List of top Questions asked in Indian Institute Of Technology Joint Admission Test for MSc- 2023

A particle (𝑝₁) of mass 𝑚 moving with speed 𝑣 collides with a stationary identical particle (𝑝₂). The particles bounce off each other elastically with 𝑝₁ getting deflected by an angle 𝜃 = 30° from its original direction. Then, which of the following statement(s) is/are true after the collision?

A spacecraft has speed 𝑣_𝑠=𝑓𝑐 with respect to the earth, where 𝑐 is the speed of light in vacuum. An observer in the spacecraft measures the time of one complete rotation of the earth to be 48 hours. The value of 𝑓 is (rounded off to two decimal places).

A single pendulum hanging vertically in an elevator has a time period 𝑇₀ when the elevator is stationary. If the elevator moves upward with an acceleration of 𝑎 = 0.2𝑔, the time period of oscillations is 𝑇₁. Here 𝑔 is the acceleration due to gravity. The ratio\( \frac{𝑇_0}{ 𝑇_1}\) is (rounded off to two decimal places).

An α particle with energy of 3 MeV is moving towards a nucleus of ⁵⁰Sn. Its minimum distance of approach to the nucleus is 𝑓×10⁻¹⁴ m. The value of 𝑓 is ________ (rounded off to one decimal place).

Two silicon diodes are connected to a battery and two resistors as shown in the figure. The current through the battery is __________ A (rounded off to two decimal places).

Given: The forward voltage drop across each diode = 0.7 V

The lattice constant (in Å) of copper, which has FCC structure, is _________ (rounded off to two decimal places).
Given: density of copper is 8.91 g cm^-3 and its atomic mass is 63.55 g mol^-1 ; Avogadro’s number = 6.023 × 10²³ mol⁻¹

A rectangular pulse of width 0.5 cm is travelling to the right on a taut string (shown by full line in the figure) that has mass per unit length 𝜇1. The string is attached to another taut string (shown by dashed line) of mass per unit length 𝜇2. If the tension in both the strings is the same, and the transmitted pulse has width 0.7 cm, the ratio 𝜇1⁄𝜇2 is _______(rounded off to two decimal places)

A rod of mass 𝑀, length 𝐿 and non-uniform mass per unit length \(λ(x)=\frac{3Mx^2}{L^3},\) is held horizontally by a pivot, as shown in the figure, and is free to move in the plane of the figure. For this rod, which of the following statements are true?

The sum of the x-components of unit vectors 𝑟̂ ̇ and 𝜃̂̇ for a particle moving with angular speed 2 rad s ^-1 at angle 𝜃 = 215° is__________ (rounded off to two decimal places)

Unit vector normal to the equipotential surface of 𝑉(𝑥, 𝑦, 𝑧) =4𝑥²+𝑦² + 𝑧 at (1,2,1) is given by (𝑎𝑖̂+ 𝑏𝑗̂+ 𝑐𝑘̂). The value of |𝑏| is (rounded off to two decimal places).

The absolute error in the value of sin𝜃 if approximated up to two terms in the Taylor’s series for 𝜃 = 60∘ is ___________ (rounded off to three decimal places).

Consider a spring mass system with mass 0.5 kg and spring constant 𝑘 = 2 Nm^-1 in a viscous medium with drag coefficient 𝑏 = 3 kg s ^-1 . The additional mass required so that the motion becomes critically damped is _______ kg (rounded off to three decimal places)

A small bar magnet is dropped through different hollow copper tubes with same length and inner diameter but with different outer diameter. The variation in the time (t) taken for the magnet to reach the bottom of the tube depends on its wall thickness (d) as

For a given vector \(\vec{F}=-y\hat{i}+z\hat{j}+x^2\hat{k}\) , the surface integral \(\int_S(\vec{▽}\times \vec{F}).\hat{r}dS\) over the surface S of a hemisphere of radius R with the centre of the base at the origin is

A fission device explodes into two pieces of rest masses 𝑚 and 0.5𝑚 with no loss of energy into any other form. These masses move apart respectively with speeds \(\frac{c}{ √13} \) and \(\frac{c}{2}\) , with respect to the stationary frame. If the rest mass of the device is 𝑓𝑚 then 𝑓 is________ (rounded off to two decimal places).

For a thermodynamic system, the coefficient of volume expansion \(\beta=\frac{1}{V}(\frac{∂V}{∂T})_P\) and compressibility \(K=-\frac{1}{V}(\frac{∂V}{∂P})_T\) , where V, T, and P are respectively the volume, temperature, and pressure. Considering that \(\frac{dV}{V}\) is a perfect differential, we get

A uniform stick of length l and mass m pivoted at its top end is oscillating with an angular frequency ω_r . Assuming small oscillations, the ratio ω_r/ω_s , where ω_s is the angular frequency of a simple pendulum of the same length, will be

A point source emitting photons of 2 eV energy and 1 W of power is kept at a distance of 1m from a small piece of a photoelectric material of area 10^-4 m² . If the efficiency of generation of photoelectrons is 10%, then the number of photoelectrons generated are 𝑓×10¹² per second. The value of 𝑓 is __________ (rounded off to two decimal places).
Given: 1eV = 1.6 × 10⁻¹⁹ J

A linearly polarized light of wavelength 590 nm is incident normally on the surface of a 20 μm thick quartz film. The plane of polarization makes an angle 30° with the optic axis. Refractive indices of ordinary and extraordinary waves differ by 0.0091, resulting in a phase difference of fπ between them after transmission. The value of f (rounded off to two decimal places) and the state of polarization of the transmitted light is

For the Maxwell-Boltzmann speed distribution, the ratio of the root-mean-square speed (v_rms) and the most probable speed (v_max) is
Given : Maxwell-Boltzmann speed distribution function for a collection of particles of mass m is
\(f(v)=(\frac{m}{2\pi k_BT})^{3/2}4\pi v^2\text{exp}(-\frac{mv^2}{2k_BT})\)
where, v is the speed and k_BT is the thermal energy.

Consider the 𝛼-decay ⁹⁰𝑇ℎ ²³²→⁸⁸𝑅𝑎 ²²⁸ . In an experiment with one gram of ⁹⁰𝑇ℎ ²³², the average count rate (integrated over the entire volume) measured by the 𝛼-detector is 3000 counts s ^-1 . If the half life of ⁹⁰𝑇ℎ ²³² is given as 4.4 × 10¹⁷ s, then the efficiency of the 𝛼-detector is ______(rounded off to two decimal places).
Given: Avogadro’s number = 6.023 × 1023 mol⁻¹

A container is occupied by a fixed number of non-interacting particles. If they are obeying Fermi-Dirac, Bose-Einstein, and Maxwell-Boltzmann statistics, the pressure in the container is P_FD, P_BE and P_MB, respectively. Then

An oil film in air of thickness 255 nm is illuminated by white light at normal incidence. As a consequence of interference, which colour will be predominantly visible in the reflected light ?
Given the refractive index of oil = 1.47

A conducting wire AB of length m has resistance of .6 Ω. It is connected to a voltage source of 0.5 V with negligible resistance as shown in the figure. The corresponding electric and magnetic fields give Poynting vectors 𝑆 (𝑟 ) all around the wire. Surface integral ∫ 𝑆 . 𝑑𝑎 is calculated over a virtual sphere of diameter 0.2 m with its centre on the wire, as shown. The value of the integral is ______W (rounded off to three decimal places)

A metallic sphere of radius 𝑅 is held at electrostatic potential 𝑉. It is enclosed in a concentric thin metallic shell of radius 2𝑅 at potential 2𝑉. If the potential at the distance \(\frac{3}{2}\) 𝑅 from the centre of the sphere is 𝑓𝑉, then the value of 𝑓 is _______ (rounded off to two decimal places).