In case of a stationary wave pattern,which of the following statements is $CORRECT$?

$A$ wave represented by the equation $y = a \cos (kx - \omega t)$ is superposed with another wave to form a stationary wave such that the point $x = 0$ is a node. The equation for the other wave is:

$A$ standing wave exists in a string of length $150 \ cm$,which is fixed at both ends with rigid supports. The displacement amplitude of a point at a distance of $10 \ cm$ from one of the ends is $5\sqrt{3} \ mm$. The nearest distance between two points,within the same loop and having a displacement amplitude equal to $5\sqrt{3} \ mm$,is $10 \ cm$. Find the maximum displacement amplitude of the particles in the string (in $mm$).

$A$ standing wave having $3$ nodes and $2$ antinodes is formed between two atoms having a distance of $1.21 \; \mathring{A}$ between them. The wavelength of the standing wave is .... $\mathring{A}$

$A$ progressive wave travelling in the positive $x$-direction given by $y=a \cos (k x-\omega t)$ meets a denser surface at $x=0, t=0$. The reflected wave is then given by

$A$ standing wave with a number of loops is produced on a string fixed at both ends. Which one of the following statements is correct?