Class XI Chapter 8 – Binomial Theorem Maths ______________________________________________________________________________ Solution **11**: It is known that T C a b r1 n nr r r Assuming that . r 1 th Tr 1 term, , in the binomial expansion of n r 1 th n x occurs in the 2n 2 2 1 1 n r r n r r r r T C x C x Comparing the indices of x Therefore, the coefficient of 2n C n in n x n x and in 2 n ! 2 n ! 2 n ! 2 ....... 1 n! 2 n n ! n! n! n! Assuming that n x occurs in the 2 1 n T C x C x 2n 2 1 1 n k k k k k k Comparing the indices of x Therefore, the coefficient of in a b term of the expansion of 2 Tr 1 , we obtain r n in the expansion of 2 n x k 1 th and in 1 x n is 1 x term of the expansion of 2 1 Tk 1 , we obtain k n 1 x n n x in the expansion of 2 1 2n 1 2n 1 ! 2n 1 ! Cn n! 2n 1 n ! n! n 1 ! 1 2 2 n. 2n 1 ! 2 n ! 2 n ! ....... 2 2 n. n! n 1 ! 2. n! n! 2 n! From (1) and (2) , it is observed that 1 2 C 2n 2n 1 n C 2 C 2n 2n 1 n n C Therefore, the coefficient of expansion of 2 1 Hence proved. n 1 x n . n x expansion of 1 x 2 n is 1 x n n is given by , we obtain , we obtain is twice the coefficient of n x in the Question 12: Find a positive value of m for which the coefficient of Solution 12: It is known that 1 th 1 x 2 x in the expansion r term, T , in the binomial expansion of a b n r 1 m is 6. is given by 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 ______________________________________________________________________________ T C a b r1 n nr r r Assuming that . 2 x occurs in the m T C x C x m 1 1 m r r r r r r Comparing the indices of x in Therefore, the coefficient of 2 x It is given that the coefficient of m C 2 6 m! 6 2! m 2 ! m m m 2m 2 ! m m1 12 2 m m 1 2 ! 6 12 0 2 m m m 4 3 12 0 m m 4 3 m 4 0 m 4 m 3 0 m 4 0 or m 3 0 m 4 or m 3 r 1 th 2 x and in is m C2 term of the expansion of Tr 1 , we obtain 1 x r 2 2 x in the expansion Thus, the positive value of m, for which the coefficient of 4. m 2 x is 6. 1 x m , we obtain in the expansion 1 x m is 6, is 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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