{"id":24868,"date":"2026-05-27T14:24:24","date_gmt":"2026-05-27T08:54:24","guid":{"rendered":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/dads-%e0%a4%a8%e0%a4%bf%e0%a4%af%e0%a4%ae\/"},"modified":"2026-06-03T13:50:14","modified_gmt":"2026-06-03T08:20:14","slug":"dads-%e0%a4%a8%e0%a4%bf%e0%a4%af%e0%a4%ae","status":"publish","type":"post","link":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/dads-%e0%a4%a8%e0%a4%bf%e0%a4%af%e0%a4%ae\/","title":{"rendered":"DADS \u0928\u093f\u092f\u092e!"},"content":{"rendered":"\n

\u0939\u092e \u090f\u0915 10 \u00d7 10 \u0915\u0947 \u0917\u094d\u0930\u093f\u0921 \u092e\u0947\u0902 \u0915\u094d\u0930\u092e\u093e\u0928\u0941\u0938\u093e\u0930 \u0932\u093f\u0916\u0940 \u0917\u093f\u0928\u0924\u0940 \u0938\u0947 \u0936\u0941\u0930\u0941\u0906\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 11 \u0915\u0947 \u0917\u0941\u0923\u091c \u0915\u094b \u0930\u0902\u0917 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u091c\u0948\u0938\u093e \u0915\u093f \u0906\u092a \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u0935\u0947 \u090f\u0915 \u0935\u093f\u0915\u0930\u094d\u0923 (diagonally) \u092e\u0947\u0902 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 100 \u0924\u0915 \u0915\u0940 \u0938\u0902\u0916\u094d\u200d\u092f\u093e \u092e\u0947\u0902 \u0905\u0902\u0915 \u0926\u094b\u0939\u0930\u093e\u090f \u091c\u093e\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n\n

\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n
1<\/td>\r\n 2<\/td>\r\n 3<\/td>\r\n 4<\/td>\r\n 5<\/td>\r\n 6<\/td>\r\n 7<\/td>\r\n 8<\/td>\r\n 9<\/td>\r\n 10<\/td>\r\n <\/tr>\r\n
11<\/td>\r\n 12<\/td>\r\n 13<\/td>\r\n 14<\/td>\r\n 15<\/td>\r\n 16<\/td>\r\n 17<\/td>\r\n 18<\/td>\r\n 19<\/td>\r\n 20<\/td>\r\n <\/tr>\r\n
21<\/td>\r\n 22<\/td>\r\n 23<\/td>\r\n 24<\/td>\r\n 25<\/td>\r\n 26<\/td>\r\n 27<\/td>\r\n 28<\/td>\r\n 29<\/td>\r\n 30<\/td>\r\n <\/tr>\r\n
31<\/td>\r\n 32<\/td>\r\n 33<\/td>\r\n 34<\/td>\r\n 35<\/td>\r\n 36<\/td>\r\n 37<\/td>\r\n 38<\/td>\r\n 39<\/td>\r\n 40<\/td>\r\n <\/tr>\r\n
41<\/td>\r\n 42<\/td>\r\n 43<\/td>\r\n 44<\/td>\r\n 45<\/td>\r\n 46<\/td>\r\n 47<\/td>\r\n 48<\/td>\r\n 49<\/td>\r\n 50<\/td>\r\n <\/tr>\r\n
51<\/td>\r\n 52<\/td>\r\n 53<\/td>\r\n 54<\/td>\r\n 55<\/td>\r\n 56<\/td>\r\n 57<\/td>\r\n 58<\/td>\r\n 59<\/td>\r\n 60<\/td>\r\n <\/tr>\r\n
61<\/td>\r\n 62<\/td>\r\n 63<\/td>\r\n 64<\/td>\r\n 65<\/td>\r\n 66<\/td>\r\n 67<\/td>\r\n 68<\/td>\r\n 69<\/td>\r\n 70<\/td>\r\n <\/tr>\r\n
71<\/td>\r\n 72<\/td>\r\n 73<\/td>\r\n 74<\/td>\r\n 75<\/td>\r\n 76<\/td>\r\n 77<\/td>\r\n 78<\/td>\r\n 79<\/td>\r\n 80<\/td>\r\n <\/tr>\r\n
81<\/td>\r\n 82<\/td>\r\n 83<\/td>\r\n 84<\/td>\r\n 85<\/td>\r\n 86<\/td>\r\n 87<\/td>\r\n 88<\/td>\r\n 89<\/td>\r\n 90<\/td>\r\n <\/tr>\r\n
91<\/td>\r\n 92<\/td>\r\n 93<\/td>\r\n 94<\/td>\r\n 95<\/td>\r\n 96<\/td>\r\n 97<\/td>\r\n 98<\/td>\r\n 99<\/td>\r\n 100<\/td>\r\n <\/tr>\r\n<\/tbody><\/table>
\u091a\u093f\u0924\u094d\u0930-1<\/figcaption><\/figure>\r\n\n

\u091c\u092c \u0939\u092e 11 \u0915\u0947 \u0909\u0928 \u0917\u0941\u0923\u091c\u094b\u0902 \u0915\u094b \u0926\u0947\u0916\u0924\u0947 \u0939\u0948\u0902, \u091c\u094b 100 \u0938\u0947 \u0905\u0927\u093f\u0915 \u0939\u0948\u0902, \u0924\u094b \u0905\u0902\u0915\u094b\u0902 \u0915\u094b \u0926\u094b\u0939\u0930\u093e\u090f \u091c\u093e\u0928\u0947 \u0935\u093e\u0932\u093e \u092a\u0948\u091f\u0930\u094d\u0928 \u092c\u0926\u0932 \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0915\u094b\u0908 \u0914\u0930 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u092a\u0948\u091f\u0930\u094d\u0928 \u0916\u094b\u091c\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0907\u0938\u0940 10 \u00d7 10 \u0917\u094d\u0930\u093f\u0921 \u092e\u0947\u0902 \u0930\u0902\u0917\u0940\u0928 \u0935\u093f\u0915\u0930\u094d\u0923 \u0915\u0947 \u0938\u092e\u093e\u0928\u093e\u0928\u094d\u200d\u0924\u0930 \u0915\u093f\u0938\u0940 \u092d\u0940 \u0905\u0928\u094d\u092f \u0935\u093f\u0915\u0930\u094d\u0923 \u0915\u094b \u0926\u0947\u0916\u0947\u0902\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \u092f\u0926\u093f \u0939\u092e 3 \u0938\u0947 \u0936\u0941\u0930\u0942 \u0939\u094b\u0928\u0947 \u0935\u093e\u0932\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 \u0915\u094b \u0932\u0947\u0902, \u0924\u094b \u0939\u092e\u0947\u0902 3, 14, 25, 36, 47, 58, 69, 80 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u092e\u093f\u0932\u0947\u0902\u0917\u0940\u0964 \u0925\u094b\u0921\u093c\u093e \u0927\u094d\u200d\u092f\u093e\u0928 \u0938\u0947 \u0926\u0947\u0916\u0928\u0947 \u092a\u0930 \u0939\u092e \u092a\u0932 \u092d\u0930 \u092e\u0947\u0902 \u0939\u0940 \u092f\u0939 \u091c\u093e\u0928 \u091c\u093e\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0939\u0930 \u0938\u0902\u0916\u094d\u200d\u092f\u093e \u092e\u0947\u0902 \u0907\u0915\u093e\u0908 \u0915\u0947 \u0905\u0902\u0915 \u0914\u0930 \u0926\u0939\u093e\u0908 \u0915\u0947 \u0905\u0902\u0915 \u0915\u0947 \u0905\u0928\u094d\u200d\u0924\u0930 \u092e\u0947\u0902 \u090f\u0915 \u092a\u0948\u091f\u0930\u094d\u0928 \u0939\u0948, \u0938\u093f\u0930\u094d\u092b\u093c \u0907\u0938 \u0935\u093f\u0915\u0930\u094d\u0923 \u0915\u0940 \u0905\u0928\u094d\u0924\u093f\u092e \u0938\u0902\u0916\u094d\u200d\u092f\u093e \u0915\u0947 \u0905\u0928\u094d\u200d\u0924\u0930 (\u091c\u094b \u0915\u093f \u22128 \u0939\u0948) \u0915\u094b \u091b\u094b\u0921\u093c\u0915\u0930, \u0905\u0928\u094d\u200d\u092f \u0938\u092d\u0940 \u0938\u0902\u0916\u094d\u200d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0907\u0915\u093e\u0908 \u0914\u0930 \u0926\u0939\u093e\u0908 \u092e\u0947\u0902 3 \u0915\u093e \u090f\u0915 \u0928\u093f\u092f\u0924 \u0905\u0928\u094d\u200d\u0924\u0930 \u0939\u0948\u0964 \u0907\u0938\u0940 \u0924\u0930\u0939 \u092f\u0926\u093f \u0939\u092e 2 \u0938\u0947 \u0936\u0941\u0930\u0942 \u0939\u094b\u0928\u0947 \u0935\u093e\u0932\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 \u0915\u094b \u0926\u0947\u0916\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0939\u092e\u0947\u0902 \u0905\u0928\u094d\u200d\u0924\u0930 \u0915\u094d\u0930\u092e\u0936\u0903 2 \u0914\u0930 \u22129 \u092e\u093f\u0932\u0924\u093e \u0939\u0948\u0964 \u0939\u092e \u092f\u0939 \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0915\u093f\u0938\u0940 \u092d\u0940 \u0935\u093f\u0915\u0930\u094d\u0923 \u0915\u0947 \u0932\u093f\u090f \u0905\u0902\u0915\u094b\u0902 \u0915\u0947 \u0905\u0928\u094d\u200d\u0924\u0930 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0939\u092e\u0947\u0902 \u091c\u094b \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 \u092a\u094d\u0930\u093e\u092a\u094d\u200d\u0924 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902 \u0935\u0947 \u090f\u0915-\u0926\u0942\u0938\u0930\u0947 \u0938\u0947 11 \u0915\u0947 \u0905\u0928\u094d\u200d\u0924\u0930 \u092a\u0930 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 \u0905\u092c 11 \u0915\u0947 \u0917\u0941\u0923\u091c\u094b\u0902 \u0935\u093e\u0932\u0947 \u0935\u093f\u0915\u0930\u094d\u0923 \u0915\u0940 \u0939\u0930\u0947\u0915 \u0938\u0902\u0916\u094d\u200d\u092f\u093e \u092e\u0947\u0902 \u0907\u0915\u093e\u0908 \u0914\u0930 \u0926\u0939\u093e\u0908 \u0915\u0947 \u0905\u0902\u0915\u094b\u0902 \u0915\u0947 \u0905\u0928\u094d\u200d\u0924\u0930 \u092a\u0930 \u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0902; \u0939\u092e \u092a\u093e\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f 100 \u0938\u0947 \u0915\u092e \u0935\u093e\u0932\u0947 11 \u0915\u0947 \u0938\u092d\u0940 \u0917\u0941\u0923\u091c\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u092f\u0939 \u0905\u0928\u094d\u200d\u0924\u0930 \u0936\u0942\u0928\u094d\u092f \u0939\u0948\u0964 <\/p>\n\n

\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n
11<\/td>\r\n 22<\/td>\r\n 33<\/td>\r\n 44<\/td>\r\n 55<\/td>\r\n 66<\/td>\r\n 77<\/td>\r\n 88<\/td>\r\n 99<\/td>\r\n 110<\/td>\r\n <\/tr>\r\n
121<\/td>\r\n 132<\/td>\r\n 143<\/td>\r\n 154<\/td>\r\n 165<\/td>\r\n 176<\/td>\r\n 187<\/td>\r\n 198<\/td>\r\n 209<\/td>\r\n 220<\/td>\r\n <\/tr>\r\n
231<\/td>\r\n 242<\/td>\r\n 253<\/td>\r\n 264<\/td>\r\n 275<\/td>\r\n 286<\/td>\r\n 297<\/td>\r\n 308<\/td>\r\n 319<\/td>\r\n 330<\/td>\r\n <\/tr>\r\n
341<\/td>\r\n 352<\/td>\r\n 363<\/td>\r\n 374<\/td>\r\n 385<\/td>\r\n 396<\/td>\r\n 407<\/td>\r\n 418<\/td>\r\n 429<\/td>\r\n 440<\/td>\r\n <\/tr>\r\n
451<\/td>\r\n 462<\/td>\r\n 473<\/td>\r\n 484<\/td>\r\n 495<\/td>\r\n 506<\/td>\r\n 517<\/td>\r\n 528<\/td>\r\n 539<\/td>\r\n 550<\/td>\r\n <\/tr>\r\n
561<\/td>\r\n 572<\/td>\r\n 583<\/td>\r\n 594<\/td>\r\n 605<\/td>\r\n 616<\/td>\r\n 627<\/td>\r\n 638<\/td>\r\n 649<\/td>\r\n 660<\/td>\r\n <\/tr>\r\n
671<\/td>\r\n 682<\/td>\r\n 693<\/td>\r\n 704<\/td>\r\n 715<\/td>\r\n 726<\/td>\r\n 737<\/td>\r\n 748<\/td>\r\n 759<\/td>\r\n 770<\/td>\r\n <\/tr>\r\n
781<\/td>\r\n 792<\/td>\r\n 803<\/td>\r\n 814<\/td>\r\n 825<\/td>\r\n 836<\/td>\r\n 847<\/td>\r\n 858<\/td>\r\n 869<\/td>\r\n 880<\/td>\r\n <\/tr>\r\n
891<\/td>\r\n 902<\/td>\r\n 913<\/td>\r\n 924<\/td>\r\n 935<\/td>\r\n 946<\/td>\r\n 957<\/td>\r\n 968<\/td>\r\n 979<\/td>\r\n 990<\/td>\r\n <\/tr>\r\n<\/tbody><\/table>
\u091a\u093f\u0924\u094d\u0930-2<\/figcaption><\/figure>\r\n\n

\u0905\u092c \u0939\u092e 3-\u0905\u0902\u0915\u0940\u092f \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u092a\u0930 \u090f\u0915 \u0928\u091c\u093c\u0930 \u0921\u093e\u0932\u0924\u0947 \u0939\u0948\u0902\u0964 \u091c\u093f\u0938\u092e\u0947\u0902 \u0939\u092e\u0947\u0902 11 \u0915\u0947 \u0917\u0941\u0923\u091c 110, 121, 132, 143 . . . . \u092e\u093f\u0932\u0924\u0947 \u0939\u0948\u0902\u0964 \u0926\u093f\u0932\u091a\u0938\u094d\u092a \u092c\u093e\u0924 \u092f\u0939 \u0939\u0948 \u0915\u093f 209 \u0924\u0915 \u092a\u0939\u0941\u0901\u091a\u0928\u0947 \u0924\u0915, \u0907\u0915\u093e\u0908 \u0915\u0947 \u0905\u0902\u0915 \u0914\u0930 \u0938\u0948\u0915\u0921\u093c\u0947 \u0915\u0947 \u0905\u0902\u0915 \u0915\u0947 \u092f\u094b\u0917 \u092e\u0947\u0902 \u0938\u0947 \u0926\u0939\u093e\u0908 \u0915\u0947 \u0905\u0902\u0915 \u0915\u094b \u0918\u091f\u093e\u0928\u0947 \u092a\u0930 \u092a\u0930\u093f\u0923\u093e\u092e 0 \u0906\u0924\u093e \u0939\u0948\u0964 209 \u092a\u0930 \u092f\u0939 \u0905\u0928\u094d\u200d\u0924\u0930 11 \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0910\u0938\u093e \u0932\u0917\u0924\u093e \u0939\u0948 \u0915\u093f \u0905\u092c \u0915\u0947\u0935\u0932 11 \u0915\u0947 \u0917\u0941\u0923\u091c\u094b\u0902 \u092a\u0930 \u0927\u094d\u092f\u093e\u0928 \u0915\u0947\u0928\u094d\u0926\u094d\u0930\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u093e \u0938\u092e\u092f \u0939\u0948\u0964 \u0910\u0938\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e 11 \u0915\u0947 \u0917\u0941\u0923\u091c\u094b\u0902 \u0915\u0940 \u0907\u0928 \u092a\u0902\u0915\u094d\u0924\u093f\u092f\u094b\u0902 \u0915\u094b \u092c\u0928\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u0938\u0940 \u092d\u0940 \u0938\u094d\u092a\u094d\u0930\u0947\u0921\u0936\u0940\u091f (\u0939\u092e\u0928\u0947 \u090f\u0915\u094d\u0938\u0947\u0932 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u0939\u0948) \u0915\u0947 \u0909\u092a\u092f\u094b\u0917 \u0915\u0940 \u0938\u0932\u093e\u0939 \u0926\u0947\u0924\u0947 \u0939\u0948\u0902\u0964 \u092f\u0926\u093f \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u094b, \u0924\u094b \u0936\u093f\u0915\u094d\u0937\u0915 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0907\u0928\u0915\u093e \u092a\u094d\u0930\u093f\u0902\u091f\u0906\u0909\u091f \u0932\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u091c\u093f\u0938\u092e\u0947\u0902 \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u0940 \u092a\u0948\u091f\u0930\u094d\u0928 \u0915\u094b \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0909\u0928 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u092e\u0947\u0902 \u0930\u0902\u0917 \u092d\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u091c\u093f\u0928\u092e\u0947\u0902 (U + H) – T = 11 \u0939\u0948\u0964<\/p>\n\n

\u091a\u093f\u0924\u094d\u0930-2 \u0915\u094b \u0926\u0947\u0916\u0947\u0902\u0964 \u092f\u0939\u093e\u0901 \u0939\u092e\u0947\u0902 209, 308, 407 . . . 902 \u0915\u093e \u090f\u0915 \u0926\u093f\u0932\u091a\u0938\u094d\u092a \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u092e\u093f\u0932\u0924\u093e \u0939\u0948 \u091c\u094b \u090f\u0915\u093e\u0928\u094d\u200d\u0924\u0930 (alternate) \u0905\u0902\u0915\u094b\u0902 \u0915\u0947 \u092f\u094b\u0917 \u0915\u093e \u0905\u0928\u094d\u200d\u0924\u0930 11 \u0926\u0947\u0924\u093e \u0939\u0948, \u091c\u092c\u0915\u093f 11 \u0915\u093e \u0939\u0930 \u0926\u0942\u0938\u0930\u093e \u0917\u0941\u0923\u091c \u090f\u0915\u093e\u0928\u094d\u200d\u0924\u0930 \u0905\u0902\u0915\u094b\u0902 \u0915\u0947 \u092f\u094b\u0917 \u0915\u0947 \u0905\u0928\u094d\u200d\u0924\u0930 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0936\u0942\u0928\u094d\u092f \u0926\u0947\u0924\u093e \u0939\u0948\u0964<\/p>\n\n

11 \u0915\u0947 4-\u0905\u0902\u0915\u0940\u092f \u0917\u0941\u0923\u091c\u094b\u0902 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u0906\u092a \u0915\u094d\u092f\u093e \u0938\u094b\u091a\u0924\u0947 \u0939\u0948\u0902? \u091a\u093f\u0924\u094d\u0930-3 \u0926\u0947\u0916\u0947\u0902\u0964 \u0939\u092e \u0926\u0947\u0916\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f (U + H) – (T + Th) = 0 \u092f\u093e 11 \u092f\u093e -11 \u0939\u0948\u0964 \u0907\u0938 \u092c\u093f\u0928\u094d\u200d\u0926\u0941 \u092a\u0930, \u0939\u092e\u0928\u0947 \u0907\u0938 \u0905\u0928\u094d\u200d\u0924\u0930 \u0915\u094b DADS (Difference of Alternate Digit Sums \u092f\u093e\u0928\u0940 \u090f\u0915\u093e\u0928\u094d\u200d\u0924\u0930 \u0905\u0902\u0915\u094b\u0902 \u0915\u0947 \u092f\u094b\u0917 \u0915\u093e \u0905\u0928\u094d\u200d\u0924\u0930) \u0928\u093e\u092e \u0926\u0947\u0928\u0947 \u0915\u093e \u0928\u093f\u0930\u094d\u0923\u092f \u0932\u093f\u092f\u093e\u0964 \u092f\u0939 \u0926\u0947\u0916\u0928\u093e \u0926\u093f\u0932\u091a\u0938\u094d\u092a \u0939\u0948 \u0915\u093f \u0915\u0948\u0938\u0947 DADS 11 \u0935\u093e\u0932\u0947 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u092c\u0921\u093c\u0947 \u0924\u094d\u0930\u093f\u092d\u0941\u091c\u094b\u0902 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0936\u0941\u0930\u0942 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902 \u0932\u0947\u0915\u093f\u0928 \u092b\u093f\u0930 \u0938\u093f\u092e\u091f\u0915\u0930 \u0915\u0947\u0935\u0932 \u090f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e 7909 \u0924\u0915 \u0930\u0939 \u091c\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 \u0907\u0938\u0940 \u0924\u0930\u0939, DADS -11 \u0935\u093e\u0932\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u0936\u0941\u0930\u0942 \u092e\u0947\u0902 \u0938\u092e\u093e\u0928 \u0935\u093f\u0928\u094d\u200d\u092f\u093e\u0938 \u0915\u0947 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0926\u093f\u0916\u093e\u0908 \u0926\u0947\u0924\u0940 \u0939\u0948\u0902, \u0932\u0947\u0915\u093f\u0928 \u092b\u093f\u0930 \u0909\u0928\u0915\u093e \u0935\u093f\u0928\u094d\u200d\u092f\u093e\u0938 \u092c\u0926\u0932\u0924\u093e \u0939\u0948 \u0914\u0930 \u0932\u0917\u0924\u093e \u0939\u0948 \u0915\u093f \u0935\u0947 \u0917\u094d\u0930\u093f\u0921 \u0915\u0947 \u0905\u0928\u094d\u0924\u093f\u092e \u091b\u094b\u0930 \u0924\u0915 \u092b\u0948\u0932\u0924\u0940 \u0939\u0948\u0902\u0964<\/p>\n\n

\u0915\u094d\u092f\u093e \u0939\u094b\u0917\u093e \u092f\u0926\u093f \u0939\u092e \u0915\u093f\u0938\u0940 \u092c\u0947\u0939\u0924\u0930 \u092a\u0948\u091f\u0930\u094d\u0928 \u0915\u0940 \u0916\u094b\u091c \u092e\u0947\u0902 \u0915\u0949\u0932\u092e \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u092c\u0926\u0932 \u0926\u0947\u0902? \u0939\u092e\u0928\u0947 9 \u0915\u0949\u0932\u092e \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0915\u094b\u0936\u093f\u0936 \u0915\u0940, \u092f\u093e\u0928\u0940 \u092a\u0939\u0932\u0940 \u092a\u0902\u0915\u094d\u0924\u093f 11 . . . 99, \u0926\u0942\u0938\u0930\u0940 \u092a\u0902\u0915\u094d\u0924\u093f 110 . . . 198 \u0906\u0926\u093f\u0964 \u0924\u0941\u0930\u0928\u094d\u200d\u0924 \u0939\u0940, \u0939\u092e\u0947\u0902 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u093e \u090f\u0915 \u0938\u094d\u092a\u0937\u094d\u091f \u092a\u0948\u091f\u0930\u094d\u0928 \u0926\u093f\u0916\u0928\u0947 \u0932\u0917\u093e\u0964 \u091a\u093f\u0924\u094d\u0930-4 \u0926\u0947\u0916\u0947\u0902\u0964 DADS 11 \u0935\u093e\u0932\u0947 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0938\u093f\u0915\u0941\u0921\u093c\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 DADS -11 \u0935\u093e\u0932\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u091c\u0917\u0939 \u092c\u0928\u093e\u0924\u0947 \u0939\u0948\u0902, \u091c\u094b \u0924\u092c \u0924\u0915 \u092c\u0922\u093c\u0924\u0947 \u0939\u0948\u0902 \u091c\u092c \u0924\u0915 \u0915\u093f \u0935\u0947 \u0932\u0917\u092d\u0917 \u092a\u0942\u0930\u0940 \u092a\u0902\u0915\u094d\u0924\u093f\u092f\u094b\u0902 \u0915\u094b \u0915\u0935\u0930 \u0928 \u0915\u0930 \u0932\u0947\u0902\u0964<\/p>\n\n

\u0907\u0938 \u092c\u093f\u0928\u094d\u200d\u0926\u0941 \u092a\u0930, \u0939\u092e \u0935\u0930\u094d\u0923\u0928\u093e\u0924\u094d\u092e\u0915 \u0924\u0930\u0940\u0915\u093c\u0947 \u0938\u0947 \u0939\u091f\u0915\u0930 ‘\u0932\u094b \u092b\u094d\u0932\u094b\u0930 \u0939\u093e\u0908 \u0938\u0940\u0932\u093f\u0902\u0917’ (Low Floor High Ceiling) \u092a\u0948\u091f\u0930\u094d\u0928 \u092a\u0930 \u0906\u0927\u093e\u0930\u093f\u0924 \u0915\u0941\u091b \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0942\u091b\u0928\u093e \u091a\u093e\u0939\u0947\u0902\u0917\u0947\u0964<\/p>\n\n

\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n
3971<\/td>\r\n 3982<\/td>\r\n 3993<\/td>\r\n 4004<\/td>\r\n 4015<\/td>\r\n 4026<\/td>\r\n 4037<\/td>\r\n 4048<\/td>\r\n 4059<\/td>\r\n 4070<\/td>\r\n <\/tr>\r\n
4081<\/td>\r\n 4092<\/td>\r\n 4103<\/td>\r\n 4114<\/td>\r\n 4125<\/td>\r\n 4136<\/td>\r\n 4147<\/td>\r\n 4158<\/td>\r\n 4169<\/td>\r\n 4180<\/td>\r\n <\/tr>\r\n
4191<\/td>\r\n 4202<\/td>\r\n 4213<\/td>\r\n 4224<\/td>\r\n 4235<\/td>\r\n 4246<\/td>\r\n 4257<\/td>\r\n 4268<\/td>\r\n 4279<\/td>\r\n 4290<\/td>\r\n <\/tr>\r\n
4301<\/td>\r\n 4312<\/td>\r\n 4323<\/td>\r\n 4334<\/td>\r\n 4345<\/td>\r\n 4356<\/td>\r\n 4367<\/td>\r\n 4378<\/td>\r\n 4389<\/td>\r\n 4400<\/td>\r\n <\/tr>\r\n
4411<\/td>\r\n 4422<\/td>\r\n 4433<\/td>\r\n 4444<\/td>\r\n 4455<\/td>\r\n 4466<\/td>\r\n 4477<\/td>\r\n 4488<\/td>\r\n 4499<\/td>\r\n 4510<\/td>\r\n <\/tr>\r\n
4521<\/td>\r\n 4532<\/td>\r\n 4543<\/td>\r\n 4554<\/td>\r\n 4565<\/td>\r\n 4576<\/td>\r\n 4587<\/td>\r\n 4598<\/td>\r\n 4609<\/td>\r\n 4620<\/td>\r\n <\/tr>\r\n
4631<\/td>\r\n 4642<\/td>\r\n 4653<\/td>\r\n 4664<\/td>\r\n 4675<\/td>\r\n 4686<\/td>\r\n 4697<\/td>\r\n 4708<\/td>\r\n 4719<\/td>\r\n 4730<\/td>\r\n <\/tr>\r\n
4741<\/td>\r\n 4752<\/td>\r\n 4763<\/td>\r\n 4774<\/td>\r\n 4785<\/td>\r\n 4796<\/td>\r\n 4807<\/td>\r\n 4818<\/td>\r\n 4829<\/td>\r\n 4840<\/td>\r\n <\/tr>\r\n
4851<\/td>\r\n 4862<\/td>\r\n 4873<\/td>\r\n 4884<\/td>\r\n 4895<\/td>\r\n 4906<\/td>\r\n 4917<\/td>\r\n 4928<\/td>\r\n 4939<\/td>\r\n 4950<\/td>\r\n <\/tr>\r\n
4961<\/td>\r\n 4972<\/td>\r\n 4983<\/td>\r\n 4994<\/td>\r\n 5005<\/td>\r\n 5016<\/td>\r\n 5027<\/td>\r\n 5038<\/td>\r\n 5049<\/td>\r\n 5060<\/td>\r\n <\/tr>\r\n
5071<\/td>\r\n 5082<\/td>\r\n 5093<\/td>\r\n 5104<\/td>\r\n 5115<\/td>\r\n 5126<\/td>\r\n 5137<\/td>\r\n 5148<\/td>\r\n 5159<\/td>\r\n 5170<\/td>\r\n <\/tr>\r\n
5181<\/td>\r\n 5192<\/td>\r\n 5203<\/td>\r\n 5214<\/td>\r\n 5225<\/td>\r\n 5236<\/td>\r\n 5247<\/td>\r\n 5258<\/td>\r\n 5269<\/td>\r\n 5280<\/td>\r\n <\/tr>\r\n
5291<\/td>\r\n 5302<\/td>\r\n 5313<\/td>\r\n 5324<\/td>\r\n 5335<\/td>\r\n 5346<\/td>\r\n 5357<\/td>\r\n 5368<\/td>\r\n 5379<\/td>\r\n 5390<\/td>\r\n <\/tr>\r\n
5401<\/td>\r\n 5412<\/td>\r\n 5423<\/td>\r\n 5434<\/td>\r\n 5445<\/td>\r\n 5456<\/td>\r\n 5467<\/td>\r\n 5478<\/td>\r\n 5489<\/td>\r\n 5500<\/td>\r\n <\/tr>\r\n
5511<\/td>\r\n 5522<\/td>\r\n 5533<\/td>\r\n 5544<\/td>\r\n 5555<\/td>\r\n 5566<\/td>\r\n 5577<\/td>\r\n 5588<\/td>\r\n 5599<\/td>\r\n 5610<\/td>\r\n <\/tr>\r\n
5621<\/td>\r\n 5632<\/td>\r\n 5643<\/td>\r\n 5654<\/td>\r\n 5665<\/td>\r\n 5676<\/td>\r\n 5687<\/td>\r\n 5698<\/td>\r\n 5709<\/td>\r\n 5720<\/td>\r\n <\/tr>\r\n
5731<\/td>\r\n 5742<\/td>\r\n 5753<\/td>\r\n 5764<\/td>\r\n 5775<\/td>\r\n 5786<\/td>\r\n 5797<\/td>\r\n 5808<\/td>\r\n 5819<\/td>\r\n 5830<\/td>\r\n <\/tr>\r\n
5841<\/td>\r\n 5852<\/td>\r\n 5863<\/td>\r\n 5874<\/td>\r\n 5885<\/td>\r\n 5896<\/td>\r\n 5907<\/td>\r\n 5918<\/td>\r\n 5929<\/td>\r\n 5940<\/td>\r\n <\/tr>\r\n<\/tbody><\/table>
\u091a\u093f\u0924\u094d\u0930-3<\/figcaption><\/figure>\r\n\n
\n

\u0932\u094b \u092b\u094d\u0932\u094b\u0930 \u0939\u093e\u0908 \u0938\u0940\u0932\u093f\u0902\u0917 \u0915\u093e \u090f\u0915 \u0938\u0902\u0915\u094d\u0937\u093f\u092a\u094d\u0924 \u092a\u0930\u093f\u091a\u092f : \u090f\u0915 \u0917\u0924\u093f\u0935\u093f\u0927\u093f \u0915\u094b \u091a\u0941\u0928\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u091c\u094b \u0938\u0930\u0932 \u0935 \u0909\u092e\u094d\u0930 \u0915\u0947 \u0939\u093f\u0938\u093e\u092c \u0938\u0947 \u091f\u093e\u0938\u094d\u0915 \u0926\u0947\u0928\u0947 \u0938\u0947 \u0936\u0941\u0930\u0942 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u0910\u0938\u093e \u091f\u093e\u0938\u094d\u0915 \u091c\u093f\u0938\u0947 \u0915\u0930\u0928\u0947 \u0915\u093e \u092a\u094d\u0930\u092f\u093e\u0938, \u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0938\u092d\u0940 \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u093f\u092f\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u094b\u0964 \u0907\u0928 \u091f\u093e\u0938\u094d\u0915\u094b\u0902 \u0915\u0940 \u091c\u091f\u093f\u0932\u0924\u093e \u092c\u095d\u0924\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948 \u0924\u093e\u0915\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u0940 \u0915\u094b \u0905\u092a\u0928\u0940 \u0905\u0927\u093f\u0915\u0924\u092e \u0915\u094d\u0937\u092e\u0924\u093e \u092a\u0930 \u0915\u093e\u092e \u0915\u0930\u0928\u0947 \u0915\u093e \u092a\u094d\u0930\u092f\u093e\u0938 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092a\u094d\u0930\u0947\u0930\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0947\u0964 \u0907\u0938\u092e\u0947\u0902 \u0938\u092d\u0940 \u0915\u0947 \u0932\u093f\u090f \u092a\u0930\u094d\u092f\u093e\u092a\u094d\u0924 \u0915\u093e\u092e \u0939\u094b\u0924\u093e \u0939\u0948; \u0932\u0947\u0915\u093f\u0928 \u091c\u0948\u0938\u0947-\u091c\u0948\u0938\u0947 \u0917\u0924\u093f\u200d\u0935\u093f\u0927\u093f\u092f\u094b\u0902 \u0915\u093e \u0938\u094d\u0924\u0930 \u091c\u091f\u093f\u0932 \u0939\u094b\u0924\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0915\u092e \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u0940 \u0939\u0940 \u0907\u0928 \u091f\u093e\u0938\u094d\u0915\u094b\u0902 \u0915\u094b \u092a\u0942\u0930\u093e \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0938\u0915\u094d\u0937\u092e \u0939\u094b \u092a\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 \u0939\u093e\u0932\u093e\u0901\u0915\u093f, \u092f\u0939\u093e\u0901 \u092e\u0939\u0924\u094d\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092f\u0939 \u0939\u0948 \u0915\u093f \u0938\u092d\u0940 \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u0940 \u0935\u094d\u092f\u0938\u094d\u0924 \u0930\u0939\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0935\u0947 \u0938\u092d\u0940 \u092a\u0942\u0930\u0947 \u091f\u093e\u0938\u094d\u0915 \u0915\u0947 \u0915\u092e-\u0938\u0947-\u0915\u092e \u090f\u0915 \u0939\u093f\u0938\u094d\u0938\u0947 \u0915\u094b \u092a\u0942\u0930\u093e \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0938\u0915\u094d\u0937\u092e \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<\/div><\/div>\n\n

\r\n\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n
3080<\/td>\r\n 3091<\/td>\r\n 3102<\/td>\r\n 3113<\/td>\r\n 3124<\/td>\r\n 3135<\/td>\r\n 3146<\/td>\r\n 3157<\/td>\r\n 3168<\/td>\r\n <\/tr>\r\n\r\n
3179<\/td>\r\n 3190<\/td>\r\n 3201<\/td>\r\n 3212<\/td>\r\n 3223<\/td>\r\n 3234<\/td>\r\n 3245<\/td>\r\n 3256<\/td>\r\n 3267<\/td>\r\n <\/tr>\r\n\r\n
3278<\/td>\r\n 3289<\/td>\r\n 3300<\/td>\r\n 3311<\/td>\r\n 3322<\/td>\r\n 3333<\/td>\r\n 3344<\/td>\r\n 3355<\/td>\r\n 3366<\/td>\r\n <\/tr>\r\n\r\n
3377<\/td>\r\n 3388<\/td>\r\n 3399<\/td>\r\n 3410<\/td>\r\n 3421<\/td>\r\n 3432<\/td>\r\n 3443<\/td>\r\n 3454<\/td>\r\n 3465<\/td>\r\n <\/tr>\r\n\r\n
3476<\/td>\r\n 3487<\/td>\r\n 3498<\/td>\r\n 3509<\/td>\r\n 3520<\/td>\r\n 3531<\/td>\r\n 3542<\/td>\r\n 3553<\/td>\r\n 3564<\/td>\r\n <\/tr>\r\n\r\n
3575<\/td>\r\n 3586<\/td>\r\n 3597<\/td>\r\n 3608<\/td>\r\n 3619<\/td>\r\n 3630<\/td>\r\n 3641<\/td>\r\n 3652<\/td>\r\n 3663<\/td>\r\n <\/tr>\r\n\r\n
3674<\/td>\r\n 3685<\/td>\r\n 3696<\/td>\r\n 3707<\/td>\r\n 3718<\/td>\r\n 3729<\/td>\r\n 3740<\/td>\r\n 3751<\/td>\r\n 3762<\/td>\r\n <\/tr>\r\n\r\n
3773<\/td>\r\n 3784<\/td>\r\n 3795<\/td>\r\n 3806<\/td>\r\n 3817<\/td>\r\n 3828<\/td>\r\n 3839<\/td>\r\n 3850<\/td>\r\n 3861<\/td>\r\n <\/tr>\r\n\r\n
3872<\/td>\r\n 3883<\/td>\r\n 3894<\/td>\r\n 3905<\/td>\r\n 3916<\/td>\r\n 3927<\/td>\r\n 3938<\/td>\r\n 3949<\/td>\r\n 3960<\/td>\r\n <\/tr>\r\n\r\n
3971<\/td>\r\n 3982<\/td>\r\n 3993<\/td>\r\n 4004<\/td>\r\n 4015<\/td>\r\n 4026<\/td>\r\n 4037<\/td>\r\n 4048<\/td>\r\n 4059<\/td>\r\n <\/tr>\r\n\r\n
4070<\/td>\r\n 4081<\/td>\r\n 4092<\/td>\r\n 4103<\/td>\r\n 4114<\/td>\r\n 4125<\/td>\r\n 4136<\/td>\r\n 4147<\/td>\r\n 4158<\/td>\r\n <\/tr>\r\n\r\n
4169<\/td>\r\n 4180<\/td>\r\n 4191<\/td>\r\n 4202<\/td>\r\n 4213<\/td>\r\n 4224<\/td>\r\n 4235<\/td>\r\n 4246<\/td>\r\n 4257<\/td>\r\n <\/tr>\r\n\r\n
4268<\/td>\r\n 4279<\/td>\r\n 4290<\/td>\r\n 4301<\/td>\r\n 4312<\/td>\r\n 4323<\/td>\r\n 4334<\/td>\r\n 4345<\/td>\r\n 4356<\/td>\r\n <\/tr>\r\n\r\n
4367<\/td>\r\n 4378<\/td>\r\n 4389<\/td>\r\n 4400<\/td>\r\n 4411<\/td>\r\n 4422<\/td>\r\n 4433<\/td>\r\n 4444<\/td>\r\n 4455<\/td>\r\n <\/tr>\r\n\r\n
4466<\/td>\r\n 4477<\/td>\r\n 4488<\/td>\r\n 4499<\/td>\r\n 4510<\/td>\r\n 4521<\/td>\r\n 4532<\/td>\r\n 4543<\/td>\r\n 4554<\/td>\r\n <\/tr>\r\n\r\n
4565<\/td>\r\n 4576<\/td>\r\n 4587<\/td>\r\n 4598<\/td>\r\n 4609<\/td>\r\n 4620<\/td>\r\n 4631<\/td>\r\n 4642<\/td>\r\n 4653<\/td>\r\n <\/tr>\r\n\r\n
4664<\/td>\r\n 4675<\/td>\r\n 4686<\/td>\r\n 4697<\/td>\r\n 4708<\/td>\r\n 4719<\/td>\r\n 4730<\/td>\r\n 4741<\/td>\r\n 4752<\/td>\r\n <\/tr>\r\n\r\n
4763<\/td>\r\n 4774<\/td>\r\n 4785<\/td>\r\n 4796<\/td>\r\n 4807<\/td>\r\n 4818<\/td>\r\n 4829<\/td>\r\n 4840<\/td>\r\n 4851<\/td>\r\n <\/tr>\r\n\r\n
4862<\/td>\r\n 4873<\/td>\r\n 4884<\/td>\r\n 4895<\/td>\r\n 4906<\/td>\r\n 4917<\/td>\r\n 4928<\/td>\r\n 4939<\/td>\r\n 4950<\/td>\r\n <\/tr>\r\n\r\n<\/tbody><\/table>
\u091a\u093f\u0924\u094d\u0930-4<\/figcaption><\/figure>\r\n\n
\n

\u0905\u092c \u0924\u0915 \u0915\u0947 \u0939\u092e\u093e\u0930\u0947 \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937\u094b\u0902 \u0915\u093e \u0938\u093e\u0930 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u0948 :<\/h3>\n\n\n\n
    \n
  1. 11 \u0915\u0947 \u0938\u092d\u0940 2-\u0905\u0902\u0915\u0940\u092f \u0917\u0941\u0923\u091c\u094b\u0902 \u092e\u0947\u0902 \u0926\u0939\u093e\u0908 \u0914\u0930 \u0907\u0915\u093e\u0908 \u0915\u0947 \u0938\u094d\u0925\u093e\u0928 \u092a\u0930 \u0905\u0902\u0915 \u0926\u094b\u0939\u0930\u093e\u090f \u091c\u093e\u0924\u0947 \u0939\u0948\u0902\u0964<\/li>\n\n\n\n
  2. 11 \u0915\u0947 3-\u0905\u0902\u0915\u0940\u092f \u0917\u0941\u0923\u091c\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f, \u0907\u0915\u093e\u0908 \u0915\u0947 \u0905\u0902\u0915 \u0914\u0930 \u0938\u0948\u0915\u0921\u093c\u0947 \u0915\u0947 \u0905\u0902\u0915 \u0915\u0947 \u092f\u094b\u0917 \u092e\u0947\u0902 \u0938\u0947 \u0926\u0939\u093e\u0908 \u0915\u0947 \u0905\u0902\u0915 \u0915\u094b \u0918\u091f\u093e\u0928\u0947 \u092a\u0930 \u092a\u0930\u093f\u0923\u093e\u092e \u092f\u093e \u0924\u094b 0 \u0906\u0924\u093e \u0939\u0948 \u092f\u093e +11 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/li>\n\n\n\n
  3. DADS (Difference of Alternate Digit Sums – \u090f\u0915\u093e\u0928\u094d\u0924\u0930 \u0905\u0902\u0915\u094b\u0902 \u0915\u0947 \u092f\u094b\u0917 \u0915\u093e \u0905\u0928\u094d\u0924\u0930) \u0915\u094b \u090f\u0915\u093e\u0928\u094d\u0924\u0930 \u0938\u094d\u0925\u093e\u0928\u094b\u0902 \u092a\u0930 \u0938\u094d\u0925\u093f\u0924 \u0905\u0902\u0915\u094b\u0902 \u0915\u0947 \u092f\u094b\u0917 \u0915\u0947 \u0905\u0928\u094d\u0924\u0930 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964<\/li>\n\n\n\n
  4. 11 \u0915\u0947 4-\u0905\u0902\u0915\u0940\u092f \u0917\u0941\u0923\u091c\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f, DADS 0, +11 \u092f\u093e – 11 \u0925\u093e\u0964<\/li>\n\n\n\n
  5. \u0935\u0947 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u091c\u093f\u0928\u094d\u0939\u094b\u0902\u0928\u0947 \u090f\u0915 \u0935\u093f\u0936\u093f\u0937\u094d\u091f DADS \u092e\u093e\u0928 \u0926\u093f\u092f\u093e, \u0935\u0947 \u090f\u0915 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0926\u093f\u0916\u093e\u0908 \u0926\u0940\u0902, \u091c\u094b 9 \u0915\u0949\u0932\u092e \u0935\u093e\u0932\u0947 \u0917\u094d\u0930\u093f\u0921 \u092e\u0947\u0902 \u0938\u094d\u092a\u0937\u094d\u091f \u0930\u0942\u092a \u0938\u0947 \u0926\u093f\u0916\u093e\u0908 \u0926\u0947 \u0930\u0939\u0940 \u0925\u0940\u0902\u0964<\/li>\n<\/ol>\n<\/div><\/div>\n\n

    \u0916\u094b\u091c-\u092c\u0940\u0928 \u0915\u0947 \u0932\u093f\u090f \u092a\u094d\u0930\u0936\u094d\u0928 :<\/h2>\n\n
      \n
    1. \u0915\u094d\u092f\u093e \u0910\u0938\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u0939\u0948\u0902 \u091c\u093f\u0928\u0915\u093e DADS 22 \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u0939\u0948?<\/li>\n\n\n\n
    2. \u0935\u0939 \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094c\u0928-\u0938\u0940 \u0939\u0948 \u091c\u093f\u0938\u0915\u093e DADS 22 \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u0939\u0948?<\/li>\n\n\n\n
    3. \u0915\u094d\u092f\u093e \u0910\u0938\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u0939\u0948\u0902 \u091c\u093f\u0928\u0915\u093e DADS \u221222 \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u0939\u0948? \u0935\u0939 \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094c\u0928-\u0938\u0940 \u0939\u0948 \u091c\u093f\u0938\u0915\u093e DADS \u221222 \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u0939\u0948?<\/li>\n\n\n\n
    4. \u0935\u0939 \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094c\u0928-\u0938\u0940 \u0939\u094b\u0917\u0940 \u091c\u093f\u0938\u0915\u093e DADS \\(11n\\) \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b? \u0907\u0938 \u0938\u0902\u0916\u094d\u092f\u093e \u092e\u0947\u0902 \u0915\u093f\u0924\u0928\u0947 \u0905\u0902\u0915 \u0939\u094b\u0902\u0917\u0947?<\/li>\n\n\n\n
    5. \\(n\\) \u0915\u0947 \u0915\u093f\u0938\u0940 \u0926\u093f\u090f \u0917\u090f \u092e\u093e\u0928 \u0915\u0947 \u0932\u093f\u090f, \\(11n\\) \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 DADS \u0935\u093e\u0932\u0940 \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0947 \u0905\u0902\u0915\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u0942\u0924\u094d\u0930 \u0916\u094b\u091c\u0947\u0902\u0964<\/li>\n\n\n\n
    6. \u0915\u094d\u092f\u093e 11 \u0915\u0947 \u0938\u092d\u0940 \u0917\u0941\u0923\u091c\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f, DADS \u0939\u092e\u0947\u0936\u093e 11 \u0915\u093e \u090f\u0915 \u0917\u0941\u0923\u091c \u0939\u094b\u0917\u093e?<\/li>\n<\/ol>\n\n

      \u0936\u093f\u0915\u094d\u0937\u0915\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0928\u094b\u091f\u094d\u0938 :<\/h2>\n\n
        \n
      1. \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u0940 DADS 22 \u0935\u093e\u0932\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f 1010101010101010101010101010101010101010101<\/span> \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u092c\u0928\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u092f\u0939\u093e\u0901 \u0938\u0947, \u0935\u0947 \u091c\u0932\u094d\u0926 \u0939\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b \u091b\u094b\u091f\u093e \u0915\u0930\u0915\u0947 2020202020202020202020 \u0915\u0930\u0928\u093e \u0936\u0941\u0930\u0942 \u0915\u0930 \u0926\u0947\u0902\u0917\u0947 \u0914\u0930 \u092f\u0939 \u0926\u0947\u0916\u0947\u0902\u0917\u0947 \u0915\u093f \u0915\u094d\u092f\u093e \u0935\u0947 \u0907\u0938\u0938\u0947 \u092d\u0940 \u091b\u094b\u091f\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/li>\n\n\n\n
      2. \u092f\u0939 \u0935\u093f\u0926\u094d\u092f\u093e\u200d\u0930\u094d\u0925\u093f\u092f\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0907\u0938 \u0916\u094b\u091c-\u092c\u0940\u0928 \u092e\u0947\u0902 \u0935\u094d\u092f\u0935\u0938\u094d\u0925\u093f\u0924 \u0930\u0942\u092a \u0938\u0947 \u0906\u0917\u0947 \u092c\u0922\u093c\u0928\u0947 \u0915\u093e \u090f\u0915 \u0905\u091a\u094d\u091b\u093e \u0905\u0935\u0938\u0930 \u0939\u0948\u0964 \u091a\u0930\u0923-1 \u0915\u0947 \u0924\u0930\u094d\u0915 \u0915\u093e \u092a\u093e\u0932\u0928 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f, \u0935\u0947 \u092c\u0939\u0941\u0924 \u091b\u094b\u091f\u0940 \u0938\u0902\u0916\u094d\u092f\u093e 909 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 \u091c\u093f\u0938\u0915\u093e DADS 18 \u0939\u0948 (\u092f\u0939 11 \u0915\u093e \u0917\u0941\u0923\u091c \u0928\u0939\u0940\u0902 \u0939\u0948)\u0964 22 \u0915\u093e DADS \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0938\u0902\u0916\u094d\u092f\u093e 40909 \u0939\u094b\u0928\u0940 \u091a\u093e\u0939\u093f\u090f\u0964<\/li>\n\n\n\n
      3. \u092f\u0939 \u090f\u0915 \u092c\u0939\u0941\u0924 \u0939\u0940 \u0926\u093f\u0932\u091a\u0938\u094d\u092a \u092c\u0926\u0932\u093e\u0935 \u0939\u0948 \u2014 \u090a\u092a\u0930 \u0926\u093f\u090f \u0917\u090f \u091a\u0930\u0923\u094b\u0902 \u0915\u0947 \u0924\u0930\u094d\u0915 \u0915\u093e \u092a\u093e\u0932\u0928 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f, \u0939\u092e \u0926\u0947\u0916\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f 409090 \u090f\u0915 \u0910\u0938\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948 \u091c\u093f\u0938\u0915\u093e DADS -22 \u0939\u0948\u0964 \u0915\u094d\u092f\u093e \u092f\u0939 \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948? \u0938\u094d\u092a\u0937\u094d\u091f \u0930\u0942\u092a \u0938\u0947, \u092f\u0926\u093f \u0907\u0915\u093e\u0908 \u0915\u0947 \u0938\u094d\u0925\u093e\u0928 \u0915\u0947 \u0938\u093e\u0925 \u090f\u0915\u093e\u0928\u094d\u200d\u0924\u0930 \u0938\u094d\u0925\u093e\u0928\u094b\u0902 \u092a\u0930 \u0917\u093c\u0948\u0930-\u0936\u0942\u0928\u094d\u092f (non-zero) \u0905\u0902\u0915 \u0939\u0948\u0902, \u0924\u094b \u0905\u0928\u094d\u092f \u0938\u094d\u0925\u093e\u0928\u094b\u0902 \u0915\u0947 \u0905\u0902\u0915\u094b\u0902 \u0915\u094b \u092c\u0921\u093c\u093e \u0939\u094b\u0928\u093e \u0939\u094b\u0917\u093e \u0924\u093e\u0915\u093f \u0905\u0902\u0924\u0930 -22 \u092c\u0928\u093e \u0930\u0939\u0947\u0964 \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u0940 \u092f\u0939 \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u090b\u0923\u093e\u0924\u094d\u092e\u0915 DADS \u0935\u093e\u0932\u0940 \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u092e\u0947\u0902 \u0905\u0902\u0915\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0938\u092e (even) \u0939\u094b\u0917\u0940 \u0914\u0930 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 DADS \u0935\u093e\u0932\u0940 \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u092e\u0947\u0902 \u0905\u0902\u0915\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0935\u093f\u0937\u092e (odd) \u0939\u094b\u0917\u0940\u0964 \u0915\u093f\u0938\u0940 \u0935\u093f\u0936\u0947\u0937 DADS \u092e\u093e\u0928 \u0935\u093e\u0932\u0940 \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b \u0926\u0930\u094d\u091c \u0915\u0930\u0928\u0947 \u0935\u093e\u0932\u0940 \u0924\u093e\u0932\u093f\u0915\u093e \u0909\u0928\u094d\u0939\u0947\u0902 \u092f\u0939 \u0905\u0935\u0932\u094b\u0915\u0928 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u092e\u0926\u0926 \u0915\u0930\u0947\u0917\u0940\u0964<\/li>\n\n\n\n
      4. \u0906\u0917\u0947 \u092c\u0922\u093c\u0924\u0947 \u0939\u0941\u090f, \u0939\u092e \u092a\u0942\u091b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0915\u093f\u0938\u0940 \u092d\u0940 \u092a\u094d\u0930\u093e\u0915\u0943\u0924 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0947 \u0932\u093f\u090f \\(11n\\) DADS \u0935\u093e\u0932\u0940 \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0947 \u0905\u0902\u0915\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094d\u092f\u093e \u0939\u094b\u0917\u0940\u0964 \u0924\u0930\u094d\u0915 \u092c\u093f\u0932\u094d\u0915\u0941\u0932 \u092a\u0939\u0932\u0947 \u091c\u0948\u0938\u093e \u0939\u0940 \u0939\u0948\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, DADS 55 \u0935\u093e\u0932\u0940 \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u092e\u0947\u0902 \u0907\u0915\u093e\u0908 \u0905\u0902\u0915 \u0938\u0947 \u0936\u0941\u0930\u0942 \u0939\u094b\u0928\u0947 \u0935\u093e\u0932\u0947 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u090f\u0915\u093e\u0928\u094d\u200d\u0924\u0930 \u0938\u094d\u0925\u093e\u0928 \u092a\u0930 \u091b\u0939 9 \u0939\u094b\u0928\u0947 \u091a\u093e\u0939\u093f\u090f \u0914\u0930 \u092b\u093f\u0930 \u0938\u092c\u0938\u0947 \u0906\u0917\u0947 \u0935\u093e\u0932\u0947 \u0905\u0902\u0915 \u092e\u0947\u0902 1 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f (55 \u00f79 = 6, \u0936\u0947\u0937\u092b\u0932 1)\u0964 \u0907\u0938\u0932\u093f\u090f, \u092f\u0939 13 \u0905\u0902\u0915\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e 1090909090909 \u0939\u094b\u0917\u0940\u0964 \u0905\u0924\u0903 \\(11n\\) \u0915\u0947 DADS \u0935\u093e\u0932\u0940 \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u0942\u0924\u094d\u0930 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u094b\u0917\u093e : \u092f\u0926\u093f \\(q\\) \u0914\u0930 \\(r\\) \u0910\u0938\u0940 \u092a\u094d\u0930\u093e\u0915\u0943\u0924 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u0939\u0948\u0902 \u0915\u093f \\(11n \\ \u00f7 \\ 9 = q\\) \u0914\u0930 \u0936\u0947\u0937\u092b\u0932 \\(r\\) \u0939\u0948 (\u092f\u093e\u0928\u0940 \\(r \\lt 9\\)), \u0924\u094b \u0935\u0939 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u094b\u0917\u0940 :

        \\( r \\times 10^{2q} \\ + \\ 9 \\times \\left( 10^{2\\left(q-1 \\right)}\\ + \\ 10^{2\\left (q-2 \\right)}) \\ + \\ … \\ + 1 \\right)\\).<\/p>

        \u092f\u0939 \\(2q + 1\\) \u0905\u0902\u0915\u094b\u0902 \u0935\u093e\u0932\u0940 \u090f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u094b\u0917\u0940\u0964 \u0939\u092e \u0907\u0938\u0947 DADS \u0928\u093f\u092f\u092e (DADS Rule) \u0915\u0939\u0924\u0947 \u0939\u0948\u0902!<\/p><\/li>\n\n\n\n

      5. \u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0947\u0902 \u0915\u093f \u092f\u0926\u093f N, 11 \u0915\u093e \u0917\u0941\u0923\u091c \u0939\u0948, \u0924\u094b DADS \u092d\u0940 11 \u0915\u093e \u0917\u0941\u0923\u091c \u0939\u094b\u0917\u093e, \u0914\u0930 \u0907\u0938\u0915\u0947 \u0935\u093f\u092a\u0930\u0940\u0924 \u092d\u0940 \u0938\u0939\u0940 \u0939\u094b\u0917\u093e :<\/strong>\u092e\u093e\u0928 \u0932\u0947\u0902 \\((2n + 1)\\) \u0905\u0902\u0915\u094b\u0902 \u0935\u093e\u0932\u0940 \u0915\u094b\u0908 \u0938\u0902\u0916\u094d\u092f\u093e N \u0939\u0948 :

        \\(a_{0} + 10a_{1} + 100a_{2} + … + 10^{2n} \\times a_{2n}\\)<\/p>\u0907\u0938\u0915\u0947 \u090f\u0915\u093e\u0928\u094d\u200d\u0924\u0930 \u0905\u0902\u0915\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 \\(a_{0} + a_{2} + … + a_{2n}\\) \u0914\u0930 \\( a_{1} + a_{3} + … + a_{2n-1}\\) \u0939\u0948\u0964\u0907\u0938\u0932\u093f\u090f N \u0915\u0947 \u0932\u093f\u090f DADS \u0939\u0948 :

        \\(\\left( a_{0}+ a_{2} +… + a_{2n} \\right) \\ – \\left( a_{1}+ a_{3} +… + a_{2-1} \\right)\\)<\/p>\u0906\u0907\u090f N – DADS \u092a\u0930 \u0935\u093f\u091a\u093e\u0930 \u0915\u0930\u0947\u0902 \u091c\u094b \u0915\u093f \u0939\u0948 :

        \\(a_{0} + 10a_{1} + 100a_{2} + … + 10^{2n}\\times a_{2n} -\\ [ \\left( a_{0} + a_{2} + … + a_{2n} \\right) \\ – \\left(a_{1} + a_{3} + … + a_{2n-1} \\right)]\\)\\( = a_{0} + 10a_{1} + 100a_{2} + … + 10^{2n} \\times a_{2n}\\ – \\left( a_{0} + a_{2} + … + a_{2n} \\right)+\\left(a_{1} + a_{3} + … + a_{2n-1} \\right)\\)\\( = 11a_{1} + 99a_{2} + 1001a_{3} + 9999a_{4} + … + \\left( 10^{2n-1} + 1 \\right)a_{2n-1} + \\left( 10^{2n} – 1 \\right)a_{2n}\\)\\( = \u2211^{n}_{k=1} [\\left( 10^{2k-1} + 1 \\right)a_{2k-1} + \\left( 10^{2k} – 1 \\right)a_{2k}]\\)<\/p><\/li>\n<\/ol>\n\n

        \u0905\u092c \\(10^{2k – 1} + 1 = \\left( 10 + 1 \\right) \\left( 10^{2k-2} \\ – \\ 10^{2k – 3} + … + 1 \\right) = 11b\\)<\/span>\u091c\u0939\u093e\u0901 \\(b\\) \u0915\u094b\u0908 \u092a\u094d\u0930\u093e\u0915\u0943\u0924 \u0938\u0902\u0916\u094d\u200d\u092f\u093e \u0939\u0948, \u092f\u093e\u0928\u0940 \\(10^{2k – 1} + 1\\) \u0935\u093f\u092d\u093e\u091c\u094d\u200d\u092f \u0939\u0948 11 \u0938\u0947\u0964 \u0915\u094d\u0930\u092e\u093f\u0915 \u0905\u092a\u0918\u091f\u0928 (decomposition) \u0915\u0947 \u0907\u0938 \u091a\u0930\u0923 \u0915\u094b \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u093f\u092f\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0938\u092e\u091d\u0928\u093e \u0906\u0938\u093e\u0928 \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948 \u092f\u0926\u093f \u0939\u092e \u090f\u0915 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902, \u091c\u0948\u0938\u0947 \u0915\u093f…<\/p>\n\n

        \n
        \n

        \\(10^{5} + 1\\)<\/p>\n<\/div>\n\n\n\n

        \n

        \\(= 10 \\cdot 10^{4} + 1 = 11 \\cdot 10^{4} \\ – \\ 1 \\cdot 10^{4} + 1\\)<\/p>\n\n\n\n

        \\(= 11 \\cdot 10^{4} \\ – \\ 10 \\cdot 10^{3} + 1 = 11 \\cdot 10^{4} \\ – \\ 11 \\cdot 10^{3} + 1 \\cdot 10^{3} + 1\\)<\/p>\n\n\n\n

        \\(= 11 \\cdot 10^{4} \\ – \\ 11 \\cdot 10^{3} + 10 \\cdot 10^{2} + 1 = 11 \\cdot 10^{4} \\ – \\ 11 \\cdot 10^{3} + 11 \\cdot 10^{2} \\ – \\ 10^{2} + 1\\)<\/p>\n\n\n\n

        \\(= 11 \\cdot 10^{4} \\ – \\ 11 \\cdot 10^{3} + 11 \\cdot 10^{2} \\ – \\ 10 \\cdot 10 + 1\\)<\/p>\n\n\n\n

        \\(= 11 \\cdot 10^{4} \\ – \\ 11 \\cdot 10^{3} + 11 \\cdot 10^{2} \\ – \\ 11 \\cdot 10 + 1 \\cdot 10 + 1\\)<\/p>\n\n\n\n

        \\(= 11 \\cdot 10^{4} \\ – \\ 11 \\cdot 10^{3} + 11 \\cdot 10^{2} \\ – \\ 11 \\cdot 10 + 11 \\ – \\ 1 + 1 = 11\\left( 10^{4} \\ – \\ 10^{3} + 10^{2} \\ – \\ 10 + 1\\right)\\)<\/p>\n<\/div>\n<\/div>\n\n

        \u091c\u094b 11 \u0915\u093e \u0917\u0941\u0923\u091c \u0939\u0948\u0964<\/p>\n\n

        \u0907\u0938 \u091a\u0930\u0923 \u0938\u0947, \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u093f\u092f\u094b\u0902 \u0915\u094b \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0940\u0915\u0930\u0923 (generalise) \u0915\u0930\u0928\u093e \u0906\u0938\u093e\u0928 \u0932\u0917 \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0935\u0947 \u092f\u0939 \u092d\u0940 \u091c\u093e\u0901\u091a \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0915\u094d\u092f\u093e \\(10^{n} + 1\\) \u0938\u092d\u0940 \\(n\\) \u0915\u0947 \u0932\u093f\u090f 11 \u0915\u093e \u0917\u0941\u0923\u091c \u0939\u0948 \u092f\u093e \u0915\u0947\u0935\u0932 \u0935\u093f\u0937\u092e \\(n\\) \u0915\u0947 \u0932\u093f\u090f\u0964<\/p>\n\n

        \u0907\u0938\u0940 \u0924\u0930\u0939 \\(10^{2k} \\ – \\ 1 = \\left( 10^{2} \\right)^{k} \\ – \\ 1 = 100^{k} \\ -\\ 1 = \\left(100 – 1 \\right) \\left( 100 ^{k – 1} + … + 1\\right) = 99c\\)<\/span> \u0915\u093f\u0938\u0940 \u092a\u094d\u0930\u093e\u0915\u0943\u0924 \u0938\u0902\u0916\u094d\u092f\u093e c \u0915\u0947 \u0932\u093f\u090f, \\(10^{2k} \\ – \\ 1\\) \u0938\u0902\u0916\u094d\u092f\u093e 99 \u0938\u0947 \u0935\u093f\u092d\u093e\u091c\u094d\u092f \u0939\u0948 \u0914\u0930 \u0907\u0938\u0932\u093f\u090f 11 \u0938\u0947 \u092d\u0940 \u0935\u093f\u092d\u093e\u091c\u094d\u092f \u0939\u0948\u0964<\/p>\n\n

        \u091a\u0942\u0901\u0915\u093f N – DADS \u0938\u0902\u0916\u094d\u092f\u093e 11 \u0938\u0947 \u0935\u093f\u092d\u093e\u091c\u094d\u092f \u0939\u0948, \u0907\u0938\u0932\u093f\u090f \u092f\u093e \u0924\u094b N \u0914\u0930 DADS \u0926\u094b\u0928\u094b\u0902 11 \u0938\u0947 \u0935\u093f\u092d\u093e\u091c\u094d\u092f \u0939\u094b\u0902\u0917\u0947 \u092f\u093e \u0926\u094b\u0928\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u0915\u094b\u0908 \u092d\u0940 \u0928\u0939\u0940\u0902 \u0939\u094b\u0917\u093e; \u0905\u0924\u0903 \u092f\u0926\u093f DADS \u0938\u0902\u0916\u094d\u092f\u093e 11 \u0915\u093e \u0917\u0941\u0923\u091c \u0939\u0948, \u0924\u094b \u092e\u0942\u0932 \u0938\u0902\u0916\u094d\u092f\u093e N \u092d\u0940 \u0939\u094b\u0917\u0940, \u0914\u0930 \u092f\u0926\u093f DADS \u0928\u0939\u0940\u0902 \u0939\u0948, \u0924\u094b N \u092d\u0940 \u0928\u0939\u0940\u0902 \u0939\u094b\u0917\u0940\u0964<\/p>\n\n

        \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937<\/h2>\n\n

        ‘\u0932\u094b \u092b\u094d\u0932\u094b\u0930 \u0939\u093e\u0908 \u0938\u0940\u0932\u093f\u0902\u0917’ \u0917\u0924\u093f\u0935\u093f\u0927\u093f\u092f\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0917\u0923\u093f\u0924\u0940\u092f \u091c\u093e\u0901\u091a-\u092a\u0921\u093c\u0924\u093e\u0932 \u090f\u0915\u0926\u092e \u0938\u091f\u0940\u0915 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902\u0964 \u092f\u0939\u093e\u0901 \u0939\u092e\u0928\u0947 \u092c\u0924\u093e\u092f\u093e \u0939\u0948 \u0915\u093f \u0915\u0948\u0938\u0947 \u090f\u0915 \u0938\u093e\u0927\u093e\u0930\u0923 \u092a\u0948\u091f\u0930\u094d\u0928 \u0915\u094b \u092a\u0939\u091a\u093e\u0928\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u0909\u0938\u0915\u0940 \u091c\u093e\u0901\u091a-\u092a\u0921\u093c\u0924\u093e\u0932 \u0915\u0940 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948, \u0909\u0938\u0915\u0947 \u0938\u093e\u0925 \u0916\u0947\u0932\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u0914\u0930 \u0909\u0938\u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0940\u0915\u0930\u0923 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u092f\u0926\u093f \u0906\u092a\u0915\u0947 \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u093f\u092f\u094b\u0902 \u0928\u0947 ‘DADS \u0928\u093f\u092f\u092e’ (DADS Rule) \u0915\u093e \u0906\u0928\u0928\u094d\u200d\u0926 \u0932\u093f\u092f\u093e \u0939\u0948, \u0924\u094b \u0909\u0928\u094d\u0939\u0947\u0902 \u0905\u0928\u094d\u092f \u0938\u0902\u0916\u094d\u092f\u093e \u092a\u0948\u091f\u0930\u094d\u0928 \u0915\u0947 \u0938\u093e\u0925 \u092d\u0940 \u0907\u0938\u0940 \u0924\u0930\u0939 \u0915\u0940 \u0935\u093f\u0927\u093f\u092f\u094b\u0902 \u0938\u0947 \u092a\u094d\u0930\u092f\u093e\u0938 \u0915\u0930\u0928\u0947 \u0926\u0947\u0902; \u0939\u092e\u0947\u0902 \u0909\u092e\u094d\u092e\u0940\u0926 \u0939\u0948 \u0915\u093f \u0935\u0947 \u0907\u0938\u092e\u0947\u0902 \u092e\u093e\u0939\u093f\u0930 \u0939\u094b \u091c\u093e\u090f\u0901\u0917\u0947!<\/p>\n\n

        \u0905\u092a\u0928\u0947 \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u093f\u092f\u094b\u0902 \u0915\u0947 \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937\u094b\u0902 \u0915\u094b ‘\u090f\u091f \u0930\u093e\u0907\u091f \u090f\u0902\u0917\u0932\u094d\u0938’ (At Right Angles) \u0915\u0947 \u0938\u093e\u0925 \u0938\u093e\u091d\u093e \u0915\u0930\u0928\u093e \u0928 \u092d\u0942\u0932\u0947\u0902\u0964<\/p>\n","protected":false},"excerpt":{"rendered":"

        \u0939\u092e \u090f\u0915 10 \u00d7 10 \u0915\u0947 \u0917\u094d\u0930\u093f\u0921 \u092e\u0947\u0902 \u0915\u094d\u0930\u092e\u093e\u0928\u0941\u0938\u093e\u0930 \u0932\u093f\u0916\u0940 \u0917\u093f\u0928\u0924\u0940 \u0938\u0947 \u0936\u0941\u0930\u0941\u0906\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 11 \u0915\u0947 \u0917\u0941\u0923\u091c \u0915\u094b \u0930\u0902\u0917 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u091c\u0948\u0938\u093e \u0915\u093f \u0906\u092a \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u0935\u0947 \u090f\u0915 \u0935\u093f\u0915\u0930\u094d\u0923 (diagonally) \u092e\u0947\u0902 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 100 \u0924\u0915 \u0915\u0940 \u0938\u0902\u0916\u094d\u200d\u092f\u093e \u092e\u0947\u0902 \u0905\u0902\u0915 \u0926\u094b\u0939\u0930\u093e\u090f \u091c\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 1 2 3 4 5 6 7 8 9 […]<\/p>\n","protected":false},"author":19,"featured_media":28587,"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":[1188,1105,379,1106],"stage-class":[1008],"magazine_category":[323],"class_list":["post-24868","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category---hi","tag-investigation","tag-1105","tag-379","tag-1106","stage-class-middle-class-6-8-hi","magazine_category-issue-15-march-2017-hi"],"acf":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2026\/05\/DADS-Rule-thumbnail.png","_links":{"self":[{"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/posts\/24868","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=24868"}],"version-history":[{"count":4,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/posts\/24868\/revisions"}],"predecessor-version":[{"id":24878,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/posts\/24868\/revisions\/24878"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/media\/28587"}],"wp:attachment":[{"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/media?parent=24868"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/categories?post=24868"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/tags?post=24868"},{"taxonomy":"stage-class","embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/stage-class?post=24868"},{"taxonomy":"magazine_category","embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/magazine_category?post=24868"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}