$P_4O_{10}$ has short and long $P-O$ bonds. The number of short $P=O$ bonds in this compound is

The mean of a set of observations is $\bar{x}$. If each observation is divided by $\alpha$ $(\alpha \neq 0)$ and then increased by $10$,what is the mean of the new set?

Two capacitors $C_1$ and $C_2 = 2C_1$ are connected in a circuit with a switch $S$ and a resistor $R$ as shown in the figure. Initially,the switch is open and $C_1$ holds charge $Q$. The switch is closed. At steady state,the charge on each capacitor will be

Two coherent narrow slits emitting light of wavelength $\lambda$ in the same phase are placed parallel to each other at a small separation of $3\lambda$. The light is collected on a screen $S$ which is placed at a distance $D$ from the slits. Find the smallest distance $x$ from the central point $O$ such that point $P$ is a maxima.

$\int \frac{\cos ^3 x+\cos ^5 x}{\sin ^2 x+\sin ^4 x} d x=$

$A$ man slides down a telegraphic pole with an acceleration equal to one-fourth of the acceleration due to gravity. The frictional force between the man and the pole is equal to which of the following in terms of the man's weight $w$?