{"id":24769,"date":"2021-06-21T10:34:09","date_gmt":"2021-06-21T05:04:09","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=24769"},"modified":"2022-03-02T10:38:12","modified_gmt":"2022-03-02T05:08:12","slug":"ncert-solutions-for-class-10-maths-chapter-1-in-hindi","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-1-in-hindi\/","title":{"rendered":"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers (Hindi Medium)"},"content":{"rendered":"
These Solutions are part of NCERT Solutions for Class 10 Maths in Hindi Medium<\/a>. Here we have given NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers.<\/p>\n Chapter 1. \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901<\/strong><\/p>\n \u0905\u092d\u094d\u092f\u093e\u0938 1.1<\/strong><\/span><\/p>\n Ex 1.1 Class 10 \u0917\u0923\u093f\u0924 \u092a\u094d\u0930.1. \u092f\u0941\u0915\u094d\u0932\u093f\u0921 \u0935\u093f\u092d\u093e\u091c\u0928 \u0905\u0932\u094d\u0917\u094b\u0930\u093f\u0925\u092e \u0915\u0947 \u092a\u094d\u0930\u092f\u094b\u0917 \u0938\u0947 HCF \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u092f\u0947 |\u00a0<\/strong><\/p>\n \u00a0(i) 135 \u0914\u0930 225 (ii) 196 \u0914\u0930 38220 (iii) 867 \u0914\u0930 255<\/strong><\/p>\n \u0939\u0932: \u00a0<\/strong><\/p>\n (1) \u00a0\u00a0 135 \u0914\u0930 225<\/strong><\/p>\n a = 225, b = 135 {\u0938\u092c\u0938\u0947 \u092c\u095c\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b\u00a0a\u00a0\u0924\u0925\u093e \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b\u00a0b\u00a0\u092e\u093e\u0928\u0924\u0947 \u0939\u0948\u00a0}<\/p>\n \u092f\u0941\u0915\u094d\u0932\u093f\u0921 \u0935\u093f\u092d\u093e\u091c\u0928 \u0905\u0932\u094d\u0917\u094b\u0930\u093f\u0925\u092e \u0915\u0947 \u092a\u094d\u0930\u092f\u094b\u0917 \u0938\u0947<\/p>\n a = bq + r (\u0924\u092c)<\/p>\n 225 = 135 \u00d71 + 90<\/p>\n 135 = 90 \u00d71 + 45<\/p>\n 90 = 45 \u00d7 2 + 0 {\u091c\u092c \u0939\u092e\u0947\u0902\u00a0r=0\u00a0\u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948 \u0924\u094b \u0939\u092e \u0906\u0917\u0947 \u0939\u0932 \u0915\u0930\u0928\u093e \u092c\u0902\u0926 \u0915\u0930 \u0926\u0947\u0924\u0947 \u0939\u0948\u00a0}<\/p>\n b = 45 {\u092b\u093f\u0930 \u0909\u0938\u092e\u0947 \u0938\u0947\u00a0b\u00a0\u0915\u093e \u092e\u093e\u0928\u00a0HCF\u00a0\u0939\u094b\u0924\u093e \u0939\u0948;}<\/p>\n HCF = 45<\/p>\n \u0939\u0932:<\/p>\n (ii) \u00a0\u00a0 196 \u0914\u0930 38220<\/strong><\/p>\n a = 38220, b = 196\u00a0\u00a0{\u0938\u092c\u0938\u0947 \u092c\u095c\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b\u00a0a\u00a0\u0924\u0925\u093e \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b\u00a0b\u00a0\u092e\u093e\u0928\u0924\u0947 \u0939\u0948\u00a0}<\/p>\n \u092f\u0941\u0915\u094d\u0932\u093f\u0921 \u0935\u093f\u092d\u093e\u091c\u0928 \u0905\u0932\u094d\u0917\u094b\u0930\u093f\u0925\u092e \u0915\u0947 \u092a\u094d\u0930\u092f\u094b\u0917 \u0938\u0947<\/p>\n a = bq + r (\u0924\u092c)<\/p>\n 38220= 196 \u00d7195 + 0 \u00a0{\u091c\u092c \u0939\u092e\u0947\u0902\u00a0r=0\u00a0\u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948 \u0924\u094b \u0939\u092e \u0906\u0917\u0947 \u0939\u0932 \u0915\u0930\u0928\u093e \u092c\u0902\u0926 \u0915\u0930 \u0926\u0947\u0924\u0947 \u0939\u0948\u00a0}<\/p>\n b = 196\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0{\u092b\u093f\u0930 \u0909\u0938\u092e\u0947 \u0938\u0947\u00a0b\u00a0\u0915\u093e \u092e\u093e\u0928\u00a0HCF\u00a0\u0939\u094b\u0924\u093e \u0939\u0948;}<\/p>\n HCF = 196<\/p>\n \u0939\u0932:<\/strong><\/p>\n (iii) \u00a0 867 \u0914\u0930 255<\/strong><\/p>\n a = 867, b = 255 {\u0938\u092c\u0938\u0947 \u092c\u095c\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b\u00a0a\u00a0\u0924\u0925\u093e \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b\u00a0b\u00a0\u092e\u093e\u0928\u0924\u0947 \u0939\u0948\u00a0}<\/p>\n \u092f\u0941\u0915\u094d\u0932\u093f\u0921 \u0935\u093f\u092d\u093e\u091c\u0928 \u0905\u0932\u094d\u0917\u094b\u0930\u093f\u0925\u092e \u0915\u0947 \u092a\u094d\u0930\u092f\u094b\u0917 \u0938\u0947<\/p>\n a = bq + r (\u0924\u092c)<\/p>\n 38220= 196 \u00d7195 + 0 {\u091c\u092c \u0939\u092e\u0947\u0902\u00a0r=0\u00a0\u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948 \u0924\u094b \u0939\u092e \u0906\u0917\u0947 \u0939\u0932 \u0915\u0930\u0928\u093e \u092c\u0902\u0926 \u0915\u0930 \u0926\u0947\u0924\u0947 \u0939\u0948\u00a0}<\/p>\n b = 196\u00a0\u00a0{\u092b\u093f\u0930 \u0909\u0938\u092e\u0947 \u0938\u0947\u00a0b\u00a0\u0915\u093e \u092e\u093e\u0928\u00a0HCF\u00a0\u0939\u094b\u0924\u093e \u0939\u0948;}<\/p>\n HCF = 196<\/p>\n Ex 1.1 Class 10 \u0917\u0923\u093f\u0924\u00a0\u092a\u094d\u0930.2. \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u0915\u094b\u0908 \u092d\u0940 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0935\u093f\u0937\u092e \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 6q\u00a0+ 1, \u092f\u093e 6q\u00a0+ 3, \u092f\u093e 6q\u00a0+ 5, \u0915\u0947 \u0930\u0942\u092a \u0915\u093e \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u0939\u093e\u0901 q \u0915\u094b\u0908 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 \u0939\u0948 |<\/strong><\/p>\n \u0939\u0932:<\/strong><\/p>\n \u0926\u0930\u094d\u0936\u093e\u0928\u093e \u0939\u0948:\u00a0a = 6q + 1, 6q+3\u00a0\u092f\u093e\u00a0\u00a06q+5<\/p>\n \u092e\u093e\u0928\u093e \u0915\u093f a \u0915\u094b\u0908 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0935\u093f\u0937\u092e \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 \u0939\u0948; \u00a0\u091c\u0939\u093e\u0901 b = 6 \u0939\u094b\u0917\u093e,<\/p>\n \u091c\u092c \u0939\u092e 6 \u0938\u0947 a \u0915\u094b \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948 \u091c\u094b \u0936\u0947\u0937\u092b\u0932 \u0915\u094d\u0930\u092e\u0936: 0, 1, 2, 3, 4 \u0914\u0930 5 \u092a\u093e\u0924\u0947 \u0939\u0948;<\/p>\n \u091c\u0939\u093e\u0901 0 \u2264\u00a0r\u00a0< b<\/p>\n \u092f\u0939\u093e\u0901 a \u090f\u0915 \u0935\u093f\u0937\u092e \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948 \u0907\u0938\u0932\u093f\u090f \u0936\u0947\u0937\u092b\u0932 \u092d\u0940 \u0935\u093f\u0937\u092e \u0938\u0902\u0916\u094d\u092f\u093e \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 |<\/p>\n \u0936\u0947\u0937\u092b\u0932 \u0939\u094b\u0917\u093e 1 \u092f\u093e 3 \u092f\u093e 5<\/p>\n \u092f\u0941\u0915\u094d\u0932\u093f\u0921 \u0935\u093f\u092d\u093e\u091c\u0928 \u0905\u0932\u094d\u0917\u094b\u0930\u093f\u0925\u092e \u0915\u0947 \u092a\u094d\u0930\u092f\u094b\u0917 \u0938\u0947 \u0939\u092e \u092a\u093e\u0924\u0947 \u0939\u0948;<\/p>\n a = 6q + 1, 6q+3\u00a0\u092f\u093e\u00a06q+5<\/p>\n Ex 1.1 Class 10 \u0917\u0923\u093f\u0924\u00a0\u092a\u094d\u0930\u09663. \u0915\u093f\u0938\u0940 \u092a\u0930\u0947\u0921 \u092e\u0947\u0902 616 \u0938\u0926\u0938\u094d\u092f\u094b\u0902 \u0935\u093e\u0932\u0940 \u090f\u0915 \u0938\u0947\u0928\u093e (\u0906\u0930\u094d\u092e\u0940) \u0915\u0940 \u091f\u0941\u0915\u095c\u0940 \u0915\u094b 32 \u0938\u0926\u0938\u094d\u092f\u094b\u0902 \u0935\u093e\u0932\u0947 \u090f\u0915 \u0906\u0930\u094d\u092e\u0940 \u092c\u0948\u0902\u0921 \u0915\u0947 \u092a\u0940\u091b\u0947 \u092e\u093e\u0930\u094d\u091a \u0915\u0930\u0928\u093e \u0939\u0948 | \u0926\u094b\u0928\u094b\u0902 \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u094b \u0938\u092e\u093e\u0928 \u0938\u0902\u0916\u094d\u092f\u093e \u0935\u093e\u0932\u0947 \u0938\u094d\u0924\u0902\u092d\u094b\u0902 \u092e\u0947\u0902 \u092e\u093e\u0930\u094d\u091a \u0915\u0930\u0928\u093e \u0939\u0948 | \u0909\u0928 \u0938\u094d\u0924\u0902\u092d\u094b\u0902 \u0915\u0940 \u0905\u0927\u093f\u0915\u0924\u092e \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094d\u092f\u093e \u0939\u0948, \u091c\u093f\u0938\u092e\u0947\u0902 \u0935\u0947 \u092e\u093e\u0930\u094d\u091a \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948 ?<\/strong><\/p>\n \u0939\u0932:<\/p>\n \u0938\u094d\u0924\u0902\u092d\u094b\u0902 \u0915\u0940 \u0905\u0927\u093f\u0915\u0924\u092e \u0938\u0902\u0916\u094d\u092f\u093e = HCF (616, 32)<\/p>\n a = 616, b = 32\u00a0 {\u0938\u092c\u0938\u0947 \u092c\u095c\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b\u00a0a\u00a0\u0924\u0925\u093e \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b\u00a0b\u00a0\u092e\u093e\u0928\u0924\u0947 \u0939\u0948\u00a0}<\/p>\n \u092f\u0941\u0915\u094d\u0932\u093f\u0921 \u0935\u093f\u092d\u093e\u091c\u0928 \u0905\u0932\u094d\u0917\u094b\u0930\u093f\u0925\u092e \u0915\u0947 \u092a\u094d\u0930\u092f\u094b\u0917 \u0938\u0947<\/p>\n a = bq + r (\u0924\u092c)<\/p>\n 616 = 32 \u00d719 + 8\u00a0\u00a0{\u091c\u092c \u0939\u092e\u0947\u0902\u00a0r=0\u00a0\u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948 \u0924\u094b \u0939\u092e \u0906\u0917\u0947 \u0939\u0932 \u0915\u0930\u0928\u093e \u092c\u0902\u0926 \u0915\u0930 \u0926\u0947\u0924\u0947 \u0939\u0948\u00a0}<\/p>\n 32 = 8 \u00d7 4 + 0<\/p>\n b = 8 {b\u00a0\u0915\u093e \u092e\u093e\u0928\u00a0HCF\u00a0\u0939\u094b\u0924\u093e \u0939\u0948}<\/p>\n HCF = 8<\/p>\n \u0907\u0938\u0932\u093f\u090f \u0938\u094d\u0924\u0902\u092d\u094b\u0902 \u0915\u0940 \u0905\u0927\u093f\u0915\u0924\u092e \u0938\u0902\u0916\u094d\u092f\u093e =\u00a08<\/p>\n Ex 1.1 Class 10 \u0917\u0923\u093f\u0924\u00a0\u092a\u094d\u0930\u09664. \u092f\u0942\u0915\u094d\u0932\u093f\u0921 \u0935\u093f\u092d\u093e\u091c\u0928 \u092a\u094d\u0930\u092e\u0947\u092f\u093f\u0915\u093e \u0915\u093e \u092a\u094d\u0930\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u0915\u093f\u0938\u0940 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 \u0915\u093e \u0935\u0930\u094d\u0917, \u0915\u093f\u0938\u0940 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 m \u0915\u0947 \u0932\u093f\u090f 3m \u092f\u093e 3m + 1 \u0915\u0947 \u0930\u0942\u092a \u0915\u093e \u0939\u094b\u0924\u093e \u0939\u0948 |<\/strong><\/p>\n \u0939\u0932<\/strong>\u00a0:<\/p>\n \u0926\u0930\u094d\u0936\u093e\u0928\u093e \u0939\u0948 : a2<\/sup>\u00a0= 3m or 3m + 1<\/p>\n a = bq + r<\/p>\n \u092e\u093e\u0928\u093e \u0915\u093f\u00a0a\u00a0\u0915\u094b\u0908 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 \u0939\u0948 \u091c\u0939\u093e\u0901\u00a0b\u00a0= 3 \u0914\u0930\u00a0r\u00a0= 0, 1, 2 \u0915\u094d\u092f\u094b\u0902\u0915\u093f 0 \u2264\u00a0r\u00a0< 3<\/p>\n \u0924\u092c\u00a0a\u00a0= 3q\u00a0+\u00a0r\u00a0 \u0915\u0941\u091b \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 \u0915\u0947 \u0932\u093f\u090f\u00a0q\u00a0\u2265 0<\/p>\n \u0907\u0938\u0932\u093f\u090f,\u00a0a\u00a0= 3q\u00a0+ 0 or 3q\u00a0+ 1 or 3q\u00a0+ 2<\/p>\n \u0905\u092c \u0939\u092e \u092a\u093e\u0924\u0947 \u0939\u0948;<\/p>\n \u21d2\u00a0a2<\/sup>\u00a0= (3q + 0)2<\/sup>\u00a0or (3q + 1)2<\/sup>\u00a0or (3q +2)2<\/sup><\/p>\n \u21d2\u00a0a2<\/sup>\u00a0= 9q2<\/sup>\u00a0or 9q2<\/sup>\u00a0+ 6q + 1 or 9q2<\/sup>\u00a0+ 12q + 4<\/p>\n \u21d2\u00a0a2<\/sup>\u00a0= 9q2<\/sup>\u00a0or 9q2<\/sup>\u00a0+ 6q + 1 or 9q2<\/sup>\u00a0+ 12q + 3 + 1<\/p>\n \u21d2\u00a0a2<\/sup>\u00a0= 3(3q2<\/sup>) or 3(3q2<\/sup>\u00a0+ 2q) + 1 or 3(3q2<\/sup>\u00a0+ 4q + 1) + 1<\/p>\n \u092f\u0926\u093f m = (3q2<\/sup>) or (3q2<\/sup>\u00a0+ 2q)\u00a0 or (3q2<\/sup>\u00a0+ 4q + 1) \u0939\u094b \u0924\u094b<\/p>\n \u0939\u092e \u092a\u093e\u0924\u0947 \u0939\u0948 \u0915\u093f ;<\/p>\n a2<\/sup>\u00a0= 3m or 3m + 1 or 3m + 1<\/p>\n Ex 1.1 Class 10 \u0917\u0923\u093f\u0924\u00a0\u092a\u094d\u0930\u09665. \u092f\u0942\u0915\u094d\u0932\u093f\u0921 \u0935\u093f\u092d\u093e\u091c\u0928 \u092a\u094d\u0930\u092e\u0947\u092f\u093f\u0915\u093e \u0915\u093e \u092a\u094d\u0930\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f \u0915\u093f\u0938\u0940 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 \u0915\u093e \u0918\u0928 9m, 9m + 1 \u092f\u093e 9m + 8 \u0915\u0947 \u0930\u0942\u092a \u0915\u093e \u0939\u094b\u0924\u093e \u0939\u0948 |<\/strong><\/p>\n \u0939\u0932<\/strong>:<\/p>\n \u092e\u093e\u0928\u093e, a \u0915\u094b\u0908 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 \u0939\u0948;<\/p>\n \u092f\u0941\u0915\u093f\u0932\u094d\u0921 \u0935\u093f\u092d\u093e\u091c\u0928 \u092a\u094d\u0930\u092e\u0947\u092f\u093f\u0915\u093e \u0915\u0947 \u092a\u094d\u0930\u092f\u094b\u0917 \u0938\u0947;<\/p>\n a = bq + r\u00a0\u091c\u0939\u093e\u0901;\u00a00 \u2264\u00a0r\u00a0< b<\/p>\n b = 9 \u0930\u0916\u0928\u0947 \u092a\u0930<\/p>\n a = 9q + r\u00a0\u091c\u0939\u093e\u0901;\u00a00 \u2264\u00a0r\u00a0< 9<\/p>\n \u091c\u092c r = 0 \u0939\u094b;<\/p>\n a = 9q + 0 = 9q<\/p>\n