List of top Questions asked in Banaras Hindu University Postgraduate Entrance Test

In the TM mode:
For a two-dimensional free electron gas, the electron density \(n\) and Fermi energy \(E_F\) are related as:
In a waveguide, which condition always holds good?
The work done by the force \( \mathbf{F} = (4\hat{i} -3\hat{j} + 2\hat{k}) \) N in giving a 1 nC charge a displacement of \( (10\hat{i} + 2\hat{j} -7\hat{k}) \) m is:
The divergence of the vector field \( \mathbf{P} = x^2 y \hat{i} + xyj \) is:
Radio waves in the frequency range 3 MHz – 30 MHz propagate through which mode of propagation?
What is the major factor for determining whether a medium is free space, lossless dielectric, loss of dielectric or good conductor?
The dominant mode for rectangular waveguide is:
At cut off the JFET channel is:
The circuit shown is used for:
Integration
If the peak rectified voltage from a full-wave rectifier is 15V, the approximate average rectified voltage will be:
A certain JFET has transconductance 4mS with an external AC drain resistance 1.5kΩ, what is the ideal voltage gain?
A certain transistor is to be operated with \( V_{CE} = 6V \). If its maximum power rating is 250 mW, what is the maximum collector current that it can handle?
The correct equivalent symbol for the AND gate with inverted inputs shown below will be:
equivalent symbol for the AND
The eigenvalues of the operator \( \sin \left( a \frac{\partial}{\partial \theta} \right) \) corresponding to the eigenfunction \( \psi_{3,2,-2}(r,\theta,\phi) \) are:
Number of bound states for the system \( V(x) = -V_0 \delta(x-a), V_0>0 \) is:
Which of the following is not correct about Pauli spin matrices?
The de-Broglie wavelength of a 10 KeV electron is equal to:
The depletion region in a semiconductor is created by:
The value of \( \frac{1}{r} \) in the \( \psi_{1,0,0}(r,\theta,\phi) \) state of a hydrogen atom is (\( a_0 \) is Bohr radius):
An electron is confined to a box of length \( L \). If the length of the box changes to \( 2L \), how would the uncertainty of momentum of the electron change?
The Lagrangian of a simple pendulum, consisting of a bob of mass \( m \) suspended by a string of length \( l \), executing oscillations of amplitude \( \theta \) about the equilibrium position is given by:
Which one of the following is \textit{not a linear operator?}
Which of the following is a Hermitian operator?
Two identical atoms of mass \( m \) are bound to each other by the Lennard-Jones potential,
\[ V = \varepsilon \left[ \left( \frac{r_0}{r} \right)^{12} - 2 \left( \frac{r_0}{r} \right)^6 \right] \] The frequency of small oscillations about the equilibrium is: