Q. The vector that is normal to the surface 2x z2 - 3x y - 4 x = 7 at the point (1, –1, 2) is             (A) 2i - 3j + ...

Q. For any real, square and non-singular matrix B , the det B-1 is (A) zero           (B) (det B)-1    (C) -(det B)   (D) det B Ans: (det B)-1 Sol: For any matrix whose inverse exists i.e. non-singular BB-1 = I |BB-1| = 1 |B||B-1| = 1 det (B-1) = (det B)-1

Q. In a certain two-dimensional lattice, the energy dispersion of the electrons is where 𝑘⃗→ = (𝑘𝑥 , 𝑘𝑦) denotes the wave vector, 𝑎 is the lattice constant and 𝑡 is a constant in units of eV. In this lattice the effective mass tensor 𝑚𝑖𝑗 of electrons calculated at the center of the ...

Q. Two events, one on the earth and the other one on the Sun, occur simultaneously in the earth’s frame. The time difference between the two events as seen by an observer in a spaceship moving with velocity 0.5c in the earth’s frame along the line joining the earth to the Sun is Δ𝑡, where c is the ...

Q. Electrons with spin in the 𝑧-direction (𝑧̂) are passed through a Stern-Gerlach (SG) set up with the magnetic field at 𝜃 = 60o from 𝑧̂ . The fraction of electrons that will emerge with their spin parallel to the magnetic field in the SG set up (rounded off to two decimal places) is         ...

Q. Consider two systems A and B each having two distinguishable particles. In both the systems, each particle can exist in states with energies 0, 1, 2 and 3 units with equal probability. The total energy of the combined system is 5 units. Assuming that the system A has energy 3 units and the ...

Q. Consider a system of three charges as shown in the figure below: For 𝑟 = 10 m; 𝜃 = 60 degrees; 𝑞 = 10−6 Coulomb, and 𝑑 = 10−3 m, the electric dipole potential in volts (rounded off to three decimal places) at a point (𝑟, 𝜃) is Ans: 0.045 Sol:

Q. In a thermally insulated container, 0.01 kg of ice at 273 K is mixed with 0.1 kg of water at 300 K. Neglecting the specific heat of the container, the change in the entropy of the system in J/K on attaining thermal equilibrium (rounded off to two decimal places) is (Specific heat of water is ...

Q. A radioactive element X has a half-life of 30 hours. It decays via alpha, beta and gamma emissions with the branching ratio for beta decay being 0.75. The partial half-life for beta decay in unit of hours is            Ans: 40 Sol:

Q. Let 𝜃 be a variable in the range − 𝜋 ≤ 𝜃 < 𝜋.  Now consider a function If its Fourier series is written as then the value of 𝑚=−∞   𝑚 |𝐶3|2 (rounded off to three decimal places) is            Ans: 0.011

Q. A projectile of mass 1 kg is launched at an angle of 30° from the horizontal direction at 𝑡 = 0 and takes time 𝑇 before hitting the ground. If its initial speed is 10 ms−1 , the value of the action integral for the entire flight in the units of kg m2s−1 (rounded off to one decimal place) is ...

Q. The ground state electronic configuration of the rare-earth ion (Nd3+) is 4f 35s25p6.Assuming LS coupling, the Land𝑒́ 𝑔-factor of this ion is 8/11 . The effective magnetic 11 moment in units of Bohr magneton 𝜇B (rounded off to two decimal places) is Ans: 3.62 Sol: