List of top Questions asked in IIT JAM

The figure shows a circuit containing two diodes \(D_1\) and \(D_2\) with threshold voltages \(V_{TH}\) of 0.7 V and 0.3 V, respectively. Considering the simplified diode model, which assumes diode I–V characteristics as shown in the plot on the right, the current through the resistor \(R\) is ......... µA.

If a function \(y(x)\) is described by the initial-value problem, \(\dfrac{d^2y}{dx^2} + 5\dfrac{dy}{dx} + 6y = 0\), with initial conditions \(y(0) = 2\) and \(\dfrac{dy}{dx}\bigg|_{x=0} = 0\), then the value of \(y\) at \(x = 1\) is ................. . (Round off to 2 decimal places)

A vehicle of mass 600 kg with an engine operating at constant power \(P\) accelerates from rest on a straight horizontal road. The vehicle covers a distance of 600 m in 1 minute. Neglecting all losses, the magnitude of \(P\) is ............. kW. (Round off to 2 decimal places)

The angular momentum of a particle relative to the origin varies with time (\(t\)) as \(\vec{L} = (4\hat{i} + \alpha t^2 \hat{j})\, \mathrm{kg \cdot m}^2/\mathrm{s}\), where \(\alpha = 1\, \mathrm{kg \cdot m}^2/\mathrm{s}^3\). The angle between \(\vec{L}\) and the torque acting on the particle becomes \(45^\circ\) after a time of ............ s.

Two transverse waves \(y_1 = 5 \cos(kx - \omega t)\) cm and \(y_2 = 5 \cos(kx + \omega t)\) cm, travel on a string along the x-axis. If the speed of a point at \(x = 0\) is zero at \(t = 0\,s,\ 0.25\,s,\) and \(0.5\,s,\) then the minimum frequency of the waves is ............ Hz.

For the AC circuit shown in the figure, \(R = 100\, \text{k}\Omega\) and \(C = 10\, \text{pF}\), the phase difference between \(V_{in}\) and \(V_{out}\) is \(90^\circ\) at the input signal frequency of ............. kHz. (Round off to 2 decimal places)

The magnetic fields in tesla in the two regions separated by the \(z = 0\) plane are given by \(\vec{B_1} = 3\hat{i} + 5\hat{j}\) and \(\vec{B_2} = 8\hat{i} + 3\hat{j} + 5\hat{k}\). The magnitude of the surface current density at the interface between the two regions is \(\alpha \times 10^6\, \text{A/m}\). Given the permeability of free space \(\mu_0 = 4\pi \times 10^{-7}\, \text{N/A}^2\), the value of \(\alpha\) is ............... . (Round off to 2 decimal places)

A body at a temperature \(T\) is brought into contact with a reservoir at temperature \(2T\). Thermal equilibrium is established at constant pressure. The heat capacity of the body at constant pressure is \(C_p\). The total change in entropy of the body and the reservoir in units of \(C_p\) is ............ (Round off to 2 decimal places)

One mole of an ideal monatomic gas at pressure \(P\), volume \(V\) and temperature \(T\) is expanded isothermally to volume \(4V\). Thereafter, the gas is heated isochorically (at constant volume) till its pressure becomes \(P\). If \(R\) is the universal gas constant, the total heat transfer in the process, in units of \(RT\), is ................... (Round off to 2 decimal places)

In the transistor circuit given in the figure, the emitter-base junction has a voltage drop of 0.7 V. A collector-emitter voltage of 14 V reverse biases the collector. Assuming the collector current to be the same as the emitter current, the value of \(R_B\) is ........... k\(\Omega\).

The radioactive nuclei \({}^{40}\text{K}\) decay to \({}^{40}\text{Ar}\) with a half-life of \(1.25 \times 10^9\) years. The \({}^{40}\text{K}/{}^{40}\text{Ar}\) isotopic ratio for a particular rock is found to be 50. The age of the rock is \(m \times 10^7\) years. The value of \(m\) is .............. (Round off to 2 decimal places)

Consider a retarder with refractive indices \(n_e = 1.551\) and \(n_o = 1.542\) along the extraordinary and ordinary axes, respectively. The thickness of this retarder for which a left circularly polarized light of wavelength \(600 \, \text{nm}\) will be converted into a right circularly polarized light is ........... µm. (Round off to 2 decimal places).

Water flows in a horizontal pipe in a streamlined manner at an absolute pressure of \(4 \times 10^5 \, \text{Pa}\) and speed of \(6 \, \text{m/s}\). If it exits the pipe at a pressure of \(10^5 \, \text{Pa}\), the speed of water at the exit point is .......... m/s (Round off to 1 decimal place).
(The density of water is \(1000 \, \text{kg/m}^3\))

Consider a thin bi-convex lens of relative refractive index \(n = 1.5\). The radius of curvature of one surface of the lens is twice that of the other. The magnitude of larger radius of curvature in units of the focal length of the lens is ............. (Round off to 1 decimal place).

One mole of an ideal gas having specific heat ratio (\(\gamma\)) of 1.6 is mixed with one mole of another ideal gas having specific heat ratio of 1.4. If \(C_V\) and \(C_P\) are the molar specific heat capacities of the gas mixture at constant volume and pressure, respectively, which of the following is/are correct? (\(R\) denotes the universal gas constant.)

A spherical dielectric shell with inner radius \(a\) and outer radius \(b\), has polarization \(\vec{P} = \dfrac{k}{r^2}\hat{r}\), where \(k\) is a constant and \(\hat{r}\) is the unit vector along the radial direction. Which of the following statements is/are correct?

For electric and magnetic fields, \(\vec{E}\) and \(\vec{B}\), due to a charge density \(\rho(\vec{r},t)\) and a current density \(\vec{J}(\vec{r},t)\), which of the following relations is/are always correct?

An object executes simple harmonic motion along the x-direction with angular frequency \(\omega\) and amplitude \(a\). The speed of the object is 4 cm/s and 2 cm/s when it is at distances 2 cm and 6 cm, respectively, from the equilibrium position. Which of the following is/are correct?

A thin rod of uniform density and length \(2\sqrt{3}\, \text{m}\) is undergoing small oscillations about a pivot point. The time period of oscillation (\(T_m\)) is minimum when the distance of the pivot point from the center-of-mass of the rod is \(x_m\). Which of the following is/are correct? (Assume acceleration due to gravity \(g = 10\, \text{m/s}^2\))

Consider a vector function \(\vec{u}(\vec{r})\) and two scalar functions \(\psi(\vec{r})\) and \(\phi(\vec{r})\). The unit vector \(\hat{n}\) is normal to the elementary surface \(dS\), \(dV\) is an infinitesimal volume, \(d\vec{l}\) is an infinitesimal line element, and \(\partial / \partial n\) denotes the partial derivative along \(\hat{n}\). Which of the following identities is/are correct?

In the circuit shown in the figure, both OPAMPs are ideal. The output for the circuit \(V_{out}\) is:

For an unbiased Silicon \(n\text{-}p\text{-}n\) transistor in thermal equilibrium, which one of the following electronic energy band diagrams is correct? (\(E_c\) = conduction band minimum, \(E_v\) = valence band maximum, \(E_F\) = Fermi level.)

Consider a one-dimensional infinite potential well of width \(a\). This system contains five non-interacting electrons, each of mass \(m\), at temperature \(T = 0 \, K\). The energy of the highest occupied state is:

A linear operator \(\hat{O}\) acts on two orthonormal states of a system \(\psi_1\) and \(\psi_2\) as per the following: \[ \hat{O}\psi_1 = \psi_2, \hat{O}\psi_2 = \frac{1}{\sqrt{2}}(\psi_1 + \psi_2) \] The system is in a superposed state defined by \[ \psi = \frac{1}{\sqrt{2}}\psi_1 + \frac{i}{\sqrt{2}}\psi_2 \] The expectation value of \(\hat{O}\) in the state \(\psi\) is:

A thin conducting square loop of side \(L\) is placed in the first quadrant of the \(xy\)-plane with one of the vertices at the origin. If a changing magnetic field \(\vec{B}(t) = B_0(52yt\,\hat{x} + xzt\,\hat{y} + 3y^2t^2\,\hat{z})\) is applied, where \(B_0\) is a constant, then the magnitude of the induced electromotive force in the loop is: