List of top Questions asked in Indian Institute Of Technology Joint Admission Test for MSc

Consider a binary number with m digits, where m is an even number. This binary number has alternating 1's and 0's, with digit 1 in the highest place value. The decimal equivalent of this binary number is

Consider a conical region of height h and base radius R with its vertex at the origin. Let the outward normal to its base be along the positive z-axis, as shown in the figure. A uniform magnetic field, \(\overrightarrow{B}=B_0\hat{z}\) exists everywhere. Then the magnetic flux through the base (\(\Phi_b\)) and that through the curved surface of the cone (\(\Phi_c\)) are

Consider a particle of mass m moving in a plane with a constant radial speed \(\dot{r}\) and a constant angular speed \(\dot{\theta}\). The acceleration of the particle in (r,\(\theta\)) coordinates is

For an ideal intrinsic semiconductor, the Fermi energy at 0 K

In a dilute gas, the number of molecules with free path length ≥ x is given by N(x) = N₀e^-x/λ, where N₀ is the total number of molecules and A is the mean free path. The fraction of molecules with free path lengths between λ and 2λ is

The current through a series RL circuit, subjected to a constant emf \(\epsilon\), obeys \(L\frac{di}{dt}+iR=\epsilon\). Let L=1mH, R=1k\(\Omega\) and \(\epsilon\)=1V. The initial condition is i(0)=0. At t=1\(\mu s\), the current in mA is

The dispersion relation for certain type of waves is given by \(\omega=\sqrt{k^2+a^2}\), where k is the wave vector and a is a constant. Which one of the following sketches represents v_g, the group velocity?

The function f(x) = e^sinx is expanded as a Taylor series in x, around x = 0, in the form f(x) = \(\sum^{\infin}_{n=0}a_nx^n\). The value of a₀ + a₁ + a₂ is