Question

The smallest natural number n, such that the coefficient of $x$ in the expansion of ${\left(x^2+\frac{1}{x^3}\right)}^n$ is ${}^n{C}_{23}$ , is :

• A. 35
• B. 38
• C. 23
• D. 58

Answer 1

Answer: (B)

$T_r={\sum }_{r=0}^n{}^n{C}_r{x}^{2n-2r}.x^{-3r}$
2n - 5r = 1 $\Rightarrow$ $2n=5r+1$
for $r=15$ $n=38$ smallest value of $n$ is $38$.