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Question: If in the expansion of \(\left( x^{3} - \frac{2}{\sqrt{x}} \right)^{n}\) a term like x<sup>2</sup> e...

If in the expansion of (x3−2x)n\left( x^{3} - \frac{2}{\sqrt{x}} \right)^{n} a term like x2 exists and 'n' is a double digit number, then least value of 'n' is -

A

-10

B

11

C

12

D

13

Answer

-10

Explanation

Solution

Let the term is Tr+1 = nCr(x3)n-r(−2x)r\left( \frac{- 2}{\sqrt{x}} \right)^{r}

\ 3n – 3r – r/2 = 2 ̃ 3n = 2 + 7r2\frac{7r}{2} ̃ n = 4+7r6\frac{4 + 7r}{6}

least value of n which is double digit = 10