if ` x = a cos^3 theta sin^2 theta and y = a cos^2 theta sin^3 theta` and `(x^2 + y^2)^p/(xy)^q` is independent of `theta`, then (A) `4p=5q` (B) `5p=4q` (C) `p+q=9` (D) `pq=20`

Explanation

To solve the problem, we need to analyze the expressions given for \( x \) and \( y \) and determine the conditions under which \( \frac{(x^2 + y^2)^p}{(xy)^q} \) is independent of \( \theta \).

### Step-by-Step Solution:

1. **Given Expressions**:
\[ x = a \cos^3 \theta \sin^2 \theta \]
...