In a photoelectric effect experiment a light of frequency \(1.5\) times the threshold frequency is made to fall on the surface of photosensitive material. Now if the frequency is halved and intensity is doubled, the number of photo electrons emitted will be _______.

For which of the following particles will it be most difficult to experimentally verify the deBroglie relationship?

An electron moves through a uniform magnetic field \(\vec{B}=B_0 \hat{i}+2 B_0 \hat{j} T\). At a particular instant of time, the velocity of electron is \(\overrightarrow{\mathrm{u}}=3 \hat{i}+5 \hat{j} \mathrm{~m} / \mathrm{s}\). If the magnetic force acting on electron is \(\vec{F}=5 e\hat kN\), where \(e\) is the charge of electron, then the value of \(\mathrm{B}_0\) is _______\(\mathrm{T}\).

The vernier constant of Vernier callipers is \(0.1 \,mm\) and it has zero error of \((-0.05) \,cm\). While measuring diameter of a sphere, the main scale reading is \(1.7 \,cm\) and coinciding vernier division is \(5\). The corrected diameter will be ........... \(\times 10^{-2} \,cm\)

A particle starts from origin at \(t=0\) with a velocity \(5 \hat{i} \mathrm{~m} / \mathrm{s}\) and moves in \(x-y\) plane under action of a force which produces a constant acceleration of \((3 \hat{i}+2 \hat{j}) \mathrm{m} / \mathrm{s}^2\). If the \(x\)-coordinate of the particle at that instant is \(84 \mathrm{~m}\), then the speed of the particle at this time is \(\sqrt{\alpha} \mathrm{m} / \mathrm{s}\). The value of \(\alpha\) is___________.

Match the List-I with List-II

	List-I		List-II
A	Radio-wave	I	is produced by Magnetron value
B	Micro-wave	II	Due to change in the vibrational modes of atoms
C	Infrared-wave	II	Due to inner shell electrons moving from higher energy level to lower energy level
D	X-ray	IV	Due to rapid acceleration of electrons

Choose the correct answer from the options given below:

Two resistors \(2 \Omega\) and \(3 \Omega\) are connected in the gaps of bridge as shown in figure. The null point is obtained with the contact of jockey at some point on wire XY . When an unknown resistor is connected in parallel with \(3 \Omega\) resistor, the null point is shifted by 22.5 cm toward Y . The resistance of unknown resistor is _________ \(\Omega\).

The light waves from two coherent sources have same intensity \({I}_{1}={I}_{2}={I}_{0} .\) In interference pattern the intensity of light at minima is zero.What will be the intensity of light at maxima?

Match the LIST-I with LIST-II:

List-I	List-II
A. Spring constant	I. \(ML ^2 T^{-2} K^{-1}\)
B. Thermal conductivity	II. \(ML ^0 T^{-2}\)
C. Boltzmann constant	III. \(ML ^2 T^{-3} A^{-2}\)
D. Inductive reactance	IV. \(MLT ^{-3} K^{-1}\)

Choose the correct answer from the options given below:

The charged particle moving in a uniform magnetic field of \((3\hat{i} + 2\hat{j})\) T has an acceleration \(\left(4\hat{i} - \dfrac{x}{2}\hat{j}\right)\) m/s\(^2\). The value of \(x\) is __________.