A prism of angle $75^{\circ}$ and refractive index $\sqrt{3}$ is coated with thin film of refractive index 1.5 only at the back exit surface. To have total internal reflection at the back exit surface the incident angle must be $\_\_\_\_$

$\left(\sin 15^{\circ}=0.25\right.$ and $\left.\sin 25^{\circ}=0.43\right)$

The current passing through a conducting loop in the form of equilateral triangle of side $4 \sqrt{3} \mathrm{~cm}$ is 2 A . The magnetic field at its centroid is $\alpha \times 10^{-5} \mathrm{~T}$. The value of $\alpha$ is $\_\_\_\_$ .

(Given : $\mu_{\mathrm{o}}=4 \pi \times 10^{-7}$ SI units)

$$ \text { For the given logic gate circuit, which of the following is the correct truth table? } $$

A small metallic sphere of diameter 2 mm and density $10.5 \mathrm{~g} / \mathrm{cm}^3$ is dropped in glycerine having viscosity 10 Poise and density $1.5 \mathrm{~g} / \mathrm{cm}^3$ respectively. The terminal velocity attained by the sphere is $\_\_\_\_$ $\mathrm{cm} / \mathrm{s}$.

$\left(\pi=\frac{22}{7}\right.$ and $\left.g=10 \mathrm{~m} / \mathrm{s}^2\right)$