$A$ fish looking up through the water sees the outside world,contained in a circular horizon. If the refractive index of water is $\frac{4}{3}$ and the fish is $12 \ cm$ below the water surface,the radius of this circle in $cm$ is

A positive ion $A$ and a negative ion $B$ has charges $6.67 \times 10^{-19}\ {C}$ and $9.6 \times 10^{-10}\ {C}$, and masses $19.2 \times 10^{-27}\ {kg}$ and $9 \times 10^{-27}\ {kg}$ respectively. At an instant, the ions are separated by a certain distance $r$. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is ${P} \times 10^{-13}$, where the value of $P$ is _________ .
(Take $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\ {Nm}^2 {C}^{-1}$ and universal gravitational constant as $6.67 \times 10^{-11}\ {Nm}^2 {kg}^{-2}$)

Mortar is a mixture of which of the following?

The uncertainties in the velocities of two particles $A$ and $B$ are $0.05 \ m/s$ and $0.02 \ m/s$ respectively. The mass of $B$ is five times that of mass $A$. What is the ratio of uncertainties $\left(\frac{\Delta x_A}{\Delta x_B}\right)$ in their positions?

Select the correct option on the basis of the following sentences regarding a gland's function:
$(I)$ Hormones increase alertness.
$(II)$ Hormones increase the heart beat.
$(III)$ Stimulate the breakdown of glycogen.
$(IV)$ Stimulate the breakdown of lipids and proteins.

$A$ plane electromagnetic wave of wave intensity $6 \, W/m^2$ strikes a small mirror of area $40 \, cm^2$,held perpendicular to the approaching wave. The momentum transferred by the wave to the mirror each second will be: