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Question

Question: Coefficient of \(f = R - \lbrack R\rbrack\) in the expansion of \(4^{2n + 1}\) is....

Coefficient of f=R[R]f = R - \lbrack R\rbrack in the expansion of 42n+14^{2n + 1} is.

A

42n4^{- 2n}

B

(2+1)6(\sqrt{2} + 1)^{6}

C

– 7

D

7

Answer

– 7

Explanation

Solution

Tr+1=8Cr(x)8r(12x)rT _ { r + 1 } = { } ^ { 8 } C _ { r } ( x ) ^ { 8 - r } \left( - \frac { 1 } { 2 x } \right) ^ { r } 100C100-^{100}C_{100}

For coefficient ofx32x^{32},(x41x3)15\left( x^{4} - \frac{1}{x^{3}} \right)^{15}15C515C_{5}

Coefficient of 15C615C_{6}= 15C415C_{4}.