{"id":94,"date":"2021-07-23T10:02:21","date_gmt":"2021-07-23T04:32:21","guid":{"rendered":"http:\/\/mcq-questions.com\/?p=94"},"modified":"2022-03-02T10:25:44","modified_gmt":"2022-03-02T04:55:44","slug":"ncert-solutions-for-class-10-maths-chapter-5-hindi","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-5-hindi\/","title":{"rendered":"NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions (Hindi Medium)"},"content":{"rendered":"

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions (Hindi Medium)<\/h2>\n

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 5 Arithmetic Progressions.<\/p>\n

Chapter 5. \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u0936\u094d\u0930\u0947\u095d\u0940<\/strong><\/p>\n

\n

\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 5.1<\/strong><\/span><\/p>\n

Ex 5.1 Class 10 \u0917\u0923\u093f\u0924 Q1. <\/strong>\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u094d\u0925\u093f\u0924\u092f\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u0915\u093f\u0928 \u0938\u094d\u0925\u093f\u0924\u092f\u094b\u0902 \u092e\u0947\u0902 \u0938\u0902\u092c\u0926\u094d\u0927 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0940 \u0938\u0942\u091a\u0940 A.P \u0939\u0948 \u0914\u0930 \u0915\u094d\u092f\u094b\u0902?<\/strong><\/p>\n

(1) \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0915\u093f\u0932\u094b\u0902 \u092e\u0940\u091f\u0930 \u0915\u0947 \u092c\u093e\u0926 \u091f\u0948\u0915\u094d\u0938\u0940 \u0915\u093e \u0915\u093f\u0930\u093e\u092f\u093e, \u091c\u092c\u0915\u093f \u092a\u094d\u0930\u0925\u092e \u0915\u093f\u0932\u094b \u092e\u0940\u091f\u0930 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u0930\u093e\u092f\u093e\u00a0<\/strong>15 \u00a0\u0930\u0941o\u00a0\u0939\u0948 \u0914\u0930 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924 \u0915\u093f\u0932\u094b \u092e\u0940\u091f\u0930 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u0930\u093e\u092f\u093e\u00a0<\/strong>8 \u0930\u0941o \u0939\u0948 |<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

\u092a\u094d\u0930\u0925\u092e \u0915\u093f\u0932\u094b\u092e\u0940\u091f\u0930 \u0915\u093e \u0915\u093f\u0930\u093e\u092f\u093e = 15 \u0930\u0941\u092a\u092f\u0947 |<\/p>\n

\u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924 \u0915\u093f\u0932\u094b\u092e\u0940\u091f\u0930 \u0915\u093e \u0915\u093f\u0930\u093e\u092f\u093e = 8 \u0930\u0941\u092a\u092f\u0947<\/p>\n

\u0936\u094d\u0930\u0943\u0902\u0916\u0932\u093e : 15, 23, 31, 39 …………………………..<\/p>\n

\u091c\u093e\u0901\u091a:<\/p>\n

a = 15<\/p>\n

d1<\/sub>\u00a0= a2<\/sub>\u00a0– a1<\/sub><\/p>\n

= 23 – 15 = 8<\/p>\n

d2<\/sub>\u00a0= a3\u00a0<\/sub>– a2<\/sub><\/p>\n

= 31 – 23 = 8<\/p>\n

d3<\/sub>\u00a0= a4\u00a0<\/sub>– a3<\/sub><\/p>\n

= 39 – 31 = 8<\/p>\n

\u091a\u0942\u0901\u0915\u093f \u0938\u092d\u0940 \u0905\u0902\u0924\u0930\u094b\u0902 \u0915\u093e \u0905\u0902\u0924\u0930 \u0938\u093e\u092e\u093e\u0928 \u0939\u0948 \u0905\u0930\u094d\u0925\u093e\u0924 \u0938\u093e\u0930\u094d\u0935\u0905\u0902\u0924\u0930 = 8 \u0939\u0948 |<\/p>\n

\u0907\u0938\u0932\u093f\u090f \u0926\u093f\u092f\u093e \u0917\u092f\u093e \u0938\u0942\u091a\u0940 A. P \u0939\u0948 |<\/p>\n

(ii) \u0915\u093f\u0938\u0940 \u092c\u0947\u0932\u0928 (cylinder) \u092e\u0947\u0902 \u0909\u092a\u0938\u094d\u0925\u093f\u0924 \u0939\u0935\u093e \u0915\u0940 \u092e\u093e\u0924\u094d\u0930\u093e, \u091c\u092c\u0915\u093f \u0935\u093e\u092f\u0941 \u0928\u093f\u0915\u093e\u0932\u0928\u0947 \u0935\u093e\u0932\u093e \u092a\u092e\u094d\u092a \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092c\u093e\u0930 \u092c\u0947\u0932\u0928 \u0915\u0940 \u0939\u0935\u093e \u0915\u093e\u00a0<\/strong>\u00bc\u00a0\u092d\u093e\u0917 \u092c\u093e\u0939\u0930 \u0928\u093f\u0915\u093e\u0932 \u0926\u0947\u0924\u093e \u0939\u0948 |<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

\u092e\u093e\u0928\u093e \u092c\u0947\u0932\u0928 \u092e\u0947\u0902 \u0939\u0935\u093e \u0915\u0940 \u092e\u093e\u0924\u094d\u0930\u093e 1 \u0939\u0948 |<\/p>\n

\"NCERT<\/p>\n

(iii) \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092e\u0940\u091f\u0930 \u0915\u0940 \u0916\u0941\u0926\u093e\u0908 \u0915\u0947 \u092c\u093e\u0926, \u090f\u0915 \u0915\u0941\u0906\u0902 \u0916\u094b\u0926\u0928\u0947 \u092e\u0947\u0902 \u0906\u0908 \u0932\u093e\u0917\u0924, \u091c\u092c\u0915\u093f \u092a\u094d\u0930\u0925\u092e \u092e\u0940\u091f\u0930 \u0916\u0941\u0926\u093e\u0908 \u0915\u0940 \u0932\u093e\u0917\u0924\u00a0<\/strong>150 \u0930\u0941o\u00a0<\/strong>\u0939\u0948 \u0914\u0930 \u092c\u093e\u0926 \u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0916\u0941\u0926\u093e\u0908 \u0915\u0940 \u0932\u093e\u0917\u0924\u00a0<\/strong>50 \u0930\u0941o \u092c\u095d\u0924\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948 |<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

\u092a\u094d\u0930\u0925\u092e \u092e\u0940\u091f\u0930 \u0915\u093e \u0932\u093e\u0917\u0924 = 150,<\/p>\n

\u0926\u0941\u0938\u0930\u0947 \u092e\u0940\u091f\u0930 \u0916\u0941\u0926\u093e\u0908 \u0915\u0940 \u0932\u093e\u0917\u0924 = 150 + 50 = 200<\/p>\n

\u0924\u0940\u0938\u0930\u0947 \u092e\u0940\u091f\u0930 \u0916\u0941\u0926\u093e\u0908 \u0915\u0940 \u0932\u093e\u0917\u0924 = 200 + 50 = 250<\/p>\n

\u0936\u094d\u0930\u0943\u0902\u0916\u0932\u093e : 150, 200, 250, 300 ………………………<\/p>\n

\u091c\u093e\u0901\u091a:<\/p>\n

a = 150<\/p>\n

d1<\/sub>\u00a0= a2<\/sub>\u00a0– a1<\/sub><\/p>\n

= 200 – 150 = 50<\/p>\n

d2<\/sub>\u00a0= a3\u00a0<\/sub>– a2<\/sub><\/p>\n

= 250 – 200 = 50<\/p>\n

d3<\/sub>\u00a0= a4\u00a0<\/sub>– a3<\/sub><\/p>\n

= 300 – 250 = 50<\/p>\n

\u0938\u093e\u0930\u094d\u0935 \u0905\u0902\u0924\u0930 = 50<\/p>\n

\u092f\u0939\u093e\u0901 \u0938\u093e\u0930\u094d\u0935 \u0905\u0902\u0924\u0930 \u0938\u092e\u093e\u0928 \u0939\u0948 \u0907\u0938\u0932\u093f\u090f \u092f\u0939 \u0936\u094d\u0930\u0943\u0902\u0916\u0932\u093e A.P \u0939\u0948 |<\/p>\n

(iv) \u0916\u093e\u0924\u0947 \u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0935\u0930\u094d\u0937 \u0915\u093e \u092e\u093f\u0936\u094d\u0930\u0927\u0928, \u091c\u092c\u0915\u093f\u00a0<\/strong>10000 \u0930\u0941o \u0915\u0940 \u0930\u093e\u0936\u093f 8 % \u0935\u093e\u0930\u094d\u0937\u093f\u0915 \u0915\u0940 \u0926\u0930 \u0938\u0947 \u091a\u0915\u094d\u0930\u0935\u0943\u0926\u094d\u0927\u093f \u092c\u094d\u092f\u093e\u091c \u092a\u0930 \u091c\u092e\u093e \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948 |<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

\u092a\u0939\u0932\u0947 \u0935\u0930\u094d\u0937 \u0915\u0940 \u0930\u093e\u0936\u093f = 10000<\/p>\n

\"NCERT<\/p>\n

\u0924\u0940\u0938\u0930\u0947 \u0935\u0930\u094d\u0937 \u0915\u0940 \u0930\u093e\u0936\u093f = 11664<\/p>\n

\u0936\u094d\u0930\u0943\u0902\u0916\u0932\u093e: 10000, 10800, 11664 …………………<\/p>\n

\u0938\u094d\u092a\u0937\u094d\u091f \u0939\u0948 \u0915\u093f \u0907\u0938 \u0936\u094d\u0930\u0943\u0902\u0916\u0932\u093e \u0915\u093e \u0938\u093e\u0930\u094d\u0935 \u0905\u0902\u0924\u0930 \u0938\u092e\u093e\u0928 \u0928\u0939\u0940\u0902 \u0939\u0948 \u0905\u0924: A.P \u0928\u0939\u0940\u0902 \u0939\u0948 |<\/p>\n

Ex 5.1 Class 10 \u0917\u0923\u093f\u0924\u00a0Q2. \u0926\u0940 \u0939\u0941\u0908 A.P \u0915\u0947 \u092a\u094d\u0930\u0925\u092e \u091a\u093e\u0930 \u092a\u0926 \u0932\u093f\u0916\u093f\u090f, \u091c\u092c\u0915\u093f \u092a\u094d\u0930\u0925\u092e \u092a\u0926 a \u0914\u0930 \u0938\u093e\u0930\u094d\u0935 \u0905\u0902\u0924\u0930 d \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0939\u0948\u0902 :<\/strong><\/p>\n

(i) \u00a0a\u00a0<\/em>= 10,\u00a0d\u00a0<\/em>= 10<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

a = 10<\/p>\n

a2<\/sub>\u00a0= a + d\u00a0\u21d2\u00a010 + 10 = 20<\/p>\n

a3<\/sub>\u00a0= a + 2d\u00a0\u21d2\u00a010 + 2 \u00d7 10 = 30<\/p>\n

a4<\/sub>\u00a0= a + 3d\u00a0\u21d2\u00a010 + 3 \u00d7 10 = 40<\/p>\n

\u0936\u094d\u0930\u0943\u0902\u0916\u0932\u093e:\u00a0<\/strong>10, 20, 30, 40 ………………….<\/p>\n

\u092a\u094d\u0930\u0925\u092e \u091a\u093e\u0930 \u092a\u0926\u00a0<\/strong>: 10, 20, 30 \u0914\u0930 40<\/p>\n

(ii)\u00a0a\u00a0<\/em>= \u20132,\u00a0d\u00a0<\/em>= 0<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

a = \u20132<\/p>\n

a2<\/sub>\u00a0= a + d\u00a0\u21d2\u00a0\u20132 + 0 = \u20132<\/p>\n

a3<\/sub>\u00a0= a + 2d\u00a0\u21d2\u00a0\u20132 + 2 \u00d7 0 = \u20132<\/p>\n

a4<\/sub>\u00a0= a + 3d\u00a0\u21d2\u00a0\u20132 + 3 \u00d7 0 = \u20132<\/p>\n

\u0936\u094d\u0930\u0943\u0902\u0916\u0932\u093e:\u00a0<\/strong>\u20132, \u20132, \u20132, \u20132 ………………….<\/p>\n

\u092a\u094d\u0930\u0925\u092e \u091a\u093e\u0930 \u092a\u0926\u00a0<\/strong>: \u20132, \u20132, \u20132 \u0914\u0930 \u20132<\/p>\n

(iii)\u00a0a\u00a0<\/em>= 4,\u00a0d\u00a0<\/em>= \u2013 3<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

a = 4<\/p>\n

a2<\/sub>\u00a0= a + d\u00a0\u21d2\u00a04 + \u2013 3 = 1<\/p>\n

a3<\/sub>\u00a0= a + 2d\u00a0\u21d2\u00a04 + 2 \u00d7 \u2013 3 = \u20132<\/p>\n

a4<\/sub>\u00a0= a + 3d\u00a0\u21d2\u00a04 + 3 \u00d7 \u2013 3 = \u20135<\/p>\n

\u0936\u094d\u0930\u0943\u0902\u0916\u0932\u093e:\u00a0<\/strong>4, 1, \u2013 3, \u20135 ………………….<\/p>\n

\u092a\u094d\u0930\u0925\u092e \u091a\u093e\u0930 \u092a\u0926\u00a0<\/strong>: 4, 1, \u2013 3 \u0914\u0930 \u20135<\/p>\n

\"NCERT<\/p>\n

(v)\u00a0a\u00a0<\/em>= \u2013 1.25,\u00a0d\u00a0<\/em>= \u2013 0.25<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

a = \u2013 1.25<\/p>\n

a2<\/sub>\u00a0= a + d\u00a0\u21d2\u00a0\u2013 1.25 + \u2013 0.25 = – 1.5<\/p>\n

a3<\/sub>\u00a0= a + 2d\u00a0\u21d2\u00a0\u2013 1.25 + 2 \u00d7 \u2013 0.25 = \u20131.75<\/p>\n

a4<\/sub>\u00a0= a + 3d\u00a0\u21d2\u00a0\u2013 1.25 + 3 \u00d7 \u2013 0.25 = \u20132<\/p>\n

\u0936\u094d\u0930\u0943\u0902\u0916\u0932\u093e:\u00a0<\/strong>\u2013 1.25, – 1.5, \u20131.75, \u20132 ………………….<\/p>\n

\u092a\u094d\u0930\u0925\u092e \u091a\u093e\u0930 \u092a\u0926\u00a0<\/strong>: \u2013 1.25, – 1.5, \u20131.75 \u0914\u0930 \u20132<\/p>\n

Ex 5.1 Class 10 \u0917\u0923\u093f\u0924\u00a0Q4. \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092e\u0947\u0902 \u0938\u0947 \u0915\u094c\u0928-\u0915\u094c\u0928 A.P \u0939\u0948\u0902? \u092f\u0926\u093f \u0915\u094b\u0908 A.P \u0939\u0948, \u0924\u094b \u0907\u0938\u0915\u093e \u0938\u093e\u0930\u094d\u0935 \u0905\u0902\u0924\u0930 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f \u0914\u0930 \u0907\u0928\u0915\u0947 \u0924\u0940\u0928 \u092a\u0926 \u0932\u093f\u0916\u093f\u090f |<\/strong><\/p>\n

(i) 3, 1, \u2013 1, \u2013 3, . . .<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

d1<\/sub>\u00a0= a2<\/sub>\u00a0– a1<\/sub><\/p>\n

= 1 – 3 = – 2<\/p>\n

d2<\/sub>\u00a0= a3\u00a0<\/sub>– a2<\/sub><\/p>\n

= -1 – (1) = – 2<\/p>\n

d3<\/sub>\u00a0= a4\u00a0<\/sub>– a3<\/sub><\/p>\n

= -3 – (-1) = -3 + 1 = – 2<\/p>\n

\u0938\u093e\u0930\u094d\u0935 \u0905\u0902\u0924\u0930 = – 2<\/p>\n

\u091a\u0942\u0901\u0915\u093f \u0938\u093e\u0930\u094d\u0935 \u0905\u0902\u0924\u0930 \u0938\u092e\u093e\u0928 \u0939\u0948 \u0907\u0938\u0932\u093f\u090f \u092f\u0939 A.P \u0939\u0948 |<\/p>\n

\u0907\u0928\u0915\u0947 \u0905\u0917\u0932\u0947 \u0924\u0940\u0928 \u092a\u0926 \u0939\u0948\u0902 :<\/p>\n

a5<\/sub>\u00a0= a + 4d = 3 + 4\u00d7(- 2) = 3 – 8 = – 5<\/p>\n

a6<\/sub>\u00a0= a + 4d = 3 + 5\u00d7(- 2) = 3 – 10 = – 7<\/p>\n

a7<\/sub>\u00a0= a + 4d = 3 + 6\u00d7(- 2) = 3 – 12 = – 9<\/p>\n

– 5, – 7, – 9<\/p>\n

\"NCERT<\/p>\n

(iii) \u2013 1.2, \u2013 3.2, \u2013 5.2, \u2013 7.2, . . .<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

a = \u2013 1.2<\/p>\n

d1<\/sub>\u00a0= a2<\/sub>\u00a0– a1<\/sub><\/p>\n

= \u20133.2 \u2013 (\u20131.2 )<\/p>\n

= \u2013 3.2 + 1.2 = \u00a0\u2013 2<\/p>\n

d2<\/sub>\u00a0= a3\u00a0<\/sub>– a2<\/sub><\/p>\n

= \u20135.2 \u2013 (\u20133.2 )<\/p>\n

= \u2013 5.2 + 3.2 = \u00a0\u2013 2<\/p>\n

d3<\/sub>\u00a0= a4\u00a0<\/sub>– a3<\/sub><\/p>\n

= \u20137.2 \u2013 (\u20135.2 )<\/p>\n

= \u2013 7.2 + 5.2 = \u00a0\u2013 2<\/p>\n

\u0938\u093e\u0930\u094d\u0935 \u0905\u0902\u0924\u0930 = \u2013 2<\/p>\n

\u091a\u0942\u0901\u0915\u093f \u0938\u093e\u0930\u094d\u0935 \u0905\u0902\u0924\u0930 \u0938\u092e\u093e\u0928 \u0939\u0948 \u0907\u0938\u0932\u093f\u090f \u092f\u0939 A.P \u0939\u0948 |<\/p>\n

\u0907\u0928\u0915\u0947 \u0905\u0917\u0932\u0947 \u0924\u0940\u0928 \u092a\u0926 \u0939\u0948\u0902 :<\/p>\n

a5<\/sub>\u00a0= a + 4d = \u2013 1.2 \u00a0+ 4\u00d7(- 2) = \u2013 1.2 – 8 = \u2013 9.2<\/p>\n

a6<\/sub>\u00a0= a + 4d = \u2013 1.2 \u00a0+ 5\u00d7(- 2) = \u2013 1.2 \u00a0– 10 = \u00a0\u2013 11.2<\/p>\n

a7<\/sub>\u00a0= a + 4d = \u2013 1.2 \u00a0+ 6\u00d7(- 2) = \u2013 1.2 \u00a0– 12 = \u2013 13.2<\/p>\n

\u21d2\u00a0\u2013 9.2, \u2013 11.2, \u2013 13.2<\/p>\n

(iv) \u2013 10, \u2013 6, \u2013 2, \u00a02, . . .<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

a = \u2013 10<\/p>\n

d1<\/sub>\u00a0= a2<\/sub>\u00a0– a1<\/sub><\/p>\n

= \u20136 \u2013 (\u201310 )<\/p>\n

= \u2013 6 + 10 = \u00a04<\/p>\n

d2<\/sub>\u00a0= a3\u00a0<\/sub>– a2<\/sub><\/p>\n

= \u20132 \u2013 (\u20136 )<\/p>\n

= \u2013 2 + 6 = \u00a04<\/p>\n

d3<\/sub>\u00a0= a4\u00a0<\/sub>– a3<\/sub><\/p>\n

= 2 \u2013 (\u20132 )<\/p>\n

= 2 + 2 = \u00a04<\/p>\n

\u0938\u093e\u0930\u094d\u0935 \u0905\u0902\u0924\u0930 = 4<\/p>\n

\u091a\u0942\u0901\u0915\u093f \u0938\u093e\u0930\u094d\u0935 \u0905\u0902\u0924\u0930 \u0938\u092e\u093e\u0928 \u0939\u0948 \u0907\u0938\u0932\u093f\u090f \u092f\u0939 A.P \u0939\u0948 |<\/p>\n

\u0907\u0928\u0915\u0947 \u0905\u0917\u0932\u0947 \u0924\u0940\u0928 \u092a\u0926 \u0939\u0948\u0902 :<\/p>\n

a5<\/sub>\u00a0= a + 4d = \u2013 10 + 4\u00d7(4) = \u2013 10 + 16 = 6<\/p>\n

a6<\/sub>\u00a0= a + 4d = \u2013 10 + 5\u00d7(4) = \u2013 10 + 20 = \u00a010<\/p>\n

a7<\/sub>\u00a0= a + 4d = \u2013 10 + 6\u00d7(4) = \u2013 10 + 24 = 14<\/p>\n

\u21d2\u00a06, 10, 14<\/p>\n<\/div>\n

<\/a>\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 5.2<\/strong><\/span><\/p>\n

\u0915\u0915\u094d\u0937\u093e – 10 (NCERT Solution)<\/strong><\/p>\n

Ex 5.2 Class 10 \u0917\u0923\u093f\u0924 Q1. \u00a0\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u093e\u0930\u0923\u0940 \u092e\u0947\u0902, \u0930\u093f\u0915\u094d\u0924 \u0938\u094d\u0925\u093e\u0928\u094b\u0902 \u0915\u094b \u092d\u0930\u093f\u090f, \u091c\u0939\u093e\u0901 A.P \u0915\u093e \u092a\u094d\u0930\u0925\u092e \u092a\u0926 a, \u0938\u093e\u0930\u094d\u0935 \u0905\u0902\u0924\u0930 d \u0914\u0930 n\u0935\u093e\u0901 \u092a\u0926 an<\/sub>\u00a0\u0939\u0948:\u00a0<\/strong><\/p>\n

\"Maths<\/p>\n

Solution:<\/strong><\/p>\n

(i) a = 7, d = 3, n = 8 an<\/sub>\u00a0= ?<\/p>\n

an<\/sub>\u00a0= a + (n – 1)d<\/p>\n

a8<\/sub>\u00a0= 7 + (8 – 1)3<\/p>\n

= 7 + 7 \u00d73 = 7 + 21<\/p>\n

= 28<\/p>\n

(ii) a = – 18, n = 10, an<\/sub>\u00a0= 0, d = ?,<\/p>\n

an<\/sub>\u00a0= a + (n – 1)d<\/p>\n

a10<\/sub>\u00a0= – 18 + (10 – 1)d<\/p>\n

0 \u00a0\u00a0\u00a0= -18 + 9d<\/p>\n

9d = 18<\/p>\n

\"NCERT<\/p>\n

(iii) \u00a0d = -3, n = 18, an<\/sub>\u00a0= -5, a = ?<\/p>\n

an<\/sub>\u00a0= a + (n – 1)d<\/p>\n

a18<\/sub>\u00a0= a + (18 – 1)d<\/p>\n

-5\u00a0\u00a0 = a + 17(- 3)<\/p>\n

-5 + 51 = a<\/p>\n

a = 46<\/p>\n

(iv) a = – 18.9, \u00a0d = 2.5, \u00a0an<\/sub>\u00a0= 3.6 \u00a0n = ?<\/p>\n

an<\/sub>\u00a0= a + (n – 1)d<\/p>\n

3.6 = – 18.9 + (n – 1)2.5<\/p>\n

3.6 + 18.9\u00a0\u00a0 = (n – 1)2.5<\/p>\n

(n – 1)2.5 \u00a0= 22.5<\/p>\n

\"NCERT<\/p>\n

(v) a = 3.5, d = 0, n = 105, an\u00a0<\/sub>= ?<\/p>\n

an<\/sub>\u00a0= a + (n – 1)d<\/p>\n

= 3.5 + (105 – 1)0<\/p>\n

= 3.5 + 0<\/p>\n

= 3.5<\/p>\n

Ex 5.2 Class 10 \u0917\u0923\u093f\u0924\u00a0Q2. \u00a0<\/strong>\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092e\u0947\u0902 \u0938\u0939\u0940 \u0909\u0924\u094d\u0924\u0930 \u091a\u0941\u0928\u093f\u090f \u0914\u0930 \u0909\u0938\u0915\u093e \u0914\u091a\u093f\u0924\u094d\u092f \u0926\u0940\u091c\u093f\u090f:<\/strong><\/p>\n

(i) A.P: 10, 7, 4, …………………. \u0915\u093e 30 \u0935\u093e\u0901 \u092a\u0926 \u0939\u0948:<\/strong><\/p>\n

(A) 97 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (B) \u00a077 \u00a0\u00a0\u00a0\u00a0 (C) \u201377 \u00a0\u00a0\u00a0 (D) \u00a0\u2013 87<\/p>\n

Solution:<\/strong><\/p>\n

a = 10, d = 7 – 10 = -3<\/p>\n

30 \u0935\u093e\u0901 \u092a\u0926 = ?<\/p>\n

a30<\/sub>\u00a0= a + 29d<\/p>\n

= 10 + 29(-3)<\/p>\n

= 10 – 87<\/p>\n

= – 77<\/p>\n

Correct Answer: (C) – 77<\/p>\n

\"NCERT
\n\"Maths
\nCorrect Answer: (B) 22<\/p>\n

Ex 5.2 Class 10 \u0917\u0923\u093f\u0924\u00a0Q3. \u00a0\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u092e\u093e\u0902\u0924\u0930 \u0936\u094d\u0930\u0947\u095d\u0940 \u092e\u0947\u0902, \u0930\u093f\u0915\u094d\u0924 \u0916\u093e\u0928\u094b\u0902 (boxes) \u0915\u0947 \u092a\u0926\u094b\u0902 \u0915\u094b \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f |\u00a0<\/strong><\/p>\n

\"Solutions<\/p>\n

(i) a = 2, b = ?, c = 26\u00a0<\/strong><\/p>\n

Solution:\u00a0<\/strong><\/p>\n

\"NCERT<\/p>\n

Solution:<\/strong>\u00a0(ii) \u00a0a2<\/sub>\u00a0= 13,<\/p>\n

\u2234\u00a0\u00a0 a + d = 13\u00a0 ……………. (1)<\/p>\n

a4<\/sub>\u00a0= 3<\/p>\n

\u2234\u00a0\u00a0 a + 3d = 3\u00a0 ……………..(2)<\/p>\n

\u0938\u092e\u0940o (2) \u092e\u0947\u0902 \u0938\u0947 (1) \u0918\u091f\u093e\u0928\u0947 \u092a\u0930<\/p>\n

a + 3d – (a + d) = 3 – 13<\/p>\n

a + 3d – a – d = -10<\/p>\n

2d = – 10<\/p>\n

\"Solutions<\/p>\n

d = -5<\/p>\n

d\u00a0 \u0915\u093e \u092e\u093e\u0928 \u0938\u092e\u0940o (1) \u092e\u0947\u0902 \u0930\u0916\u0928\u0947 \u092a\u0930<\/p>\n

a + d = 13<\/p>\n

a + (- 5) = 13<\/p>\n

a = 13 + 5<\/p>\n

a = 18<\/p>\n

a3<\/sub>\u00a0= a + 2d = 18 + 2 (-5)<\/p>\n

= 18 – 10 = 8<\/p>\n

\u0905\u0924:\u00a018<\/strong>, 13,\u00a08<\/strong>, 3<\/p>\n

Ex 5.2 Class 10 \u0917\u0923\u093f\u0924\u00a0Q4. \u00a0A.P. : 3, 8, 13, 18, . . . \u0915\u093e \u0915\u094c\u0928 \u0938\u093e \u092a\u0926 78 \u0939\u0948 ?<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

a = 3, d = 8 – 3 = 5, an\u00a0<\/sub>= 78<\/p>\n

an\u00a0<\/sub>\u00a0= a + (n – 1) d<\/p>\n

78 = 3 + (n – 1) 5<\/p>\n

78 – 3 = (n – 1) 5<\/p>\n

75 = (n – 1) 5<\/p>\n

n – 1 = 75\/5<\/p>\n

n – 1 = 15<\/p>\n

n = 15 + 1<\/p>\n

n = 16<\/p>\n

\u0905\u0924: 16 \u0935\u093e\u0901 \u092a\u0926 78 \u0939\u0948 |<\/p>\n

Ex 5.2 Class 10 \u0917\u0923\u093f\u0924\u00a0Q5. \u00a0\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u092e\u093e\u0902\u0924\u0930 \u0936\u094d\u0930\u0947\u0922\u093f\u092f\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0936\u094d\u0930\u0947\u095d\u0940 \u092e\u0947\u0902 \u0915\u093f\u0924\u0928\u0947 \u092a\u0926 \u0939\u0948\u0902 ?<\/strong><\/p>\n

(i) 7, 13, 19, …………….. , 205<\/p>\n

Solution:<\/strong><\/p>\n

a = 7, d = 13 – 7 = 6, an\u00a0<\/sub>= 205<\/p>\n

an\u00a0<\/sub>\u00a0= a + (n – 1) d<\/p>\n

205 = 7 + (n – 1) 6<\/p>\n

205 – 7 = (n – 1) 6<\/p>\n

198 = (n – 1) 6<\/p>\n

\"NCERT<\/p>\n

n – 1 = 33<\/p>\n

n = 33 + 1<\/p>\n

n = 34<\/p>\n

\u0907\u0938 \u0936\u094d\u0930\u0947\u095d\u0940 \u092e\u0947\u0902 34 \u092a\u0926 \u0939\u0948\u0902 |<\/p>\n

\"CBSE<\/p>\n

\u0907\u0938 \u0936\u094d\u0930\u0947\u095d\u0940 \u092e\u0947\u0902 27 \u092a\u0926 \u0939\u0948\u0902 |<\/p>\n

Ex 5.2 Class 10 \u0917\u0923\u093f\u0924\u00a0Q6. \u00a0<\/strong>\u0915\u094d\u092f\u093e\u00a0<\/strong>A.P., 11, 8, 5, 2 . . .<\/strong>\u00a0\u0915\u093e \u090f\u0915 \u092a\u0926 – 150 \u0939\u0948 ? \u0915\u094d\u092f\u094b\u0902 ?<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

a = 11, d = 8 – 11 = – 3 \u0914\u0930 an\u00a0<\/sub>= – 150<\/p>\n

an\u00a0<\/sub>\u00a0= a + (n – 1) d<\/p>\n

– 150 = 11 + (n – 1) – 3<\/p>\n

– 150 – 11 = (n – 1) -3<\/p>\n

– 161 = (n – 1) – 3<\/p>\n

\"NCERT<\/p>\n

n – 1 = 53. 66<\/p>\n

n = 53.66 + 1<\/p>\n

n = 54.66<\/p>\n

\u092f\u0939\u093e\u0901 n \u090f\u0915 \u092d\u093f\u0928\u094d\u0928\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948 \u091c\u094b n \u0915\u0947 \u0932\u093f\u090f \u0938\u0902\u092d\u0935 \u0928\u0939\u0940\u0902 \u0939\u0948<\/p>\n

\u0907\u0938\u0932\u093f\u090f – 150 \u0926\u093f\u090f \u0917\u090f A.P \u0915\u093e \u092a\u0926 \u0928\u0939\u0940\u0902 \u0939\u0948 |<\/p>\n

Ex 5.2 Class 10 \u0917\u0923\u093f\u0924\u00a0Q7.\u00a0<\/strong>\u0909\u0938\u00a0<\/strong>A.P<\/strong>\u00a0\u0915\u093e\u00a0<\/strong>31<\/strong>\u0935\u093e\u0901 \u092a\u0926 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f<\/strong>,\u00a0<\/strong>\u091c\u093f\u0938\u0915\u093e\u00a0<\/strong>11<\/strong>\u0935\u093e\u0901 \u092a\u0926\u00a0<\/strong>38\u00a0<\/strong>\u0939\u0948 \u0914\u0930\u00a0<\/strong>16<\/strong>\u0935\u093e\u0901 \u092a\u0926\u00a0<\/strong>73\u00a0<\/strong>\u0939\u0948\u0964<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

31\u0935\u093e\u0901 \u092a\u0926 = ?<\/p>\n

a11<\/sub>\u00a0= 38<\/p>\n

\u21d2a + 10d = 38 ………………… (1)<\/p>\n

a16<\/sub>\u00a0= 73<\/p>\n

\u21d2\u00a0a + 15d = 73 ………………… (2)<\/p>\n

\u0938\u092e\u0940o (2) \u092e\u0947\u0902 \u0938\u0947 (1) \u0918\u091f\u093e\u0928\u0947 \u092a\u0930<\/p>\n

a + 15d – (a + 10d ) = 73 – 38<\/p>\n

a + 15d – a – 10d = 35<\/p>\n

5d = 35<\/p>\n

\"NCERT<\/p>\n

d = 7<\/p>\n

\u0938\u092e\u0940o (1) \u092e\u0947\u0902 d \u0915\u093e \u092e\u093e\u0928 7 \u0930\u0916\u0928\u0947 \u092a\u0930<\/p>\n

a + 10d = 38<\/p>\n

a = 10 (7) = 38<\/p>\n

a = 38 – 70<\/p>\n

a = – 32<\/p>\n

\u0905\u092c, a31\u00a0<\/sub>= a + 30d<\/p>\n

\u21d2\u00a0a31\u00a0<\/sub>= – 32 + 30(7)<\/p>\n

\u21d2\u00a0a31\u00a0<\/sub>= – 32 + 210<\/p>\n

\u21d2\u00a0a31\u00a0<\/sub>= 178<\/p>\n

\u0905\u0924: 31 \u0935\u093e\u0901 \u092a\u0926 178 \u0939\u0948 |<\/p>\n

Ex 5.2 Class 10 \u0917\u0923\u093f\u0924\u00a0Q8.\u00a0<\/strong>\u090f\u0915\u00a0<\/strong>A.P<\/strong>\u00a0\u092e\u0947\u0902\u00a0<\/strong>50<\/strong>\u00a0\u092a\u0926 \u0939\u0948\u0902<\/strong>,\u00a0<\/strong>\u091c\u093f\u0938\u0915\u093e \u0924\u0940\u0938\u0930\u093e \u092a\u0926\u00a0<\/strong>12<\/strong>\u00a0\u0939\u0948 \u0914\u0930 \u0905\u0902\u0924\u093f\u092e \u092a\u0926\u00a0<\/strong>106<\/strong>\u00a0\u0939\u0948\u0964 \u0907\u0938\u0915\u093e\u00a0<\/strong>29<\/strong>\u0935\u093e\u0901 \u092a\u0926<\/strong>\u00a0\u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

A.P \u092e\u0947\u0902 50 \u092a\u0926 \u0939\u0948\u0902 |<\/p>\n

\u0905\u0924: n = 50<\/p>\n

a3<\/sub>\u00a0= 12<\/p>\n

\u21d2\u00a0a + 2d = 12 ………………… (1)<\/p>\n

\u0914\u0930 \u0905\u0902\u0924\u093f\u092e \u092a\u0926 106 \u0939\u0948\u0964<\/p>\n

an\u00a0<\/sub>= 106<\/p>\n

\u092f\u093e a50\u00a0<\/sub>= 106<\/p>\n

\u21d2\u00a0a + 49d = 106 ………………… (2)<\/p>\n

\u0938\u092e\u0940o (2) \u092e\u0947\u0902 \u0938\u0947 (1) \u0918\u091f\u093e\u0928\u0947 \u092a\u0930<\/p>\n

a + 49d – (a + 2d ) = 106 – 12<\/p>\n

a + 49d – a – 2d = 94<\/p>\n

47d = 94<\/p>\n

\"CBSE<\/p>\n

d = 2<\/p>\n

\u0938\u092e\u0940o (1) \u092e\u0947\u0902 d \u0915\u093e \u092e\u093e\u0928 2 \u0930\u0916\u0928\u0947 \u092a\u0930<\/p>\n

a + 2d = 12<\/p>\n

a = 2(2) = 12<\/p>\n

a = 12 – 4<\/p>\n

a = 8<\/p>\n

\u0905\u092c, a29<\/sub>\u00a0= a + 28d<\/p>\n

\u21d2\u00a0a29<\/sub>\u00a0= 8 + 28(2)<\/p>\n

\u21d2\u00a0a29<\/sub>\u00a0= 8 + 56<\/p>\n

\u21d2\u00a0a29<\/sub>\u00a0= 64<\/p>\n

\u0905\u0924: 29 \u0935\u093e\u0901 \u092a\u0926 64 \u0939\u0948 |<\/p>\n

Ex 5.2 Class 10 \u0917\u0923\u093f\u0924\u00a0Q9. \u00a0<\/strong>\u092f\u0926\u093f \u0915\u093f\u0938\u0940\u00a0<\/strong>A.P<\/strong>\u00a0\u0915\u0947 \u0924\u0940\u0938\u0930\u0947 \u0914\u0930 \u0928\u094c\u0935\u0947\u0902 \u092a\u0926 \u0915\u094d\u0930\u092e\u0936\u0903\u00a0<\/strong>4<\/strong>\u00a0\u0914\u0930 –<\/strong>8<\/strong>\u00a0\u0939\u0948\u0902<\/strong>,\u00a0<\/strong>\u0924\u094b \u0907\u0938\u0915\u093e \u0915\u094c\u0928-\u0938\u093e \u092a\u0926 \u0936\u0942\u0928\u094d\u092f\u00a0<\/strong>\u0939\u094b\u0917\u093e<\/strong>?<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

a3<\/sub>\u00a0= 4<\/p>\n

\u21d2\u00a0a + 2d = 4 ………………… (1)<\/p>\n

\u0914\u0930 \u0928\u094c\u0935\u093e \u092a\u0926 – 8 \u0939\u0948\u0964<\/p>\n

a9\u00a0<\/sub>= – 8<\/p>\n

\u21d2\u00a0a + 8d = – 8 ………………… (2)<\/p>\n

\u0938\u092e\u0940o (2) \u092e\u0947\u0902 \u0938\u0947 (1) \u0918\u091f\u093e\u0928\u0947 \u092a\u0930<\/p>\n

a + 8d – (a + 2d ) = – 8 – 4<\/p>\n

a + 8d – a – 2d = – 12<\/p>\n

6d = – 12<\/p>\n

\"NCERT<\/p>\n

d = – 2<\/p>\n

\u0938\u092e\u0940o (1) \u092e\u0947\u0902 d \u0915\u093e \u092e\u093e\u0928 2 \u0930\u0916\u0928\u0947 \u092a\u0930<\/p>\n

a + 2d = 4<\/p>\n

a = 2(-2) = 4<\/p>\n

a = 4 + 4<\/p>\n

a = 8<\/p>\n

\u0905\u0924: a = 8, \u0914\u0930 d = – 2<\/p>\n

\u092e\u093e\u0928\u093e n \u0935\u093e\u0901 \u092a\u0926 \u0936\u0942\u0928\u094d\u092f \u0939\u0948 |<\/p>\n

an<\/sub>\u00a0= 0<\/p>\n

an\u00a0<\/sub>\u00a0= a + (n – 1) d<\/p>\n

\u21d2\u00a00 = \u00a08 \u00a0+ (n – 1) -2<\/p>\n

\u21d2\u00a0– 8 = (n – 1) -2<\/p>\n

\"NCERT<\/p>\n

\u21d2\u00a0n – 1 = 4<\/p>\n

\u21d2\u00a0n = 4 + 1 = 5<\/p>\n

\u0905\u0924: 5 \u0935\u093e\u0901 \u092a\u0926 \u0936\u0942\u0928\u094d\u092f \u0939\u0948 |<\/p>\n

Ex 5.2 Class 10 \u0917\u0923\u093f\u0924\u00a0Q10.\u00a0<\/strong>\u00a0\u0915\u093f\u0938\u0940\u00a0<\/strong>A.P<\/strong>\u00a0\u0915\u093e 17\u0935\u093e\u0901 \u092a\u0926 \u0909\u0938\u0915\u0947 10\u0935\u0947\u0902 \u092a\u0926 \u0938\u0947 7 \u0905\u0927\u093f\u0915 \u0939\u0948\u0964 \u0907\u0938\u0915\u093e \u0938\u093e\u0930\u094d\u0935 \u0905\u0902\u0924\u0930 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

\u091a\u0942\u0901\u0915\u093f 17\u0935\u093e\u0901 \u092a\u0926 \u0909\u0938\u0915\u0947 10\u0935\u0947\u0902 \u092a\u0926 \u0938\u0947 7 \u0905\u0927\u093f\u0915 \u0939\u0948\u0964<\/p>\n

\u2234\u00a0a17\u00a0<\/sub>\u00a0– a10<\/sub>\u00a0= 7<\/p>\n

\u21d2\u00a0a + 16d – (a + 9d) = 7<\/p>\n

\u21d2a + 16d – a – 9d = 7<\/p>\n

\u21d2\u00a07d = 7<\/p>\n

\u21d2\u00a0d = 1<\/p>\n

\u0938\u093e\u0930\u094d\u0935 \u0905\u0902\u0924\u0930 = 1<\/p>\n

Ex 5.2 Class 10 \u0917\u0923\u093f\u0924\u00a0Q11.\u00a0<\/strong>\u00a0A.P. : 3, 15, 27,\u00a0 39, ………<\/strong>\u00a0\u0915\u093e \u0915\u094c\u0928-\u0938\u093e \u092a\u0926 \u0909\u0938\u0915\u0947 54\u0935\u0947\u0902 \u092a\u0926 \u0938\u0947 132 \u0905\u0927\u093f\u0915 \u0939\u094b\u0917\u093e<\/strong>?<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

a = 3, d = 15 – 3 = 12<\/p>\n

a54<\/sub>\u00a0= a + 53d<\/p>\n

= 3 + 53(12)<\/p>\n

= 3 + 636<\/p>\n

= 639<\/p>\n

\u0935\u0939 \u092a\u0926 \u091c\u094b 54 \u0935\u0947\u0902 \u092a\u0926 \u0938\u0947 132 \u0905\u0927\u093f\u0915 \u0939\u094b\u0917\u093e<\/p>\n

an<\/sub>\u00a0= a54<\/sub>\u00a0+ 132<\/p>\n

= 639 + 132<\/p>\n

= 771<\/p>\n

an\u00a0<\/sub>\u00a0= a + (n – 1) d<\/p>\n

\u21d2\u00a0771 = \u00a03 \u00a0+ (n – 1) 12<\/p>\n

\u21d2\u00a0771 – 3 = (n – 1) 12<\/p>\n

\u21d2\u00a0768 = (n – 1) 12<\/p>\n

\"NCERT
\n\u21d2\u00a0n – 1 = 64<\/p>\n

\u21d2n = 64 + 1 = 65<\/p>\n

\u0905\u0924: 65 \u0935\u093e\u0901 \u092a\u0926 54\u0935\u0947\u0902 \u092a\u0926 \u0938\u0947 132 \u0905\u0927\u093f\u0915 \u0939\u0948 |<\/p>\n

Ex 5.2 Class 10 \u0917\u0923\u093f\u0924\u00a0Q12.\u00a0<\/strong>\u00a0\u0926\u094b \u0938\u092e\u093e\u0902\u0924\u0930 \u0936\u094d\u0930\u0947\u0922\u093f\u093c\u092f\u094b\u0902 \u0915\u093e \u0938\u093e\u0930\u094d\u0935 \u0905\u0902\u0924\u0930 \u0938\u092e\u093e\u0928 \u0939\u0948\u0964 \u092f\u0926\u093f \u0907\u0928\u0915\u0947 100\u0935\u0947\u0902 \u092a\u0926\u094b\u0902 \u0915\u093e \u0905\u0902\u0924\u0930 100 \u0939\u0948<\/strong>,\u00a0<\/strong>\u0924\u094b \u0907\u0928\u0915\u0947 1000\u0935\u0947\u0902 \u092a\u0926\u094b\u0902 \u0915\u093e \u0905\u0902\u0924\u0930 \u0915\u094d\u092f\u093e \u0939\u094b\u0917\u093e<\/strong>?<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

\u092e\u093e\u0928\u093e \u092a\u094d\u0930\u0925\u092e A.P \u0915\u093e \u092a\u094d\u0930\u0925\u092e \u092a\u0926 = a<\/p>\n

\u0914\u0930 \u0926\u0941\u0938\u0930\u0947 A.P \u0915\u093e \u092a\u094d\u0930\u0925\u092e \u092a\u0926 = a’ \u0939\u0948 |<\/p>\n

\u0914\u0930 \u0938\u093e\u0930\u094d\u0935 \u0905\u0902\u0924\u0930 d \u0939\u0948 [\u091a\u0942\u0901\u0915\u093f \u0938\u093e\u0930\u094d\u0935 \u0905\u0902\u0924\u0930 \u0938\u092e\u093e\u0928 \u0939\u0948 ] \u0926\u093f\u092f\u093e \u0939\u0948<\/p>\n

\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0928\u0941\u0938\u093e\u0930,<\/p>\n

a100<\/sub>\u00a0– a’100\u00a0<\/sub>= 100<\/p>\n

a + 99d – (a’ + 99d) = 100<\/p>\n

a + 99d – a’ – 99d = 100<\/p>\n

a – a’ = 100 ……………. (1)<\/p>\n

a1000<\/sub>\u00a0– a’1000\u00a0<\/sub>= a + 999d – (a’ + 999d)<\/p>\n

= a + 999d – a’ – 999d<\/p>\n

= a + a’<\/p>\n

\u091a\u0942\u0901\u0915\u093f a + a’ = 100 \u0939\u0948 \u0938\u092e\u0940o (1) \u0938\u0947<\/p>\n

\u0907\u0938\u0932\u093f\u090f,\u00a01000\u0935\u0947\u0902 \u092a\u0926\u094b\u0902 \u0915\u093e \u0905\u0902\u0924\u0930 \u092d\u0940 100 \u0939\u0948 |<\/strong><\/p>\n

Ex 5.2 Class 10 \u0917\u0923\u093f\u0924\u00a0Q13. \u00a0\u0924\u0940\u0928 \u0905\u0902\u0915\u094b\u0902 \u0935\u093e\u0932\u0940 \u0915\u093f\u0924\u0928\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 7 \u0938\u0947 \u0935\u093f\u092d\u093e\u091c\u094d\u092f \u0939\u0948\u0902?<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

\u0924\u0940\u0928 \u0905\u0902\u0915\u094b \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e 100 ……………… 999 \u0915\u0947 \u092c\u0940\u091a \u0939\u094b\u0924\u0940 \u0939\u0948 |<\/p>\n

\u0905\u0924: 7 \u0938\u0947 \u0935\u093f\u092d\u093e\u091c\u094d\u092f \u0938\u0902\u0916\u094d\u092f\u093e\u092f\u0947\u0902 \u0939\u0948:<\/p>\n

105, 112, 119, …………………… 994<\/p>\n

\u0907\u0938\u0938\u0947 \u0939\u092e\u0947\u0902 \u090f\u0915 A.P \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 |<\/p>\n

\u2234\u00a0a = 105, d = 7 \u0914\u0930 an<\/sub>\u00a0= 994<\/p>\n

an\u00a0<\/sub>\u00a0= a + (n – 1) d<\/p>\n

\u21d2\u00a0994 = \u00a0105 \u00a0+ (n – 1) 7<\/p>\n

\u21d2\u00a0994 – 105 = (n – 1) 7<\/p>\n

\u21d2\u00a0889 = (n – 1) 7<\/p>\n

\"NCERT<\/p>\n

\u21d2\u00a0n – 1 = 127<\/p>\n

\u21d2\u00a0n = 127 + 1 = 128<\/p>\n

\u0905\u0924: \u0924\u0940\u0928 \u0905\u0902\u0915\u094b\u0902 \u0935\u093e\u0932\u0940 7 \u0938\u0947 \u0935\u093f\u092d\u093e\u091c\u094d\u092f \u0938\u0902\u0916\u094d\u092f\u093e 128 \u0939\u0948\u0902 |<\/p>\n

Ex 5.2 Class 10 \u0917\u0923\u093f\u0924\u00a0Q14. \u00a010 \u0914\u0930 250 \u0915\u0947 \u092c\u0940\u091a \u092e\u0947\u0902 4 \u0915\u0947 \u0915\u093f\u0924\u0928\u0947 \u0917\u0941\u0923\u091c \u0939\u0948\u0902?<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

10 \u0914\u0930 250 \u0915\u0947 \u092c\u0940\u091a 4 \u0915\u0947 \u0917\u0941\u0923\u091c \u0915\u0947 \u0932\u093f\u090f A.P \u0939\u0948 |<\/p>\n

12, 16, 20, …………………… 248<\/p>\n

\u2234\u00a0a = 12, d = 4 \u0914\u0930 an<\/sub>\u00a0= 248<\/p>\n

an\u00a0<\/sub>\u00a0= a + (n – 1) d<\/p>\n

\u21d2\u00a0248 = \u00a012 \u00a0+ (n – 1) 4<\/p>\n

\u21d2\u00a0248 – 12 = (n – 1) 4<\/p>\n

\u21d2\u00a0236 = (n – 1) 4<\/p>\n

\"NCERT<\/p>\n

\u21d2\u00a0n – 1 = 59<\/p>\n

\u21d2\u00a0n = 59 + 1 = 60<\/p>\n

10 \u0914\u0930 250 \u0915\u0947 \u092c\u0940\u091a 4 \u0915\u0947 \u0917\u0941\u0923\u091c\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e 60 \u0939\u0948\u0902 |<\/p>\n

Ex 5.2 Class 10 \u0917\u0923\u093f\u0924\u00a0Q15.\u00a0<\/strong>\u00a0n \u0915\u0947 \u0915\u093f\u0938 \u092e\u093e\u0928 \u0915\u0947 \u0932\u093f\u090f<\/strong>,\u00a0<\/strong>\u0926\u094b\u0928\u094b\u0902 \u0938\u092e\u093e\u0902\u0924\u0930 \u0936\u094d\u0930\u0947\u0922\u093f\u093c\u092f\u094b\u0902 63, 65,\u00a0<\/strong>67<\/strong>, ………. \u0914\u0930 3, 10, 17, ……………… \u0915\u0947 n \u0935\u0947\u0902 \u092a\u0926 \u092c\u0930\u093e\u092c\u0930<\/strong>\u00a0\u0939\u094b\u0902\u0917\u0947<\/strong>?<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

\u092a\u094d\u0930\u0925\u092e A.P: \u00a063, 65, 67, ……….<\/p>\n

\u091c\u093f\u0938\u092e\u0947\u0902, a = 63, d = 65 – 63 = 2<\/p>\n

an\u00a0<\/sub>\u00a0= a + (n – 1) d<\/p>\n

= 63 + (n – 1) 2<\/p>\n

= 63 + 2n – 2<\/p>\n

= 61 + 2n ……………….. (1)<\/p>\n

\u0926\u094d\u0935\u093f\u0924\u0940\u092f A.P: 3, 10, 17, ………………<\/p>\n

\u091c\u093f\u0938\u092e\u0947\u0902 , a = 3, d = 10 – 3 = 7<\/p>\n

an\u00a0<\/sub>\u00a0= a + (n – 1) d<\/p>\n

= 3 + (n – 1) 7<\/p>\n

= 3 + 7n – 7<\/p>\n

= – 4 + 7n ……………….. (1)<\/p>\n

\u091a\u0942\u0901\u0915\u093f n \u0935\u093e\u0901 \u092a\u0926 \u092c\u0930\u093e\u092c\u0930 \u0939\u0948\u0902, \u0907\u0938\u0932\u093f\u090f (1) \u0924\u0925\u093e (2) \u0938\u0947<\/p>\n

61 + 2n = – 4 + 7n<\/p>\n

61 + 4 = 7n – 2n<\/p>\n

5n = 65<\/p>\n

n = 65\/5<\/p>\n

n = 13<\/p>\n

\u0905\u0924: \u0926\u094b\u0928\u094b\u0902 A.P \u0915\u093e 13 \u0935\u093e\u0901 \u092a\u0926 \u092c\u0930\u093e\u092c\u0930 \u0939\u0948\u0902 |<\/p>\n

Ex 5.2 Class 10 \u0917\u0923\u093f\u0924\u00a0Q16.\u00a0<\/strong>\u00a0\u0935\u0939 A.P \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f \u091c\u093f\u0938\u0915\u093e \u0924\u0940\u0938\u0930\u093e \u092a\u0926 16 \u0939\u0948 \u0914\u0930 7\u0935\u093e\u0901 \u092a\u0926 5\u0935\u0947\u0902 \u092a\u0926 \u0938\u0947 12 \u0905\u0927\u093f\u0915 \u0939\u0948\u0964<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

\u092e\u093e\u0928\u093e \u092a\u094d\u0930\u0925\u092e \u092a\u0926 = a, \u0914\u0930 \u0938\u093e\u0930\u094d\u0935 \u0905\u0902\u0924\u0930 = d \u0924\u094b,<\/p>\n

a3<\/sub>\u00a0= 16<\/p>\n

a + 2d = 16 ………………… (1)<\/p>\n

a7<\/sub>\u00a0– a5\u00a0<\/sub>= 12<\/p>\n

\u21d2\u00a0a + 6d – (a + 4d) = 12<\/p>\n

\u21d2\u00a0a + 6d – a – 4d = 12<\/p>\n

\u21d2\u00a02d = 12<\/p>\n

\u21d2\u00a0d = 6<\/p>\n

\u0905\u092c d \u0915\u093e \u092e\u093e\u0928 \u0938\u092e\u0940\u0915\u0930\u0923 (1) \u092e\u0947\u0902 \u0930\u0916\u0928\u0947 \u092a\u0930 ‘<\/p>\n

a + 2d = 16<\/p>\n

a + 2(6) = 16<\/p>\n

a + 12 = 16<\/p>\n

a = 16 – 12<\/p>\n

a = 4<\/p>\n

a, a + d, a + 2d, a + 3d ………………<\/p>\n

\u21d2\u00a04, 4 + 6, 4 + 2(6), 4 + 3(6), ……………<\/p>\n

\u0905\u0924: \u0905\u092d\u0940\u0937\u094d\u091f A.P:\u00a0\u21d2\u00a04, 10, 16, 22 …………………………<\/p>\n

Ex 5.2 Class 10 \u0917\u0923\u093f\u0924\u00a0Q17.\u00a0<\/strong>A.P. : 3, 8, 13, …,<\/strong>\u00a0253 \u092e\u0947\u0902 \u0905\u0902\u0924\u093f\u092e \u092a\u0926 \u0938\u0947 20\u0935\u093e\u0901 \u092a\u0926 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

\u0926\u093f\u092f\u093e \u0917\u092f\u093e A.P. : 3, 8, 13, …, 253 \u0939\u0948 |<\/p>\n

\u092a\u094d\u0930\u0925\u092e \u092a\u0926 \u0915\u0940 \u0913\u0930 \u0938\u0947 a = 3, d = 8 – 3 = 5<\/p>\n

\u092a\u0930\u0928\u094d\u0924\u0941 \u0905\u0902\u0924\u093f\u092e \u092a\u0926 \u0938\u0947 a = 253, n = 20,<\/p>\n

\u0914\u0930 \u0938\u093e\u0930\u094d\u0935 \u0905\u0902\u0924\u0930 d = – 5, [\u091a\u0942\u0901\u0915\u093f \u0905\u0902\u0924\u093f\u092e \u092a\u0926 \u0938\u0947 d \u0915\u093e \u092e\u093e\u0928 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0939\u094b \u091c\u093e\u092f\u0947\u0917\u093e ]<\/p>\n

a20<\/sub>\u00a0= a + 19d<\/p>\n

= 253 + 19(-5)<\/p>\n

= 253 – 95<\/p>\n

= 158<\/p>\n

\u0905\u0924: \u0905\u0902\u0924\u093f\u092e \u092a\u0926 \u0938\u0947 20 \u0935\u093e\u0901 \u092a\u0926 158 \u0939\u0948 |<\/p>\n

Ex 5.2 Class 10 \u0917\u0923\u093f\u0924\u00a0Q18. \u0915\u093f\u0938\u0940 A.P. \u00a0\u0915\u0947 \u091a\u094c\u0925\u0947 \u0914\u0930 8\u0935\u0947\u0902 \u092a\u0926\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 24 \u0939\u0948 \u0924\u0925\u093e \u091b\u0920\u0947 \u0914\u0930 10\u0935\u0947\u0902 \u092a\u0926\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 44 \u0939\u0948\u0964 \u0907\u0938 A.P. \u00a0\u0915\u0947 \u092a\u094d\u0930\u0925\u092e \u0924\u0940\u0928 \u092a\u0926 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

a4<\/sub>\u00a0+ a8<\/sub>\u00a0= 24<\/p>\n

\u092f\u093e \u00a0\u00a0 a + 3d + a + 7d = 24<\/p>\n

\u092f\u093e \u00a0\u00a0 2a + 10d = 24<\/p>\n

\u092f\u093e \u00a0\u00a0 2(a + 5d) = 24<\/p>\n

\"NCERT<\/p>\n

\u092f\u093e \u00a0\u00a0 a + 5d = 12\u00a0 \u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026. (1)<\/p>\n

\u0907\u0938\u0940\u092a\u094d\u0930\u0915\u093e\u0930,<\/p>\n

A6<\/sub>\u00a0+ a10<\/sub>\u00a0= 44<\/p>\n

\u092f\u093e \u00a0\u00a0 a + 5d + a + 9d = 44<\/p>\n

\u092f\u093e \u00a0\u00a0 2a + 14d = 44<\/p>\n

\u092f\u093e \u00a0\u00a0 2(a + 7d) = 44<\/p>\n

\"NCERT<\/p>\n

\u092f\u093e \u00a0\u00a0 a + 7d = 22\u00a0 \u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026. (2)<\/p>\n

\u0938\u092e\u0940\u0915\u0930\u0923 (2) \u092e\u0947\u0902 \u0938\u0947 (1) \u0918\u091f\u093e\u0928\u0947 \u092a\u0930<\/p>\n

(a + 7d) \u2013 (a + 5d) \u00a0= 22\u00a0 – 12<\/p>\n

\u092f\u093e \u00a0\u00a0 a + 7d \u2013 a – 5d \u00a0= 10<\/p>\n

\u092f\u093e \u00a0\u00a0 2d = 10<\/p>\n

\u092f\u093e\u00a0\u00a0\u00a0 d = 5<\/p>\n

\u0938\u092e\u0940\u0915\u0930\u0923 (1) \u092e\u0947\u0902 d = 5 \u0930\u0916\u0928\u0947 \u092a\u0930<\/p>\n

a + 5(5) = 12<\/p>\n

\u092f\u093e \u00a0\u00a0 a + 25 = 12<\/p>\n

\u092f\u093e \u00a0\u00a0 a = 12 \u2013 25<\/p>\n

\u092f\u093e\u00a0 \u00a0 a = – 13<\/p>\n

\u0905\u0924: A.P \u0915\u0947 \u092a\u094d\u0930\u0925\u092e 3 \u092a\u0926 \u0939\u0948 :<\/p>\n

-13, -13 + 5, -13 + 2(5)<\/p>\n

-13, – 8, – 3<\/p>\n

Ex 5.2 Class 10 \u0917\u0923\u093f\u0924\u00a0Q19. \u0938\u0941\u092c\u094d\u092c\u093e \u0930\u093e\u0935 \u0928\u0947 1995 \u092e\u0947\u0902 D 5000 \u0915\u0947 \u092e\u093e\u0938\u093f\u0915 \u0935\u0947\u0924\u0928 \u092a\u0926 \u0915\u093e\u0930\u094d\u092f \u0906\u0930\u0902\u092d \u0915\u093f\u092f\u093e \u0914\u0930 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0935\u0930\u094d\u0937 200 \u0915\u0940 \u0935\u0947\u0924\u0928 \u0935\u0943\u0926\u094d\u0927\u093f \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0940\u0964 \u0915\u093f\u0938 \u0935\u0930\u094d\u0937 \u092e\u0947\u0902 \u0909\u0938\u0915\u093e \u0935\u0947\u0924\u0928 D 7000 \u0939\u094b \u0917\u092f\u093e?<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

\u0926\u093f\u090f \u0917\u090f \u0938\u0941\u091a\u0928\u093e \u0938\u0947 \u0939\u092e\u0947\u0902 \u090f\u0915 A.P \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 :<\/p>\n

A.P: 5000, 5200, 5400, \u2026\u2026\u2026\u2026\u2026\u2026\u2026.. 7000<\/p>\n

a = 5000, d = 200, an<\/sub>\u00a0= 7000<\/p>\n

an<\/sub>\u00a0= a + (n \u2013 1)d<\/p>\n

7000 = 5000 + (n \u2013 1)200<\/p>\n

7000 \u2013 5000 = (n \u2013 1)200<\/p>\n

2000 = (n \u2013 1)200<\/p>\n

\"NCERT<\/p>\n

n – 1 = 20<\/p>\n

n = 20 + 1<\/p>\n

n = 21 \u0935\u0930\u094d\u0937<\/p>\n

\u0905\u0924: 21 \u0935\u0930\u094d\u0937 \u092c\u093e\u0926 \u0909\u0938\u0915\u093e \u0935\u0947\u0924\u0928 7000 \u0939\u094b \u091c\u093e\u092f\u0947\u0917\u093e |<\/p>\n

1995 + 21 = 2016 \u092e\u0947\u0902 \u0939\u094b \u091c\u093e\u092f\u0947\u0917\u093e |<\/p>\n

Ex 5.2 Class 10 \u0917\u0923\u093f\u0924\u00a0Q20. \u0930\u093e\u092e\u0915\u0932\u0940 \u0928\u0947 \u0915\u093f\u0938\u0940 \u0935\u0930\u094d\u0937 \u0915\u0947 \u092a\u094d\u0930\u0925\u092e \u0938\u092a\u094d\u0924\u093e\u0939 \u092e\u0947\u0902 D 5 \u0915\u0940 \u092c\u091a\u0924 \u0915\u0940 \u0914\u0930 \u092b\u093f\u0930 \u0905\u092a\u0928\u0940 \u0938\u093e\u092a\u094d\u0924\u093e\u0939\u093f\u0915 \u092c\u091a\u0924 D 1.75 \u092c\u0922\u093c\u093e\u0924\u0940 \u0917\u0908\u0964 \u092f\u0926\u093f n \u0935\u0947\u0902 \u0938\u092a\u094d\u0924\u093e\u0939 \u092e\u0947\u0902 \u0909\u0938\u0915\u0940 \u0938\u093e\u092a\u094d\u0924\u093e\u0939\u093f\u0915 \u092c\u091a\u0924 D 20.75 \u0939\u094b \u091c\u093e\u0924\u0940 \u0939\u0948, \u0924\u094b n \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

\u0907\u0938 \u0938\u0941\u091a\u0928\u093e \u0938\u0947 \u090f\u0915 A.P \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948 :<\/p>\n

A.P: 5, 6.75, 8.50, ………………………, 20.75<\/p>\n

A = 5, d = 1.75, an<\/sub>\u00a0= 20.75<\/p>\n

an<\/sub>\u00a0= a + (n \u2013 1)d<\/p>\n

20.75 = 5 + (n \u2013 1)1.75<\/p>\n

20.75 \u2013 5 = (n \u2013 1)1.75<\/p>\n

15.75 = (n \u2013 1)1.75<\/p>\n

\"NCERT<\/p>\n

n – 1 = 9<\/p>\n

n = 9 + 1<\/p>\n

n = 10<\/p>\n

<\/a>\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 5.3<\/strong><\/span><\/p>\n

Ex 5.3 Class 10 \u0917\u0923\u093f\u0924 <\/strong>Q1. \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u092e\u093e\u0902\u0924\u0930 \u0936\u094d\u0930\u0947\u0922\u093f\u092f\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f :<\/p>\n

(i) 2, 7, 12, . . ., 10 \u092a\u0926\u094b\u0902 \u0924\u0915<\/p>\n

(ii) \u201337, \u201333, \u201329, . . ., 12 \u092a\u0926\u094b\u0902 \u0924\u0915<\/p>\n

(iii) 0.6, 1.7, 2.8, . . ., 100 \u092a\u0926\u094b\u0902 \u0924\u0915<\/p>\n

\"NCERT
\n\"NCERT<\/p>\n

Solution:<\/strong><\/p>\n

(ii) \u201337, \u201333, \u201329, . . ., 12 \u092a\u0926\u094b\u0902 \u0924\u0915<\/p>\n

a = \u201337, d = \u201333 \u2013 (\u201337) = \u201333 + 37 = 4, n = 12<\/p>\n

\"NCERT<\/p>\n

Solution:<\/strong><\/p>\n

(iii) 0.6, 1.7, 2.8, . . ., 100 \u092a\u0926\u094b\u0902 \u0924\u0915<\/p>\n

a = 0.6, d = 1.7 \u2013 0.6 = 1.1, n = 100,<\/p>\n

\"NCERT
\n\"NCERT<\/p>\n

Ex 5.3 Class 10 \u0917\u0923\u093f\u0924\u00a0<\/strong>Q2. \u0928\u0940\u091a\u0947 \u0926\u093f\u090f \u0939\u0941\u090f \u092f\u094b\u0917\u094d\u092b\u093e\u0932\u094b\u0902 \u0915\u094b \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u092f\u0947:<\/p>\n

\"Download<\/p>\n

(ii) 34 + 32 + 30 + . . . + 10<\/p>\n

(iii) \u20135 + (\u20138) + (\u201311) + . . . + (\u2013230)<\/p>\n

Solution:\u00a0<\/strong><\/p>\n

\"NCERT
\n\"NCERT<\/p>\n

(ii) 34 + 32 + 30 + . . . + 10<\/p>\n

Solution:<\/strong><\/p>\n

a = 34, d = 32 \u2013 34 = -2, an<\/sub>\u00a0= 10<\/p>\n

an\u00a0<\/sub>= a + (n -1)d<\/p>\n

10 = 34 + (n \u2013 1)-2<\/p>\n

10 \u2013 34 = (n \u2013 1)-2<\/p>\n

-24 = (n \u2013 1)-2<\/p>\n

\"NCERT<\/p>\n

(iii) \u20135 + (\u20138) + (\u201311) + . . . + (\u2013230)<\/p>\n

Solution:<\/strong><\/p>\n

a = \u20135, d = (\u20138) \u2013 (\u20135) = \u20138 + 5 = \u20133, an<\/sub>\u00a0= \u00a0\u2013230<\/p>\n

an\u00a0<\/sub>= a + (n -1)d<\/p>\n

\u2013230 = \u20135 + (n \u2013 1)\u20133<\/p>\n

\u2013230 + 5 = (n \u2013 1) \u20133<\/p>\n

\u2013225= (n \u2013 1)\u20133<\/p>\n

\"Maths<\/p>\n

Ex 5.3 Class 10 \u0917\u0923\u093f\u0924\u00a0Q3. \u090f\u0915 A.P. \u092e\u0947\u0902,<\/strong><\/p>\n

(i) a = 5, d = 3 \u0914\u0930 an<\/sub>\u00a0= 50 \u0926\u093f\u092f\u093e \u0939\u0948\u00a0<\/strong>\u0964<\/strong>\u00a0n \u0914\u0930 Sn<\/sub>\u00a0\u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u00a0<\/strong>\u0964<\/strong><\/p>\n

\"NCERT<\/p>\n

(ii) a = 7 \u0914\u0930 a13<\/sub>\u00a0= 35 \u0926\u093f\u092f\u093e \u0939\u0948 \u0964 d \u0914\u0930 S13<\/sub>\u00a0\u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f \u0964<\/strong><\/p>\n

\"Solutions<\/p>\n

(iii) a12<\/sub>\u00a0= 37 \u0914\u0930 d = 3 \u0926\u093f\u092f\u093e \u0939\u0948 \u0964 a \u0914\u0930 S12<\/sub>\u00a0\u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f \u0964<\/strong><\/p>\n

\"NCERT<\/p>\n

\u0905\u0924: a = 4 \u0914\u0930 S12<\/sub>\u00a0= 246 \u0939\u0948 |<\/p>\n

(iv) a3<\/sub>\u00a0= 15 \u0914\u0930 S10<\/sub>\u00a0= 125 \u0926\u093f\u092f\u093e \u0939\u0948 \u0964 d \u0914\u0930 a10<\/sub>\u00a0\u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f \u0964<\/strong><\/p>\n

\"Maths<\/p>\n

\u092a\u094d\u0930\u0924\u093f\u0938\u094d\u0925\u093e\u092a\u0928 \u0935\u093f\u0927\u093f \u0938\u0947 \u0938\u092e\u0940\u0915\u0930\u0923 (i) \u0914\u0930 (ii) \u0915\u093e \u0939\u0932 \u0915\u0930\u0928\u0947 \u092a\u0930<\/p>\n

\u0938\u092e\u0940\u0915\u0930\u0923 (i) \u0938\u0947<\/p>\n

\"Solutions<\/p>\n

(v) d = 5 \u0914\u0930 S9<\/sub>\u00a0= 75 \u0926\u093f\u092f\u093e \u0939\u0948 \u0964 a \u0914\u0930 a9<\/sub>\u00a0\u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f \u0964<\/strong><\/p>\n

\u0939\u0932 :<\/strong>\u00a0d = 5 \u0914\u0930 S9<\/sub>\u00a0= 75 \u0926\u093f\u092f\u093e \u0939\u0948<\/p>\n

S9<\/sub>\u00a0= 75<\/p>\n

\"NCERT
\n\"NCERT<\/p>\n

(vi) a = 2, d = 8 \u0914\u0930 Sn<\/sub>\u00a0= 90 \u0926\u093f\u092f\u093e \u0939\u0948 \u0964 n \u0914\u0930 an<\/sub>\u00a0\u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f \u0964<\/strong><\/p>\n

\u0939\u0932 :<\/strong>\u00a0a = 2, d = 8 \u0914\u0930 Sn<\/sub>\u00a0= 90 \u0926\u093f\u092f\u093e \u0939\u0948 \u0964<\/p>\n

Sn<\/sub>\u00a0= 90<\/p>\n

\"CBSE<\/p>\n

(vii) a = 8, an<\/sub>\u00a0= 62 \u0914\u0930 Sn<\/sub>\u00a0= 210 \u0926\u093f\u092f\u093e \u0939\u0948 \u0964 n \u0914\u0930 d \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f \u0964<\/strong><\/p>\n

\"CBSE<\/p>\n

\u0905\u0924: \u0905\u0902\u0924\u093f\u092e \u092a\u0926 = 62 \u0914\u0930 \u0938\u093e\u0930\u094d\u0935\u0905\u0902\u0924\u0930 = 54\/5<\/p>\n

(viii) an<\/sub>\u00a0= 4, d = 2 \u0914\u0930 Sn\u00a0<\/sub>= \u201314 \u0926\u093f\u092f\u093e \u0939\u0948 \u0964 n \u0914\u0930 a \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f \u0964<\/strong><\/p>\n

\"NCERT<\/p>\n

=> n = 7 \u0914\u0930 \u00a0n = – 2 (Not Applicable \u0915\u094d\u092f\u094b\u0902\u0915\u093f n \u0939\u092e\u0947\u0936\u093e \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0939\u094b\u0924\u093e \u0939\u0948)<\/p>\n

\u0905\u0924: n = 7<\/p>\n

n = 7 \u0915\u093e \u092e\u093e\u0928 (i) \u092e\u0947\u0902 \u0930\u0916\u0928\u0947 \u092a\u0930<\/p>\n

a = 6 – 2n\u00a0\u00a0 …………… (i)<\/p>\n

a = 6 – 2(7)<\/p>\n

a = 6 – 14<\/p>\n

a = – 8<\/p>\n

\u0905\u0924: n = 7 \u0914\u0930 a = – 8 \u0939\u0948 |<\/p>\n

(ix) a = 3, n = 8 \u0914\u0930 S = 192 \u0926\u093f\u092f\u093e \u0939\u0948 \u0964 d \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f \u0964<\/strong><\/p>\n

\"NCERT<\/p>\n

(x)\u00a0<\/strong>l\u00a0<\/em><\/strong>= 28, S = 144 \u0914\u0930 \u0915\u0941\u0932 9 \u092a\u0926 \u0939\u0948\u0902 \u0964\u00a0a\u00a0<\/em>\u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f \u0964<\/strong><\/p>\n

\"NCERT<\/p>\n

Ex 5.3 Class 10 \u0917\u0923\u093f\u0924\u00a0Q4. 636 \u092f\u094b\u0917 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, A.P. :\u00a0<\/strong>9, 17, 25 ……….. \u0915\u0947 \u0915\u093f\u0924\u0928\u0947 \u092a\u0926 \u0932\u0947\u0928\u0947 \u091a\u093e\u0939\u093f\u090f ?<\/strong><\/p>\n

\u0939\u0932 :<\/strong>\u00a0\u0926\u093f\u092f\u093e \u0939\u0948 : A.P. : 9, 17, 25 ………..<\/p>\n

a = 9, d = 17 – 9 = 8, Sn<\/sub>\u00a0= 636 \u0914\u0930 n = ?<\/p>\n

\u0905\u092c, Sn<\/sub>\u00a0= 636<\/p>\n

\"NCERT<\/p>\n

Ex 5.3 Class 10 \u0917\u0923\u093f\u0924\u00a0Q5. \u0915\u093f\u0938\u0940\u00a0<\/strong>A.P.<\/strong>\u00a0\u0915\u093e \u092a\u094d\u0930\u0925\u092e \u092a\u0926 5<\/strong>, \u0905\u0902\u0924\u093f\u092e \u092a\u0926 45 \u0914\u0930 \u092f\u094b\u0917 400 \u0939\u0948\u0964 \u092a\u0926\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0914\u0930 \u0938\u093e\u0930\u094d\u0935 \u0905\u0902\u0924\u0930 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/strong><\/p>\n

\u0939\u0932 :<\/strong>\u00a0\u0926\u093f\u092f\u093e \u0939\u0948 : a = 5, an<\/sub>\u00a0= 45 \u0914\u0930 Sn<\/sub>\u00a0= 400<\/p>\n

\u0905\u092c, an<\/sub>\u00a0= 45<\/p>\n

\"NCERT<\/p>\n

Ex 5.3 Class 10 \u0917\u0923\u093f\u0924\u00a0Q6. \u0915\u093f\u0938\u0940\u00a0<\/strong>A.P.<\/strong>\u00a0\u0915\u0947 \u092a\u094d\u0930\u0925\u092e \u0914\u0930 \u0905\u0902\u0924\u093f\u092e \u092a\u0926 \u0915\u094d\u0930\u092e\u0936\u0903 17 \u0914\u0930 350 \u0939\u0948\u0902\u0964 \u092f\u0926\u093f \u0938\u093e\u0930\u094d\u0935 \u0905\u0902\u0924\u0930 9 \u0939\u0948<\/strong>, \u0924\u094b \u0907\u0938\u092e\u0947\u0902 \u0915\u093f\u0924\u0928\u0947 \u092a\u0926 \u0939\u0948\u0902 \u0914\u0930 \u0907\u0928\u0915\u093e \u092f\u094b\u0917 \u0915\u094d\u092f\u093e \u0939\u0948?<\/strong><\/p>\n

\u0939\u0932 :<\/strong>\u00a0a1<\/sub>\u00a0= 17, an<\/sub>\u00a0= 350 \u0914\u0930 d = 9<\/p>\n

\u0905\u092c, an<\/sub>\u00a0= 350<\/p>\n

\"NCERT<\/p>\n

Ex 5.3 Class 10 \u0917\u0923\u093f\u0924\u00a0Q7. \u0909\u0938\u00a0<\/strong>A.P. \u0915\u0947\u00a0<\/strong>\u092a\u094d\u0930\u0925\u092e 22 \u092a\u0926\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f<\/strong>, \u091c\u093f\u0938\u092e\u0947\u0902 d = 7 \u0939\u0948 \u0914\u0930 22\u0935\u093e\u0901 \u092a\u0926 149 \u0939\u0948\u0964<\/strong><\/p>\n

\u0939\u0932 :<\/strong>\u00a0\u0926\u093f\u092f\u093e \u0939\u0948 : a22\u00a0<\/sub>= 149 d = 7 \u0914\u0930 n = 22<\/p>\n

a22\u00a0<\/sub>= a + 21 d<\/p>\n

149 = a + 21\u00d77<\/p>\n

149 = a + 147<\/p>\n

a = 149 – 147<\/p>\n

a = 2<\/p>\n

\"NCERT<\/p>\n

Ex 5.3 Class 10 \u0917\u0923\u093f\u0924\u00a0Q8. \u0909\u0938\u00a0<\/strong>A.P. \u0915\u0947<\/strong>\u00a0\u092a\u094d\u0930\u0925\u092e 51 \u092a\u0926\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f<\/strong>, \u091c\u093f\u0938\u0915\u0947 \u0926\u0942\u0938\u0930\u0947 \u0914\u0930 \u0924\u0940\u0938\u0930\u0947 \u092a\u0926 \u0915\u094d\u0930\u092e\u0936\u0903 14 \u0914\u0930 18 \u0939\u0948\u0902\u0964<\/strong><\/p>\n

\u0939\u0932 :<\/strong>\u00a0\u0926\u093f\u092f\u093e \u0939\u0948 :<\/p>\n

a2<\/sub>\u00a0= 14<\/p>\n

=> a + d = 14\u00a0 ………… (i)<\/p>\n

a3\u00a0\u00a0<\/sub>= 18<\/p>\n

d = a3<\/sub>\u00a0– a2<\/sub><\/p>\n

= 18 – 14<\/p>\n

= 4<\/p>\n

d \u0915\u093e \u092e\u093e\u0928 \u0938\u092e\u0940\u0915\u0930\u0923 (i) \u092e\u0947\u0902 \u0930\u0916\u0928\u0947 \u092a\u0930<\/p>\n

\"NCERT<\/p>\n

Ex 5.3 Class 10 \u0917\u0923\u093f\u0924\u00a0Q9. \u092f\u0926\u093f \u0915\u093f\u0938\u0940\u00a0<\/strong>A.P. \u0915\u0947<\/strong>\u00a0\u092a\u094d\u0930\u0925\u092e 7 \u092a\u0926\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 49 \u0939\u0948 \u0914\u0930 \u092a\u094d\u0930\u0925\u092e 17 \u092a\u0926\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 289 \u0939\u0948<\/strong>, \u0924\u094b \u0907\u0938\u0915\u0947 \u092a\u094d\u0930\u0925\u092e n \u092a\u0926\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/strong><\/p>\n

\"Download
\n\"Download<\/p>\n

Ex 5.3 Class 10 \u0917\u0923\u093f\u0924\u00a0Q<\/em><\/strong>10<\/strong>.<\/em><\/strong>\u00a0\u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f\u00a0<\/strong>a1<\/sub>, a2<\/sub>, . . ., an<\/sub>, . .<\/strong>\u00a0.<\/em><\/strong>\u00a0\u0938\u0947 \u090f\u0915\u00a0<\/strong>A.P.<\/strong>\u00a0\u092c\u0928\u0924\u0940 \u0939\u0948<\/strong>,\u00a0<\/em><\/strong>\u092f\u0926\u093f\u00a0<\/strong>an<\/sub><\/strong>\u00a0\u0928\u0940\u091a\u0947 \u0926\u093f\u090f \u0905\u0928\u0941\u0938\u093e\u0930 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0939\u0948:<\/strong><\/p>\n

(i) an<\/sub>\u00a0= 3 + 4n (ii) an<\/sub>\u00a0= 9 \u2013 5n<\/strong><\/p>\n

\u0938\u093e\u0925 \u0939\u0940<\/strong>,\u00a0<\/em><\/strong>\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0938\u094d\u0925\u093f\u0924\u093f \u092e\u0947\u0902<\/strong>,\u00a0<\/em><\/strong>\u092a\u094d\u0930\u0925\u092e 15 \u092a\u0926\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/strong><\/p>\n

\"NCERT
\n\"NCERT<\/p>\n

Ex 5.3 Class 10 \u0917\u0923\u093f\u0924\u00a0Q<\/strong>11<\/strong>.<\/em><\/strong>\u00a0\u092f\u0926\u093f \u0915\u093f\u0938\u0940\u00a0<\/strong>A.P.<\/strong>\u00a0\u0915\u0947 \u092a\u094d\u0930\u0925\u092e n \u092a\u0926\u094b\u0902 \u0915\u093e \u092f\u094b\u0917\u00a0<\/strong>4n \u2013 n2<\/sup><\/strong>\u00a0\u0939\u0948<\/strong>,\u00a0<\/em><\/strong>\u0924\u094b \u0907\u0938\u0915\u093e \u092a\u094d\u0930\u0925\u092e \u092a\u0926 (\u0905\u0930\u094d\u0925\u093e\u0924\u094d\u00a0<\/strong>S1<\/sub><\/strong>\u00a0) \u0915\u094d\u092f\u093e \u0939\u0948<\/strong>?<\/strong>\u00a0\u00a0\u092a\u094d\u0930\u0925\u092e \u0926\u094b \u092a\u0926\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 \u0915\u094d\u092f\u093e \u0939\u0948<\/strong>?<\/em><\/strong>\u00a0\u00a0\u0926\u0942\u0938\u0930\u093e \u092a\u0926 \u0915\u094d\u092f\u093e \u0939\u0948<\/strong>?<\/em><\/strong>\u00a0\u00a0\u0907\u0938\u0940 \u092a\u094d\u0930\u0915\u093e\u0930<\/strong>,<\/em><\/strong>\u00a0\u00a0\u0924\u0940\u0938\u0930\u0947<\/strong>,\u00a0<\/em><\/strong>10\u0935\u0947\u0902 \u0914\u0930 n \u0935\u0947\u0902 \u092a\u0926 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/strong><\/p>\n

\u0939\u0932 :<\/strong>\u00a0\u092a\u094d\u0930\u0925\u092e n \u092a\u0926\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 4n \u2013 n2<\/sup>\u00a0\u0939\u0948<\/p>\n

Sn<\/sub>\u00a0= 4n \u2013 n2<\/sup>\u00a0…………\u00a0<\/em>(i)<\/p>\n

n \u0915\u0940 \u091c\u0917\u0939 n\u00a0–<\/em>\u00a01 \u0930\u0916\u0928\u0947 \u092a\u0930<\/p>\n

Sn-1<\/sub>\u00a0= 4(n\u00a0–<\/em>1) \u2013 (n\u00a0–<\/em>\u00a01)2<\/sup><\/p>\n

= 4n\u00a0–<\/em>\u00a04 \u2013 (n2<\/sup>\u00a0–<\/em>\u00a02n + 1)<\/p>\n

= 4n\u00a0–<\/em>\u00a04 \u2013 n2<\/sup>\u00a0+ 2n\u00a0–<\/em>\u00a01<\/p>\n

= \u2013 n2<\/sup>\u00a0+ 6n\u00a0–<\/em>\u00a05\u00a0\u00a0\u00a0\u00a0\u00a0 …………… (ii)<\/p>\n

\u0905\u0924: n \u0935\u093e\u0901 \u092a\u0926 (an<\/sub>) = Sn<\/sub>\u00a0–<\/em>\u00a0Sn-1<\/sub><\/p>\n

=> (an<\/sub>) = Sn<\/sub>\u00a0–<\/em>\u00a0Sn-1<\/sub><\/p>\n

\u0939\u0932 :<\/strong>\u00a0\u092a\u094d\u0930\u0925\u092e n \u092a\u0926\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 4n \u2013 n2<\/sup>\u00a0\u0939\u0948<\/p>\n

Sn<\/sub>\u00a0= 4n \u2013 n2<\/sup>\u00a0…………\u00a0<\/em>(i)<\/p>\n

n \u0915\u0940 \u091c\u0917\u0939 n\u00a0–<\/em>\u00a01 \u0930\u0916\u0928\u0947 \u092a\u0930<\/p>\n

Sn-1<\/sub>\u00a0= 4(n\u00a0–<\/em>1) \u2013 (n\u00a0–<\/em>\u00a01)2<\/sup><\/p>\n

= 4n\u00a0–<\/em>\u00a04 \u2013 (n2<\/sup>\u00a0–<\/em>\u00a02n + 1)<\/p>\n

= 4n\u00a0–<\/em>\u00a04 \u2013 n2<\/sup>\u00a0+ 2n\u00a0–<\/em>\u00a01<\/p>\n

= \u2013 n2<\/sup>\u00a0+ 6n\u00a0–<\/em>\u00a05\u00a0\u00a0\u00a0\u00a0\u00a0 …………… (ii)<\/p>\n

\u0905\u0924: n \u0935\u093e\u0901 \u092a\u0926 (an<\/sub>) = Sn<\/sub>\u00a0–<\/em>\u00a0Sn-1<\/sub><\/p>\n

=> (an<\/sub>) = Sn<\/sub>\u00a0–<\/em>\u00a0Sn-1<\/sub><\/p>\n

=> (an<\/sub>) = 4n \u2013 n2<\/sup>\u00a0–<\/em>\u00a0(\u2013 n2<\/sup>\u00a0+ 6n\u00a0–<\/em>\u00a05)<\/p>\n

=> (an<\/sub>) = 4n \u2013 n2<\/sup>\u00a0+ n2<\/sup>\u00a0–<\/em>\u00a06n + 5<\/p>\n

=> (an<\/sub>) =\u00a0–<\/em>\u00a02n + 5<\/p>\n

\u0905\u092c, S1<\/sub>\u00a0= 4(1) \u2013 (1)2<\/sup>\u00a0= 4 – 1 = 3<\/p>\n

\u092a\u094d\u0930\u0925\u092e \u0926\u094b \u092a\u0926\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 (S2<\/sub><\/em>) = 4(2) \u2013 (2)2<\/sup>\u00a0= 8 – 4 = 4<\/p>\n

(an<\/sub>) =\u00a0–<\/em>\u00a02n + 5<\/p>\n

\u0926\u0942\u0938\u0930\u093e \u092a\u0926 (a2<\/sub>) =\u00a0–<\/em>\u00a02(2) + 5\u00a0 =\u00a0–<\/em>\u00a04 + 5 = 1<\/p>\n

\u0924\u0940\u0938\u0930\u093e \u092a\u0926 (a3<\/sub>) =\u00a0–<\/em>\u00a02(3) + 5\u00a0 =\u00a0–<\/em>\u00a06 + 5 =\u00a0–<\/em>1<\/p>\n

10 \u0935\u093e\u0901 \u092a\u0926 (a10<\/sub>) =\u00a0–<\/em>\u00a02(10) + 5\u00a0 =\u00a0–<\/em>\u00a020 + 5 =\u00a0–<\/em>15<\/p>\n

(an<\/sub>) = 4n \u2013 n2<\/sup>\u00a0–<\/em>\u00a0(\u2013 n2<\/sup>\u00a0+ 6n\u00a0–<\/em>\u00a05)<\/p>\n

=> (an<\/sub>) = 4n \u2013 n2<\/sup>\u00a0+ n2<\/sup>\u00a0–<\/em>\u00a06n + 5<\/p>\n

=> (an<\/sub>) =\u00a0–<\/em>\u00a02n + 5<\/p>\n

\u0905\u092c, S1<\/sub>\u00a0= 4(1) \u2013 (1)2<\/sup>\u00a0= 4 – 1 = 3<\/p>\n

\u092a\u094d\u0930\u0925\u092e \u0926\u094b \u092a\u0926\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 (S2<\/sub><\/em>) = 4(2) \u2013 (2)2<\/sup>\u00a0= 8 – 4 = 4<\/p>\n

(an<\/sub>) =\u00a0–<\/em>\u00a02n + 5<\/p>\n

\u0926\u0942\u0938\u0930\u093e \u092a\u0926 (a2<\/sub>) =\u00a0–<\/em>\u00a02(2) + 5\u00a0 =\u00a0–<\/em>\u00a04 + 5 = 1<\/p>\n

\u0924\u0940\u0938\u0930\u093e \u092a\u0926 (a3<\/sub>) =\u00a0–<\/em>\u00a02(3) + 5\u00a0 =\u00a0–<\/em>\u00a06 + 5 =\u00a0–<\/em>1<\/p>\n

10 \u0935\u093e\u0901 \u092a\u0926 (a10<\/sub>) =\u00a0–<\/em>\u00a02(10) + 5\u00a0 =\u00a0–<\/em>\u00a020 + 5 =\u00a0–<\/em>15<\/p>\n

Ex 5.3 Class 10 \u0917\u0923\u093f\u0924\u00a0Q12. \u0910\u0938\u0947 \u092a\u094d\u0930\u0925\u092e 40 \u0927\u0928 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f \u091c\u094b 6 \u0938\u0947 \u0935\u093f\u092d\u093e\u091c\u094d\u092f \u0939\u0948\u0902\u0964<\/strong><\/p>\n

\"NCERT<\/p>\n

Ex 5.3 Class 10 \u0917\u0923\u093f\u0924\u00a0Q13. 8 \u0915\u0947 \u092a\u094d\u0930\u0925\u092e 15 \u0917\u0941\u0923\u091c\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/strong><\/p>\n

\"Maths<\/p>\n

Ex 5.3 Class 10 \u0917\u0923\u093f\u0924\u00a0Q14. 0 \u0914\u0930 50 \u0915\u0947 \u092c\u0940\u091a \u0915\u0940 \u0935\u093f\u0937\u092e \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u093e \u092f\u094b\u0917 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/strong><\/p>\n

\"NCERT<\/p>\n

Ex 5.3 Class 10 \u0917\u0923\u093f\u0924\u00a0Q15. \u0928\u093f\u0930\u094d\u092e\u093e\u0923 \u0915\u093e\u0930\u094d\u092f \u0938\u0947 \u0938\u092e\u094d\u092c\u0928\u094d\u0927\u0940 \u0915\u093f\u0938\u0940 \u0920\u0947\u0915\u0947 \u092e\u0947\u0902<\/strong>,\u00a0<\/em><\/strong>\u090f\u0915 \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0924\u093f\u0925\u093f \u0915\u0947 \u092c\u093e\u0926 \u0915\u093e\u0930\u094d\u092f \u0915\u094b \u0935\u093f\u0932\u0902\u092c \u0938\u0947 \u092a\u0942\u0930\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f<\/strong>,\u00a0<\/em><\/strong>\u091c\u0941\u0930\u094d\u092e\u093e\u0928\u093e \u0932\u0917\u093e\u0928\u0947 \u0915\u093e \u092a\u094d\u0930\u093e\u0935\u0927\u0928 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u0948: \u092a\u0939\u0932\u0947 \u0926\u093f\u0928 \u0915\u0947 \u0932\u093f\u090f 200 \u0930\u0941<\/strong>,\u00a0<\/em><\/strong>\u0926\u0942\u0938\u0930\u0947 \u0926\u093f\u0928 \u0915\u0947 \u0932\u093f\u090f 250 \u0930\u0941<\/strong>,\u00a0<\/em><\/strong>\u0924\u0940\u0938\u0930\u0947 \u0926\u093f\u0928 \u0915\u0947 \u0932\u093f\u090f 300 \u0930\u0941 \u0907\u0924\u094d\u092f\u093e\u0926\u093f<\/strong>,\u00a0<\/em><\/strong>\u0905\u0930\u094d\u0925\u093e\u0924\u094d \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0909\u0924\u0930\u094b\u0924\u094d\u0924\u0930 \u0926\u093f\u0928 \u0915\u093e \u091c\u0941\u0930\u094d\u092e\u093e\u0928\u093e \u0905\u092a\u0928\u0947 \u0938\u0947 \u0920\u0940\u0915 \u092a\u0939\u0932\u0947 \u0926\u093f\u0928 \u0915\u0947 \u091c\u0941\u0930\u094d\u092e\u093e\u0928\u0947 \u0938\u0947 50 \u0930\u0941 \u0905\u0927\u093f\u0915 \u0939\u0948\u0964 \u090f\u0915 \u0920\u0947\u0915\u0947\u0926\u093e\u0930 \u0915\u094b \u091c\u0941\u0930\u094d\u092e\u093e\u0928\u0947 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0915\u093f\u0924\u0928\u0940 \u0930\u093e\u0936\u093f \u0905\u0926\u093e \u0915\u0930\u0928\u0940 \u092a\u0921\u093c\u0947\u0917\u0940<\/strong>,\u00a0<\/em><\/strong>\u092f\u0926\u093f \u0935\u0939 \u0907\u0938 \u0915\u093e\u0930\u094d\u092f \u092e\u0947\u0902 30 \u0926\u093f\u0928 \u0915\u093e \u0935\u093f\u0932\u0902\u092c \u0915\u0930 \u0926\u0947\u0924\u093e \u0939\u0948\u00a0<\/strong>?<\/strong><\/p>\n

\"Solutions<\/p>\n

Ex 5.3 Class 10 \u0917\u0923\u093f\u0924\u00a0Q16. \u0915\u093f\u0938\u0940 \u0938\u094d\u0915\u0942\u0932 \u0915\u0947 \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u093f\u092f\u094b\u0902 \u0915\u094b \u0909\u0928\u0915\u0947 \u0938\u092e\u0917\u094d\u0930 \u0936\u0948\u0915\u094d\u0937\u093f\u0915 \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u0928 \u0915\u0947 \u0932\u093f\u090f 7 \u0928\u0915\u0926 \u092a\u0941\u0930\u0938\u094d\u0915\u093e\u0930 \u0926\u0947\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f 700 \u0930\u0941 \u0915\u0940 \u0930\u093e\u0936\u093f \u0930\u0916\u0940 \u0917\u0908 \u0939\u0948\u0964 \u092f\u0926\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092a\u0941\u0930\u0938\u094d\u0915\u093e\u0930 \u0905\u092a\u0928\u0947 \u0938\u0947 \u0920\u0940\u0915 \u092a\u0939\u0932\u0947 \u092a\u0941\u0930\u0938\u094d\u0915\u093e\u0930 \u0938\u0947 20 \u0930\u0941 \u0915\u092e \u0939\u0948<\/strong>,\u00a0<\/em><\/strong>\u0924\u094b \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092a\u0941\u0930\u0938\u094d\u0915\u093e\u0930 \u0915\u093e \u092e\u093e\u0928 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/strong><\/p>\n

\"NCERT<\/p>\n

Ex 5.3 Class 10 \u0917\u0923\u093f\u0924\u00a0Q1<\/strong>7<\/em><\/strong>. \u090f\u0915 \u0938\u094d\u0915\u0942\u0932 \u0915\u0947 \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u093f\u092f\u094b\u0902 \u0928\u0947 \u0935\u093e\u092f\u0941 \u092a\u094d\u0930\u0926\u0941\u0937\u0923 \u0915\u092e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0938\u094d\u0915\u0942\u0932 \u0915\u0947 \u0905\u0928\u094d\u0926\u0930 \u0914\u0930 \u092c\u093e\u0939\u0930 \u092a\u0947\u095c \u0932\u0917\u093e\u0928\u0947 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u0938\u094b\u0902\u091a\u093e\u00a0<\/strong>\u0964<\/strong>\u00a0\u092f\u0939 \u0928\u093f\u0930\u094d\u0923\u092f \u0932\u093f\u092f\u093e \u0917\u092f\u093e \u0915\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0915\u0915\u094d\u0937\u093e \u0915\u093e \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0905\u0928\u0941\u092d\u093e\u0917 \u0905\u092a\u0928\u0940 \u0915\u0915\u094d\u0937\u093e \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u092a\u0947\u095c \u0932\u0917\u093e\u090f\u0917\u093e\u00a0<\/strong>\u0964<\/strong>\u00a0\u0909\u0926\u093e\u0939\u0930\u0923\u093e\u0930\u094d\u0925, \u0915\u0915\u094d\u0937\u093e I \u0915\u093e \u090f\u0915 \u0905\u0928\u0941\u092d\u093e\u0917 \u090f\u0915 \u092a\u0947\u095c \u0932\u0917\u093e\u090f\u0917\u093e, \u0915\u0915\u094d\u0937\u093e II \u0915\u093e \u090f\u0915 \u0905\u0928\u0941\u092d\u093e\u0917 2 \u092a\u0947\u095c \u0932\u0917\u093e\u090f\u0917\u093e, \u0915\u0915\u094d\u0937\u093e III \u0915\u093e \u090f\u0915 \u0905\u0928\u0941\u092d\u093e\u0917 3 \u092a\u0947\u095c \u0932\u0917\u093e\u090f\u0917\u093e, \u0907\u0924\u094d\u092f\u093e\u0926\u093f \u0914\u0930 \u0910\u0938\u093e \u0939\u0940 \u0915\u0915\u094d\u0937\u093e XII \u0924\u0915 \u0915\u0947 \u0932\u093f\u090f \u091a\u0932\u0924\u093e \u0930\u0939\u0947\u0917\u093e\u00a0<\/strong>\u0964<\/strong>\u00a0\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0924\u0940\u0928 \u0905\u0928\u0941\u092d\u093e\u0917 \u0939\u0948\u0902\u00a0<\/strong>\u0964<\/strong>\u00a0\u0907\u0938 \u0935\u093f\u0926\u094d\u092f\u093e\u0932\u092f \u0915\u0947 \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u093f\u092f\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u0932\u0917\u093e\u090f \u0917\u090f \u0915\u0941\u0932 \u092a\u0947\u095c\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u093f\u0924\u0928\u0940 \u0939\u094b\u0917\u0940 ?<\/strong><\/p>\n

\u0939\u0932 :<\/strong><\/p>\n

\u0915\u0915\u094d\u0937\u093e 1 \u0938\u0947 12 \u0924\u0915 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0905\u0928\u0941\u092d\u093e\u0917 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u092a\u0947\u095c \u0932\u0917\u093e\u0924\u093e \u0939\u0948 \u0964<\/p>\n

\u0905\u0924: 1, 2, 3, 4, …………………. 12<\/p>\n

\u091a\u0942\u0901\u0915\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0924\u0940\u0928 \u0905\u0928\u0941\u092d\u093e\u0917 \u0939\u0948 \u0964<\/p>\n

\u0905\u0924: \u0905\u092c \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0915\u0915\u094d\u0937\u093e \u0926\u094d\u0935\u093e\u0930\u093e \u0932\u0917\u093e\u090f \u0917\u090f \u092a\u0947\u095c \u0939\u094b \u091c\u093e\u092f\u0947\u0902\u0917\u0947 \u0964<\/p>\n

\u0907\u0938\u0932\u093f\u090f, 3(1), 3(2), 3(3), 3(4) ……………………. 3(12)<\/p>\n

\u092f\u093e\u00a0\u00a0\u00a0\u00a0\u00a0 3, 6, 9, 12, ………………….. 36<\/p>\n

a = 3, d = 3 \u0914\u0930 n = 12<\/p>\n

\u0915\u0941\u0932 \u092a\u0947\u095c\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e = S12<\/sub><\/p>\n

\"Maths<\/p>\n

Ex 5.3 Class 10 \u0917\u0923\u093f\u0924\u00a0Q18. \u0915\u0947\u0902\u0926\u094d\u0930 A \u0938\u0947 \u092a\u094d\u0930\u093e\u0930\u0902\u092d \u0915\u0930\u0924\u0947 \u0939\u0941\u090f, \u092c\u093e\u0930\u0940-\u092c\u093e\u0930\u0940 \u0938\u0947 \u0915\u0947\u0928\u094d\u0926\u094d\u0930\u094b\u0902 A \u0914\u0930 B \u0915\u094b \u0932\u0947\u0924\u0947 \u0939\u0941\u090f, \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e\u0913\u0902 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm …. \u0935\u093e\u0932\u0947 \u0909\u0924\u094d\u0924\u0930\u094b\u0924\u094d\u0924\u0930 \u0905\u0930\u094d\u0927\u0935\u0943\u0924\u094b\u0902 \u0915\u094b \u0916\u0940\u0902\u091a\u0915\u0930 \u090f\u0915 \u0938\u0930\u094d\u092a\u093f\u0932 (spiral) \u092c\u0928\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948, \u091c\u0948\u0938\u093e \u0915\u093f \u0906\u0915\u0943\u0924\u093f \u092e\u0947\u0902 \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948 | \u0924\u0947\u0930\u0939 \u0915\u094d\u0930\u092e\u093e\u0917\u0924 \u0905\u0930\u094d\u0927\u0935\u0943\u0924\u094b\u0902 \u0938\u0947 \u092c\u0928\u0947 \u0907\u0938 \u0938\u0930\u094d\u092a\u093f\u0932 \u0915\u0940 \u0915\u0941\u0932 \u0932\u0902\u092c\u093e\u0908 \u0915\u094d\u092f\u093e \u0939\u0948 ?\u00a0<\/strong><\/p>\n

\"NCERT<\/p>\n

\u0939\u0932 :<\/strong>\u00a0\u0926\u093f\u092f\u093e \u0939\u0948 \u0905\u0930\u094d\u0927\u0935\u0943\u0924\u094b\u0902 \u0915\u0940 \u0932\u092e\u094d\u092c\u093e\u0908\u092f\u093e\u0901\u00a0l1<\/sub>, l2<\/sub>, l3<\/sub>, l4<\/sub><\/em>\u00a0\u0915\u094d\u0930\u092e\u0936: \u00a0\u0907\u0924\u094d\u092f\u093e\u0926\u093f \u0905\u0930\u094d\u0927\u0935\u0943\u0924\u094d\u0924 \u0939\u0948\u0902 \u0964<\/p>\n

\"Solutions
\n\"NCERT<\/p>\n

Ex 5.3 Class 10 \u0917\u0923\u093f\u0924\u00a0Q19.<\/strong>\u00a0200 \u0932\u091f\u094d\u0920\u094b\u0902\u00a0<\/strong>(logs)<\/strong>\u00a0\u0915\u094b \u0922\u0947\u0930\u0940 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0930\u0916\u093e \u091c\u093e\u0924\u093e \u0939\u0948: \u0938\u092c\u0938\u0947 \u0928\u0940\u091a\u0947 \u0935\u093e\u0932\u0940 \u092a\u0902\u0915\u094d\u0924\u093f \u092e\u0947\u0902<\/strong>\u00a020 \u0932\u091f\u094d\u0920\u0947<\/strong>,<\/em><\/strong>\u00a0\u00a0\u0909\u0938\u0938\u0947 \u0905\u0917\u0932\u0940 \u092a\u0902\u0915\u094d\u0924\u093f \u092e\u0947\u0902 19 \u0932\u091f\u094d\u0920\u0947<\/strong>,\u00a0<\/em><\/strong>\u00a0\u0909\u0938\u0938\u0947 \u0905\u0917\u0932\u0940 \u092a\u0902\u0915\u094d\u0924\u093f \u092e\u0947\u0902 18 \u0932\u091f\u094d\u0920\u0947<\/strong>,<\/em><\/strong>\u00a0\u00a0\u0907\u0924\u094d\u092f\u093e\u0926\u093f\u00a0<\/strong>(<\/strong>\u0926\u0947\u0916\u093f\u090f<\/strong>\u00a0\u0906\u0915\u0943\u0924\u093f )<\/strong>\u0964 \u092f\u0947 200 \u0932\u0920\u094d\u0920\u0947 \u0915\u093f\u0924\u0928\u0940 \u092a\u0902\u0915\u094d\u0924\u093f\u092f\u094b\u0902 \u092e\u0947\u0902 \u0930\u0916\u0947 \u0917\u090f \u0939\u0948\u0902 \u0924\u0925\u093e \u0938\u092c\u0938\u0947 \u090a\u092a\u0930\u0940 \u092a\u0902\u0915\u094d\u0924\u093f \u092e\u0947\u0902 \u0915\u093f\u0924\u0928\u0947<\/strong>\u00a0\u0932\u091f\u094d\u0920\u0947 \u0939\u0948\u0902<\/strong>?<\/em><\/strong><\/p>\n

\"NCERT
\n\"CBSE<\/p>\n

\u092f\u0939\u093e\u0901\u00a0–<\/em>\u00a04 \u0938\u0902\u092d\u0935 \u0928\u0939\u0940\u0902 \u0939\u0948 \u0905\u0924: \u0905\u0902\u0924\u093f\u092e \u0905\u0930\u094d\u0925\u093e\u0924 \u0938\u092c\u0938\u0947 \u0909\u092a\u0930\u0940 \u092a\u0902\u0915\u094d\u0924\u093f \u092e\u0947\u0902 \u0932\u0920\u094d\u0920\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e 5 \u0939\u0948 \u0914\u0930 \u092a\u0902\u0915\u094d\u0924\u093f\u092f\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e 16 \u0939\u0948 |<\/p>\n

Ex 5.3 Class 10 \u0917\u0923\u093f\u0924\u00a0Q20.\u00a0<\/strong>\u090f\u0915 \u0906\u0932\u0942 \u0926\u094c\u0921\u093c\u00a0<\/strong>(potato race)<\/strong>\u00a0\u092e\u0947\u0902<\/strong>,\u00a0<\/em><\/strong>\u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0938\u094d\u0925\u093e\u0928 \u092a\u0930 \u090f\u0915 \u092c\u093e\u0932\u094d\u091f\u0940 \u0930\u0916\u0940 \u0939\u0941\u0908 \u0939\u0948<\/strong>,\u00a0<\/em><\/strong>\u091c\u094b \u092a\u0939\u0932\u0947 \u0906\u0932\u0942<\/strong>\u00a0\u0938\u0947 5m \u0915\u0940 \u0926\u0942\u0930\u0940 \u092a\u0930 \u0939\u0948<\/strong>,\u00a0<\/em><\/strong>\u0924\u0925\u093e \u0905\u0928\u094d\u092f \u0906\u0932\u0941\u0913\u0902 \u0915\u094b \u090f\u0915 \u0938\u0940\u0927\u0940 \u0930\u0947\u0916\u093e \u092e\u0947\u0902 \u092a\u0930\u0938\u094d\u092a\u0930 3m \u0915\u0940 \u0926\u0942\u0930\u093f\u092f\u094b\u0902 \u092a\u0930 \u0930\u0916\u093e<\/strong>\u00a0\u0917\u092f\u093e \u0939\u0948\u0964 \u0907\u0938 \u0930\u0947\u0916\u093e \u092a\u0930 10 \u0906\u0932\u0942 \u0930\u0916\u0947 \u0917\u090f \u0939\u0948\u0902\u00a0<\/strong>(<\/strong>\u0926\u0947\u0916\u093f\u090f \u0906\u0915\u0943\u0924\u093f) \u0964 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092a\u094d\u0930\u0924\u093f\u092f\u094b\u0917\u0940 \u092c\u093e\u0932\u094d\u091f\u0940 \u0938\u0947 \u091a\u0932\u0928\u093e \u092a\u094d\u0930\u093e\u0930\u0902\u092d \u0915\u0930\u0924\u0940 \u0939\u0948<\/strong>,\u00a0<\/em><\/strong>\u0928\u093f\u0915\u091f\u0924\u092e \u0906\u0932\u0942 \u0915\u094b \u0909\u0920\u093e\u0924\u0940 \u0939\u0948<\/strong>,\u00a0<\/em><\/strong>\u0909\u0938\u0947 \u0932\u0947\u0915\u0930 \u0935\u093e\u092a\u0938 \u0906\u0915\u0930 \u0926\u094c\u0921\u093c\u0915\u0930 \u092c\u093e\u0932\u094d\u091f\u0940 \u092e\u0947\u0902 \u0921\u093e\u0932\u0924\u0940 \u0939\u0948<\/strong>,\u00a0<\/em><\/strong>\u0926\u0942\u0938\u0930\u093e \u0906\u0932\u0942 \u0909\u0920\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0935\u093e\u092a\u0938 \u0926\u094c\u0921\u093c\u0924\u0940 \u0939\u0948<\/strong>,\u00a0<\/em><\/strong>\u0909\u0938\u0947 \u0909\u0920\u093e\u0915\u0930 \u0935\u093e\u092a\u0938 \u092c\u093e\u0932\u094d\u091f\u0940 \u092e\u0947\u0902 \u0921\u093e\u0932\u0924\u0940 \u0939\u0948<\/strong>,\u00a0<\/em><\/strong>\u00a0\u0914\u0930 \u0935\u0939 \u0910\u0938\u093e \u0924\u092c \u0924\u0915 \u0915\u0930\u0924\u0940 \u0930\u0939\u0924\u0940 \u0939\u0948<\/strong>,\u00a0<\/em><\/strong>\u091c\u092c \u0924\u0915 \u0938\u092d\u0940 \u0906\u0932\u0942 \u092c\u093e\u0932\u094d\u091f\u0940 \u092e\u0947\u0902 \u0928 \u0906 \u091c\u093e\u090f\u0901\u0964 \u0907\u0938\u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u093f\u092f\u094b\u0917\u0940 \u0915\u094b \u0915\u0941\u0932 \u0915\u093f\u0924\u0928\u0940 \u0926\u0942\u0930\u0940 \u0926\u094c\u0921\u093c\u0928\u0940 \u092a\u0921\u093c\u0947\u0917\u0940<\/strong>?<\/em><\/strong><\/p>\n

\"NCERT<\/p>\n

<\/a>\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 5.4<\/span><\/strong><\/p>\n

Ex 5.4 Class 10 \u0917\u0923\u093f\u0924 Q1.<\/strong> A.P : 121,117,113,…., \u0915\u093e \u0915\u094c\u0928 -\u0938\u093e \u092a\u0926 \u0938\u092c\u0938\u0947 \u092a\u0939\u0932\u093e \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u092a\u0926 \u0939\u094b\u0917\u093e ?<\/p>\n

[\u0938\u0902\u0915\u0947\u0924 : an<\/sub><0 \u0915\u0947 \u0932\u093f\u090f n \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f | ]<\/p>\n

\"UP<\/p>\n

Ex 5.4 Class 10 \u0917\u0923\u093f\u0924\u00a0Q2.<\/strong> \u0915\u093f\u0938\u0940 A.P. \u0915\u0947 \u0924\u0940\u0938\u0930\u0947 \u0914\u0930 \u0938\u093e\u0924\u0935\u0947\u0902 \u092a\u0926\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 6 \u0939\u0948 \u0914\u0930 \u0909\u0928\u0915\u093e \u0917\u0941\u0923\u0928\u092b\u0932 8 \u0939\u0948 | \u0907\u0938 A.P. \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u0915\u0947 \u092a\u094d\u0930\u0925\u092e 16 \u092a\u0926\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f |
\n\"UP
\n\"UP<\/p>\n

Ex 5.4 Class 10 \u0917\u0923\u093f\u0924\u00a0Q3.<\/strong> \u00a0\u090f\u0915 \u0938\u0940\u095d\u0940 \u0915\u0947 \u0915\u094d\u0930\u092e\u093e\u0917\u0924 \u0921\u0902\u0921\u0947 \u092a\u0930\u0938\u094d\u092a\u0930 25 cm \u0915\u0940 \u0926\u0941\u0930\u0940 \u092a\u0930 \u0939\u0948\u0902| (\u0926\u0947\u0916\u093f\u090f \u0906\u0915\u0943\u0924\u093f 5.7) |<\/p>\n

\"NCERT<\/p>\n

\u0921\u0902\u0921\u094b\u0902 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 \u090f\u0915 \u0938\u092e\u093e\u0928 \u0930\u0942\u092a \u0938\u0947 \u0918\u091f\u0924\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948 \u0924\u0925\u093e \u0938\u092c\u0938\u0947 \u0928\u093f\u091a\u0932\u0947 \u0921\u0902\u0921\u0947 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 45 cm \u0939\u0948 \u00a0 \u00a0 \u00a0 \u00a0 \u0914\u0930 \u0938\u092c\u0938\u0947 \u090a\u092a\u0930 \u0935\u093e\u0932\u0947 \u0921\u0902\u0921\u0947 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 25 cm \u0939\u0948 | \u092f\u0926\u093f \u090a\u092a\u0930\u0940 \u0914\u0930 \u0928\u093f\u091a\u0932\u0947 \u0921\u0902\u0921\u0947 \u0915\u0947 \u092c\u0940\u091a \u0915\u0940 \u0926\u0941\u0930\u0940 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 2,1\/2 m \u0939\u0948, \u0924\u094b \u0921\u0902\u0921\u094b\u0902 \u0915\u094b \u092c\u0928\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0932\u0915\u095c\u0940 \u0915\u0940 \u0915\u093f\u0924\u0928\u0940 \u0932\u0902\u092c\u093e\u0908 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u094b\u0917\u0940 ?<\/p>\n

[\u0938\u0902\u0915\u0947\u0924 : \u0921\u0902\u0921\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e = 250\/ 25 \u0939\u0948\u0902 |]
\n\"UP
\n\"UP
\n\"UP<\/p>\n

Ex 5.4 Class 10 \u0917\u0923\u093f\u0924\u00a0Q4.<\/strong> \u090f\u0915 \u092a\u0902\u0915\u094d\u0924\u093f \u0915\u0947 \u092e\u0915\u093e\u0928\u094b\u0902 \u0915\u094b \u0915\u094d\u0930\u092e\u093e\u0917\u0924 \u0930\u0942\u092a \u0938\u0947 \u0938\u0902\u0916\u094d\u092f\u093e 1 \u0938\u0947 49 \u0924\u0915 \u0905\u0902\u0915\u093f\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948 | \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u0926\u0930\u094d\u0936\u093e\u0907\u090f \u0915\u093f x \u0915\u093e \u090f\u0915 \u0910\u0938\u093e \u092e\u093e\u0928 \u0939\u0948 x \u0938\u0947 \u0905\u0902\u0915\u093f\u0924 \u092e\u0915\u093e\u0928 \u0938\u0947 \u092a\u0939\u0932\u0947 \u0915\u0947 \u092e\u0915\u093e\u0928\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u093e \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u092f\u094b\u0917 \u0909\u0938\u0915\u0947 \u092c\u093e\u0926 \u0935\u093e\u0932\u0947 \u092e\u0915\u093e\u0928\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u092f\u094b\u0917 \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u0939\u0948 | x \u0915\u093e \u092e\u093e\u0928 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f |<\/p>\n

[ \u0938\u0902\u0915\u0947\u0924 : Sx – 1 =\u00a0<\/sub>S49 \u00a0<\/sub>– Sx\u00a0<\/sub>\u00a0\u0939\u0948 | ]
\n\"UP
\n\"UP
\n\"UP<\/p>\n

Ex 5.4 Class 10 \u0917\u0923\u093f\u0924\u00a0Q5.<\/strong> \u090f\u0915 \u092b\u0941\u091f\u092c\u0949\u0932 \u0915\u0947 \u092e\u0948\u0926\u093e\u0928 \u092e\u0947\u0902 \u090f\u0915 \u091b\u094b\u091f\u093e \u091a\u092c\u0942\u0924\u0930\u093e \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 15 \u0938\u0940\u0922\u0940\u092f\u093e\u0901 \u092c\u0928\u0940 \u0939\u0941\u0908 \u0939\u0948\u0902 | \u0907\u0928 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u0938\u0940\u0922\u0940\u092f\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 50m \u0939\u0948 \u0935\u0939 \u0920\u094b\u0938 \u0915\u0902\u0915\u094d\u0930\u0940\u091f ( concrete) \u0915\u0940 \u092c\u0928\u0940 \u0939\u0948 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u0938\u0940\u095d\u0940 \u092e\u0947\u0902 1\/4 m \u0915\u0940 \u091a\u094c\u095c\u093e\u0908 \u0939\u0948 \u0914\u0930 1\/2 m \u0915\u093e \u092b\u0948\u0932\u093e\u0935 \u00a0(\u091a\u094c\u095c\u093e\u0908) \u0939\u0948 | (\u0926\u0947\u0916\u093f\u090f \u0906\u0915\u0943\u0924\u093f 5.8 )| \u0907\u0938<\/p>\n

\u091a\u092c\u0942\u0924\u0930\u0947 \u0915\u094b \u092c\u0928\u093e\u0928\u0947 \u092e\u0947\u0902 \u0932\u0917\u0940 \u0915\u0902\u0915\u094d\u0930\u0940\u091f \u0915\u093e \u0915\u0941\u0932 \u0906\u092f\u0924\u0928 \u092a\u0930\u093f\u0915\u0932\u093f\u0924 \u0915\u0940\u091c\u093f\u090f |<\/p>\n

[ \u0938\u0902\u0915\u0947\u0924 : \u092a\u0939\u0932\u0940 \u0938\u0940\u095d\u0940 \u0915\u094b \u092c\u0928\u093e\u0928\u0947 \u092e\u0947\u0902 \u0932\u0917\u0940 \u0915\u0902\u0915\u094d\u0930\u0940\u091f \u0915\u093e \u0906\u092f\u0924\u0928 = 1\/4 x 1\/2 x 50m3\u00a0\u0939\u0948 |]
\n<\/sup><\/p>\n

\"NCERT
\n\"UP
\n\"UP
\n\"UP<\/p>\n

Hope given NCERT Solutions for Class 10 Maths Chapter 5\u00a0are helpful to complete your homework.<\/p>\n","protected":false},"excerpt":{"rendered":"

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions (Hindi Medium) These Solutions are part of NCERT Solutions for Class 10 Maths in Hindi Medium. Here we have given NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions. Chapter 5. \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u0936\u094d\u0930\u0947\u095d\u0940 \u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 5.1 Ex 5.1 Class 10 \u0917\u0923\u093f\u0924 Q1. \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u094d\u0925\u093f\u0924\u092f\u094b\u0902 \u092e\u0947\u0902 …<\/p>\n

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions (Hindi Medium)<\/span> Read More »<\/a><\/p>\n","protected":false},"author":5,"featured_media":7611,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[2],"tags":[23,22,11,20,12,21],"yoast_head":"\nNCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions (Hindi Medium) - MCQ Questions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-5-hindi\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions (Hindi Medium) - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions (Hindi Medium) These Solutions are part of NCERT Solutions for Class 10 Maths in Hindi Medium. 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Chapter 5. \u0938\u092e\u093e\u0928\u094d\u0924\u0930 \u0936\u094d\u0930\u0947\u095d\u0940 \u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 5.1 Ex 5.1 Class 10 \u0917\u0923\u093f\u0924 Q1. \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u094d\u0925\u093f\u0924\u092f\u094b\u0902 \u092e\u0947\u0902 … NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions (Hindi Medium) Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-5-hindi\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ Questions\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/NCERTSolutionsGuru\/\" \/>\n<meta property=\"article:published_time\" content=\"2021-07-23T04:32:21+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-03-02T04:55:44+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mcq-questions.com\/wp-content\/uploads\/2019\/09\/NCERT-Solutions-for-Class-10-Maths-Chapter-5-Arithmetic-Progressions-Hindi-Medium.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1280\" \/>\n\t<meta property=\"og:image:height\" content=\"720\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@ncertsolguru\" \/>\n<meta name=\"twitter:site\" content=\"@ncertsolguru\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Raju\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"8 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mcq-questions.com\/#website\",\"url\":\"https:\/\/mcq-questions.com\/\",\"name\":\"MCQ Questions\",\"description\":\"MCQ Questions for Class 1 to 12\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mcq-questions.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-5-hindi\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/i2.wp.com\/mcq-questions.com\/wp-content\/uploads\/2019\/09\/NCERT-Solutions-for-Class-10-Maths-Chapter-5-Arithmetic-Progressions-Hindi-Medium.png?fit=1280%2C720&ssl=1\",\"contentUrl\":\"https:\/\/i2.wp.com\/mcq-questions.com\/wp-content\/uploads\/2019\/09\/NCERT-Solutions-for-Class-10-Maths-Chapter-5-Arithmetic-Progressions-Hindi-Medium.png?fit=1280%2C720&ssl=1\",\"width\":1280,\"height\":720,\"caption\":\"NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions (Hindi Medium)\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-5-hindi\/#webpage\",\"url\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-5-hindi\/\",\"name\":\"NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions (Hindi Medium) - 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Here we have given NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions. 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