Find (a) the coefficient of `x^7 ` in the epansion of `(ax^2+1/(bx))^11`
(b) The coefficient of `x^(-7)` in the expansion of `(ax^2+1/(bx))^11`
Also , find the relation between a and b, so that these coefficients are equal .

Explanation

To solve the problem, we need to find the coefficients of \(x^7\) and \(x^{-7}\) in the expansion of \((ax^2 + \frac{1}{bx})^{11}\).

### Step-by-Step Solution

**(a) Coefficient of \(x^7\)**

1. **Identify the General Term**: The general term \(T_{r+1}\) in the binomial expansion of \((ax^2 + \frac{1}{bx})^{11}\) is given by:
\[
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