A planet having mass $$9 \mathrm{Me}$$ and radius $$4 \mathrm{R}_{\mathrm{e}}$$, where $$\mathrm{Me}$$ and $$\mathrm{Re}$$ are mass and radius of earth respectively, has escape velocity in $$\mathrm{km} / \mathrm{s}$$ given by:

(Given escape velocity on earth $$\mathrm{V}_{\mathrm{e}}=11.2 \times 10^{3} \mathrm{~m} / \mathrm{s}$$ )

The figure shows a liquid of given density flowing steadily in horizontal tube of varying cross - section. Cross sectional areas at $$\mathrm{A}$$ is $$1.5 \mathrm{~cm}^{2}$$, and $$\mathrm{B}$$ is $$25 \mathrm{~mm}^{2}$$, if the speed of liquid at $$\mathrm{B}$$ is $$60 \mathrm{~cm} / \mathrm{s}$$ then $$\left(\mathrm{P}_{\mathrm{A}}-\mathrm{P}_{\mathrm{B}}\right)$$ is :

(Given $$\mathrm{P}_{\mathrm{A}}$$ and $$\mathrm{P}_{\mathrm{B}}$$ are liquid pressures at $$\mathrm{A}$$ and $$\mathrm{B}$$% points.

density $$\rho=1000 \mathrm{~kg} \mathrm{~m}^{-3}$$

$$\mathrm{A}$$ and $$\mathrm{B}$$ are on the axis of tube

A vessel of depth '$$d$$' is half filled with oil of refractive index $$n_{1}$$ and the other half is filled with water of refractive index $$n_{2}$$. The apparent depth of this vessel when viewed from above will be-

The difference between threshold wavelengths for two metal surfaces $$\mathrm{A}$$ and $$\mathrm{B}$$ having work function $$\phi_{A}=9 ~\mathrm{eV}$$ and $$\phi_{B}=4 \cdot 5 ~\mathrm{eV}$$ in $$\mathrm{nm}$$ is:

$$\{$$ Given, hc $$=1242 ~\mathrm{eV} \mathrm{nm}\}$$