{"id":21648,"date":"2026-02-25T15:42:15","date_gmt":"2026-02-25T10:12:15","guid":{"rendered":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/%e0%a4%ae%e0%a5%88%e0%a4%a8%e0%a4%bf%e0%a4%aa%e0%a5%8d%e0%a4%af%e0%a5%82%e0%a4%b2%e0%a5%87%e0%a4%9f%e0%a4%bf%e0%a4%b5%e0%a5%8d%e0%a4%b8-%e0%a4%b8%e0%a4%be%e0%a4%ae%e0%a4%97%e0%a5%8d-3\/"},"modified":"2026-05-25T09:18:42","modified_gmt":"2026-05-25T03:48:42","slug":"%e0%a4%ae%e0%a5%88%e0%a4%a8%e0%a4%bf%e0%a4%aa%e0%a5%8d%e0%a4%af%e0%a5%82%e0%a4%b2%e0%a5%87%e0%a4%9f%e0%a4%bf%e0%a4%b5%e0%a5%8d%e0%a4%b8-%e0%a4%b8%e0%a4%be%e0%a4%ae%e0%a4%97%e0%a5%8d%e0%a4%b0%e0%a5%80","status":"publish","type":"post","link":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/%e0%a4%ae%e0%a5%88%e0%a4%a8%e0%a4%bf%e0%a4%aa%e0%a5%8d%e0%a4%af%e0%a5%82%e0%a4%b2%e0%a5%87%e0%a4%9f%e0%a4%bf%e0%a4%b5%e0%a5%8d%e0%a4%b8-%e0%a4%b8%e0%a4%be%e0%a4%ae%e0%a4%97%e0%a5%8d%e0%a4%b0%e0%a5%80\/","title":{"rendered":"\u092e\u0948\u0928\u093f\u092a\u094d\u200d\u092f\u0942\u0932\u0947\u091f\u093f\u0935\u094d\u200d\u0938 \u0938\u093e\u092e\u0917\u094d\u0930\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e : \u091f\u0947\u0928-\u092b\u094d\u0930\u0947\u092e\u094d\u200d\u0938"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u091f\u0947\u0928-\u092b\u094d\u0930\u0947\u092e\u094d\u0938 \u092d\u093e\u0930\u0924 \u092e\u0947\u0902 \u092c\u0939\u0941\u0924 \u0905\u0927\u093f\u0915 \u092a\u094d\u0930\u0938\u093f\u0926\u094d\u0927 \u0928\u0939\u0940\u0902 \u0939\u0948\u0902\u0964 \u0932\u0947\u0915\u093f\u0928 \u0907\u0928\u0915\u0947 \u0915\u0941\u091b \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0932\u093e\u092d \u0939\u0948\u0902 \u0914\u0930 \u0907\u0928\u094d\u0939\u0947\u0902 \u092c\u0939\u0941\u0924 \u0906\u0938\u093e\u0928\u0940 \u0938\u0947 \u092c\u0928\u093e\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0915\u0908 \u0935\u0947\u092c\u0938\u093e\u0907\u091f\u094b\u0902 \u092a\u0930 \u0935\u0930\u094d\u091a\u0941\u0905\u0932 (\u0921\u093f\u091c\u093f\u091f\u0932) \u091f\u0947\u0928-\u092b\u094d\u0930\u0947\u092e \u092d\u0940 \u0909\u092a\u0932\u092c\u094d\u0927 \u0939\u0948\u0902\u0964  <\/p>\n\n<p class=\"wp-block-paragraph\">\u090f\u0915 \u091f\u0947\u0928-\u092b\u094d\u0930\u0947\u092e 2 \u00d7 5 \u0915\u093e \u0922\u093e\u0901\u091a\u093e \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u0916\u093e\u0928\u0947 (\u0938\u094d\u0932\u0949\u091f) \u092c\u0928\u0947 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u091c\u093f\u0928 \u092a\u0930 10 \u0924\u0915 \u0915\u0940 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093e\u0909\u0902\u091f\u0930\u094d\u0938 \u0930\u0916\u0947 \u091c\u093e\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"194\" height=\"82\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-1.png\" alt=\"Ten-frames fig 1\" class=\"wp-image-21579\"\/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-1<\/figcaption><\/figure>\n\n<p class=\"wp-block-paragraph\">\u092f\u0939 \u092c\u091a\u094d\u091a\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0917\u093f\u0928\u0924\u0940 \u0938\u0940\u0916\u0928\u0947 \u0915\u0940 \u0936\u0941\u0930\u0941\u0906\u0924 \u092e\u0947\u0902 \u092c\u0939\u0941\u0924 \u0909\u092a\u092f\u094b\u0917\u0940 \u0939\u0948\u0902\u0964 \u092b\u094d\u0930\u0947\u092e \u092a\u0930 \u0915\u093e\u0909\u0902\u091f\u0930 \u0930\u0916\u0928\u0947 \u0915\u0940 \u0915\u094d\u0930\u093f\u092f\u093e \u0915\u0947 \u0932\u093f\u090f \u0906\u0901\u0916\u094b\u0902 \u0914\u0930 \u0939\u093e\u0925\u094b\u0902 \u0915\u0947 \u0938\u092e\u0928\u094d\u0935\u092f (eye-hand coordination) \u0915\u0947 \u0938\u093e\u0925-\u0938\u093e\u0925 \u0917\u093f\u0928\u0928\u0947 \u0915\u0940 \u0915\u094d\u0937\u092e\u0924\u093e \u0915\u0940 \u092d\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u091f\u0947\u0928-\u092b\u094d\u0930\u0947\u092e \u092a\u0930 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0928\u0947 \u0915\u0947 \u0926\u094b \u0938\u092e\u094d\u200d\u092d\u093e\u0935\u093f\u0924 \u0924\u0930\u0940\u0915\u0947 \u0939\u0948\u0902 :  <\/p>\n\n<ol class=\"wp-block-list\">\n<li>\u092b\u094d\u0930\u0947\u092e \u0915\u094b \u0926\u094b \u092a\u0902\u0915\u094d\u0924\u093f\u092f\u094b\u0902 \u0914\u0930 \u092a\u093e\u0901\u091a \u0938\u094d\u0924\u092e\u094d\u200d\u092d\u094b\u0902 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u0935\u0938\u094d\u0925\u093f\u0924 \u0915\u0930\u0947\u0902\u0964 \u090a\u092a\u0930\u0940 \u092a\u0902\u0915\u094d\u0924\u093f \u0915\u0947 \u0916\u093e\u0928\u094b\u0902 \u0915\u094b \u092d\u0930\u0947\u0902 \u2013 \u092c\u093e\u090f\u0901 \u0938\u0947 \u0926\u093e\u090f\u0901 \u2013 \u0914\u0930 \u092b\u093f\u0930 \u0928\u093f\u091a\u0932\u0940 \u092a\u0902\u0915\u094d\u0924\u093f \u0915\u094b\u0964 <\/li>\n<\/ol>\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1025\" height=\"193\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-2.png\" alt=\"Ten-frames fig 2\" class=\"wp-image-21582\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-2.png 1025w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-2-640x121.png 640w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-2-360x68.png 360w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-2-768x145.png 768w\" sizes=\"auto, (max-width: 1025px) 100vw, 1025px\" \/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-2<\/figcaption><\/figure>\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li>\u092b\u094d\u0930\u0947\u092e \u0915\u094b \u092a\u093e\u0901\u091a \u092a\u0902\u0915\u094d\u0924\u093f\u092f\u094b\u0902 \u0914\u0930 \u0926\u094b \u0938\u094d\u0924\u092e\u094d\u200d\u092d\u094b\u0902 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u0935\u0938\u094d\u0925\u093f\u0924 \u0915\u0930\u0947\u0902\u0964 \u0938\u092c\u0938\u0947 \u0928\u0940\u091a\u0947 \u0935\u093e\u0932\u0940 \u092a\u0902\u0915\u094d\u0924\u093f \u0915\u0947 \u0916\u093e\u0928\u094b\u0902 \u0915\u094b \u092d\u0930\u0947\u0902 \u2013 \u092a\u0939\u0932\u0947 \u092c\u093e\u090f\u0901, \u092b\u093f\u0930 \u0926\u093e\u090f\u0901 \u2013 \u0914\u0930 \u090a\u092a\u0930 \u0915\u0940 \u0913\u0930 \u092c\u095d\u0947\u0902 (\u091a\u093f\u0924\u094d\u0930-3)\u0964 <\/li>\n<\/ol>\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1226\" height=\"202\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-3.png\" alt=\"Ten-frames fig 3\" class=\"wp-image-21585\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-3.png 1226w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-3-640x105.png 640w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-3-360x59.png 360w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-3-768x127.png 768w\" sizes=\"auto, (max-width: 1226px) 100vw, 1226px\" \/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-3<\/figcaption><\/figure>\n\n<p class=\"wp-block-paragraph\">\u0926\u094b\u0928\u094b\u0902 \u0935\u094d\u092f\u0935\u0938\u094d\u0925\u093e\u0913\u0902 \u0915\u0947 \u0905\u092a\u0928\u0947 \u0932\u093e\u092d \u0939\u0948\u0902\u0964 \u0926\u094b\u0928\u094b\u0902 \u0939\u0940 10 \u092c\u0928\u093e\u0928\u0947 \u0935\u093e\u0932\u0947 \u0938\u0902\u0916\u094d\u092f\u093e \u092f\u0941\u0917\u094d\u092e\u094b\u0902 (\u091c\u0948\u0938\u0947 7+3, 6+4) \u0915\u094b \u092f\u093e\u0926 \u0915\u0930\u0928\u0947 \u092f\u093e \u0938\u094d\u0935\u091a\u093e\u0932\u093f\u0924 (automatize)1 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u092e\u0926\u0926 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u092f\u0939 \u0926\u094b \u0924\u0930\u0939 \u0938\u0947 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u2013 (i) \u092d\u0930\u0947 \u0939\u0941\u090f \u0916\u093e\u0928\u094b\u0902 \u0914\u0930 \u0916\u093e\u0932\u0940 \u0916\u093e\u0928\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u092a\u0930 \u0935\u093f\u091a\u093e\u0930 \u0915\u0930\u0915\u0947, \u0914\u0930 (ii) \u092b\u094d\u0930\u0947\u092e \u0915\u094b \u092d\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0926\u094b \u0930\u0902\u0917\u094b\u0902 \u0915\u0947 \u0915\u093e\u0909\u0902\u091f\u0930\u094d\u0938 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 (\u091a\u093f\u0924\u094d\u0930-4)\u0964    <\/p>\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1218\" height=\"95\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-4.png\" alt=\"Ten-frames fig 4\" class=\"wp-image-21588\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-4.png 1218w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-4-640x50.png 640w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-4-360x28.png 360w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-4-768x60.png 768w\" sizes=\"auto, (max-width: 1218px) 100vw, 1218px\" \/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-4<\/figcaption><\/figure>\n\n<p class=\"wp-block-paragraph\">\u092a\u0939\u0932\u0940 \u0935\u094d\u092f\u0935\u0938\u094d\u0925\u093e (\u0915\u094d\u0937\u0948\u0924\u093f\u091c) \u090f\u0915\u0932-\u0905\u0902\u0915\u094b\u0902 \u0915\u0947 \u092f\u094b\u0917 \u0924\u0925\u094d\u092f\u094b\u0902 \u0915\u094b \u092f\u093e\u0926 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u092e\u0926\u0926 \u0915\u0930\u0924\u0940 \u0939\u0948, \u0935\u093f\u0936\u0947\u0937 \u0930\u0942\u092a \u0938\u0947 \u0909\u0928 \u092f\u094b\u0917\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u091c\u094b \u0926\u0938 \u0938\u0947 \u0905\u0927\u093f\u0915 \u0939\u0948\u0902\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f 6 + 7 \u092a\u0930 \u0935\u093f\u091a\u093e\u0930 \u0915\u0930\u0947\u0902\u0964 \u092f\u0926\u093f \u092a\u0939\u0932\u0947 \u092b\u094d\u0930\u0947\u092e \u0915\u094b \u0918\u0941\u092e\u093e\u0915\u0930 \u0926\u0942\u0938\u0930\u0947 \u0915\u0947 \u0938\u093e\u0925 \u0930\u0916\u093e \u091c\u093e\u090f, \u0924\u094b \u092c\u0940\u091a \u0915\u0940 \u0926\u094b \u092a\u0902\u0915\u094d\u0924\u093f\u092f\u093e\u0901 \u092e\u093f\u0932\u0915\u0930 \u090f\u0915 \u092a\u0942\u0930\u093e \u092b\u094d\u0930\u0947\u092e \u092f\u093e\u0928\u0940 &#8216;\u0926\u0938&#8217; \u092c\u0928\u093e \u0926\u0947\u0924\u0940 \u0939\u0948\u0902\u0964 \u092f\u0939 \u0914\u0930 \u0936\u0947\u0937 \u092c\u091a\u0947 \u090f\u0915 \u0914\u0930 \u0926\u094b \u092e\u093f\u0932\u0915\u0930 13 \u0939\u094b \u091c\u093e\u0924\u0947 \u0939\u0948\u0902 (\u091a\u093f\u0924\u094d\u0930-5)\u0964 \u092f\u0939\u093e\u0901, 6 \u0914\u0930 7 \u0915\u093e \u20185 + \u0915\u0941\u091b\u2019 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0939\u094b\u0928\u093e \u092e\u0939\u0924\u094d\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0939\u0948\u0964 \u0907\u0938 \u0936\u094d\u0930\u0947\u0923\u0940 \u0915\u0947 \u0905\u0928\u094d\u092f \u0909\u0926\u093e\u0939\u0930\u0923 5 + 6, 5 + 7, 5 + 8, 5 + 9, 6 + 6, 6 + 8, 6 + 9, 7 + 7, 7 + 8, 7 + 9, 8 + 8, 8 + 9 \u0914\u0930 9 + 9 \u0939\u0948\u0902\u0964 \u0907\u0938\u0940 \u092a\u094d\u0930\u0915\u093e\u0930, \u0915\u094b\u0908 7 + 4 (\u091a\u093f\u0924\u094d\u0930-6), 8 + 3, 8 + 4, 9 + 2, 9 + 3 \u0914\u0930 9 + 4 \u0915\u093e \u092d\u0940 \u092a\u0924\u093e \u0932\u0917\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964      <\/p>\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"564\" height=\"195\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-5.png\" alt=\"Ten-frames fig 5\" class=\"wp-image-21611\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-5.png 564w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-5-360x124.png 360w\" sizes=\"auto, (max-width: 564px) 100vw, 564px\" \/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-5<\/figcaption><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"234\" height=\"139\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-6.png\" alt=\"Ten-frames fig-6\" class=\"wp-image-21616\"\/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-6<\/figcaption><\/figure>\n<\/div>\n<\/div>\n\n<p class=\"wp-block-paragraph\">\u0907\u0938\u0932\u093f\u090f, \u091c\u092c \u092c\u091a\u094d\u091a\u0947 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u0938\u0940\u0916\u0928\u0947 \u0915\u0940 \u0936\u0941\u0930\u0941\u0906\u0924 \u092e\u0947\u0902 &#8216;\u091f\u0947\u0928-\u092b\u094d\u0930\u0947\u092e\u094d\u0938&#8217; (ten-frames) \u0915\u0947 \u0938\u093e\u0925 \u0916\u0947\u0932\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0935\u0947 \u0938\u094d\u0935\u092f\u0902 \u0907\u0928 \u0926\u0943\u0936\u094d\u092f\u094b\u0902 (visuals) \u0915\u094b \u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u0915\u0908 \u091a\u0940\u091c\u093c\u094b\u0902 \u0915\u093e \u0905\u0935\u0932\u094b\u0915\u0928 \u0915\u0930\u0928\u093e \u0936\u0941\u0930\u0942 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0938\u092e\u094d\u200d\u092c\u0928\u094d\u200d\u0927 \u092c\u0928\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<p class=\"wp-block-paragraph\">\u0907\u0938\u0940 \u0924\u0930\u0939, \u0926\u0942\u0938\u0930\u0940 \u0935\u094d\u092f\u0935\u0938\u094d\u0925\u093e (\u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930) \u0905\u0928\u093f\u0935\u093e\u0930\u094d\u092f \u0930\u0942\u092a \u0938\u0947 \u0938\u092e \u0914\u0930 \u0935\u093f\u0937\u092e \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0924\u0940 \u0939\u0948\u0964 \u0907\u0928\u0915\u0947 \u0928\u093e\u092e\u094b\u0902 \u0915\u094b &#8216;\u0906\u0915\u0943\u0924\u093f\u092f\u094b\u0902&#8217; \u0938\u0947 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u091c\u094b\u0921\u093c\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 : <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u0935\u093f\u0937\u092e (Odd) : \u0935\u0947 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u091c\u093f\u0928\u0915\u0947 \u0936\u0940\u0930\u094d\u0937 \u092a\u0930 \u090f\u0915 \u0905\u0915\u0947\u0932\u093e (single) \u0915\u093e\u0909\u0902\u091f\u0930 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/li>\n\n\n\n<li>\u0938\u092e (Even) : \u0935\u0947 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u091c\u093f\u0928\u0915\u0947 \u0936\u0940\u0930\u094d\u0937 \u092a\u0930 \u090f\u0915 \u091c\u094b\u0921\u093c\u0940 (pair) \u0939\u094b\u0924\u0940 \u0939\u0948 (\u091a\u093f\u0924\u094d\u0930-7)\u0964<\/li>\n<\/ul>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"481\" height=\"429\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-7.png\" alt=\"Ten-frames fig 7\" class=\"wp-image-21597\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-7.png 481w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-7-404x360.png 404w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-7-226x202.png 226w\" sizes=\"auto, (max-width: 481px) 100vw, 481px\" \/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-7<\/figcaption><\/figure>\n<\/div>\n<\/div>\n\n<p class=\"wp-block-paragraph\">\u0907\u0938 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924\u093f (representation) \u0915\u094b \u092b\u093f\u0930 \u0935\u093f\u0937\u092e \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0932\u093f\u090f 2<em>n<\/em> + 1 \u092f\u093e 2<em>n<\/em> &#8211; 1 \u0914\u0930 \u0938\u092e \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0932\u093f\u090f 2<em>n<\/em> \u0915\u0947 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u0930\u0942\u092a\u094b\u0902 (algebraic forms) \u0938\u0947 \u091c\u094b\u0921\u093c\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0907\u0938 \u091a\u093f\u0924\u094d\u0930 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u092f\u0939 \u092a\u0942\u0930\u0940 \u0924\u0930\u0939 \u0938\u094d\u092a\u0937\u094d\u091f \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0907\u0928 \u0924\u0940\u0928\u094b\u0902 \u092e\u093e\u092e\u0932\u094b\u0902 \u092e\u0947\u0902 <em>n<\/em> \u0915\u093e \u0915\u094d\u092f\u093e \u0905\u0930\u094d\u0925 \u0939\u0948 : \u0938\u092e 2<em>n<\/em>, \u0935\u093f\u0937\u092e 2<em>n<\/em> + 1 \u0914\u0930 \u0935\u093f\u0937\u092e 2<em>n<\/em> &#8211; 1\u0964 <\/p>\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-top is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<p class=\"wp-block-paragraph\">\u0907\u0938\u0938\u0947 \u092f\u0939 \u092d\u0940 \u0938\u094d\u092a\u0937\u094d\u091f \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0907\u0928 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u091c\u094b\u0921\u093c\u0928\u0947 \u092a\u0930 \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948 (\u091a\u093f\u0924\u094d\u0930-7)\u0964 \u0938\u094d\u092a\u0937\u094d\u091f \u0930\u0942\u092a \u0938\u0947, \u090f\u0915 \u0938\u092e \u0938\u0902\u0916\u094d\u092f\u093e \u091c\u094b\u0921\u093c\u0928\u0947 \u0938\u0947 \u0938\u092e-\u0935\u093f\u0937\u092e \u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f (parity) \u0928\u0939\u0940\u0902 \u092c\u0926\u0932\u0924\u0940 \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0935\u0939 \u0938\u0902\u0916\u094d\u092f\u093e \u0926\u0942\u0938\u0930\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0947 \u0928\u0940\u091a\u0947 \u0906\u0938\u093e\u0928\u0940 \u0938\u0947 \u092b\u093f\u091f \u0939\u094b \u091c\u093e\u0924\u0940 \u0939\u0948\u0964 \u0907\u0938\u0932\u093f\u090f, \u0938\u092e + \u0938\u092e = \u0938\u092e, \u0914\u0930 \u0935\u093f\u0937\u092e + \u0938\u092e = \u0935\u093f\u0937\u092e \u0930\u0939\u0924\u093e \u0939\u0948\u0964 \u0938\u093e\u0925 \u0939\u0940, \u0915\u094b\u0908 \u092f\u0939 \u0926\u0947\u0916 \u0938\u0915\u0924\u093e \u0939\u0948 \u0915\u093f \u0926\u094b \u0935\u093f\u0937\u092e \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u093e \u092f\u094b\u0917 \u0938\u092e \u0915\u0948\u0938\u0947 \u0939\u094b\u0924\u093e \u0939\u0948 \u0915\u094d\u092f\u094b\u0902\u0915\u093f &#8216;\u0905\u0915\u0947\u0932\u0947 \u0935\u093e\u0932\u0947&#8217; \u0915\u093e\u0909\u0902\u091f\u0930 \u0906\u092a\u0938 \u092e\u0947\u0902 \u091c\u094b\u0921\u093c\u0940 \u092c\u0928\u093e \u0932\u0947\u0924\u0947 \u0939\u0948\u0902! \u092f\u0939\u093e\u0901 \u0907\u0938 \u092a\u0930 \u092d\u0940 \u091a\u0930\u094d\u091a\u093e \u0915\u0940 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948 \u0915\u093f \u0936\u0942\u0928\u094d\u092f \u0938\u092e \u0939\u0948 \u092f\u093e \u0935\u093f\u0937\u092e \u0914\u0930 \u0915\u094d\u092f\u094b\u0902\u0964    <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u092e\u0939\u0924\u094d\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092c\u093e\u0924 \u092f\u0939 \u0939\u0948 \u0915\u093f \u0907\u0938\u0947 \u092c\u0921\u093c\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0924\u0915 \u0935\u093f\u0938\u094d\u0924\u093e\u0930\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 9 \u0938\u0947 \u092c\u0921\u093c\u0940 \u0915\u094b\u0908 \u092d\u0940 \u0938\u0902\u0916\u094d\u092f\u093e &#8216;\u0926\u0939\u093e\u0908&#8217; \u0914\u0930 &#8216;\u0907\u0915\u093e\u0908&#8217; \u0938\u0947 \u092c\u0928\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u0926\u0939\u093e\u0908, \u0938\u0948\u0915\u0921\u093c\u093e, \u0939\u091c\u093c\u093e\u0930 \u0906\u0926\u093f \u0915\u0947 \u0938\u092d\u0940 \u0938\u092e\u0942\u0939 \u0938\u092e \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 \u0907\u0938\u0932\u093f\u090f, \u0915\u0947\u0935\u0932 \u0907\u0915\u093e\u0907\u092f\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0940 \u0915\u093f\u0938\u0940 \u092d\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0947 \u0938\u092e \u092f\u093e \u0935\u093f\u0937\u092e \u0939\u094b\u0928\u0947 \u0915\u093e \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u0923 \u0915\u0930\u0924\u0940 \u0939\u0948\u0964 \u0907\u0938\u0947 \u091f\u0947\u0928-\u092b\u094d\u0930\u0947\u092e \u0915\u0947 \u0938\u093e\u0925 \u0938\u094d\u092a\u0937\u094d\u091f \u0930\u0942\u092a \u0938\u0947 \u0926\u0947\u0916\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u2013 \u0926\u0947\u0916\u0947\u0902 \u0915\u093f 25 \u092f\u093e 34 \u0915\u0948\u0938\u0947 \u0926\u093f\u0916\u0924\u0947 \u0939\u0948\u0902 (\u091a\u093f\u0924\u094d\u0930-8)\u0964      <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u091c\u0948\u0938\u093e \u0915\u093f \u092a\u0939\u0932\u0947 \u0909\u0932\u094d\u0932\u0947\u0916 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948, \u0915\u0908 \u0935\u0947\u092c\u0938\u093e\u0907\u091f\u094b\u0902 \u092a\u0930 \u0935\u0930\u094d\u091a\u0941\u0905\u0932 \u091f\u0947\u0928-\u092b\u094d\u0930\u0947\u092e \u0909\u092a\u0932\u092c\u094d\u0927 \u0939\u0948\u0902\u0964 \u0907\u0928\u0915\u093e \u0935\u093f\u0935\u0930\u0923 \u092f\u0939\u093e\u0901 \u0926\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948 :<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"198\" height=\"720\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-8.jpg\" alt=\"Ten-frames fig 8\" class=\"wp-image-21607\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-8.jpg 198w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-8-99x360.jpg 99w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-8<\/figcaption><\/figure>\n<\/div>\n<\/div>\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/toytheater.com\/two-color-counter-ten-frame\/\" target=\"_blank\" rel=\"noreferrer noopener\">Toy Theater<\/a> : \u0938\u0930\u0932 \u092b\u094d\u0930\u0947\u092e \u0914\u0930 \u0926\u094b \u0930\u0902\u0917\u094b\u0902 \u092e\u0947\u0902 \u0915\u093e\u0909\u0902\u091f\u0930 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u0909\u092a\u092f\u094b\u0917\u0915\u0930\u094d\u0924\u093e \u0915\u094b \u092b\u094d\u0930\u0947\u092e \u092a\u0930 \u0915\u093e\u0909\u0902\u091f\u0930 \u0909\u0938\u0940 \u0924\u0930\u0939 \u0930\u0916\u0928\u0947 \u0939\u094b\u0902\u0917\u0947 \u091c\u0948\u0938\u0947 \u090f\u0915 \u0905\u0938\u0932\u0940 \u092b\u094d\u0930\u0947\u092e \u092e\u0947\u0902 \u0930\u0916\u0947 \u091c\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 \u0939\u093e\u0932\u093e\u0901\u0915\u093f, \u092b\u094d\u0930\u0947\u092e \u0915\u093e \u0913\u0930\u093f\u090f\u0902\u091f\u0947\u0936\u0928 (\u0926\u093f\u0936\u093e) \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0939\u0948, \u0914\u0930 \u090f\u0915 \u0938\u0947 \u0905\u0927\u093f\u0915 \u092b\u094d\u0930\u0947\u092e \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u093e \u0938\u092e\u094d\u200d\u092d\u0935 \u0928\u0939\u0940\u0902 \u0939\u0948\u0964 \u0907\u0938\u0932\u093f\u090f, \u092f\u0939 \u0936\u0941\u0930\u0941\u0906\u0924\u0940 \u0938\u0940\u0916\u0928\u0947 \u0935\u093e\u0932\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0924\u094b \u0905\u091a\u094d\u091b\u093e \u0939\u0948, \u0932\u0947\u0915\u093f\u0928 \u0907\u0938\u0915\u093e \u0926\u093e\u092f\u0930\u093e \u0938\u0940\u092e\u093f\u0924 \u0939\u0948\u0964   <\/p>\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/apps.mathlearningcenter.org\/number-frames\/\" target=\"_blank\" rel=\"noreferrer noopener\">Math Learning Center<\/a> : \u092f\u0939 \u091f\u0947\u0928-\u092b\u094d\u0930\u0947\u092e \u0915\u0947 \u0938\u093e\u0925-\u0938\u093e\u0925 \u0926\u094b \u0930\u0902\u0917\u094b\u0902 \u092e\u0947\u0902 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0938\u0939\u093f\u0924 \u092b\u094d\u0930\u0947\u092e \u0915\u0940 \u090f\u0915 \u0935\u093f\u0938\u094d\u0924\u0943\u0924 \u0936\u0943\u0902\u0916\u0932\u093e \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u094b \u0938\u094d\u0915\u094d\u0930\u0940\u0928 \u092a\u0930 \u090f\u0915\u0932, \u092a\u093e\u0901\u091a \u0915\u0947 \u0938\u092e\u0942\u0939\u094b\u0902 \u0914\u0930 \u0926\u0938 \u0915\u0947 \u0938\u092e\u0942\u0939\u094b\u0902 \u092e\u0947\u0902 \u0932\u093e\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u092b\u094d\u0930\u0947\u092e \u0915\u093e \u0913\u0930\u093f\u090f\u0902\u091f\u0947\u0936\u0928 (\u0926\u093f\u0936\u093e) \u092c\u0926\u0932\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u0914\u0930 \u090f\u0915 \u0938\u093e\u0925 \u0915\u0908 \u092b\u094d\u0930\u0947\u092e \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u0947 \u0930\u0902\u0917 \u092d\u0940 \u092c\u0926\u0932\u0947 \u091c\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u0905\u0928\u094d\u092f \u092a\u0942\u0930\u094d\u0935-\u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u092b\u094d\u0930\u0947\u092e 1 \u00d7 5, 2 \u00d7 10 \u0914\u0930 10 \u00d7 10 \u0939\u0948\u0902\u0964 2 \u00d7 10 \u0915\u093e \u092b\u094d\u0930\u0947\u092e \u0909\u0928 \u091c\u094b\u0921\u093c \u0915\u0947 \u0924\u0925\u094d\u092f\u094b\u0902 (addition facts) \u0915\u094b \u0938\u094d\u0935\u091a\u093e\u0932\u093f\u0924 (automatize) \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u092f\u094b\u0917\u0940 \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948 \u091c\u093f\u0928\u0915\u093e \u092f\u094b\u0917 20 \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u092f\u093e \u0909\u0938\u0938\u0947 \u0915\u092e \u0939\u0948\u0964 \u0935\u0947 \u091a\u093f\u0924\u094d\u0930 5-6 (\u091a\u093f\u0924\u094d\u0930-9) \u0915\u0947 \u0905\u0928\u0941\u0930\u0942\u092a \u0935\u0948\u0915\u0932\u094d\u092a\u093f\u0915 \u0926\u0943\u0936\u094d\u092f \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u092f\u0939 \u0938\u093e\u0907\u091f \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0930\u0942\u092a \u0938\u0947 \u092c\u0939\u0941\u0924 \u0905\u0927\u093f\u0915 \u0938\u092e\u094d\u200d\u092d\u093e\u0935\u0928\u093e\u090f\u0901\/\u0905\u0935\u0938\u0930 \u0926\u0947\u0924\u0940 \u0939\u0948\u0964       <\/p>\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"482\" height=\"286\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-9.png\" alt=\"Ten-frames fig 9\" class=\"wp-image-21603\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-9.png 482w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-9-340x202.png 340w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/02\/Ten-frames-fig-9-480x286.png 480w\" sizes=\"auto, (max-width: 482px) 100vw, 482px\" \/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-9<\/figcaption><\/figure>\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/polypad.amplify.com\/p#number-frames\" target=\"_blank\" rel=\"noreferrer noopener\">Mathigon Polypad<\/a> : \u0907\u0938\u092e\u0947\u0902 \u091f\u0947\u0928-\u092b\u094d\u0930\u0947\u092e \u0914\u0930 \u0926\u094b \u0930\u0902\u0917\u094b\u0902 \u0915\u0947 \u0915\u093e\u0909\u0902\u091f\u0930 \u0936\u093e\u092e\u093f\u0932 \u0939\u0948\u0902\u0964 \u092b\u094d\u0930\u0947\u092e \u0915\u093e \u0913\u0930\u093f\u090f\u0902\u091f\u0947\u0936\u0928 (\u0926\u093f\u0936\u093e) \u0914\u0930 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u0947 \u0930\u0902\u0917 \u092c\u0926\u0932\u0947 \u091c\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u091a\u093f\u0924\u094d\u0930 4-8 \u0907\u0938\u0940 \u0938\u093e\u0907\u091f \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u092c\u0928\u093e\u090f \u0917\u090f \u0939\u0948\u0902\u0964 \u0938\u093e\u0925 \u0939\u0940, \u090f\u0915 \u0938\u0947 \u0905\u0927\u093f\u0915 \u092b\u094d\u0930\u0947\u092e \u0915\u093e \u092d\u0940 \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0915\u0947 \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924, \u0907\u0938\u092e\u0947\u0902 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u092a\u0939\u0932\u0947 \u0938\u0947 \u0939\u0940 &#8216;\u0938\u092e-\u0935\u093f\u0937\u092e&#8217; (odd-even) \u092a\u094d\u0930\u093e\u0930\u0942\u092a \u092e\u0947\u0902 \u0938\u092e\u0942\u0939\u093f\u0924 (grouped) \u0939\u0948\u0902, \u091c\u093f\u0928\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u091a\u093f\u0924\u094d\u0930 7-8 \u092e\u0947\u0902 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964 \u092f\u0947 \u0924\u094d\u0935\u0930\u093f\u0924 \u0939\u0947\u0930\u092b\u0947\u0930 (quick manipulation) \u0915\u0940 \u0938\u0941\u0935\u093f\u0927\u093e \u0926\u0947\u0915\u0930 \u0905\u0928\u094d\u0935\u0947\u0937\u0923 \u0915\u0940 \u0915\u0908 \u0938\u092e\u094d\u200d\u092d\u093e\u0935\u0928\u093e\u090f\u0901 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964     <\/p>\n\n<p class=\"wp-block-paragraph\">\u0926\u093f\u0932\u091a\u0938\u094d\u092a \u092c\u093e\u0924 \u092f\u0939 \u0939\u0948 \u0915\u093f \u0915\u094b\u0908 \u092d\u0940 \u0938\u093e\u0907\u091f &#8216;5 + \u0915\u0941\u091b&#8217; \u0935\u093e\u0932\u093e \u092a\u094d\u0930\u0940-\u0917\u094d\u0930\u0941\u092a \u0938\u0902\u0938\u094d\u0915\u0930\u0923 \u0928\u0939\u0940\u0902 \u0926\u0947\u0924\u0940 \u0939\u0948, \u0932\u0947\u0915\u093f\u0928 \u0909\u0928\u094d\u0939\u0947\u0902 \u0906\u0938\u093e\u0928\u0940 \u0938\u0947 \u092c\u0928\u093e\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 <a href=\"https:\/\/sites.google.com\/apu.edu.in\/mathspace\/matherials#h.a21m13dektic\" target=\"_blank\" rel=\"noreferrer noopener\">\u092e\u0948\u0925 \u0938\u094d\u092a\u0947\u0938<\/a> (Math Space) \u0915\u0940 \u0935\u0947\u092c\u0938\u093e\u0907\u091f \u092a\u0930 \u0909\u092a\u0932\u092c\u094d\u200d\u0927 \u0939\u0948\u0902 :  <\/p>\n\n<ul class=\"wp-block-list\">\n<li>\u091f\u0947\u0928-\u092b\u094d\u0930\u0947\u092e \u092c\u0928\u093e\u0928\u0947 \u0915\u0947 \u0924\u0930\u0940\u0915\u0947 \u2013 3 \u0938\u0902\u0938\u094d\u0915\u0930\u0923 : (i) \u092c\u091a\u094d\u091a\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0916\u093e\u0932\u0940 \u092b\u094d\u0930\u0947\u092e : \u0924\u093e\u0915\u093f \u0935\u0947 \u0938\u094d\u0935\u092f\u0902 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u094b \u0930\u0916\u0915\u0930 \u0905\u092d\u094d\u092f\u093e\u0938 \u0915\u0930 \u0938\u0915\u0947\u0902\u0964 (ii) \u0936\u093f\u0915\u094d\u0937\u0915\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u092a\u0939\u0932\u0947 \u0938\u0947 \u092d\u0930\u0947 \u0939\u0941\u090f \u092b\u094d\u0930\u0947\u092e : \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u0928 \u0914\u0930 \u0909\u0926\u093e\u0939\u0930\u0923 \u0926\u0947\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f\u0964 (iii) \u092a\u0939\u0932\u0947 \u0938\u0947 \u0938\u092e\u0942\u0939\u093f\u0924 (\u092d\u0930\u0947 \u0939\u0941\u090f \u0914\u0930 \u0915\u091f\u0947 \u0939\u0941\u090f) \u0938\u0902\u0938\u094d\u0915\u0930\u0923 : \u092c\u0921\u093c\u0947 \u092c\u091a\u094d\u091a\u094b\u0902 \u0914\u0930 \u0905\u0927\u093f\u0915 \u091c\u091f\u093f\u0932 \u0917\u0924\u093f\u0935\u093f\u0927\u093f\u092f\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f\u0964 \u0907\u0938\u092e\u0947\u0902 \u0926\u094b \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0947 \u0932\u0947\u0906\u0909\u091f \u0936\u093e\u092e\u093f\u0932 \u0939\u0948\u0902 \u2014 &#8216;\u0938\u092e-\u0935\u093f\u0937\u092e&#8217; (odd-even) \u0914\u0930 &#8216;5 + \u0915\u0941\u091b&#8217; \u0964   <\/li>\n\n\n\n<li>\u091c\u094b\u0921\u093c \u0915\u0947 \u0938\u0902\u0916\u094d\u092f\u093e \u092a\u0948\u091f\u0930\u094d\u0928 \u0915\u094b \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u093f\u0924 \u0915\u0930\u0928\u0947 \u0935\u093e\u0932\u0947 \u092a\u094b\u0938\u094d\u091f\u0930 : (i) \u20185 + \u0915\u0941\u091b\u2019 \u092a\u094d\u0930\u093e\u0930\u0942\u092a \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u093e : (\u091c\u0948\u0938\u0947 7 \u0915\u094b &#8216;5 + 2&#8217; \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0926\u093f\u0916\u093e\u0928\u093e)\u0964 (ii) \u0938\u092e-\u0935\u093f\u0937\u092e \u0932\u0947\u0906\u0909\u091f : (\u091c\u094b\u0921\u093c\u093f\u092f\u094b\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0940 \u0938\u0902\u0930\u091a\u0928\u093e \u0926\u093f\u0916\u093e\u0928\u093e)\u0964  <\/li>\n<\/ul>\n\n<p class=\"fs-6 wp-block-paragraph\"><sup>1<\/sup> \u0932\u0917\u092d\u0917 \u092c\u093f\u0928\u093e \u0938\u094b\u091a\u0947 \u0924\u0941\u0930\u0928\u094d\u200d\u0924 \u091c\u0935\u093e\u092c \u0926\u0947\u0928\u0947 \u0915\u0940 \u0915\u094d\u0937\u092e\u0924\u093e, \u0938\u093e\u0925 \u0939\u0940 \u092a\u0942\u091b\u0947 \u091c\u093e\u0928\u0947 \u092a\u0930 \u0909\u0938\u0947 \u0938\u0939\u0940 \u0920\u0939\u0930\u093e\u0928\u0947 \u0915\u0940 \u0915\u094d\u0937\u092e\u0924\u093e (\u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0924\u0925\u094d\u092f \u0915\u094b \u0938\u092e\u091d\u093e \u0914\u0930 \u0906\u0924\u094d\u092e\u0938\u093e\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948, \u092f\u0939 \u0907\u0938\u0947 \u0930\u091f\u0928\u0947 \u0938\u0947 \u0905\u0932\u0917 \u092c\u0928\u093e\u0924\u093e \u0939\u0948)\u0964<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u091f\u0947\u0928-\u092b\u094d\u0930\u0947\u092e\u094d\u0938 \u092d\u093e\u0930\u0924 \u092e\u0947\u0902 \u092c\u0939\u0941\u0924 \u0905\u0927\u093f\u0915 \u092a\u094d\u0930\u0938\u093f\u0926\u094d\u0927 \u0928\u0939\u0940\u0902 \u0939\u0948\u0902\u0964 \u0932\u0947\u0915\u093f\u0928 \u0907\u0928\u0915\u0947 \u0915\u0941\u091b \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0932\u093e\u092d \u0939\u0948\u0902 \u0914\u0930 \u0907\u0928\u094d\u0939\u0947\u0902 \u092c\u0939\u0941\u0924 \u0906\u0938\u093e\u0928\u0940 \u0938\u0947 \u092c\u0928\u093e\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0915\u0908 \u0935\u0947\u092c\u0938\u093e\u0907\u091f\u094b\u0902 \u092a\u0930 \u0935\u0930\u094d\u091a\u0941\u0905\u0932 (\u0921\u093f\u091c\u093f\u091f\u0932) \u091f\u0947\u0928-\u092b\u094d\u0930\u0947\u092e \u092d\u0940 \u0909\u092a\u0932\u092c\u094d\u0927 \u0939\u0948\u0902\u0964 \u090f\u0915 \u091f\u0947\u0928-\u092b\u094d\u0930\u0947\u092e 2 \u00d7 5 \u0915\u093e \u0922\u093e\u0901\u091a\u093e \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u0916\u093e\u0928\u0947 (\u0938\u094d\u0932\u0949\u091f) \u092c\u0928\u0947 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u091c\u093f\u0928 \u092a\u0930 10 \u0924\u0915 \u0915\u0940 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b 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