At $x=0.3\,m$

$y=0.02 \cos (\pi / 2+50 \pi \times t) \cos (3 \pi)=-0.02 \cos (\pi / 2+50 \pi \times t)$ (It is

right)

Now compare the given equation by the standard stationary wave equation,

$y=A \cos (\phi+\omega \times t) \cos (2 \pi \lambda \times x)$

$2 \pi \lambda=10 \pi, \lambda=0.2\,m$ (it is also right)

$\text { At } x=0.15\,m$

$y=0.02 \cos (\pi / 2+50 \pi \times t) \cos (\pi / 2)$

and

$v = A \omega=0.02 * 50 \pi=\pi ms ^{-1}$

Hence, option " $C$ " is wrong.