Consider the following statements $A$ and $B$ and identify the correct answer given below:
$(A)$ $A$ body initially at rest is acted upon by a constant force. The rate of change of its kinetic energy varies linearly with time.
$(B)$ When a body is at rest,it must be in equilibrium.

$A$ body is sliding down a rough inclined plane. The coefficient of friction between the body and the plane is $0.5$. The ratio of the net force required for the body to slide down and the normal reaction on the body is $1:2$. Then the angle of the inclined plane is: (in $^{\circ}$)

If $ad \neq 0$ and two of the lines represented by $ax^3+3bx^2y+3cxy^2+dy^3=0$ are perpendicular,then

Which of the following transitions in a hydrogen atom emits a photon of the highest frequency?

$A$ star initially has $10^{40}$ deuterons. It produces energy via the processes:
${}_1H^2 + {}_1H^2 \to {}_1H^3 + p$
${}_1H^2 + {}_1H^3 \to {}_2He^4 + n$
The masses of the nuclei are as follows: $M(H^2) = 2.014 \, amu$,$M(p) = 1.007 \, amu$,$M(n) = 1.008 \, amu$,$M(He^4) = 4.001 \, amu$. If the average power radiated by the star is $10^{16} \, W$,the deuteron supply of the star is exhausted in a time of the order of:

Two small drops of mercury,each of radius $R$,coalesce to form a single large drop. The ratio of the total surface energies before and after the change is