List of top Questions asked in IIT JAM PH- 2019

The amount of work done to increase the speed of an electron from \( v = c/3 \) to \( v = 2c/3 \) is \[ c = 3 \times 10^8 \, \text{m/s}, \text{ rest mass of electron is } 0.511 \, \text{MeV} \]

For a quantum particle confined inside a cubic box of side \( L \), the ground state energy is given by \( E_0 \). The energy of the first excited state is

In a heat engine based on the Carnot cycle, heat is added to the working substance at constant

Isothermal compressibility is given by

For using a transistor as an amplifier, choose the correct option regarding the resistances of base-emitter \( (R_{BE}) \) and base-collector \( (R_{BC}) \) junctions.

A thin lens of refractive index \( \frac{3}{2} \) is kept inside a liquid of refractive index \( \frac{4}{3} \). If the focal length of the lens in air is 10 cm, then its focal length inside the liquid is

The Fermi-Dirac distribution function \( [n(\epsilon)] \) is \[ n(\epsilon) = \frac{1}{e^{(\epsilon - \epsilon_F) / k_B T} + 1} \] where \( k_B \) is the Boltzmann constant, \( T \) is the temperature and \( \epsilon_F \) is the Fermi energy.

If \( \phi(x,y,z) \) is a scalar function which satisfies the Laplace equation, then the gradient of \( \phi \) is

The function \( f(x) = \frac{8x}{x^2 + 9} \) is continuous everywhere except at