In a photoelectric experiment a parallel beam of monochromatic light with power of $$200$$ $$W$$ is incident on a perfectly absorbing cathode of work function $$6.25$$ $$ev.$$ The frequency of light is just above the threshold frequency so that the photoelectrons are emitted with negligible kinetic energy. Assume that the photoelectron emission efficiency is $$100\% $$. A potential difference of $$500$$ $$V$$ is applied between the cathode and the anode. All the emitted electrons are incident normally on the anode and are absorbed. The anode experiences a force $$F = n \times {10^{ - 4}}$$ $$N$$ due to the impact of the electrons. The value of $$n$$ is ______________. Mass of the electron $${M_e} = 9 \times {10^{ - 31}}\,kg$$ and $$1.0eV = 1.6 \times {10^{ - 19}}\,J.$$

The electric field $$E$$ is measured at a point $$P(0,0,d)$$ generated due to various charge distributions and the dependence of $$E$$ on $$d$$ is found to be different for different charge distributions. List-$${\rm I}$$ contains different relations between $$E$$ and $$d$$. List-$${\rm II}$$ describes different electric charge distributions, along with their locations. Match the functions in List-$${\rm I}$$ with the related charge distributions in List-$${\rm II}$$.

LIST - I		LIST - II
P.	$$E$$ is independent of $$d$$	1.	A point charge Q at the origin
Q.	$$E\, \propto \,1/d$$	2.	A small dipole with point charges $$Q$$ at $$\left( {0,0,l} \right)$$ and $$-Q$$ at $$\left( {0,0, - l} \right).$$ Take $$2l < < d$$
R.	$$E\, \propto \,1/{d^2}$$	3.	An infinite line charge coincident with the x-axis, with uniform linear charge density $$\lambda $$
S.	$$E\, \propto \,1/{d^3}$$	4.	Two infinite wires carrying uniform linear charge density parallel to the $$x$$-axis. The one along $$\left( {y = 0,z = l} \right)$$ has a charge density $$ + \lambda $$ and the one along $$\left( {y = 0,z = - l} \right)$$ has a charge density Take
		5.	Infinite plane charge coincident with the $$xy$$-plane with uniform surface charge density

A planet of mass $$M,$$ has two natural satellites with masses $${m_1}$$ and $${m_2}.$$ The radii of their circular orbits are $${R_1}$$ and $${R_2}$$ respectively, Ignore the gravitational force between the satellites. Define $${v_1},{L_1},{K_1}$$ and $${T_1}$$ to be , respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite $$1$$; and $${v_2},{L_2},{K_2},$$ and $${T_2}$$ to be the corresponding quantities of satellite $$2.$$ Given $${m_1}/{m_2} = 2$$ and $${R_1}/{R_2} = 1/4,$$ match the ratios in List-$${\rm I}$$ to the numbers in List-$${\rm II}.$$

LIST - I		LIST - II
P.	v1/v2	1.	1/8
Q.	L1/L2	2.	1
R.	K1/K2	3.	2
S.	T1/T2	4.	8

One mole of a monatomic ideal gas undergoes four thermodynamic processes as shown schematically in the $$PV$$-diagram below. Among these four processes, one is isobaric, one is isochoric, one is isothermal and one is adiabatic. Match the processes mentioned in List-I with the corresponding statements in List-II.

LIST - I		LIST - II
P.	In process I	1.	Work done by the gas is zero
Q.	In process II	2.	Temperature of the gas remains unchanged
R.	In process III	3.	No heat is exchanged between the gas and its surroundings
S.	In process IV	4.	Work done by the gas is 6P0V0