Class XI Chapter 8 – Binomial Theorem Maths ______________________________________________________________________________ 4 4 4 4 3 4 2 2 4 3 4 4 a b C a C a b C a b C ab C b 0 1 2 3 4 4 4 4 4 3 4 2 2 4 3 4 4 a b C a C a b C a b C ab C b 0 1 2 3 4 4 4 4 4 4 3 4 2 2 4 3 4 4 4 4 4 3 4 2 2 4 3 4 4 0 1 2 3 4 0 1 2 3 4 a b a b C a C a b C a b C ab C b C a C a b C a b C ab C b 4 3 4 3 3 3 C1a b C3ab a b ab 2 2 4 4 8ab a By putting b 2 2 a 3 and b 2 , we obtain 4 4 2 2 3 2 3 2 8 3 2 3 2 8 63 2 40 6 Question 12: 6 6 Find x1 x1 Solution 12: 6 6 2 1 2 1 . Hence or otherwise evaluate. Using Binomial Theorem, the expression, 6 x 1 and 6 6 6 6 6 5 6 4 6 3 6 2 6 6 x 1 C x C x C x C x C x C x C x 1 0 1 2 3 4 5 6 6 6 6 6 5 6 4 6 3 6 2 6 6 1 x C x C x C x C x C x C x C 0 1 2 3 4 5 6 6 6 6 6 6 4 6 2 6 0 2 4 6 x 1 x 1 2 C x C x C x C 6 4 2 2 x 15x 15x 1 By putting x 2 we obtain 2 1 6 2 1 6 2 2 6 15 2 4 15 2 2 1 2 8 15 4 15 2 1 2 8 60 30 1 2 99 198 , can be expanded as Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 8 – Binomial Theorem Maths ______________________________________________________________________________ Question 13: Show that Solution 13: n 1 9 8n 9 In order to show that where k is some natural number By Binomial Theorem, is divisible by 64, whenever n is a positive integer. n 1 9 8n 9 2 m m m m m m 0 1 2 m 1 a C C a C a .... C a For a 8 and mn1 , we obtain is divisible by 64, it has to be prove that, n1 n1 n1 n1 2 n1 n1 C0 C1 C2 C n 1 18 8 8 .... 8 1 n1 2 n1 n1 n1 9 1 n 1 8 8 C2 C3 8 .... C 1 8 n n 1 n1 n1 n1 n1 9 9 8n 64 C2 C3 8 .... C 1 8 n n 1 n1 n1 n1 n1 9 8n 9 64 k, where k C2 C3 8 .... C 1 8 n n Thus, n 1 9 8n 9 is divisible by 64, whenever n is a positive integer. n 1 9 8n 9 64 is a natural number k , Question 14: Prove that n r0 r n 3 C 4 Solution 14: By Binomial Theorem, n r0 C a b a b n nr r r By putting n r0 n C n r0 r b 3 r and 1 3 13 n r r n r n 3 C 4 Hence proved. r n n n a 1 in the above equation, we obtain Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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