The threshold frequency of a metal with work function \(6.63\  \mathrm{eV}\) is:

Match the LIST-I with LIST-II

LIST-I	LIST-II
(A) Boltzmann constant	I. \(\mathrm{ML}^2 \mathrm{~T}^{-1}\)
(B) Coefficient of viscosity	II. \(\mathrm{MLT}^{-3} \mathrm{~K}^{-1}\)
(C) Planck's constant	III. \(\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\)
(D) Thermal conductivity	IV. \(\mathrm{ML}^{-1} \mathrm{~T}^{-1}\)

Choose the correct answer from the options given below :

As per the given figure, a small ball \(P\) slides down the quadrant of a circle and hits the other ball \(Q\) of equal mass which is initially at rest. Neglecting the effect of friction and assume the collision to be elastic, the velocity of ball \(Q\) after collision will be \(............\,m/s\) \(:\left( g =10\,m / s ^2\right)\)

A convex lens is made from glass material having refractive index of \(1.4\) with same radius of curvature on both sides. The ratio of its focal length and radius of curvature is ______.

When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises upto certain height h. If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by 1% each, then the height of the liquid in the tube will change by __________ %.

Four identical particles of mass \(m\) are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is \(\left(\frac{2 \sqrt{2}+1}{32}\right) \frac{\mathrm{Gm}^2}{\mathrm{~L}^2}\), the length of the sides of the square is _______.

Sliding contact of a potentiometer is in the middle of the potentiometer wire having resistance \(R_p=1 \Omega\) as shown in the figure. An external resistance of \(R_e=2 \Omega\) is connected via the sliding contact. The electric current in the circuit is :

A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The rational between temperature and volume for the process is \(TV^x =\) constant, then \(x\) is

In figure, the optical fiber is \(I = 2\,m\) long and has a diameter of \(d = 20\,\mu \,m\). If a ray of light is incident on one end of the fiber at angle \({\theta _1} = {40^o}\) , the number of reflection it makes before emerging from the other end is close to

Three blocks \(\mathrm{M}_1, \mathrm{M}_2, \mathrm{M}_3\) having masses \(4 \mathrm{~kg}, 6 \mathrm{~kg}\) and \(10 \mathrm{~kg}\) respectively are hanging from a smooth pully using rope 1,2 and 3 as shown in figure. The tension in the rope \(1, \mathrm{~T}_1\) when they are moving upward with acceleration of \(2 \mathrm{~ms}^{-2}\) is _______ \(\mathrm{N}\) (if \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) )

Match the LIST-I with LIST-II.

LIST-I	LIST-II
(A) \(_0^1n + _{92}^{235}U \rightarrow _{54}^{140}Xe + _{38}^{94}Sr + 2_0^1n\)	(I) Chemical reaction
(B) \(2H_2 + O_2 \rightarrow 2H_2O\)	(II) Fusion with +ve Q value
(C) \(_1^2H + _1^2H \rightarrow _2^3He + _0^1n\)	(III) Fission
(D) \(_1^1H + _1^3H \rightarrow _1^2H + _1^2H\)	(IV) Fusion with -ve Q value

Choose the correct answer from the options given below :