List of top Questions asked in IIT JAM

In a dielectric medium of relative permittivity 5, the amplitudes of the displacement current and conduction current are equal for an applied sinusoidal voltage of frequency f = 1 MHz. The value of conductivity (in Ω^-1m^-1) of the medium at this frequency is

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

In an extrinsic p-type semiconductor, which of the following schematic diagram depicts the variation of the Fermi energy level (E_F) with temperature (T) ?

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

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

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

Inverse of the matrix \(\begin{bmatrix} 1 & 1 & 0 \\ 2 & 3 & 0 \\ 1 & 0 & 1 \end{bmatrix}\) is

An objective lens with half angular aperture 𝛼 is illuminated with light of wavelength 𝜆. The refractive index of the medium between the sample and the objective is 𝑛. The lateral resolving power of the optical system can be increased by

The spectral energy density u_T(λ) vs wavelength (λ) curve of a black body shows a peak at λ = λ_max. If the temperature of the black body is doubled, then

The state of a harmonic oscillator is given as Ψ =\(\frac{1}{ √3}\) 𝜓₀ -\(\frac{1}{ √6}\) 𝜓₁+\(\frac{1}{ √2}\) 𝜓₂ , where 𝜓₀, 𝜓₁ and 𝜓₂ are the normalized wave functions of ground, first excited, and second excited states, respectively. Which of the following statement(s) is/are true?

Temperature (T) dependence of the total specific heat (C_v) for a two dimensional metallic solid at low temperatures is

For a cubic unit cell, the dashed arrow in which of the following figures represents the direction [220] ?

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

For the following circuit, choose the correct waveform corresponding to the output signal (V_out). Given V_in = 5 sin(200πt) V, forward bias voltage of the diodes (D and Z) = 0.7 V and reverse Zener voltage = 3 V.

A wave travelling along the x-axis with y representing its displacement is described by (𝑣 is the speed of the wave)

In the given circuit, with an ideal op-amp for what value of \(\frac{R_1}{R_2}\) the output of the amplifier V_out = V₂ - V₁ ?

Which of the following statements about the viscosity of a dilute ideal gas is correct ?

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

Which of the following schematic plots correctly represent(s) a first order phase transition occurring at temperature 𝑇=𝑇_c? Here 𝑔, 𝑠, 𝑣 are specific Gibbs free energy, entropy and volume, respectively

The plot of the function f(x) = ||x| - 1| is

A periodic function f(x) = x² for -π < x < π is expanded in a Fourier series. Which of the following statement(s) is/are correct ?

A production function at time 𝑡 is given by
\(Y_t=A_tK^a_tL^{1-a}_t\) , 𝛼 ∈ (0, 1), 𝛼 ≠ 0.5, 
where 𝑌 is output, 𝐾 is capital, 𝐿 is labour and 𝐴 is the level of Total Factor Productivity. Define per capita output as \(𝑦_𝑡 ≡ \frac{𝑌_𝑡}{ 𝐿_𝑡} \)and capital-output ratio as \(𝑘_𝑡 ≡\frac{ 𝐾_𝑡}{ 𝑌_𝑡}\) . For any variable 𝑥𝑡 , denote \(\frac{𝑑𝑥_𝑡}{ 𝑑𝑡}\) by 𝑥̇ . The per capita output growth rate is

Let 𝑌 ∼ 𝑁𝑜𝑟𝑚𝑎𝑙(3, 1), 𝑊 ∼ 𝑁𝑜𝑟𝑚𝑎𝑙(1, 2) and 𝑋 ∼ 𝐵𝑒𝑟𝑛𝑜𝑢𝑙𝑙𝑖 (𝑝 = 0.9) where 𝑋 = 1 is success and 𝑋 = 0 is failure. Let 𝑆 = 𝑋𝑌 + (1 − 𝑋)𝑊. Then 𝐸(𝑆) = _________ (round off to 1 decimal place)

A number 𝑥 is randomly chosen from the set of the first 100 natural numbers. The probability that 𝑥 satisfies the condition \(𝑥 + \frac{300}{𝑥} > 65\) is ______ (round off to 2 decimal places).

Let 𝜋 be the proportion of a population vaccinated against a disease. An estimate ̂𝜋 = 0.64 is found using a sample of 100 individuals from the population. The 𝑧 test statistic for the null hypothesis 𝐻₀ : 𝜋 = 0.58 is ________ (round off to 2 decimal places).