0930 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u090a\u092a\u0930 \u0935\u093e\u0932\u0947 \u091a\u093f\u0924\u094d\u0930 \u0915\u094b \u0915\u093f\u0938\u0940 \u0932\u092e\u094d\u200d\u092c\u0935\u0924 \u0930\u0947\u0916\u093e \u0915\u0947 \u0905\u0928\u0941\u0926\u093f\u0936 \u092a\u0930\u093e\u0935\u0930\u094d\u0924\u093f\u0924 (reflect) \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902?<\/li>\n\n\n\n<li><b>\u091a\u093f\u0924\u094d\u0930-8<\/b> \u0915\u0947 \u0932\u093f\u090f \u092f\u0939 \u0932\u092e\u094d\u200d\u092c\u0935\u0924 \u0930\u0947\u0916\u093e \u092f\u093e \u0926\u0930\u094d\u092a\u0923 (mirror) \u0915\u0939\u093e\u0901 \u092a\u0930 \u0938\u094d\u0925\u093f\u0924 \u0939\u0948?<sup>2<\/sup><\/li>\n\n\n\n<li>\u0909\u0938 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b \u0927\u094d\u092f\u093e\u0928 \u0938\u0947 \u0926\u0947\u0916\u0947\u0902 \u091c\u093f\u0938\u0938\u0947 \u0939\u094b\u0915\u0930 \u092f\u0939 \u0926\u0930\u094d\u092a\u0923 (mirror) \u0917\u0941\u091c\u0930 \u0930\u0939\u093e \u0939\u0948\u0964 \u0906\u092a 5 \u0914\u0930 -1 \u0938\u0947 \u092f\u0939 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0948\u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902?<\/li>\n\n\n\n<li>\u0915\u094d\u092f\u093e \u0906\u092a <b>\u091a\u093f\u0924\u094d\u0930-9<\/b> \u0915\u0947 \u0932\u093f\u090f \u092d\u0940 \u0910\u0938\u093e \u0939\u0940 \u090f\u0915 \u0926\u0930\u094d\u092a\u0923 \u0922\u0942\u0901\u0922\u093c \u0938\u0915\u0924\u0947 \u0939\u0948\u0902? \u092f\u0939 \u0915\u093f\u0938 \u0938\u0902\u0916\u094d\u092f\u093e \u0938\u0947 \u0939\u094b\u0915\u0930 \u0917\u0941\u091c\u0930\u0924\u093e \u0939\u0948? \u0906\u092a 2 \u0914\u0930 -5 \u0938\u0947 \u092f\u0939 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0948\u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902?<sup>3<\/sup><\/li>\n\n\n\n<li>(-2) + (-4) \u0914\u0930 (-4) + (-2) \u0915\u0947 \u0932\u093f\u090f \u092d\u0940 \u0907\u0938\u0940 \u0924\u0930\u0939 \u0915\u093e \u0905\u0935\u0932\u094b\u0915\u0928 \u0915\u0930\u0947\u0902\u0964 3 + 4 \u0914\u0930 4 + 3 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u0906\u092a\u0915\u093e \u0915\u094d\u092f\u093e \u0935\u093f\u091a\u093e\u0930 \u0939\u0948?<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0907\u0938\u0947 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u091c\u094b\u0921\u093c\u094b\u0902 (pairs) \u0915\u0947 \u0938\u093e\u0925 \u0906\u091c\u093c\u092e\u093e\u090f\u0901\u0964 \u0906\u092a \u0915\u094d\u092f\u093e \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 \u0928\u093f\u0915\u093e\u0932\u0924\u0947 \u0939\u0948\u0902?<sup>4<\/sup><\/p>\n\n\n\n<ol start=\"8\" class=\"wp-block-list mb-1\">\n<li class=\"has-custom-css wp-custom-css-d0886ad6\"><strong>\u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u0918\u091f\u093e\u0928\u093e<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"mb-1 wp-block-paragraph\">\u091c\u092c \u0939\u092e \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u0918\u091f\u093e\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0939\u092e \u090f\u0915 \u0928\u0939\u0940\u0902, \u092c\u0932\u094d\u0915\u093f \u0915\u0908 \u0915\u093c\u0926\u092e ____________ (\u0926\u093e\u0908\u0902\/\u092c\u093e\u0908\u0902) \u0913\u0930 \u091a\u0932\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0906\u092a ____________ (\u0932\u093e\u0932\/\u0939\u0930\u0947) \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u094b \u0939\u091f\u093e\u0924\u0947 \u0939\u0948\u0902\u0964\n\n [\u0905\u092c \u0906\u092a\u0915\u094b \u092a\u0924\u093e \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f \u0915\u093f \u0915\u093e\u0909\u0902\u091f\u0930 \u0916\u0924\u094d\u092e \u0939\u094b\u0928\u0947 \u092a\u0930 \u0915\u094d\u092f\u093e \u0915\u0930\u0928\u093e \u0939\u0948\u0964]<\/p>\n\n\n\n<p class=\"mb-1 wp-block-paragraph\">(\u0915) -5 \u092e\u0947\u0902 \u0938\u0947 -3 \u0918\u091f\u093e\u090f\u0901        (\u0916) 3 \u092e\u0947\u0902 \u0938\u0947 -4 \u0918\u091f\u093e\u090f\u0901       (\u0917) -2 \u092e\u0947\u0902 \u0938\u0947 -6 \u0918\u091f\u093e\u090f\u0901<\/p>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-a  mb-1\">\n<li>(-5) \u2013 (-3) : -5 \u0915\u0947 ____________ (\u092c\u093e\u0908\u0902\/\u0926\u093e\u0908\u0902) \u0913\u0930 _______ \u0915\u093c\u0926\u092e \u091a\u0932\u0947\u0902, \u0939\u0930 \u0915\u093c\u0926\u092e \u092a\u0930 1 \u0915\u093e\u0909\u0902\u091f\u0930 \u0939\u091f\u093e\u0924\u0947 \u091c\u093e\u090f\u0901\u0964<\/li>\n\n\n\n<li>3 \u2013 (-4) : 3 \u0915\u0947 ____________ (\u092c\u093e\u0908\u0902\/\u0926\u093e\u0908\u0902) \u0913\u0930 _______ \u0915\u093c\u0926\u092e \u091a\u0932\u0947\u0902, \u0939\u0930 \u0915\u093c\u0926\u092e \u092a\u0930 1 \u0915\u093e\u0909\u0902\u091f\u0930 \u0939\u091f\u093e\u0924\u0947 \u091c\u093e\u090f\u0901\u0964 \u092f\u0926\u093f \u0939\u092e \u0936\u0942\u0928\u094d\u092f-\u091c\u094b\u0921\u093c\u0947 (zero-pairs) \u091c\u094b\u0921\u093c\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0935\u0939 \u0915\u093f\u0928 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u091c\u094b\u0921\u093c\u0928\u0947 \u0915\u0947 \u0938\u092e\u0924\u0941\u0932\u094d\u092f \u0939\u0948? (<b>\u091a\u093f\u0924\u094d\u0930-10<\/b>  \u0926\u0947\u0916\u0947\u0902)<br>\u0915\u094d\u092f\u093e \u0906\u092a \u0907\u0928 \u091a\u0930\u0923\u094b\u0902 \u0915\u094b \u092a\u0942\u0930\u093e \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902? \u0905\u0928\u094d\u0924\u093f\u092e \u091a\u0930\u0923 \u092e\u0947\u0902 3 \u0915\u0947 \u092c\u093e\u0926 \u0915\u094d\u092f\u093e \u0906\u0924\u093e \u0939\u0948? 3 \u2013 (-4) = 3 \u2013 (-4) + 0 = 3 \u2013 (-4) + _______ + (- _______) = 3 _______<br>\u0915\u094d\u092f\u093e \u0906\u092a\u0915\u094b \u0926\u094b\u0928\u094b\u0902 \u092c\u093e\u0930 \u090f\u0915 \u0939\u0940 \u0909\u0924\u094d\u0924\u0930 \u092e\u093f\u0932\u093e?<\/li>\n\n\n\n<li>\u2013 (-6) : -2 \u0915\u0947 ____________ (\u092c\u093e\u0908\u0902\/\u0926\u093e\u0908\u0902) \u0913\u0930 _______ \u0915\u093c\u0926\u092e \u091a\u0932\u0947\u0902, \u0939\u0930 \u0915\u093c\u0926\u092e \u092a\u0930 1 \u0915\u093e\u0909\u0902\u091f\u0930 \u0939\u091f\u093e\u0924\u0947 \u091c\u093e\u090f\u0901\u0964 \u092f\u0926\u093f \u0939\u092e \u0907\u0938\u0915\u0947 \u092c\u091c\u093e\u092f \u0936\u0942\u0928\u094d\u092f-\u091c\u094b\u0921\u093c\u0947 \u091c\u094b\u0921\u093c\u0924\u0947 \u0939\u0948\u0902 \u0924\u094b \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948? \u0939\u092e\u0947\u0902 \u0915\u093f\u0924\u0928\u0947 \u0936\u0942\u0928\u094d\u092f-\u091c\u094b\u0921\u093c\u094b\u0902 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u094b\u0917\u0940? \u0915\u094d\u092f\u093e \u0906\u092a \u0907\u0928 \u091a\u0930\u0923\u094b\u0902 \u0915\u094b \u092a\u0942\u0930\u093e \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902? [\u0938\u0902\u0915\u0947\u0924: <b>\u091a\u093f\u0924\u094d\u0930-11<\/b> \u0926\u0947\u0916\u0947\u0902] \n\n(-2) \u2013 (-6) = (-2) \u2013 (-6) + 0 = (-2) \u2013 (-6) + _______ + (- _______) = (-2) _______ \u0915\u094d\u092f\u093e \u0906\u092a\u0915\u094b \u0935\u0939\u0940 \u0909\u0924\u094d\u0924\u0930 \u092e\u093f\u0932\u093e?<\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-group is-vertical is-content-justification-center is-layout-flex wp-container-core-group-is-layout-524f8de7 wp-block-group-is-layout-flex\">\n<figure class=\"wp-block-image size-thumbnail\"><img loading=\"lazy\" decoding=\"async\" width=\"347\" height=\"202\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure10-347x202.jpg\" alt=\"\" class=\"wp-image-27818\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure10-347x202.jpg 347w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure10-619x360.jpg 619w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure10-768x447.jpg 768w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure10.jpg 1200w\" sizes=\"auto, (max-width: 347px) 100vw, 347px\" \/><figcaption class=\"wp-element-caption\"><strong>\u091a\u093f\u0924\u094d\u0930-10<\/strong><\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-thumbnail\"><img loading=\"lazy\" decoding=\"async\" width=\"354\" height=\"202\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure11-354x202.jpg\" alt=\"\" class=\"wp-image-27821\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure11-354x202.jpg 354w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure11-632x360.jpg 632w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure11-768x438.jpg 768w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/colors_Figure11.jpg 1200w\" sizes=\"auto, (max-width: 354px) 100vw, 354px\" \/><figcaption class=\"wp-element-caption\"><strong>\u091a\u093f\u0924\u094d\u0930-11<\/strong><\/figcaption><\/figure>\n<\/div>\n\n\n\n<i><div class=\"ui-comments\" style=\"line-height:175% !important; background-color:#fdf7e5 !important; margin-bottom: 2rem;\">\n  <p style=\"margin-bottom:0.5rem !important;\">\u0907\u0938\u0932\u093f\u090f, \u091c\u0948\u0938\u0947-\u091c\u0948\u0938\u0947 \u0939\u092e \u092f\u0947 \u0915\u093c\u0926\u092e \u092c\u0922\u093c\u093e\u0924\u0947 \u0939\u0948\u0902, \u0939\u092e ___________ (\u0927\u0928\u093e\u0924\u094d\u092e\u0915\/\u090b\u0923\u093e\u0924\u094d\u092e\u0915) \u0915\u093e\u0909\u0902\u091f\u0930 \u091c\u094b\u0921\u093c \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<p style=\"margin-bottom:0.5rem !important;\"> \u0924\u094b, \u090f\u0915 <span style=\"color:#068006;\">\u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e<\/span> \u0915\u094b \u0918\u091f\u093e\u0928\u093e \u0907\u0938\u0915\u0947 \u0938\u092e\u0924\u0941\u0932\u094d\u092f \u0939\u0948 :<\/p>\n  \n  <ol style=\"margin-bottom: 0rem !important; list-style-type: lower-roman;\">\n    <li>(\u091c\u094b\u0921\u093c\u0928\u093e\/\u0939\u091f\u093e\u0928\u093e) <span style=\"color:#FF0000;\">\u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902<\/span> \u0915\u094b ______________ (\u091c\u094b\u0921\u093c\u0928\u093e\/\u0939\u091f\u093e\u0928\u093e)<\/li>\n    <li><span style=\"color:#068006;\">\u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902<\/span> \u0915\u094b  ______________ (\u091c\u094b\u0921\u093c\u0928\u093e\/\u0939\u091f\u093e\u0928\u093e)\n    <\/li>\n<\/ol>\n<p style=\"margin-bottom: 0rem !important;\">\u0915\u094d\u092f\u093e \u092f\u0939 \u0935\u0948\u0938\u093e \u0939\u0940 \u0939\u0948 \u091c\u0948\u0938\u093e \u0939\u092e \u092a\u0939\u0932\u0947 \u0939\u0940 \u0915\u0941\u091b \u0915\u0930 \u091a\u0941\u0915\u0947 \u0939\u0948\u0902? <br>\n\u0924\u094b, \u090f\u0915 <span style=\"color:#FF0000;\">\u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e<\/span> \u0915\u094b \u0918\u091f\u093e\u0928\u093e, \u090f\u0915 <span style=\"color:#068006;\">\u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e<\/span> \u0915\u094b ______________ (\u091c\u094b\u0921\u093c\u0928\u0947\/\u0918\u091f\u093e\u0928\u0947) \u0915\u0947 \u0938\u092e\u0924\u0941\u0932\u094d\u092f \u0939\u0948\u0964<br>\u092f\u0947 \u0926\u094b\u0928\u094b\u0902 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u0906\u092a\u0938 \u092e\u0947\u0902 \u0915\u093f\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u092e\u094d\u092c\u0928\u094d\u0927\u093f\u0924 \u0939\u0948\u0902?<sup>5<\/sup><\/p>\n<\/div><\/i>\n\n\n\n<p class=\"mb-1 wp-block-paragraph\"><em><strong>\u092f\u0939 \u0915\u0930\u0915\u0947 \u0926\u0947\u0916\u0947\u0902 :<\/strong><\/em><\/p>\n\n\n\n<ol start=\"12\" style=\"list-style-type:upper-roman\" class=\"wp-block-list mb-1\">\n<li><strong>6 \u2013 (-2)<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-a nested-list mb-1\">\n<li>\u0915\u094d\u092f\u093e \u0906\u092a \u0907\u0938\u0915\u0947 \u0932\u093f\u090f \u0938\u0902\u0916\u094d\u092f\u093e \u0930\u0947\u0916\u093e \u092a\u0930 0 \u0924\u0915 \u092a\u0939\u0941\u0901\u091a\u0924\u0947 \u0939\u0948\u0902\/\u092f\u093e 0 \u0915\u094b \u092a\u093e\u0930 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902?<\/li>\n\n\n\n<li>\u0906\u092a\u0915\u094b \u0915\u093f\u0924\u0928\u0947 \u0936\u0942\u0928\u094d\u092f-\u091c\u094b\u0921\u093c\u0947 (zero pairs) \u091c\u094b\u0921\u093c\u0928\u0947 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u0948?<\/li>\n\n\n\n<li>\u0907\u0938\u0947 \u090f\u0915 \u092c\u093e\u0930 \u092e\u0947\u0902 \u090f\u0915 \u0915\u093c\u0926\u092e \u0915\u0930\u0915\u0947 \u0906\u091c\u093c\u092e\u093e\u090f\u0901\u0964 \u0906\u092a \u0915\u093f\u0924\u0928\u0947 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930 \u091c\u094b\u0921\u093c\u0924\u0947 \u0939\u0948\u0902?<\/li>\n\n\n\n<li>\u0906\u092a \u0907\u0928 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u094b \u0915\u093f\u0938 \u0938\u0902\u0916\u094d\u092f\u093e \u092e\u0947\u0902 \u091c\u094b\u0921\u093c\u0924\u0947 \u0939\u0948\u0902?<\/li>\n\n\n\n<li>\u0924\u094b, _______ \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u094b _______ \u092e\u0947\u0902 \u091c\u094b\u0921\u093c\u0928\u093e _______ + _______ \u0939\u0948\u0964 \u092f\u0939 6 \u2013 (-2) \u0938\u0947 \u0915\u093f\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u092e\u094d\u200d\u092c\u0928\u094d\u0927\u093f\u0924 \u0939\u0948?<\/li>\n\n\n\n<li>\u0936\u0942\u0928\u094d\u092f-\u091c\u094b\u0921\u093c\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0914\u0930 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0906\u092a\u0938 \u092e\u0947\u0902 \u0915\u093f\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u092e\u094d\u200d\u092c\u0928\u094d\u0927\u093f\u0924 \u0939\u0948\u0902?<\/li>\n<\/ul>\n\n\n\n<ol start=\"13\" style=\"list-style-type:upper-roman\" class=\"wp-block-list mb-1\">\n<li><strong>(-3) \u2013 (-4)<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-a nested-list\">\n<li>\u0915\u094d\u092f\u093e \u0906\u092a \u0907\u0938\u0915\u0947 \u0932\u093f\u090f \u0938\u0902\u0916\u094d\u092f\u093e \u0930\u0947\u0916\u093e \u092a\u0930 0 \u0924\u0915 \u092a\u0939\u0941\u0901\u091a\u0924\u0947 \u0939\u0948\u0902\/\u092f\u093e 0 \u0915\u094b \u092a\u093e\u0930 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902?<\/li>\n\n\n\n<li>\u0906\u092a\u0915\u094b \u0915\u093f\u0924\u0928\u0947 \u0936\u0942\u0928\u094d\u092f-\u091c\u094b\u0921\u093c\u0947 \u091c\u094b\u0921\u093c\u0928\u0947 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u0948?<\/li>\n\n\n\n<li>\u0907\u0938\u0947 \u090f\u0915 \u092c\u093e\u0930 \u092e\u0947\u0902 \u090f\u0915 \u0915\u093c\u0926\u092e \u0915\u0930\u0915\u0947 \u0906\u091c\u093c\u092e\u093e\u090f\u0901\u0964 \u0906\u092a \u0915\u093f\u0924\u0928\u0947 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930 \u091c\u094b\u0921\u093c\u0924\u0947 \u0939\u0948\u0902?<\/li>\n\n\n\n<li>\u0906\u092a \u0907\u0928 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u094b \u0915\u093f\u0938 \u0938\u0902\u0916\u094d\u092f\u093e \u092e\u0947\u0902 \u091c\u094b\u0921\u093c\u0924\u0947 \u0939\u0948\u0902?<\/li>\n\n\n\n<li>\u0924\u094b, _______ \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u094b _______ \u092e\u0947\u0902 \u091c\u094b\u0921\u093c\u0928\u093e _______ + _______ \u0939\u0948\u0964 \u092f\u0939 (-3) \u2013 (-4) \u0938\u0947 \u0915\u093f\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u092e\u094d\u200d\u092c\u0928\u094d\u0927\u093f\u0924 \u0939\u0948?<\/li>\n\n\n\n<li>\u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0914\u0930 \u0936\u0942\u0928\u094d\u092f-\u091c\u094b\u0921\u093c\u094b\u0902 \u0915\u0940 \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u0938\u0902\u0916\u094d\u092f\u093e \u0906\u092a\u0938 \u092e\u0947\u0902 \u0915\u093f\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u092e\u094d\u200d\u092c\u0928\u094d\u0927\u093f\u0924 \u0939\u0948\u0902?<\/li>\n<\/ul>\n\n\n\n<p class=\"mb-1 wp-block-paragraph\"><em><strong>\u0938\u094b\u091a\u0947\u0902 :<\/strong><\/em><\/p>\n\n\n\n<ul class=\"wp-block-list mb-1 list-type-alpha start-i is-uppercase\">\n<li>\u0938\u0930\u094d\u0926\u093f\u092f\u094b\u0902 \u0915\u0940 \u090f\u0915 \u092c\u0947\u0939\u0926 \u0938\u0930\u094d\u0926 \u0930\u093e\u0924 \u092e\u0947\u0902, \u0936\u094d\u0930\u0940\u0928\u0917\u0930 \u0915\u093e \u0924\u093e\u092a\u092e\u093e\u0928 -6\u00b0C \u0925\u093e, \u091c\u092c\u0915\u093f \u0932\u0947\u0939 \u0915\u093e \u0924\u093e\u092a\u092e\u093e\u0928 -17\u00b0C \u0914\u0930 \u0917\u0902\u0917\u091f\u094b\u0915 \u0915\u093e \u0924\u093e\u092a\u092e\u093e\u0928 8\u00b0C \u0925\u093e\u0964<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-a  nested-list mb-1\">\n<li>\u0915\u094c\u0928-\u0938\u093e \u0936\u0939\u0930 \u0905\u0927\u093f\u0915 \u0920\u0923\u094d\u200d\u0921\u093e \u0925\u093e : \u0936\u094d\u0930\u0940\u0928\u0917\u0930 \u092f\u093e \u0932\u0947\u0939?<\/li>\n\n\n\n<li>_______ \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u092e\u0947\u0902 _______ \u0905\u0927\u093f\u0915 \u0920\u0923\u094d\u200d\u0921\u093e \u0925\u093e, \u091c\u094b \u0915\u093f (_______ \u2013 _______) = _______ \u00b0C \u0939\u0948\u0964<\/li>\n\n\n\n<li>\u0917\u0902\u0917\u091f\u094b\u0915, \u0936\u094d\u0930\u0940\u0928\u0917\u0930 \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u092e\u0947\u0902 \u0905\u0927\u093f\u0915 \u0917\u0930\u094d\u092e \u0925\u093e, \u091c\u094b \u0915\u093f (_______ \u2013 _______) = _______ \u00b0C \u0939\u0948\u0964<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-j is-uppercase mb-1\">\n<li>\u0924\u093f\u0924\u093f\u0930 \u0914\u0930 \u091f\u093f\u0902\u0915\u0942 \u0928\u0947 \u0926\u093f\u0928 \u0915\u0940 \u0936\u0941\u0930\u0941\u0906\u0924 \u20b9100-\u20b9100 \u0915\u0947 \u0938\u093e\u0925 \u0915\u0940\u0964 \u0924\u093f\u0924\u093f\u0930 \u0915\u094b \u20b9300 \u0915\u093e \u0932\u093e\u092d \u0939\u0941\u0906, \u091c\u092c\u0915\u093f \u091f\u093f\u0902\u0915\u0942 \u0915\u094b \u20b9200 \u0915\u093e \u0928\u0941\u0915\u0938\u093e\u0928 (loss) \u0939\u0941\u0906\u0964<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-a  nested-list mb-1\">\n<li>\u0926\u093f\u0928 \u0915\u0947 \u0905\u0928\u094d\u200d\u0924 \u092e\u0947\u0902 \u0926\u094b\u0928\u094b\u0902 \u0915\u0947 \u092a\u093e\u0938 \u0915\u093f\u0924\u0928\u0947-\u0915\u093f\u0924\u0928\u0947 \u20b9 \u0925\u0947?<\/li>\n\n\n\n<li>\u0926\u093f\u0928 \u0915\u0947 \u0905\u0928\u094d\u200d\u0924 \u092e\u0947\u0902 \u0926\u094b\u0928\u094b\u0902 \u0915\u0947 \u092a\u093e\u0938 \u0915\u093f\u0924\u0928\u0947-\u0915\u093f\u0924\u0928\u0947 \u20b9 \u0925\u0947?<\/li>\n\n\n\n<li>\u0915\u094c\u0928 \u0905\u0927\u093f\u0915 \u0905\u092e\u0940\u0930 \u0925\u093e \u0914\u0930 \u0915\u093f\u0924\u0928\u0947 \u20b9 \u0938\u0947?<\/li>\n\n\n\n<li>____________ (\u0924\u093f\u0924\u093f\u0930\/\u091f\u093f\u0902\u0915\u0942) \u0905\u0927\u093f\u0915 \u0905\u092e\u0940\u0930 \u0939\u0948 \u0914\u0930 _______ \u2013 _______ = _______ \u0938\u0947 \u0939\u0948\u0964<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-k is-uppercase mb-1\">\n<li>\u0905\u0917\u0932\u0947 \u0938\u092a\u094d\u0924\u093e\u0939, \u0909\u0928\u094d\u0939\u094b\u0902\u0928\u0947 \u092b\u093f\u0930 \u0938\u0947 \u20b9100-\u20b9100 \u0915\u0947 \u0938\u093e\u0925 \u0936\u0941\u0930\u0941\u0906\u0924 \u0915\u0940, \u0932\u0947\u0915\u093f\u0928 \u0926\u094b\u0928\u094b\u0902 \u0915\u094b \u0928\u0941\u0915\u0938\u093e\u0928 \u0939\u0941\u0906 \u2013 \u0924\u093f\u0924\u093f\u0930 \u0915\u094b \u20b9500 \u0915\u093e \u0914\u0930 \u091f\u093f\u0902\u0915\u0942 \u0915\u094b \u20b9300 \u0915\u093e\u0964<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list list-type-alpha start-a  nested-list mb-1\">\n<li>\u0926\u093f\u0928 \u0915\u0947 \u0905\u0928\u094d\u200d\u0924 \u092e\u0947\u0902 \u0926\u094b\u0928\u094b\u0902 \u0915\u0947 \u092a\u093e\u0938 \u0915\u093f\u0924\u0928\u0947-\u0915\u093f\u0924\u0928\u0947 \u20b9 \u0925\u0947?<\/li>\n\n\n\n<li>\u0924\u093f\u0924\u093f\u0930 \u0915\u0947 \u092a\u093e\u0938 \u0905\u0928\u094d\u200d\u0924 \u092e\u0947\u0902 _______ \u20b9 \u092c\u091a\u0947, \u091c\u092c\u0915\u093f \u091f\u093f\u0902\u0915\u0942 \u0915\u0947 \u092a\u093e\u0938 _______ \u20b9 \u092c\u091a\u0947\u0964<\/li>\n\n\n\n<li>____________ (\u0924\u093f\u0924\u093f\u0930\/\u091f\u093f\u0902\u0915\u0942) \u0905\u0927\u093f\u0915 \u0905\u092e\u0940\u0930 \u0939\u0948 \u0914\u0930 _______ \u2013 _______ = _______ \u0938\u0947 \u0939\u0948\u0964<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0928\u094b\u091f : \u0907\u0938 \u0932\u0947\u0916 \u0915\u093e \u0935\u093f\u091a\u093e\u0930 \u0905\u091c\u093c\u0940\u092e \u092a\u094d\u0930\u0947\u092e\u091c\u0940 \u092f\u0942\u0928\u093f\u0935\u0930\u094d\u0938\u093f\u091f\u0940 \u092e\u0947\u0902 \u090f\u092e\u090f \u090f\u091c\u0941\u0915\u0947\u0936\u0928 \u0915\u0947 \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u093f\u092f\u094b\u0902, \u091c\u094c\u0939\u0930 \u0915\u0947. \u090f\u092e. \u0914\u0930 \u0928\u093e\u0917\u0947\u0902\u0926\u094d\u0930 \u0938\u093f\u0902\u0939 \u0926\u094d\u0935\u093e\u0930\u093e \u0915\u0940 \u0917\u0908 \u090f\u0915 \u0916\u094b\u091c \u0938\u0947 \u092a\u094d\u0930\u0947\u0930\u093f\u0924 \u0939\u0948, \u091c\u094b \u0909\u0928\u0915\u0947 &#8216;\u092a\u093e\u0920\u094d\u092f\u091a\u0930\u094d\u092f\u093e \u0938\u093e\u092e\u0917\u094d\u0930\u0940 \u0935\u093f\u0915\u093e\u0938 \u2013 \u0917\u0923\u093f\u0924&#8217; \u092a\u093e\u0920\u094d\u092f\u0915\u094d\u0930\u092e \u0915\u093e \u090f\u0915 \u0939\u093f\u0938\u094d\u0938\u093e \u0925\u093e\u0964<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u092b\u0941\u091f\u0928\u094b\u091f :<\/h2>\n\n\n\n<ol start=\"1\" style=\"margin-bottom:0.5rem !important;\">\n  <li style=\"font-size: 16px;\">&#8211;<i>n<\/i> \u0915\u094b \u091c\u094b\u0921\u093c\u0928\u093e <i>n<\/i> \u0915\u094b \u0918\u091f\u093e\u0928\u0947 \u0915\u0947 \u0938\u092e\u0924\u0941\u0932\u094d\u092f \u0939\u0948, \u091c\u094b \u0915\u093f \u0907\u0938\u0915\u093e \u092f\u094b\u091c\u094d\u092f \u092a\u094d\u0930\u0924\u093f\u0932\u094b\u092e (additive opposite) \u0939\u0948\u0964<\/li>\n  <li style=\"font-size: 16px;\"><b>\u091a\u093f\u0924\u094d\u0930-8<\/b> : \u0926\u0930\u094d\u092a\u0923 <i>x<\/i> = 2 = (5 + (-1))\/2 \u2026 \u092a\u0930 \u0939\u0948\u2026 \u0907\u0938\u0947 \u0926\u094b\u0928\u094b\u0902 \u0906\u0930\u0947\u0916\u094b\u0902 \u0915\u0947 \u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920 (common) \u092d\u093e\u0917 \u0914\u0930 \u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920 \u0905\u0928\u094d\u200d\u0924\u0930\u093e\u0932 \u0915\u094b \u0926\u0947\u0916\u0915\u0930, \u0914\u0930 \u092b\u093f\u0930 \u0909\u0938 \u0905\u0928\u094d\u200d\u0924\u0930\u093e\u0932 \u0915\u093e \u092e\u0927\u094d\u092f\u092c\u093f\u0928\u094d\u200d\u0926\u0941 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0915\u0947 \u0938\u092e\u091d\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/li>\n<\/ol>\n\n\n\n<ol start=\"3\">\n  <li style=\"font-size: 16px;\"><b>\u091a\u093f\u0924\u094d\u0930-9<\/b> : \u0926\u0930\u094d\u092a\u0923 (mirror) <i>x<\/i> = -1.5 = ((-5) + 2) \/ 2 \u092a\u0930 \u0939\u0948<\/li>\n  <li style=\"font-size: 16px;\">\u0930\u094d\u0923\u093e\u0902\u0915\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u092f\u094b\u0917 \u0915\u093e \u0915\u094d\u0930\u092e\u0935\u093f\u0928\u093f\u092e\u0947\u092f \u0917\u0941\u0923 (Commutative property of addition for integers)<\/li>\n  <li style=\"font-size: 16px;\">&#8211;<i>n<\/i> \u0915\u094b \u0918\u091f\u093e\u0928\u093e <i>n<\/i> \u0915\u094b \u091c\u094b\u0921\u093c\u0928\u0947 \u0915\u0947 \u0938\u092e\u0924\u0941\u0932\u094d\u092f \u0939\u0948, \u091c\u094b \u0915\u093f \u0907\u0938\u0915\u093e \u092f\u094b\u091c\u094d\u092f \u092a\u094d\u0930\u0924\u093f\u0932\u094b\u092e (additive opposite) \u0939\u0948\u0964<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u0915\u0941\u091b \u0906\u092f\u0924\u093e\u0915\u093e\u0930 \u092c\u093f\u0928\u094d\u200d\u0926\u0941 \u0935\u093e\u0932\u0940 \u0936\u0940\u091f (rectangular dot sheets), \u0926\u094b \u0935\u093f\u092a\u0930\u0940\u0924 \u0930\u0902\u0917\u094b\u0902 \u0915\u0947 \u0938\u094d\u0915\u0947\u091a-\u092a\u0947\u0928 (\u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \u0932\u093e\u0932 \u0914\u0930 \u0939\u0930\u093e), \u090f\u0915 \u0938\u094d\u0915\u0947\u0932 \u0914\u0930 \u090f\u0915 \u092a\u0947\u0902\u0938\u093f\u0932 \u0932\u0947\u0902\u0964 \u0938\u092c\u0938\u0947 \u092a\u0939\u0932\u0947 \u090a\u092a\u0930 \u0938\u0947 \u0926\u0942\u0938\u0930\u0947 \u0928\u092e\u094d\u200d\u092c\u0930 \u0915\u0940 \u0930\u0947\u0916\u093e \u0915\u0947 \u092c\u093f\u0928\u094d\u200d\u0926\u0941\u0913\u0902 \u0915\u094b \u0906\u092a\u0938 \u092e\u0947\u0902 \u091c\u094b\u095c\u0947\u0902\u0964 \u092b\u093f\u0930 \u092f\u0939\u0940 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e 5\u0935\u0940\u0902, 8\u0935\u0940\u0902, 11\u0935\u0940\u0902, \u2026 \u0930\u0947\u0916\u093e\u0913\u0902 \u0915\u0947 \u0932\u093f\u090f \u092d\u0940 \u0926\u094b\u0939\u0930\u093e\u090f\u0901, \u0924\u093e\u0915\u093f \u092c\u093f\u0928\u094d\u200d\u0926\u0941\u0913\u0902 \u0915\u0940 \u0939\u0930 [&hellip;]<\/p>\n","protected":false},"author":19,"featured_media":27663,"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":[1189,1191,686,1234,1232,1233],"stage-class":[1008],"magazine_category":[358],"class_list":["post-28033","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category---hi","tag-addition","tag-repeated-subtraction","tag-word-problems-hi","tag-1234","tag-1232","tag-1233","stage-class-middle-class-6-8-hi","magazine_category-issue-31-july-2022-hi"],"acf":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/09\/Coloured-counters.jpg","_links":{"self":[{"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/posts\/28033","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\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/comments?post=28033"}],"version-history":[{"count":14,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/posts\/28033\/revisions"}],"predecessor-version":[{"id":28126,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/posts\/28033\/revisions\/28126"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/media\/27663"}],"wp:attachment":[{"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/media?parent=28033"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/categories?post=28033"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/tags?post=28033"},{"taxonomy":"stage-class","embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/stage-class?post=28033"},{"taxonomy":"magazine_category","embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/magazine_category?post=28033"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}