$P V=\frac{1}{3} m n V_{r m s}^{2}=\frac{2}{3} \times \frac{1}{2} m n v_{\text {rms }}^{2}=\frac{2}{3} k T$

Boyle's law state that at constant temperature average $K E$ is constant, So, $v_{\text {rms }}$ Memains unchanged. If volume increases pressure of gas decreases.

i.e., $P V=$ constant .

Charle's law state that if we allow the volume to change to maintain constant pressure the volume will increase with increasing temperature

$\text { i.e., } V=K T$

$\therefore$ Option $(c)$ is correct.