Q. The link lengths of a planar four bar mechanism are AB = 100 mm, BC = 25 mm, CD = 75 mm and DA = 90 mm. For achieving the full rotation of both the input (crank) as well as the output (follower) links, the link that needs to be fixed is Ans: BC […]
Q. Match the crystal structure in Column A with the corresponding packing fractions in Column B of the table Column A Column B 1 Simple cubic P 0.74 2 Hexagonal close-packed Q 0.68 3 Body-centered cubic R 0.52 4 Face-centered cubic (A) 1-P, 2-R, 3-Q, 4-Q (B) 1-R, 2-P, 3-R, 4-Q (C) 1-R, 2-P,
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 + 8k (B) 2i + 3j + 4k (C) 7i – 3j + 8k (D) 7i – 5j + 8k Ans: 7i – 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
For any real, square and non-singular matrix B , the det B-1 is Read More »
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 Brillouin zone has
In a certain two-dimensional lattice, the energy dispersion of the electrons is Read More »
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
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 system
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:
Consider a system of three charges as shown in the figure below Read More »
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
