List of practice Questions

The Zener current $ I_Z $ for the given circuit is .............. mA.

The value of emitter current in the given circuit is ............ μA.

For the input voltage $ V_i = (200 \, \text{mV}) \sin (400t) $, the amplitude of the output voltage $ V_0 $ of the given OPAMP circuit is ............. V.

The flux of the function $ \mathbf{F} = (y^2) \hat{x} + (3xy - z^2) \hat{y} + (4yz) \hat{z} $ passing through the surface ABCD along $ \hat{n} $ is ............

A ball of mass m is falling freely under gravity through a viscous medium in which the drag force is proportional to the instantaneous velocity $v$ of the ball. Neglecting the buoyancy force of the medium, which one of the following figures best describes the variation of $v$ as a function of time $t$?

During the charging of a capacitor C in a series RC circuit, the typical variations in the magnitude of the charge $q(t)$ deposited on one of the capacitor plates, and the current $i(t)$ in the circuit, respectively are best represented by

In the given phase diagram for a pure substance, regions I, II, III, IV, respectively represent

The location of Cs$^+$ and Cl$^-$ ions inside the unit cell of CsCl crystal is shown in the figure. The Bravais lattice of CsCl is

For a forward biased p-n junction diode, which one of the following energy-band diagrams is correct? ($ \epsilon_F $ is the Fermi energy)

The output of the following logic circuit can be simplified to \[ \text{(Logic circuit diagram provided)} \]

Consider the normal incidence of a plane electromagnetic wave with electric field given by \[ \vec{E} = E_0 \exp{[i(k_1 z - \omega t)]} \hat{x} \] over an interface at $ z = 0 $ separating two media [wave velocities $ v_1 $ and $ v_2 $ (with $ v_2>v_1 $) and wave vectors $ k_1 $ and $ k_2 $, respectively], as shown in the figure. The magnetic field vector of the reflected wave is

A small spherical ball having charge $ q $ and mass $ m $, is tied to a thin massless non-conducting string of length $ l $. The other end of the string is fixed to an infinitely extended thin non-conducting sheet with uniform surface charge density $ \sigma $. Under equilibrium, the string makes an angle of 45° with the sheet as shown in the figure. Then $ \sigma $ is given by \[ g \text{ is the acceleration due to gravity and } \epsilon_0 \text{ is the permittivity of free space.} \]

The eigenvalues of

\[ \begin{pmatrix} 3 & i & 0 \\ -i & 3 & 0 \\ 0 & 0 & 6 \end{pmatrix} \]

are

A unit vector perpendicular to the plane containing $ \vec{A} = i + j - 2k $ and $ \vec{B} = 2i - j + k $ is

Which one of the following crystallographic planes represent $ (101) $ Miller indices of a cubic unit cell?

In the thermal neutron induced fission of $^{235}U$, the distribution of relative number of the observed fission fragments (Yield) versus mass number (A) is given by

A classical particle has total energy $ E $. The plot of potential energy $ U(r) $ as a function of distance $ r $ from the centre of force located at $ r = 0 $ is shown in the figure. Which of the regions are forbidden for the particle?

A proton is confined within a nucleus of size $ 10^{-13} \, \text{cm} $. The uncertainty in its velocity is ........... $ \times 10^8 \, \text{m/s} $.

Given the wave function of a particle $ \psi(x) = \sqrt{\frac{2}{L}} \sin \left( \frac{\pi x}{L} \right) $ for $ 0<x<L $ and 0 elsewhere, the probability of finding the particle between $ x = 0 $ and $ x = L/2 $ is .............

If the diameter of the Earth is increased by 4% without changing the mass, then the length of the day is ...... hours.
(Take the length of the day before the increment as 24 hours. Assume the Earth to be a sphere with uniform density.)

A diatomic gas undergoes adiabatic expansion against the piston of a cylinder. As a result, the temperature of the gas drops from 1150 K to 400 K. The number of moles of the gas required to obtain 2300 J of work from the expansion is .................

The decimal equivalent of the binary number 110.101 is ................

The 7th bright fringe in the Young’s double slit experiment using a light of wavelength 550 nm shifts to the central maxima after covering the two slits with two sheets of different refractive indices $n_1$ and $n_2$ but having the same thickness 6 µm. The value of $ |n_1 - n_2| $ is .............

If the wavelength of Kα2 X-ray line of an element is 1.544 Å, then the atomic number $ Z $ of the element is ................

An object of 2 cm height is placed at a distance of 30 cm in front of a concave mirror with radius of curvature 40 cm. The height of the image is ............. cm.