JEST Joint Entrance Screening Test 2018 Physics Sample Question Paper
Name of the University : Indira Gandhi Centre for Atomic Research
Exam : Joint Entrance Screening Test JEST 2018
Document Type : Sample Question Paper
Category or Subject : Physics
Website : https://www.jest.org.in/
Download Model Question Paper : https://www.pdfquestion.in/uploads/23159-jest2017.pdf
Joint Entrance Screening Test Question
** Applicants seeking admission for a Ph.D / Integrated Ph.D Programme in Physics or Theoretical Computer Science or Neuroscience or Computational Biology in one of the Participating Institutes may appear for the Joint Entrance Screening Test (JEST) at one of the Exam Centers.
Related : Abhimanu IAS Test Series 2017 Sample Question Paper : www.pdfquestion.in/23153.html
Eligibility
** Participating Institutes have their own eligibility criteria.
** Applicants who are expected to complete their final examinations by August of each year are also eligible to appear for the JEST exam of that year.
Instructions
Please Read The Instructions Carefully :
1. Do not open the seal of the question paper before 10:00 AM.
2. You are given a question paper including a few blank sheets, and a machine readable Optical Mark Reader (OMR) sheet.
3. Enter your registration number on top of this question paper with black/blue pen.
4. Part A contains 15 questions, and carry 3 (three) marks each for correct answer, and -1 (negative one) mark for incorrect answer. Part B contains 10 questions and each carries 3 (three marks). These questions must be answered by integers of 4 digits each. Answer these questions on the OMR by filling in bubbles in the OMR sheet.
Note that if the answer is, e.g. 25, you must fill in 0025 and if it is, e.g. 5, you must fill in 0005. If it is 0, you must fill in 0000. If the zeros are not filled in (where required), the answer will be not be credited. There are NO NEGATIVE MARKS for these questions. Part C contains 25 questions, and each carries 1 (one) mark for the correct answer, and -1/3 (negative one third) mark for incorrect answer. Multiple choice questions have only one correct answer.
5. On the OMR sheet, enter the appropriate Question Booklet Series (X, Y or Z) that is mentioned on the top right of the question paper.
6. On the OMR sheet, enter your name, registration number, and signature at the appropriate places. Strictly follow the instructions written on the OMR sheet.
7. On the OMR sheet, completely darken the bubble corresponding to your answer. Strictly follow the instructions written on the OMR sheet.
8. Only non-programmable scientific calculator is allowed, and exchange of calculators among the candidates is not permitted. Use of other items like electronic diary, writing pads, pencil box, beeper, cameras, mobile phones, palmtops, laptops, pagers etc., are not permitted inside the examination hall.
9. For rough work, use only the blank pages attached at the end of the question paper.
10. At the end of the examination, carefully separate the OMR sheet at the marked position, and return the original copy of the OMR sheet to the invigilator. Candidates are allowed to take away the candidates’ copy of the OMR, and the question paper.
Physics – Sample Paper
Part-A
3-Mark Questions :
1. Given a matrix M =2 11 2 , which of the following represents cos(M=6)?
2. The wavefunction of a hydrogen atom is given by the following superposition of energy eigenfunctions nlm(~r) (n; l;m are the usual quantum numbers)
3. It is found that when the resistance R indicated in the figure below is changed from 1 k to 10 k, the current flowing through the resistance R0 does not change. What is the value of the resistor R0?
(A) 5 k
(B) 100
(C) 10 k
(D) 1 k
4. A hoop of radius a rotates with constant angular velocity ! about the vertical axis as shown in the figure. A bead of mass m can slide on the hoop without friction. If g < !2a, at what angle apart from 0 and is the bead stationary
(A) tan = g=!2a
(B) sin = g=!2a
(C) cos = g=!2a
(D) tan = g=!2a
5. A spin-1/2 particle in a uniform external magnetic field has energy eigenstates j1i and j2i. The system is prepared in ket-state (j1i + j2i)= p 2 at time t = 0. It evolves to the state described by the ket (j1i ?? j2i)= p 2 in time T. The minimum energy difference between two levels is:
(A) h=6T
(B) h=4T
(C) h=2T
(D) h=T
6. You receive on average 5 emails per day during a 365-days year. The number of days on average on which you do not receive any emails in that year are:
(A) More than 5
(B) More than 2
(C) 1
(D) None of the above
7. The H2 molecule has a reduced mass M = 8:35 10??28 kg and an equilibrium internuclear distance R = 0:742 10??10 m. The rotational energy in terms of the rotational quantum number J is:
(A) Erot(J) = 7J(J ?? 1) meV
(B) Erot(J) = 5 2J(J + 1) meV
(C) Erot(J) = 7J(J + 1) meV
(D) Erot(J) = 5 2J(J ?? 1) meV
8. The maximum relativistic kinetic energy of particles from a radioactive nucleus is equal to the rest mass energy of the particle. A magnetic field is applied perpendicular to the beam of particles, which bends it to a circle of radius R. The field is given by:
(A) 3m0c=eR
(B) p 2m0c=eR
(C) p 3m0c=eR
(D) p 3m0c=2eR
9. The central force which results in the orbit r = a(1 + cos ) for a particle is proportional to:
(A) r
(B) r2
(C) r??2
(D) None of the above
11. A transistor in common base configuration has ratio of collector current to emitter current and ratio of collector to base current . Which of the following is true?
(A) = =( + 1)
(B) = ( + 1)=
(C) = =( ?? 1)
(D) = ( ?? 1)=
The energy of a particle is given by E = jpj + jqj, where p and q are the generalized momentum and coordinate, respectively. All the states with E E0 are equally probable and states with E > E0 are inaccessible. The probability density of finding the particle at coordinate q, with q > 0 is
(A) (E0 + q)=E2 0
(B) q=E2 0
(C) (E0 ?? q)=E2 0
(D) 1=E0
Part-B
3-Mark Questions :
16. A proton is confined in an infinite square well of width 4 femtometer. Calculate the energy of the photon emitted when the proton undergoes a transition from the excited state (n = 11) to the ground state (n = 1). Find the answer only up to the first four significant digits.
18. A solid insulating ball of radius a = 1 cm is surrounded by a conducting spherical shell with an inner radius of b = 2 cm and outer radius c = 2:2 cm. The inner ball has a charge Q1 = 10 C, which is uniformly distributed throughout its volume. The conducting spherical shell contains a charge of Q2 = ??10 C. Determine the electrostatic potential (in Volts) at a point r = 1:5 cm. Consider 1 40 = 9 109 Nm2=C2.
19. What is the smallest possible time necessary to freeze 2 kg of water at 273 K if a 50 watt motor is available and the outside air (hot reservoir) is at 300 K.
20. A bead slides along a smooth wire bent in the shape of parabola z = cr2. The bead rotates in a circle of radius 10 cm, when the wire is rotating about its verticle symmetry axis with angular velocity 10 radians/s. Take g = 10 m/s. Find the value of c
21. A 5 V supply is across a series combination of a Si diode, a Ge diode and a 100 resistor. Find the power dissipated in the resistor.
22. A point like charge Q = 10 C is split into two charges Q1 C and (Q ?? Q1) C. What should be the magnitude of Q1 so as to obtain maximal repulsive force between the two charges?
24. A particle (in one dimension) is described by the wave function (x) = 0 for x < 0 and (x) = Ce??x(1 ?? e??x) for x > 0, where x is in nanometers and C is a constant. Calculate the average position for the particle. Express your answer in units of 10??3nm.
25. A spacecraft in an orbit about earth has the spped of 10,160 m/s at a perigee of 6680 km from earth’s center. What speed does the spacecraft have at apogee of 42, 200 km?
Part-C
1-Mark Questions :
26. The adjoint of a differential operator d dx acting on a wavefunction (x) for a quantum mechanical system is
27. In Millikan’s oil-drop experiment an oil drop of radius r, mass m and charge q = 6r(v1+v2)=E is moving upwards with a terminal velocity v2 due to an applied electric field of magnitude E, where is the coefficient of viscosity. The acceleration due to gravity is given by
28. The electric field ~E = E0 sin(!t ?? kz)^x + 2E0 sin(!t ?? kz + =2)^y represents:
(A) a linearly polarized wave
(B) a right-hand circularly polarized wave
(C) a left-hand circularly polarized wave
(D) an elliptically polarized wave
29. An ideal gas has a specific heat ratio CP=CV = 2. Starting at a temperature T1 the gas undergoes an isothermal compression to increase its density by a factor of two. After this an adiabatic compression increases its pressure by a factor of two. The temperature of the gas at the end of the second process would be
30. Suppose yz plane forms the boundary between two linear dielectric media I and II with dielectric constant I = 3 and II = 4, respectively. If the electric field in region I at the interface is given by ~EI = 4^x + 3^y + 5^z, then the electric field ~EII at the interface in region II is
32. Circular fringes are obtained with a Michelson interferometer using 600nm laser light. What minimum displacement of one mirror will make the central fringe from bright to dark?
(A) 600 nm
(B) 300 nm
(C) 150 nm
(D) 120 °
33. If ~k is the wavevector of incident light (j~kj = 2=, is the wavelength of light) and ~G is a reciprocal lattice vector, then the Bragg’s law can be written as:
(A) ~k + ~G = 0
(B) 2~k ~G + G2 = 0
(C) 2~k ~G + k2 = 0
(D) ~k ~G = 0
34. A gas contains particles of type A with fraction 0:8, and particles of type B with fraction 0:2. The probability that among 3 randomly chosen particles at least one is of type A is:
(A) 0:8
(B) 0:25
(C) 0:33
(D) 0:992
35. The number of different Bravais lattices possible in two dimensions is:
(A) 2
(B) 3
(C) 5
(D) 6