List of top Questions asked in IIT JAM

A proton is confined within a nucleus of size \( 10^{-13} \, \text{cm} \). The uncertainty in its velocity is ........... \( \times 10^8 \, \text{m/s} \).
Given the wave function of a particle \( \psi(x) = \sqrt{\frac{2}{L}} \sin \left( \frac{\pi x}{L} \right) \) for \( 0<x<L \) and 0 elsewhere, the probability of finding the particle between \( x = 0 \) and \( x = L/2 \) is .............
If the diameter of the Earth is increased by 4% without changing the mass, then the length of the day is ...... hours.
(Take the length of the day before the increment as 24 hours. Assume the Earth to be a sphere with uniform density.)
A diatomic gas undergoes adiabatic expansion against the piston of a cylinder. As a result, the temperature of the gas drops from 1150 K to 400 K. The number of moles of the gas required to obtain 2300 J of work from the expansion is .................
The decimal equivalent of the binary number 110.101 is ................
The 7th bright fringe in the Young’s double slit experiment using a light of wavelength 550 nm shifts to the central maxima after covering the two slits with two sheets of different refractive indices \(n_1\) and \(n_2\) but having the same thickness 6 µm. The value of \( |n_1 - n_2| \) is .............
If the wavelength of Kα2 X-ray line of an element is 1.544 Å, then the atomic number \( Z \) of the element is ................
An object of 2 cm height is placed at a distance of 30 cm in front of a concave mirror with radius of curvature 40 cm. The height of the image is ............. cm.
The electrostatic energy (in units of \( \frac{1}{4\pi \epsilon_0} \, \text{J} \)) of a uniformly charged spherical shell of total charge 5 C and radius 4 m is ...........
An infinitely long very thin straight wire carries uniform line charge density \( 8\pi \times 10^{-2} \, \text{C/m} \). The magnitude of electric displacement vector at a point located 20 mm away from the axis of the wire is ......... C/m².
An atomic nucleus X with half-life \( T_X \) decays to a nucleus Y, which has half-life \( T_Y \). The condition(s) for secular equilibrium is/are
In a typical human body, the amount of radioactive \(^{40}K\) is \(3.24 \times 10^{-5}\) percent of its mass. The activity due to \(^{40}K\) in a human body of mass 70 kg is .................. kBq.
Sodium (Na) exhibits body-centered-cubic (BCC) crystal structure with atomic radius 0.186 nm. The lattice parameter of Na unit cell is ................... nm.
Light of wavelength 680 nm is incident normally on a diffraction grating having 4000 lines/cm. The diffraction angle (in degrees) corresponding to the third-order maximum is ........
Two gases having molecular diameters \( D_1 \) and \( D_2 \), and mean free paths \( \lambda_1 \) and \( \lambda_2 \), respectively, are trapped separately in identical containers. If \( D_2 = 2D_1 \), then \( \lambda_1 / \lambda_2 = \) ..........
Which of the following statement(s) is/are true?
For an underdamped harmonic oscillator with velocity \( v(t) \),
Out of the following statements, choose the correct option(s) about a perfect conductor.
In the X-ray diffraction pattern recorded for a simple cubic solid (lattice parameter \( a = 1 \) Å) using X rays of wavelength 1 Å, the first order diffraction peak(s) would appear for the
Consider a classical particle subjected to an attractive inverse-square force field. The total energy of the particle is \( E \) and the eccentricity is \( \epsilon \). The particle will follow a parabolic orbit if
The relation between the nuclear radius \( R \) and the mass number \( A \), given by \( R = 1.2 A^{1/3} \) fm, implies that
Consider an object moving with a velocity \( \vec{v} \) in a frame which rotates with a constant angular velocity \( \vec{\omega} \). The Coriolis force experienced by the object is
The gradient of a scalar field \( S(x, y, z) \) has the following characteristic(s).
A thermodynamic system is described by the \( P, V, T \) coordinates. Choose the valid expression(s) for the system.
The maximum number of intensity minima that can be observed in the Fraunhofer diffraction pattern of a single slit (width 10 µm) illuminated by a laser beam (wavelength 0.630 µm) will be