Class XI Chapter 8 – Binomial Theorem Maths ______________________________________________________________________________ Miscellaneous Exercise Question 1: Find a, b and n in the expansion of a b n if the first three terms of the expansion are 729, 7290 and 30375, respectively. Solution 1: It is known that term, T C a b n nr r . r1 r r 1 th Tr 1 , in the binomial expansion of n a b is given by The first three terms of the expansion are given as 729, 7290 and 30375 respectively. Therefore, we obtain T C a b a n n0 0 n 1 0 729 ...... 1 T C a b na b n n1 1 n1 2 1 7290 ...... 2 n n2 2 n n1 n2 2 T2 C1a b a b 30375 ...... 3 2 Dividing (2) by (1), we obtain na a n1 n b 7290 729 nb 10 ....... 4 a Dividing (3) by (2), we obtain 2 2 n n n 1 a b 30375 n1 2na b 7290 n1 b 30375 2a 7290 n1 b 30375 2 25 a 7290 3 nb b 25 a a 3 25 10 b Using 4 a 3 b 25 5 10 ..... 5 a 3 3 From (4) and (5), we obtain n 5 10 3 n 6 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 ______________________________________________________________________________ Substituting 729 n 6 a 6 729 3 From (5), we obtain b 5 b 5 3 3 Thus, a3, b 5, and in equation (1), we obtain n 6 . 6 a Question 2: Find a Solution 2: if the coefficients of It is known that T C a b n nr r . r1 r Assuming that 2 x r 1 th 2 x term, and 3 x in the expansion of 9 3 ax are equal. T , in the binomial expansion of n r 1 occurs in the r 1 th 9 9 9 9 1 3 r r 3 r r r r r r T C ax C a x Comparing the indices of x r 2 Thus, the coefficient of 9! 2!7! 2 x is in 2 x 3 3 363 and in 9 9 2 2 7 2 7 2 C2 a a a Assuming that 3 x occurs in the k 1 th 9 9 9 9 1 3 k k 3 k k k k k k T C ax C a x Comparing the indices of x Thus, the coefficient of 9! 3!6! 3 x is in 3 x 3 3 843 and in 9 9 3 3 6 3 6 3 C3 a a a It is given that the coefficient of 6 3 7 2 84 3 a 36 3 84a 363 363 104 a 84 84 a 2 x and a b term in the expansion of 9 Tr 1 , we obtain 3 ax term in the expansion of 9 Tk 1 , we obtain k 3 3 x are the same. 3 ax is given by , we obtain , we obtain Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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Class XI Chapter 12 - Introduction

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Class XI Chapter 13 - Limits and De

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Class XI Chapter 15 - Statistics Ma

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