List of practice Questions

Out of the following statements, choose the correct option(s) about a perfect conductor.

In the X-ray diffraction pattern recorded for a simple cubic solid (lattice parameter \( a = 1 \) Å) using X rays of wavelength 1 Å, the first order diffraction peak(s) would appear for the

Consider a classical particle subjected to an attractive inverse-square force field. The total energy of the particle is \( E \) and the eccentricity is \( \epsilon \). The particle will follow a parabolic orbit if

The relation between the nuclear radius \( R \) and the mass number \( A \), given by \( R = 1.2 A^{1/3} \) fm, implies that

Consider an object moving with a velocity \( \vec{v} \) in a frame which rotates with a constant angular velocity \( \vec{\omega} \). The Coriolis force experienced by the object is

The gradient of a scalar field \( S(x, y, z) \) has the following characteristic(s).

A thermodynamic system is described by the \( P, V, T \) coordinates. Choose the valid expression(s) for the system.

The maximum number of intensity minima that can be observed in the Fraunhofer diffraction pattern of a single slit (width 10 µm) illuminated by a laser beam (wavelength 0.630 µm) will be

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

Let the Taylor polynomial of degree 20 for \( \frac{1}{(1-x)^3} \) at \( x = 0 \) be

\[ \sum_{n=0}^{20} a_n x^n \]

Then \( a_{15} \) equals