There are two identical small holes of cross-sectional area $a$ on the opposite sides of a tank containing a liquid of density $\rho$. The difference in height between the holes is $h$. The tank is resting on a smooth horizontal surface. The horizontal force which will have to be applied on the tank to keep it in equilibrium is

Regarding the molecular orbital $(MO)$ energy levels for homonuclear diatomic molecules, the $\text{INCORRECT}$ statement$(s)$ is$($are$)$
$(A)$ Bond order of $Ne _2$ is zero.
$(B)$ The highest occupied molecular orbital $\text{(HOMO)}$ of $F_2$ is $\sigma$-type.
$(C)$ Bond energy of $O _2^{+}$is smaller than the bond energy of $O _2$.
$(D)$ Bond length of $Li _2$ is larger than the bond length of $B _2$

The sensitivity of a galvanometer is $60 \text{ div/A}$. When a shunt is used,its sensitivity becomes $10 \text{ div/A}$. If the resistance of the galvanometer is $20 \ \Omega$,then the value of the shunt used is: (in $\Omega$)

If $\alpha$ and $\beta$ are imaginary cube roots of unity,then the value of $\alpha^4 + \beta^{28} + \frac{1}{\alpha\beta}$ is:

Which one of the following is employed as a tranquilizer drug?

If $y=\tan ^{-1}\left(\frac{\sqrt{1+a^2 x^2}-1}{a x}\right)$,then $\left(1+a^2 x^2\right) y^{\prime \prime}+2 a^2 x y^{\prime}$ is equal to