List of top Questions asked in IIT JAM PH

Which one of the following is an impossible magnetic field \(\vec{B}\)?
If the motion of a particle is described by \( x = 5 \cos(8\pi t), y = 5 \sin(8\pi t) \) and \( z = 5t \), then the trajectory of the particle is
A $\gamma$-ray photon emitted from a $^{137}$Cs source collides with an electron at rest. If the Compton shift of the photon is $3.25 \times 10^{-13}$ m, then the scattering angle is closest to (Planck’s constant $h = 6.626 \times 10^{-34}$ J s, electron mass $m_e = 9.109 \times 10^{-31}$ kg and velocity of light in free space $c = 3 \times 10^8$ m/s)
During free expansion of an ideal gas under adiabatic condition, the internal energy of the gas
Light of wavelength \(\lambda\) (in free space) propagates through a dispersive medium with refractive index \(n(\lambda) = 1.5 + 0.6\lambda\). The group velocity of a wave traveling inside this medium in units of \(10^8\) m/s is
A red star having radius \( r_R \) at a temperature \( T_R \) and a white star having radius \( r_W \) at a temperature \( T_W \), radiate the same total power. If these stars radiate as perfect black bodies, then
The mass per unit length of a rod (length 2 m) varies as \( \rho = 3 \, \text{kg/m} \). The moment of inertia (in kg m\(^2\)) of the rod about a perpendicular-axis passing through the tip of the rod (at \( x = 0 \)) is
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

The function $f(x)=\begin{cases}-x,\; -\pi<x<0 \\ x,\; 0<x<\pi\end{cases}$ is expanded as a Fourier series of the form $a_0 + \sum_{n=1}^{\infty}a_n\cos(nx)+\sum_{n=1}^{\infty}b_n\sin(nx)$. Which of the following is true? 
 

An infinitely long solenoid, with its axis along $\hat{k}$, carries a current $I$. In addition, there is a uniform line charge density $\lambda$ along the axis. If $\vec{S}$ is the energy flux, in cylindrical coordinates $(\hat{\rho}, \hat{\phi}, \hat{k})$, then
 

Given a spherically symmetric charge density $\rho(r)=\begin{cases}kr^2, & r<R \\ 0, & r>R\end{cases}$ (k being a constant), the electric field for $r<R$ is (take the total charge as $Q$) 
 

A long solenoid is carrying a time dependent current such that the magnetic field inside has the form $\vec{B}(t)=B_0 t^2 \hat{k}$, where $\hat{k}$ is along the axis of the solenoid. The displacement current at the point $P$ on a circle of radius $r$ in a plane perpendicular to the axis

Which one of the following graphs shows the correct variation of $v_o$ with $v_i$? Here, $v_d$ is the voltage drop across the diode and the Op-Amp is assumed to be ideal. 

Which one of the figures correctly represents the T–S diagram of a Carnot engine? 

Two vehicles A and B are approaching an observer O at rest with equal speed as shown in the figure. Both vehicles have identical sirens blowing at a frequency $f_s$. The observer hears these sirens at frequency $f_A$ and $f_B$, respectively. Which one of the following is correct? 

Which one of the following arrangements of optical components can be used to distinguish between unpolarised light and circularly polarised light? 

Three planets orbit a star at distances $a,\;4a,\;9a$. Their orbital periods are proportional to $r^{3/2}$. If the smallest planet has period $T$, after how long will all three be aligned again?