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

One mole of an ideal monoatomic gas is heated in a closed container, first from 273K to 303K, and then from 303K to 373K. The net change in the entropy is ______R. (Rounded off to two decimal places) (R is the ideal gas constant)

In a Newton’s rings experiment (using light of free space wavelength 580nm), there is an air gap of height d between the glass plate and a plano-convex lens (see figure). The central fringe is observed to be bright.

The least possible value of d (in nm) is:

The value of the line integral for the vector,
\(\overrightarrow𝑣=2𝑥̂ +𝑦𝑧 ^2𝑦̂ +(3𝑦+𝑧 ^2 )𝑧̂ \)
along the closed path OABO (as shown in the figure) is: 

(Path AB is the arc of a circle of unit radius)

A vector field is expressed in the cylindrical coordinate system (s, ϕ, z) as,
\(\overrightarrow𝐹=\frac{𝐴}{𝑠} 𝑠̂+ \frac{𝐵}{𝑠} 𝑧̂. \)
If this field represents an electrostatic field, then the possible values of A and B, respectively, are:

If the electric field of an electromagnetic wave is given by,
𝐸⃗ = (4𝑥̂ + 3𝑦̂)𝑒 ^{𝑖(𝜔𝑡+𝑎𝑥−600𝑦)} 
then the value of a is: (all values are in the SI units)

Given that the rest mass of electron is 0.511MeV/c ² , the speed (in units of c) of an electron with kinetic energy 5.11MeV is closest to:

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 cylinder-piston system contains N atoms of an ideal gas. If 𝑡_𝑎𝑣𝑔 is the average time between successive collisions of a given atom with other atoms. If the temperature T of the gas is increased isobarically, then 𝑡_𝑎𝑣𝑔 is proportional to :

Linearly polarized light (free space wavelength 𝜆₀= 600nm) is incident normally on a retarding plate (𝑛_𝑒-𝑛_𝑜 = 0.05 at 𝜆₀= 600nm). The emergent light is observed to be linearly polarized, irrespective of the angle between the direction of polarization and the optic axis of the plate. The minimum thickness (in µm) of the plate is:

In the x-y plane, a vector is given by
\(\overrightarrow𝐹 (𝑥, 𝑦) = \frac{−𝑦𝑥̂ + 𝑥𝑦̂}{𝑥^ 2 + 𝑦^2} . \)
The magnitude of the flux of \(\overrightarrow∇ ×\overrightarrow 𝐹\) , through a circular loop of radius 2, centered at the origin, is:

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).

A particle moving along the x-axis approaches 𝑥=0 from 𝑥 =−∞ with a total energy E. It is subjected to a potential 𝑉(𝑥). For time 𝑡→∞, the probability density P(x) of the particle is schematically shown in the figure.

The correct option for the potential 𝑉(𝑥) is:

A one-dimensional infinite square-well potential is given by:
\(v(x)=0\,\,for\,\,-\frac{a}{2}<x<+\frac{a}{2}\)= ∞ elsewhere
Let 𝐸_𝑒 (𝑥) and ψ_𝑒 (𝑥) be the ground state energy and the corresponding wave function, respectively, if an electron (e) is trapped in that well. Similarly, let 𝐸_µ(𝑥) and ψ_µ (𝑥) be the corresponding quantities, if a muon (µ) is trapped in the well. Choose the correct option:

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)

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)

The ultraviolet catastrophe in the classical (Rayleigh-Jeans) theory of cavity radiation is attributed to the assumption that

If two traveling waves, given by
𝑦₁=𝐴₀ sin(α𝑘𝑥 -𝜔𝑡) and 𝑦₂=𝐴₀ sin(α𝑘𝑥 − β𝜔𝑡) 
are superposed, which of the following statements is correct?

Suppose that there is a dispersive medium whose refractive index depends on the wavelength as given by \(n(λ) = n_0 +\frac{ a}{λ^2}-\frac{b}{λ^4}\) . The value of 𝜆 at which the group and phase velocities would be the same, is:

A tank, placed on the ground, is filled with water up to a height ℎ. A small hole is made at a height ℎ1 such that ℎ1 < ℎ. The water jet emerging from the hole strikes

the ground at a horizontal distance D, as shown schematically in the figure. Which of the following statements is correct? (g is the acceleration due to gravity)

The sum of three binary numbers, 10110.10, 11010.01, and 10101.11, in decimal system is:

Which of the following matrices is Hermitian as well as unitary?

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

The magnitudes of spin magnetic moments of electron, proton and neutron are μ_e, μ_p and μ_n, respectively. Then

A crystal plane of a lattice intercepts the principal axes \(\overrightarrow𝑎_1, \overrightarrow𝑎_2,\) and  \(\overrightarrow{a_3}\) at 3𝑎₁, 4𝑎₂, and 2𝑎₃, respectively. The Miller indices of the plane are:

An incompressible fluid is flowing through a vertical pipe (height h and crosssectional area 𝐴_𝑜). A thin mesh, having n circular holes of area 𝐴_ℎ is fixed at the bottom end of the pipe. The speed of the fluid entering the top-end of the pipe is 𝑣_𝑜. The volume flow rate from an individual hole of the mesh is given by:
(g is the acceleration due to gravity)