If the coefficient of 4th and 13th terms in the expansion of $\left(x^2 \, + \, \dfrac{1}{x}\right)^n$ be equal then find the term which is independent of x.

#### Solution

$^nC_3 \, = \, ^nC_{12} \, \Rightarrow \, n \, = \, 15$
$\left ( x^2 \, + \, \dfrac{1}{x} \right )^{15}.$  We have to find the term independent of x . It will be 11th term
$T_{11} \, = \, ^{15}C_{10} \, (x^2)^5 \, \left (\dfrac{1}{x} \right )^{10} \, = \, ^{15}C_5 \, = \, 3003$