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Question: If in the expansion of\(\frac{2}{5}\), the coefficient of x and \(\frac{\sqrt{2}}{5}\)are 3 and – 6 ...

If in the expansion of25\frac{2}{5}, the coefficient of x and 25\frac{\sqrt{2}}{5}are 3 and – 6 respectively, then m is.

A

6

B

9

C

12

D

24

Answer

12

Explanation

Solution

nCknC_{k}

nCnk1nC_{n - k - 1}

9950+1005099^{50} + 100^{50}+.........

Given, m – n = 3 or n = m – 3

Hence 10150101^{50}

9950+1005099^{50} + 100^{50}

10150101^{50}

(1+x)nnx1(1 + x)^{n} - nx - 1