Q. The Hamiltonian for a quantum harmonic oscillator of mass 𝑚 in three dimensions is where 𝜔 is the angular frequency. The expectation value of 𝑟2 in the first excited state of the oscillator in units of (rounded off to one decimal place) is Ans: 2.5 Sol:

Q. The electric field of an electromagnetic wave in vacuum is given by The wave is reflected from the 𝑧 = 0 surface. If the pressure exerted on the surface is 𝛼𝜖0𝐸20, the value of 𝛼 (rounded off to one decimal place) is                        Ans: 0.8 Sol:

Q. An infinitely long thin cylindrical shell has its axis coinciding with the z-axis. It carries a surface charge density 𝜎0cos𝜙, where 𝜙 is the polar angle and 𝜎0 is a constant. The magnitude of the electric field inside the cylinder is Ans:

Q. A massive particle X in free space decays spontaneously into two photons. Which of the following statements is true for X? (A) X is charged  (B) Spin of X must be greater than or equal to 2  (C) X is a boson  (D) X must be a baryon Ans: X is a boson

Q. In order to estimate the specific heat of phonons, the appropriate method to apply would be (A) Einstein model for acoustic phonons and Debye model for optical phonons  (B) Einstein model for optical phonons and Debye model for acoustic phonons  (C) Einstein model for both optical and ...

Q. Consider a one-dimensional gas of 𝑁 non-interacting particles of mass 𝑚 with the Hamiltonian for a single particle given by , The high temperature specific heat in units of 𝑅 = 𝑁𝑘𝐵 (𝑘𝐵 is the Boltzmann constant) is (A) 1(B) 1.5(C) 2(D) 2.5 Ans: 1

Q. Considering baryon number and lepton number conservation laws, which of the following processes is/are allowed? (i)   𝑝 → 𝜋0 + 𝑒+ + 𝜈𝑒 (ii) 𝑒+ + 𝜈𝑒 → 𝜇+ + 𝜈𝜇 (A) both (i) and (ii)(B) only (i) (C) only (ii) (D) neither (i) nor (ii) Ans: only (ii)

Q. In a water flooding experiment, the pressure gradients in the displacing and displaced phases are 400 psi/ft and 350 psi/ft, respectively. Assume that the displacement front is stable in the absence of capillary and gravity forces. Consider that only water flows upstream and only oil flows ...

Q. In an active water drive during a certain period, the rate of production and reservoir pressure remain constant. The water influx into the reservoir from the aquifer is 6000 bbl/day. The surface oil and water production rates are 3000 STB/day and 1500 STB/day, respectively. The current ...

Q. Cement weighing 100 kg is mixed with 50 liters of water. The specific gravity of cement is 3.14 and the density of water is 1000 kg/m3. Neglecting volume changes, the resulting density of the slurry is______kg/m3 (round off to 1 decimal place). Ans: 1820-1880 Sol:

Q. In a drilling rig, the crown block and the traveling block have three and two sheaves, respectively. A single wireline connects the hoisting drum to the deadline anchor as shown in the figure. Neglect the weight of the pulleys and the wireline, and friction between the sheaves and wireline. The ...

Q. A vertical well of 8000 ft is producing below bubble point pressure. Oil and water each is produced at the rate of 500 bbl/day. The indicated bottom hole pressure is 3000 psi. If the same gas to liquid ratio (GLR) is maintained, using the given figure, the new bottom hole pressure at 5000 ft ...