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

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?
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:
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:
The first non-zero Fourier coefficient in the expansion of \( \sin^3(x) \) is:
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:
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 unit vectors \( \hat{\theta} \) and \( \hat{\phi} \) (where \( \theta \) and \( \phi \) are the polar and azimuthal angles, respectively), in the spherical coordinate system, under the operation of inversion (i.e., reflection through the origin) have:
Displacement \( x^i \) is a contravariant vector. The work done by a force is an invariant scalar. Therefore, force and hence momentum are:
Evaluate the integral:
\[ \int_{0}^{\infty} e^{-x} \delta(\lambda^2 - 4)dx \]
The matrix \( A = \begin{bmatrix} -2 & 1 & 2
1 & 2 & 1
2 & 1 & -2 \end{bmatrix} \) is:
The only possible real eigenvalue of a Skew-Hermitian matrix is:
A photon recoils back after striking an electron at rest. The change in wavelength of the photon 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:
The de-Broglie wavelength \( \lambda \) associated with an electron of energy \( V \) electron volt is:
Two inductors \( L_1 \) and \( L_2 \) are connected such that their fluxes are in opposite directions. The total inductance \( L \) will be:
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:
Above Curie temperature, the ferromagnetic material behaves as:
Polarization \( \vec{P} \) and electric susceptibility \( \chi \) are related as:
The Clausius-Mossotti relation holds best for:
Which of the following is an optically active substance?