Two waves represented by $y_1 = 10 \sin(200\pi t)$ and $y_2 = 20 \sin(200\pi t + \pi/2)$ are superimposed at a point. The amplitude of the resultant wave is

If the coordinate axes are the bisectors of the angles between the pair of lines $ax^2 + 2hxy + by^2 = 0$ where $h^2 > ab$ and $a \neq b$,then

If the $x$-coordinate of a point $P$ on the line joining the points $Q(2, 2, 1)$ and $R(5, 2, -2)$ is $4$,then the $z$-coordinate of $P$ is:

When acetaldehyde is reacted with $LiAlH_4$,what is the product formed?

In a biprism experiment,if the $5^{\text{th}}$ bright band with wavelength $\lambda_1$ coincides with the $6^{\text{th}}$ dark band with wavelength $\lambda_2$,then the ratio $\left(\frac{\lambda_2}{\lambda_1}\right)$ is:

$A$ $2 ~kg$ ball moving at $24 ~ms^{-1}$ undergoes an inelastic head-on collision with a $4 ~kg$ ball moving in the opposite direction at $48 ~ms^{-1}$. If the coefficient of restitution is $2/3$,what are their velocities in $ms^{-1}$ after the impact?