List of top Questions asked in IIT JAM

In the circuit shown, assuming the current gain β = 100 and V_BE = 0.7 V, what will be the collector voltage V_C in V ?
Given : V_CC = 15 V, R₁ = 100 kΩ, R₂ = 50 kΩ, R_C = 4.7 kΩ, and R_E = 3.3 kΩ

Which of the following statement(s) is/are true for a LC circuit with 𝐿=25 mH and 𝐶=4 µF?

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

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

For a particle moving in a general central force field, which of the following statement(s) is/are true?

Water from a tank is flowing down through a hole at its bottom with velocity 5 ms^-1. If this water falls on a flat surface kept below the hole at a distance of 0.1 m and spreads horizontally, the pressure (in kNm^-2) exerted on the flat surface is closest to
Given: acceleration due to gravity = 9.8 ms^-2 and density of water = 1000 kgm^-3

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

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

At the planar interface of two dielectrics, which of the following statements related to the electric field (\(\vec{𝐸}\) ), electric displacement (\(\vec{D}\)) and polarization (\(\vec{P}\) ) is true ?

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).

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).

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).

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)

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)

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).

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.

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)

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).

In a X-Ray tube operating at 20 kV, the ratio of the de-Broglie wavelength of the incident electrons to the shortest wavelength of the generated X-rays is ________ (rounded off to two decimal places).
Given: e/m ratio for an electron = 1.76×10¹¹ Ckg-1 and the speed of light in vacuum is 3×10⁸ ms ^-1

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

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

In the Thomson model of hydrogen atom, the nuclear charge is distributed uniformly over a sphere of radius 𝑅. The average potential energy of an electron confined within this atom can be taken as \(V=\frac{e^2}{4{\pi}e_0R}\) . Taking the uncertainty in position to be the radius of the atom, the minimum value of 𝑅 for which an electron will be confined within the atom is estimated to be 𝑓 × 10⁻¹¹ m. The value of 𝑓 is _______ (rounded off to one decimal place). 
Given: The uncertainty product of momentum and position is ℏ = 1×10⁻³⁴ Js ^-1 ,e=1.6 × 10⁻¹⁹C, and \(\frac{1}{4{\pi}e_0}\)= 9 × 10⁹ Nm2C ⁻²

The sum of the eigenvalues 𝜆₁ and 𝜆₂ of matrix 𝐵 = 𝐼+𝐴+𝐴² , where
\( \left[ {\begin{array}{cc}  2&1 \\     -0.5 &0.5 \\   \end{array} } \right]\)
 is_____ (rounded off to two decimal places).

A container of volume 𝑉 has helium gas in it with 𝑁 number of He atoms. The mean free path of these atoms is 𝜆_He. Another container has argon gas with the same number of Ar atoms in volume 2𝑉 with their mean free path being 𝜆_Ar. Taking the radius of Ar atoms to be 1.5 times the radius of He atoms, the ratio 𝜆_Ar⁄𝜆_He is__________ (rounded off to two decimal places).

Three frames 𝐹₀, 𝐹₁ and 𝐹₂ are in relative motion. The frame 𝐹₀ is at rest, 𝐹₁ is moving with velocity 𝑣1𝑖̂with respect to 𝐹₀ and 𝐹₂ is moving with velocity 𝑣₂𝑖̂ with respect to 𝐹₁. A particle is moving with velocity 𝑣3𝑖̂ with respect to 𝐹₂. If 𝑣₁ = 𝑣₂ = 𝑣₃= \(\frac{𝑐}{2}\), where 𝑐 is the speed of light, the speed of the particle with respect to 𝐹₀ is 𝑓𝑐. The value of 𝑓 is ____________ (rounded off to two decimal places)