The value of $\int\limits_{-\pi / 2}^{\pi / 2}\left(p \sin ^3 x+q \sin ^4 x+r \sin ^5 x\right) d x$ depends on:

p q r p and q

q

$I=\int\limits_{-\pi / 2}^{\pi / 2}\left(p \sin ^3 x+q \sin ^4 x+r \sin ^5 x\right) d x$ $=q \int\limits_{-\pi / 2}^{\pi / 2} \sin ^4 x dx = q $  (Since sin3x and sin5x are odd functions) Hence (2) is the correct answer.