A conducting square loop is placed in a magnetic field $B$ with its plane perpendicular to the field. The sides of the loop start shrinking at a constant rate $\alpha$. The induced emf in the loop at an instant when its side is ' $a$ ' is

If $\operatorname{cosec} \theta = \frac{p+q}{p-q}$,then $\cot \left(\frac{\pi}{4} + \frac{\theta}{2}\right)$ is equal to

Which of the following has the maximum boiling point?

$50 \ mL$ of $H_2O$ is added to $50 \ mL$ of $1 \times 10^{-3} \ M$ barium hydroxide solution. What is the $pH$ of the resulting solution?

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

If $(2+\sin x) \frac{dy}{dx} + (y+1) \cos x = 0$ and $y(0) = 1$,then $y\left(\frac{\pi}{2}\right)$ is