List of top Questions asked in Indian Institute Of Technology Joint Admission Test for MSc

The divergence of a 3-dimensional vector \(\frac{𝑟̂}{𝑟^3}\) (𝑟̂ is the unit radial vector) is:

The plane 𝑧=0 separates two linear dielectric media with relative permittivities 𝜀_𝑟1=4 and 𝜀_𝑟2=3, respectively. There is no free charge at the interface. If the electric field in the medium 1 is 𝐸⃗ ₁=3𝑥̂+2𝑦̂ +4𝑧̂, then the displacement vector \(\overrightarrow{D_2}\) in medium 2 is: (𝜀₀ is the permittivity of free space)

A gas consists of particles, each having three translational and three rotational degrees of freedom. The ratio of specific heats, Cp/Cv, is: (C_p and C_v are the specific heats at constant pressure and constant volume, respectively).

Which of the following types of motion may be represented by the trajectory,
𝑦(𝑥)=𝑎𝑥 ²+𝑏𝑥+𝑐 ? 
(Here a, b, and c are constants; x, y are the position coordinates)

A 15.7mW laser beam has a diameter of 4mm. If the amplitude of the associated magnetic field is expressed as \(\frac{𝐴}{\sqrt{ε_0𝑐^3}}\) , the value of A is: (𝜀₀ is the free space permittivity and 𝑐 is the speed of light)

A plane electromagnetic wave is incident on an interface AB separating two media (refractive indices 𝑛₁ = 1.5 and 𝑛₂ = 2.0) at Brewster angle 𝜃𝐵, as schematically shown in the figure. The angle 𝛼 (in degrees) between the reflected wave and the refracted wave is:

One mole of an ideal monoatomic gas, initially at temperature 𝑇_𝑜 is expanded from an initial volume 𝑉_𝑜 to 2.5𝑉_𝑜. Which of the following statements is(are) correct?
(R is the ideal gas constant)

A whistle S of sound frequency f is oscillating with angular frequency 𝜔 along the x-axis. Its instantaneous position and the velocity are given by 𝑥(𝑡) = 𝑎 sin(𝜔𝑡) and 𝑣(𝑡)=𝑣₀ cos (𝜔𝑡), respectively. An observer P is located on the y-axis at a distance L from the origin (see figure). Let 𝑣_𝑃𝑆(𝑡) be the component of 𝑣(𝑡) along the line joining the source and the observer. Choose the correct option(s):
(Here 𝑎 and 𝑣₀ are constants)

For the LCR AC-circuit (resonance frequency ω_o) shown in the figure below, choose the correct statement(s).

A pure Si crystal can be converted to an n-type crystal by doping with

The inertial frame 𝑆' is moving away from the inertial frame S with a speed 𝑣 = 0.6𝑐 along the negative x-direction (see figure). The origins 𝑂’ and 𝑂 of the frames coincide at 𝑡=𝑡’=0. As observed in the frame 𝑆′, two events occur simultaneously at two points on the 𝑥′-axis with a separation of ∆𝑥′=5m. If, ∆𝑡 and ∆𝑥 are the magnitudes of the time interval and the space interval, respectively, between the events in S, then which of the following statements is(are) correct?

(c = 3×10⁸ m/s)

Consider two different Compton scattering experiments, in which X-rays and γ rays of wavelength (λ) 1.024Å and 0.049Å, respectively, are scattered from stationary free electrons. The scattered wavelength (λ′) is measured as a function of the scattering angle (θ). If Compton shift is 𝛥λ=λ′−λ, then which of the following statement(s) is/are true:
( h = 6.63 x10^-34J.s, m_e = 9.11x10^-31 kg, c = 3 x 10⁸m/s )

In the following OP-AMP circuit, 𝑣_𝑖𝑛 and 𝑣_𝑜𝑢𝑡 represent the input and output signals, respectively.

Choose the correct statement(s):

A spring-mass system (spring constant 80N/m and damping coefficient 40N-s/m), initially at rest, is lying along the y-axis in the horizontal plane. One end of the spring is fixed and the mass (5kg) is attached at its other end. The mass is pulled along the y-axis by 0.5m from its equilibrium position and then released. Choose the correct statement(s).
(Ignore mass of the spring)

A particle of mass m, having an energy E and angular momentum L, is in a parabolic trajectory around a planet of mass M. If the distance of the closest approach to the planet is r_m, which of the following statement(s) is(are) true?
(G is the Gravitational constant)

A stationary nitrogen (\(^{14}_7N\)) nucleus is bombarded with α- particle (\(^{4}_2He\)) and the following nuclear reaction takes place:

If the kinetic energies of \(^4_2\) and \(^4_2H\) are 5.314MeV and 4.012MeV, respectively, then the kinetic energy of \(^{17}_80\) is MeV. (Rounded off to one decimal place) 
(Masses are given in units of 𝑢 = 931.5MeV/c² )

The moment of inertia of a solid hemisphere (mass 𝑀 and radius 𝑅) about the axis passing through the hemisphere and parallel to its flat surface is \(\frac{2}{5}\) 𝑀𝑅² . The distance of the axis from the center of mass of the hemisphere (in units of 𝑅) is______. (Rounded off to two decimal places)

Consider a p-n junction diode which has 10²³ acceptor-atoms/m³ in the p-side and 10²² donor-atoms/m³ in the n-side. If the depletion width in the p-side is 0.16µm, then the value of depletion width in the n-side will be ______µm. (Rounded off to one decimal place)

A charge of −9C is placed at the center of a concentric spherical shell made of a linear dielectric material (relative permittivity 9) and having inner and outer radii of 0.1m and 0.2m, respectively. The total charge induced on its inner surface is ______C. (Rounded off to two decimal place)

A transistor (β=100, 𝑉𝐵𝐸 = 0.7𝑉) is connected as shown in the circuit below.

The current IC will be mA. (Rounded off to two decimal places)

An unstable particle created at a point P moves with a constant speed of 0.998c until it decays at a point Q. If the lifetime of the particle in its rest frame is 632ns, the distance between points P and Q is ______m. (Rounded off to the nearest integer)
(c=3×108 m/s)

In the Taylor expansion of function, 𝐹(𝑥)=𝑒^𝑥 sin 𝑥, around 𝑥 = 0, the coefficient of 𝑥⁵ is ______. (Rounded off to three decimal places)

A satellite of mass 10kg, in a circular orbit around a planet, is having a speed 𝑣=200m/s. The total energy of the satellite is _______kJ. (Rounded off to nearest integer)

The Fermi energy of a system is 5.5eV. At 500K, the energy of a level for which the probability of occupancy is 0.2, is ________eV. (Rounded off to two decimal places) (Boltzmann constant 𝑘_𝐵 = 8.62x10⁻⁵ eV/K)

A Zener diode (rating 10V, 2W) and a normal diode (turn-on voltage 0.7V) are connected in a circuit as shown in the figure. The voltage drop 𝑉_𝐿 across the 2kΩ resistance is ____V. (Rounded off to one decimal place)