List of top Questions asked in IIT JAM PH

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)}
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)}
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 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)}
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)}
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}.}
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.)}
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)}
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?
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
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)
Two solid cylinders of the same density are found to have the same moment of inertia about their respective principal axes. The length of the second cylinder is 16 times that of the first cylinder. If the radius of the first cylinder is 4 cm, the radius of the second cylinder is \rule{1cm{0.15mm} cm. (in integer)}