List of top Questions asked in IIT JAM PH- 2025

Consider a volume V enclosed by a closed surface S having unit surface normal \(\hat{n}\). For \(\mathbf{r} = x\hat{i} + y\hat{j} + z\hat{k}\), the value of the surface integral \(\frac{1}{9} \oint_{S} \mathbf{r} \cdot \hat{n} \,dS\) is
For a Zener diode as shown in the circuit diagram below, the Zener voltage \(V_Z\) is 3.7 V. For a load resistance (\(R_L\)) of 1 k\(\Omega\), a current \(I_1\) flows through the load. If \(R_L\) is decreased to 500 \(\Omega\), the current changes to \(I_2\). The ratio \(\frac{I_2}{I_1}\) is \rule{1cm{0.15mm}. (up to two decimal places)}
The shortest distance between an object and its real image formed by a thin convex lens of focal length 20 cm is _____ cm. (in integer)
If \(\left(\frac{1-i}{1+i}\right)^{n/2} = -1\), where \(i = \sqrt{-1}\), one possible value of n is
In a two-level atomic system, the excited state is 0.2 eV above the ground state. Considering the Maxwell-Boltzmann distribution, the temperature at which 2% of the atoms will be in the excited state is _____ K. (up to two decimal places)
(Boltzmann constant \(k_B = 8.62 \times 10^{-5}\) eV/K)

At a particular temperature T, Planck's energy density of black body radiation in terms of frequency is \(\rho_T(\nu) = 8 \times 10^{-18} \text{ J/m}^3 \text{ Hz}^{-1}\) at \(\nu = 3 \times 10^{14}\) Hz. Then Planck's energy density \(\rho_T(\lambda)\) at the corresponding wavelength (\(\lambda\)) has the value \rule{1cm}{0.15mm} \(\times 10^2 \text{ J/m}^4\). (in integer) 
[Speed of light \(c = 3 \times 10^8\) m/s] 
(Note: The unit for \(\rho_T(\nu)\) in the original problem was given as J/m³, which is dimensionally incorrect for a spectral density. The correct unit J/(m³·Hz) or J·s/m³ is used here for the solution.)

The ratio of the density of atoms between the (111) and (110) planes in a simple cubic (sc) lattice is ____. (up to two decimal places)
The packing fraction for a two-dimensional hexagonal lattice having sides 2r with atoms of radii r placed at each vertex and at the center is _____. (up to two decimal places)
Consider a vector \(\mathbf{F} = \frac{1}{\pi}[-\sin y \hat{i} + x(1 - \cos y)\hat{j}]\). The value of the integral \(\oint \mathbf{F} \cdot d\mathbf{r}\) over a circle \(x^2 + y^2 = 1\) evaluated in the anti-clockwise direction is _____. (in integer)
A light beam given by \(\mathbf{E}(z, t) = E_{01} \sin(kz - \omega t)\hat{i} + E_{02} \sin(kz - \omega t + \frac{\pi}{6})\hat{j}\) passes through an ideal linear polarizer whose transmission axis is tilted by 60\(^\circ\) from x-axis (in x-y plane). If \(E_{01} = 4\) V/m and \(E_{02} = 2\) V/m, the electric field amplitude of the emerging light beam from the polarizer is ______ V/m. (up to two decimal places)
A wedge-shaped thin film is formed using soap-water solution. The refractive index of the film is 1.25. At near normal incidence, when the film is illuminated by a monochromatic light of wavelength 600 nm, 10 interference fringes per cm are observed. The wedge angle (in radians) is ______ \(\times 10^{-5}\). (in integer)
In an orthorhombic crystal, the lattice constants are 3.0 \AA, 3.2 \AA, and 4.0 \AA. The distance \(d_{101}\) between the successive (101) planes is \rule{1cm{0.15mm} \AA. (up to one decimal place)}
Consider a chamber at room temperature (27 \(^\circ\)C) filled with a gas having a molecular diameter of 0.35 nm. The pressure (in Pascal) to which the chamber needs to be evacuated so that the molecules have a mean free path of 1 km is \rule{1cm{0.15mm} \(\times 10^{-5}\) Pa. (up to two decimal places)
(Boltzmann constant \(k_B = 1.38 \times 10^{-23}\) J/K)}
A NPN bipolar junction transistor (BJT) is connected in common emitter (CE) configuration as shown in the circuit diagram below. The amplifier is operating in the saturation regime. The collector-emitter saturation voltage (\(V_{CE,sat}\)) is 0.2 V. The current gain \(\beta = 100\). The maximum value of base resistance \(R_{BB}\) is \rule{1cm{0.15mm} k\(\Omega\). (in integer)}
One kg of water at 27\(^\circ\)C is brought in contact with a heat reservoir kept at 37\(^\circ\)C. Upon reaching thermal equilibrium, this mass of water is brought in contact with another heat reservoir kept at 47\(^\circ\)C. The final temperature of water is 47\(^\circ\)C. The change in entropy of the whole system in this entire process is \rule{1cm{0.15mm} cal/K. (up to two decimal places)
Take specific heat at constant pressure of water as 1 cal/(g K)}
A particle is moving with a constant angular velocity 2 rad/s in an orbit on a plane. The radial distance of the particle from the origin at time t is given by \(r = r_0 e^{2\beta t}\) where \(r_0\) and \(\beta\) are positive constants. The radial component of the acceleration vanishes for \(\beta = \) \rule{1cm{0.15mm} rad/s. (in integer)}
A planet rotates in an elliptical orbit with a star situated at one of the foci. The distance from the center of the ellipse to any foci is half of the semi-major axis. The ratio of the speed of the planet when it is nearest (perihelion) to the star to that at the farthest (aphelion) is \rule{1cm{0.15mm}. (in integer)}
Consider two media 1 and 2 having permittivities \(\epsilon_0\) and \(\epsilon_2 (= 2\epsilon_0)\), respectively. The interface between the two media aligns with the x-y plane. An electric field \(\mathbf{E}_1 = 4\hat{i} - 5\hat{j} - \hat{k}\) exists in medium 1. The magnitude of the displacement vector \(\mathbf{D}_2\) in medium 2 is \rule{1cm{0.15mm} \(\epsilon_0\). (up to two decimal places)}
G1 and G2 are two ideal gases at temperatures \(T_1\) and \(T_2\), respectively. The molecular weight of the constituents of G1 is half that of G2. If the average speeds of the molecules of both gases are equal, then assuming Maxwell-Boltzmann distributions for the molecular speeds, the ratio \(\frac{T_2}{T_1}\) is \rule{1cm{0.15mm}.}
An ideal p-n junction diode (ideality factor \(\eta = 1\)) is operating in forward bias at room temperature (thermal energy = 26 meV). If the diode current is 26 mA for an applied bias of 1.0 V, the dynamic resistance (\(r_{ac}\)) is \rule{1cm{0.15mm} \(\Omega\). (up to two decimal places)}
Neutrons of energy 8 MeV are incident on a potential step of height 48 MeV. As they penetrate the classically forbidden region, the distance at which the probability density of finding neutrons decreases by a factor of 100 is \rule{1cm{0.15mm} fm. (up to two decimal places)
(Take \(\hbar c = 200\) MeV fm, and the rest mass energy of neutron = 1 GeV.)}
Which of the following relations is(are) valid for linear dielectrics?
\(E\) = Electric field, \(P\) = Polarization, \(D\) = Electric displacement, \(\epsilon_0\) = Permittivity of free space, \(\epsilon\) = Dielectric permittivity, \(\chi_e\) = Electric susceptibility, \(\rho_f\) = Free charge density, \(\rho_b\) = Bound charge density
Three gaseous systems, \(G_1, G_2\), and \(G_3\) with pressure and volume (\(P_1, V_1\)), (\(P_2, V_2\)), and (\(P_3, V_3\)), respectively, are such that
(I) when \(G_1\) and \(G_2\) are in thermal equilibrium, \(P_1V_1 - P_2V_2 + \alpha P_2 = 0\), is satisfied, and
(II) when \(G_1\) and \(G_3\) are in thermal equilibrium, \(P_3V_3 - P_1V_1 + \frac{\beta P_1V_1}{V_3} = 0\), is satisfied.
The relation(s) valid at thermal equilibrium is(are)
(\(\alpha\) and \(\beta\) are constants of appropriate dimensions)
An ideal mono-atomic gas is expanded adiabatically from A to B. It is then compressed in an isobaric process from B to C. Finally, the pressure is increased in an isochoric process from C to A. The cyclic process is shown in the figure below. For this system, which of the following is(are) correct?
For a body centered cubic (bcc) system, the x-ray diffraction peaks are observed for the following \(h^2+k^2+l^2\) value(s)