List of top Questions asked in IIT JAM

A fission device explodes into two pieces of rest masses 𝑚 and 0.5𝑚 with no loss of energy into any other form. These masses move apart respectively with speeds \(\frac{c}{ √13} \) and \(\frac{c}{2}\) , with respect to the stationary frame. If the rest mass of the device is 𝑓𝑚 then 𝑓 is________ (rounded off to two decimal places).

A conducting wire AB of length m has resistance of .6 Ω. It is connected to a voltage source of 0.5 V with negligible resistance as shown in the figure. The corresponding electric and magnetic fields give Poynting vectors 𝑆 (𝑟 ) all around the wire. Surface integral ∫ 𝑆 . 𝑑𝑎 is calculated over a virtual sphere of diameter 0.2 m with its centre on the wire, as shown. The value of the integral is ______W (rounded off to three decimal places)

A metallic sphere of radius 𝑅 is held at electrostatic potential 𝑉. It is enclosed in a concentric thin metallic shell of radius 2𝑅 at potential 2𝑉. If the potential at the distance \(\frac{3}{2}\) 𝑅 from the centre of the sphere is 𝑓𝑉, then the value of 𝑓 is _______ (rounded off to two decimal places).

The Jacobian matrix for transforming from (x, y) to another orthogonal coordinates system (u, v) as shown in the figure is

Consider a system of large number of particles that can be in three energy states with energies 0 meV, 1 meV, and 2 meV. At temperature T = 300 K, the mean energy of the system (in meV) is closest to
Given: Boltzmann constant k_B = 0.086 meVK^-1

The equation \(z^2+\bar{z}^2=4\) in the complex plane (where \(\bar{z}\) is the complex conjugate of z) represents

A rocket (S') moves at a speed \(\frac{c}{2}\)m/s along the positive x-axis, where c is the speed of light. When it crosses the origin, the clocks attached to the rocket and the one with a stationary observer (S) located at x = 0 are both set to zero. If S observes an event at (x, t), the same event occurs in the S' frame at

Consider a classical ideal gas of N molecules in equilibrium at temperature T. Each molecule has two energy levels, -∈ and ∈. The mean energy of the gas is

At a temperature T, let \(\beta\) and \(\kappa\) denote the volume expansivity and isothermal compressibility of a gas, respectively. Then \(\frac{\beta}{\kappa}\) is equal to

The resultant of the binary subtraction 1110101-0011110 is

Consider a particle trapped in a three-dimensional potential well such that U(x, y, z) = 0 for 0 ≤ x ≤ a, 0 ≤ y ≤ a, 0 ≤ z≤a and U(x, y, z) = ∞ everywhere else. The degeneracy of the 5^th excited state is

A particle of mass m and angular momentum L moves in space where its potential energy is U(r) = kr² (k > 0) and r is the radial coordinate.
If the particle moves in a circular orbit, then the radius of the orbit is

Consider a two-dimensional force field
\(\overrightarrow{F}(x,y) = (5x^2 + ay^2 + bxy)\hat{x} + (4x^2 + 4xy + y^2) \hat{y}\).
If the force field is conservative, then the values of a and b are

Consider an electrostatic field \(\overrightarrow{E}\) in a region of space. Identify the INCORRECT statement.

Which one of the following figures correctly depicts the intensity distribution for Fraunhofer diffraction due to a single slit? Here, x denotes the distance from the centre of the central fringe and I denotes the intensity.

The function f(x) = e^sinx is expanded as a Taylor series in x, around x = 0, in the form f(x) = \(\sum^{\infin}_{n=0}a_nx^n\). The value of a₀ + a₁ + a₂ is

Consider a unit circle C in the xy plane, centered at the origin. The value of the integral \(\oint\)[(sin x - y)dx - (sin y - x)dy] over the circle C, traversed anticlockwise, is

The current through a series RL circuit, subjected to a constant emf \(\epsilon\), obeys \(L\frac{di}{dt}+iR=\epsilon\). Let L=1mH, R=1k\(\Omega\) and \(\epsilon\)=1V. The initial condition is i(0)=0. At t=1\(\mu s\), the current in mA is

An ideal gas in equilibrium at temperature T expands isothermally to twice its initial volume. If ΔS, ΔU and ΔF denote the changes in its entropy, internal energy and Helmholtz free energy respectively, then

In a dilute gas, the number of molecules with free path length ≥ x is given by N(x) = N₀e^-x/λ, where N₀ is the total number of molecules and A is the mean free path. The fraction of molecules with free path lengths between λ and 2λ is

Consider a particle of mass m moving in a plane with a constant radial speed \(\dot{r}\) and a constant angular speed \(\dot{\theta}\). The acceleration of the particle in (r,\(\theta\)) coordinates is

A planet of mass m moves in an elliptical orbit. Its maximum and minimum distances from the Sun are R and r, respectively. Let G denote the universal gravitational constant, and M the mass of the Sun. Assuming M >> m, the angular momentum of the planet with respect to the center of the Sun is

Consider a conical region of height h and base radius R with its vertex at the origin. Let the outward normal to its base be along the positive z-axis, as shown in the figure. A uniform magnetic field, \(\overrightarrow{B}=B_0\hat{z}\) exists everywhere. Then the magnetic flux through the base (\(\Phi_b\)) and that through the curved surface of the cone (\(\Phi_c\)) are

A radioactive nucleus has a decay constant \(\lambda\) and its radioactive daughter nucleus has a decay constant 10\(\lambda\). At time t = 0, N₀ is the number of parent nuclei and there are no daughter nuclei present. N₁(t) and N₂(t) are the number of parent and daughter nuclei present at time t, respectively The ratio \(\frac{N_2(t)}{N_1(t)}\) is

A uniform magnetic field \(\overrightarrow{B}=B_0\hat{z}\), where \(B_0\gt0\) exists as shown in the figure. A charged particle of mass m and charge \(q(q\gt0)\) is released at the origin, in the yz-plane, with a velocity \(\overrightarrow v\) directed at an angle \(\theta\)= 45° with respect to the positive z-axis. Ignoring gravity, which one of the following is TRUE.