$A$ bag contains $5$ black balls,$4$ white balls and $3$ red balls. If a ball is selected at random,the probability that it is a black or a red ball is:

$\int_0^{\pi / 2} \frac{d x}{1+\tan ^3 x}$ is equal to :

$A$ horizontal uniform glass tube of $100 \ cm$ length, sealed at both ends, contains a $10 \ cm$ mercury column in the middle. The initial temperature and pressure of air on either side of the mercury column are $31^{\circ} C$ and $76 \ cm$ of mercury, respectively. If the air column at one end is kept at $0^{\circ} C$ and the other end at $273^{\circ} C$, then the pressure of the air at $0^{\circ} C$ is (in $cm$ of $Hg$):

Which one of the following is most effective in causing the coagulation of an $As_2S_3$ sol?

Two plane mirrors $A$ and $B$ are placed parallel to each other as shown in the figure. $A$ light ray is incident at an angle of $30^{\circ}$ at a point on mirror $A$. The plane of incidence coincides with the plane of the figure. What is the maximum number of reflections (including the first one) the ray will undergo before it emerges?

$A$ pendulum is oscillating with frequency $n$ on the surface of the earth. It is taken to a depth $d = \frac{R}{2}$ below the surface of the earth. What is the new frequency of oscillation at this depth? [$R$ is the radius of the earth]