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

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):
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:
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:
Which one of the following is \textit{not a linear operator?}
Which of the following is a Hermitian operator?
The distance between the Sun and the Earth is 1 astronomical unit (1 AU). Jupiter takes about 11.9 Earth years to orbit around the Sun. The distance between the Sun and Jupiter, in AU, is about:
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:
The types of constraints on the mechanical system consisting of a cylinder rolling (and possibly sliding) down an inclined plane of angle \( \alpha \) are:
For inverse square law forces, the mathematical statement of the virial theorem is (where \( \langle T \rangle \) and \( \langle V \rangle \) are the averages of kinetic and potential energies):
The moment of inertia of a solid circular cylinder of radius \( a \) and height \( h \) about its axis is:
The magnitude of Coriolis acceleration (expressed in terms of \( g \), the acceleration due to Earth's gravity) for a particle of mass \( m \) moving with a velocity \( 10^4 \) cm/s horizontally along Earth's surface at the North Pole is about:
A term of the type \( \frac{\partial T}{\partial q_k} \), where \( T \) and \( q_k \) are the kinetic energy and a generalized coordinate, respectively, if occurring in the equation of motion of a system is called a:
Displacement \( x^i \) is a contravariant vector. The work done by a force is an invariant scalar. Therefore, force and hence momentum are:
A photon recoils back after striking an electron at rest. The change in wavelength of the photon is:
A solenoid has length \( l \), number of turns \( N \), and area of cross-section \( A \). Its self-inductance \( L \) is:
A coil of inductance 2 mH and resistance 15Ω is connected in parallel with a capacitor of 0.01 μF. The peak oscillator current at resonance is:
The de-Broglie wavelength \( \lambda \) associated with an electron of energy \( V \) electron volt is:
The loss of energy due to hysteresis when 5 kg of iron is subjected for 1 hour to cyclic magnetic changes of frequency 25 cycles/sec, if the hysteresis loop represents a loss of \( 2.5 \times 10^3 \) erg cm\(^3\) cycle\(^{-1}\) and density of iron is 7.8 gm cm\(^{-3}\), is:
Two inductors \( L_1 \) and \( L_2 \) are connected such that their fluxes are in opposite directions. The total inductance \( L \) will be:
Polarization \( \vec{P} \) and electric susceptibility \( \chi \) are related as:
Which of the following is an optically active substance?
The Clausius-Mossotti relation holds best for:
Using Langevin's theory, the susceptibility \( \chi \) of a paramagnetic substance is given by: