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  #1  
Old January 24th, 2014, 03:23 PM
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Join Date: Nov 2011
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Here I am sharing the previous year Physics Question paper of JEST exam, can you please provide me the same??

Joint Entrance Screening Test (JEST) is entrance test for admission in Ph.D Courses.

As per your request, I am giving you question paper of the JEST physics. hope it will be fruitful for you.

Q 1. If a person has a meter scale and he has to measure a length of 50 m. Each time he
measures the measurement lies from 99.8 to 100.2 cm. Estimate the net error, when takes
measurement 50 times?
(a) 0.2 cm (b) 0.4 cm (c) 0.82 cm (d) 10 cm.

Q 2. If coherent source of light through A,B has wavelength λ such AB = 4λ . If the detector
is moving along the loop of radius R such that R>> AB then if the radius is increased
gradually what effect will it have on the no. of maxima detected by detector D?
(a) increase (b) decrease (c) first increase than decrease (d) none

Q 3. Slit separation = d
Slit width = w
A plane wavefront incident, when will the 3rd maxima will be missing
(a) 3d = 2w (b) 2d = 3w (c) d = 2w

Q 4. Find
0
lim
z→
( 2 ) ( 2 )
2
Real z Img z
z
+
(a) i (b) 1 (c)-1 (d) limit do not exist

Q 5. If 2P −1 = Prime no.
(a) P is a odd no. (b) P can composite no. (c) P is necessarily composite no.
(d) P is Prime no.

Q 6. Find the velocity of box
(a) v cosθ (b) v sinθ (c) v tanθ

Q 7. What is the volume of a sphere in 4-dimensional space of unit radius?
(a)
2
16
π
(b) 4
3
π
(c) 4π i

Q 8. A heard ball dropped from a 1 m height and rebounces to 95 cm. Calculate the total
distance travelled by ball?
(a) 1880 cm (b) 2160 cm

Q 9. Evaluate 3
1
2 2 3
z
π i z z i
⎫⎬
+ − ⎭ 􀁶∫
(a) 0, (b) 2π i

Q 10. If EM waveE 􀁇
is filed component along y in with magnitude Eo, travelling along x-axis
with frequency w. represent this
Ans. cos ( ) o E = E Kx − wt yλ

Q 11. If an astronaut knows the maximum and min distance between the moon of a planet and
the planet maximum orbital velocity of moon is know which quantity of the following
can’t be calculated.
A
B
A, B are known
(a) mass of planet (b) mass of moon (c) Time of the orbit (d) semi major axis.

Q 12. If P and q are two distinct prime numbers then how many divisors p2q3 have?

Q 13. represent carnot cycle in T – S diagram

Q 14. If proton and α − particle accelerated by same potential v, find the ratio of debroglie
wavelength ?
(a) 2 2:1 (b) 2:1 (c) 1 : 2 (d) none of these

Q 15. The difference in arithmetic and geometric mean of two positive integer m and n is equal
to 1. Then
2
m and
2
n are
(a) perfect square
(b)

Q 16. Net capacitance
(a) C1 +C2 +C3 (b)
1 2 3
1 1 1
C C C
+ + (c) 2 3
1
2 3
C C C
C C
+
+

Q 17. Two events are taking place at a distance 5 km with a time interval 5μ s. In an inertial
frame. An observer observes two events as simultaneous. Determine the speed of
observer.

Q 18. Find the time taken for blue light λ = 400nm, to cover a distance of 80 km in optical
fiber having refractive .Index = 1.6
Ans. 427 μ sec.

Q 19. Find ( ) 5
1 1
1 2 ...
k
k l
l
= =
ΣΣ + +

Q 20. ( )
3
, 1 cos o
a r E r
r
φ θ θ
⎡ ⎛ ⎞ ⎤ = − ⎢ −⎜ ⎟ ⎥
⎢⎣ ⎝ ⎠ ⎥⎦
(Potential distribution of sphere of change q)
Find the change distribution
(a) 2 o E ∈cosθ (b) cos o ∈E θ

Q 21. A small mass m moving with velocity collides with turnable table get attached after
collision and moves with angular velocity w? find w?

Q 22. Find the solution of given differential equation.
x dy 3y x2
dx
− =
(a) y = x2 + cx2 (b) (c) (d)

Q 23. If x and y both are non-zero then the value of x2 + xy + y2
(a) always +ve (b) always –ve (c) 0 (d) sometimes +ve and sometime –ve

Q 24. ( )
2 3
x 2 3
V = kx + Lx (a potential fn for a particle in a box)
(a) V is oscillatory (b) v is never osicllater (c)

Q 25. Find eigen value and eigen vector
2 2
2 1
⎡ ⎤
⎢ ⎥
⎢⎣ ⎥⎦

Q 26. Then
(a) B Cl F E = E = E (b) B Cl F E = E ≤ E (c) F B Cl E > E > E (d) F B Cl E > E = E

Q 27. A curve moves from origin to a point P(1, 1) then ( 2 2 )
0
P ∫ y′ + yy′ + y dx will be stationary
for
(a) y = x (b) y = x2

Q 28. A proton accelerated by a potential difference of 1000 V and enter into magnetic field B
= 1000 T along a circular path of r = 20 cm. Determine the velocity of proton during
circular motion.
(a) 1 m/s (b) 105m/s (c) 100 m/s (d) none

Q 29. A mass m is attached to a spring with one end to a rigid support and to other end a spring
is connected which is attached to a mass m. having same spring constant calculate the
node frequency.

Q 30. A particle moving with velocity v hits the uniform circular disc at rest with impact
parameter (b < R) afterwards both particles and disc rotates with same angular velocity
ω . then ω in terms of v is,

Q 31. If donors are added to n-type semiconductor then
(i) Electrons increases holes remain constant
(ii) Electrons increases holes decreases
(iii) Electrons increases holes increases
(iv) No effect will takes place.

Q 32. A particle X of mass M at rest decays into a particle A of mass mA and another particle of
zero mass. Determine the energy of A.

Q 33. If B/A decreases with increases atomic number, then what does it indicate about nuclear
number, than what does it indicate about nuclear forces?
(a) charge dependent
(b) Charge independent

Q 34. The spin and parity of 12C and 17O?
(a) 0 , 5
2
+
+ (b) 0 , 5
2

+ (c) 1 , 7
2 2
+ +
(d) 0 , 3
2
+


Q 35. A charge q drops from rest from height d to infinite grounded conducting plates.
Calculate the time to reach the charge to plates.
For more questions, consider the attachments.






Attached Files Available for Download
File Type: pdf JEST physics 2012 paper.pdf (383.6 KB, 91 views)
File Type: pdf JEST physics 2013 paper-2.pdf (255.7 KB, 83 views)
File Type: pdf JEST physics 2014 paper.pdf (250.1 KB, 92 views)

Last edited by Aakashd; October 18th, 2019 at 02:13 PM.
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  #2  
Old January 26th, 2014, 11:15 AM
Super Moderator
 
Join Date: Jun 2013
Default Re: Previous year Physics Papers of JEST exam

Joint Entrance Screening Test (JEST) is conducted for the candidates who are interested to get admission in to Ph.D. Programs in the subjects of Physics / Theoretical Computer Science / Neuroscience.

Here I am sharing the Physics Question paper of Joint Entrance Screening Test (JEST) Exam

1. If Jx; Jy; Jz are angular momentum operators, the eigenvalues of the operator (Jx + Jy)=_h are
a) real and discrete with rational spacing
b) real and discrete with irrational spacing
c) real and continuous
d) not all real
2. Compute
lim
z!0
Re(z2) + Im(z2)
z2 :
a) The limit does not exist.
b) 1
c) _i
d) _1
3. The electric _elds outside (r > R) and inside (r < R) a solid sphere with a uniform volume charge
density are given by ~Er>R =
1
4__0
q
r2 ^r and ~Er 1
4__0
q
R3 r ^r respectively, while the electric _eld
outside a spherical shell with a uniform surface charge density is given by ~Er>R =
1
4__0
q
r2 ^r, q be-
ing the total charge. The correct ratio of the electrostatic energies for the second case to the _rst case is
a) 1:3
b) 9:16
c) 3:8
d) 5:6
4. A particle of mass m is thrown upward with velocity v and there is retarding air resistance proportional
to the square of the velocity with proportonality constant k. If the particle attains a maximum height
after time t, and g is the gravitational acceleration, what is the velocity v?
a) sk
g
tan(rg
k
t)
b) pgk tan(rg
k
t)
c) rg
k
tan(pgkt)
d) pgk tan(pgkt)
5. A quantum mechanical particle in a harmonic oscillator potential has the initial wavefunction
0(x) + 1(x); where 0 and 1 are the real wavefunctions in the ground and _rst excited states
of the harmonic oscillator Hamiltonian. For convenience we take m = _h = ! = 1 for the oscillator.
What is the probability density of _nding the particle at x at time t = _?
1
a) ( 1(x) _ 0(x))2
b) ( 1(x))2 _ ( 0(x))2
c) ( 1(x) + 0(x))2
d) _ 1(x))2 + ( 0(x)_2
6. A K meson (with a rest mass of 494 MeV) at rest decays into a muon (with a rest mass of 106 MeV)
and a neutrino. The energy of the neutrino, which can be taken to be massless, is approximately
a) 120 MeV
b) 236 MeV
c) 300 MeV
d) 388 MeV
7. There are on average 20 buses per hour at a point, but at random times. The probability that there
are no buses in _ve minutes is closest to
a) 0.07
b) 0.60
c) 0.36
d) 0.19
8. Two drunks start out together at the origin, each having equal probability of making a step simulta-
neously to the left or right along the x axis. The probability that they meet after n steps is
a)
1
4n
2n!
n!2
b)
1
2n
2n!
n!2
c)
1
2n 2n!
d)
1
4n n!
9. If, in a Kepler potential, the pericentre distance of a particle in a parabolic orbit is rp while the radius
of the circular orbit with the same angular momentum is rc, then
a) rc = 2rp
b) rc = rp
c) 2rc = rp
d) rc = p2rp
10. Under a Galilean transformation, the coordinates and momenta of any particle/system transform as:
t0 = t, ~r0 = ~r + ~vt and ~p0 = ~p + m~v, where ~v is the velocity of the boosted frame with respect to the
original frame. A unitary operator carrying out these transformations for a system having total mass
M, total momentum ~P and center of mass coordinate ~X is
2
a) eiM~v: ~X =_heit~v: ~P=_h
b) eiM~v: ~X =_he_it~v: ~P=_he_iMv2t=(2_h)
c) eiM~v: ~X =_heit~v: ~P=_heiMv2t=(2_h)
d) eit~v: ~P=_he_iMv2t=(2_h)
11. The equation describing the shape of a curved mirror with the property that the light from a point
source at the origin will be reected in a beam of rays parallel to the x-axis is (with a as some constant)
a) y2 = ax + a2
b) 2y = x2 + a2
c) y2 = 2ax + a2
d) y2 = ax3 + 2a2
12. The vector _eld xz^i + y^j in cylindrical polar coordinates is
a) _(z cos2 _ + sin2 _)^e_ + _ sin _ cos _(1 _ z)^e_
b) _(z cos2 _ + sin2 _)^e_ + _ sin _ cos _(1 + z)^e_
c) _(z sin2 _ + cos2 _)^e_ + _ sin _ cos _(1 + z)^e_
d) _(z sin2 _ + cos2 _)^e_ + _ sin _ cos _(1 _ z)^e_
13. A spherical planet of radius R has a uniform density _ and does not rotate. If the planet is made up
of some liquid, the pressure at any point r from the center is
a)
4__2G
3
(R2 _ r2)
b)
4__G
3
(R2 _ r2)
c)
2__2G
3
(R2 _ r2)
d)
_G
2
(R2 _ r2)
14. A simple model of a helium-like atom with electron-electron interaction is replaced by Hooke's law
force is described by hamiltonian __h2
2m _r2
1 + r2
2 _+ 1
2m!2 _r2
1 + r2
2__ _
4m!2j~r1_~r2j2: What is the exact
ground state energy?
a) E = 3=2_h! _1 + p1 + __
b) E = 3=2_h! _1 + p__ c) E = 3=2_h!p1 _ _
d) E = 3=2_h! _1 + p1 _ __
3
15. Consider the state 0B@
1=2
1=2
1=p2
1CA
corresponding to the angular momentum l = 1 in the Lz basis of states
with m = +1; 0;_1. If L2
z is measured in this state yielding a result 1, what is the state after the
measurement?
a) 0B@
1
0
0
1CA
b) 0B@
1=p3
0 p2=3
1CA
c) 0B@
0
0
1
1CA
d) 0B@
1=p2
0
1=p2
1CA
16. A particle of mass m is contained in a one-dimensional in_nite well extending from x = _L=2 to
x = L=2. The particle is in its ground state given by 0(x) = p2=L cos(_x=L). The walls of the box
are moved suddenly to form a box extending from x = _L to x = L. What is the probability that the
particle will be in the ground state after this sudden expansion?
a) (8=3_)2
b) 0
c) (16=3_)2
d) (4=3_)2
17. Consider a system of two particles A and B. Each particle can occupy one of three possible quan-
tum states j1i, j2i, and j3i. The ratio of the probability that the two particles are in the same state
to the probability that the two particles are in di_erent states is calculated for bosons and classical
(Maxwell-Boltzman) particles. They are respectively
a) 1; 0
b) 1=2; 1
c) 1; 1=2
d) 0; 1=2
18. For a diatomic ideal gas near room temperature, what fraction of the heat supplied is available for
external work if the gas is expanded at constant pressure?
a) 1/7
b) 5/7
c) 3/4
d) 2/7
19. A box contains 100 coins out of which 99 are fair coins and 1 is a double-headed coin. Suppose you
4
choose a coin at random and toss it 3 times. It turns out that the results of all 3 tosses are heads.
What is the probability that the coin you have drawn is the double-headed one?
a) 0.99
b) 0.925
c) 0.075
d) 0.01
20. The free fall time of a test mass on an object of mass M from a height 2R to R is
a) (_=2 + 1)s R3
GM
b) s R3
GM
c) (_=2)s R3
GM
d) _s2R3
GM
21. A at surface is covered with non-overlapping disks of same size. What is the largest fraction of the
area that can be covered?
a)
3
_
b)
5_
6
c)
6
7
d)
_
2p3
22. In an observer's rest frame, a particle is moving towards the observer with an energy E and momentum
p. If c denotes the velocity of light in vacuum, the energy of the particle in another frame moving in
the same direction as the particle with a constant velocity v is
a)
(E + vp)
p1 _ (v=c)2
b)
(E _ vp)
p1 _ (v=c)2
c)
(E + vp)
[1 _ (v=c)2]2
d)
(E _ vp)
[1 _ (v=c)2]2
23. Consider a uniform distribution of particles with volume density n in a box. The particles have an
isotropic velocity distribution with constant magnitude v. The rate at which the particles will be
emitted from a hole of area A on one side of this box is
5
a) nvA
b) nvA=2
c) nvA=4
d) none of the above
24. A metal su_ers a structural phase transition from face-centred cubic (FCC) to the simple cubic (SC)
structure. It is observed that this phase transition does not involve any change of volume. The near-
est neighbour distances dfc and dsc for the FCC and the SC structures respectively are in the ratio
(dfc=dsc) [Given 21=3 = 1:26]
a) 1.029
b) 1.122
c) 1.374
d) 1.130
25. At `equilibrium' there can not be any free charge inside a metal. However, if you forcibly put charge in
the interior then it takes some _nite time to `disappear', i.e. move to the surface. If the conductivity,
_, of a metal is 106 (m)_1 and the dielectric constant _0 = 8:85 _ 10_12 Farad/m, this time will be
approximately:
a) 10_5 sec
b) 10_11 sec
c) 10_9 sec
d) 10_17 sec
PART B: ONE MARK QUESTIONS
26. What is the value of the following series?
_1 _
1
2!
+
1
4! _ _ _ __2
+ _1 _
1
3!
+
1
5! _ _ _ __2
a) 0
b) e
c) e2
d) 1
27. The operator _ d
dx _ x__ d
dx
+ x_
is equivalent to
6
a)
d2
dx2 _ x2
b)
d2
dx2 _ x2 + 1
c)
d2
dx2 _ x
d
dx
x2 + 1
d)
d2
dx2 _ 2x
d
dx _ x2
28. The coordinate transformation
x0 = 0:8x + 0:6y; y0 = 0:6x _ 0:8y
represents
a) a translation.
b) a proper rotation.
c) a reection.
d) none of the above.
29. An electromagnetic wave of frequency ! travels in the x-direction through vacuum. It is polarized in
the y-direction and the amplitude of the electric _eld is E0. With k = !=c where c is the speed of
light in vacuum, the electric and the magnetic _elds are then conventionally given by
a) ~E = E0 cos(ky _ !t) ^x and ~B =
E0
c
cos(ky _ !t) ^z
b) ~E = E0 cos(kx _ !t) ^y and ~B =
E0
c
cos(kx _ !t) ^z
c) ~E = E0 cos(kx _ !t) ^z and ~B =
E0
c
cos(kx _ !t) ^y
d) ~E = E0 cos(kx _ !t) ^x and ~B =
E0
c
cos(ky _ !t) ^y
30. Consider a particle with three possible spin states: s = 0 and _1. There is a magnetic _eld h present
and the energy for a spin state s is _hs. The system is at a temperature T. Which of the following
statements is true about the entropy S(T)?
a) S(T) = ln 3 at T = 0, and 3 at high T
b) S(T) = ln 3 at T = 0, and zero at high T
c) S(T) = 0 at T = 0, and 3 at high T
d) S(T) = 0 for T = 0, and ln 3 at high T
31. Consider three situations of 4 particles in a one dimensional box of width L with hard walls. In case
(i), the particles are fermions, in case (ii) they are bosons, and in case (iii) they are classical. If the
total ground state energy of the four particles in these three cases are EF , EB and Ecl respectively,
which of the following is true?
7
a) EF = EB = Ecl
b) EF > EB = Ecl
c) EF < EB < Ecl
d) EF > EB > Ecl
32. If a proton were ten times lighter, the ground state energy of the electron in a hydrogen atom would be
a) less
b) more
c) the same
d) less, more or equal depending on the electron mass
33. The hermitian conjugate of the operator (_@=@x) is
a) @=@x
b) _@=@x
c) i@=@x
d) _i@=@x
34. What are the eigenvalues of the operator H = ~_ _ ~a, where ~_ are the three Pauli matrices and ~a is a
vector?
a) ax + ay and az
b) ax + az _ iay
c) _(ax + ay + az)
d) _j~aj
35. If the expectation value of the momentum is hpi for the wavefunction (x), then the expectation value
of momentum for the wavefunction eikx=_h (x) is
a) k
b) hpi _ k
c) hpi + k
d) hpi
36. If ~ E1 = xy^i + 2yz^j + 3xz^k and ~ E2 = y2^i + (2xy + z2)^j + 2yz^k then
a) Both are impossible electrostatic _elds.
b) Both are possible electrostatic _elds.
c) Only ~ E1 is a possible electrostatic _eld.
d) Only ~ E2 is a possible electrostatic _eld.
37. A light beam is propagating through a block of glass with index of refraction n. If the glass is moving
at constant velocity v in the same direction as the beam, the velocity of the light in the glass block as
8
measured by an observer in the laboratory is approximately
a) u =
c
n
+ v _1 _
1
n2_
b) u =
c
n _ v _1 _
1
n2_
c) u =
c
n
+ v _1 +
1
n2_
d) u =
c
n
38. A thin uniform ring carrying charge Q and mass M rotates about its axis. What is the gyromagnetic
ratio (de_ned as ratio of magnetic dipole moment to the angular momentum) of this ring?
a) Q=(2_M)
b) Q=M
c) Q=(2M)
d) Q=(_M)
39. The velocity of a particle at which the kinetic energy is equal to its rest energy is (in terms of c, the
speed of light in vacuum)
a) p3c=2
b) 3c=4
c) p3=5c
d) c=p2
40. Two electrons are con_ned in a one dimensional box of length L. The one-electron states are given by
n(x) = p2=L sin(n_x=L). What would be the ground state wave function (x1; x2) if both electrons
are arranged to have the same spin state?
a) (x1; x2) =
1
p2 _2
L
sin__x1
L _sin_2_x2
L _+
2
L
sin_2_x1
L _sin__x2
L __
b) (x1; x2) =
1
p2 _2
L
sin__x1
L _sin_2_x2
L __
2
L
sin_2_x1
L _sin__x2
L __
c) (x1; x2) =
2
L
sin__x1
L _sin_2_x2
L _
d) (x1; x2) =
2
L
sin_2_x1
L _sin__x2
L _
41. If the distribution function of x is f(x) = xe_x=_ over the interval 0 < x < 1, the mean value of x is
a) _
b) 2_
c) _=2
d) 0
9
42. A charge q is placed at the centre of an otherwise neutral dielectric sphere of radius a and relative
permittivity _r. We denote the expression q=4__0r2 by E(r). Which of the following statements is
false?
a) The electric _eld inside the sphere, r < a, is given by E(r)=_r.
b) The _eld outside the sphere, r > a, is given by E(r).
c) The total charge inside a sphere of radius r > a is given by q.
d) The total charge inside a sphere of radius r < a is given by q.
43. A small mass M hangs from a thin string and can swing like a pendulum. It is attached above the
window of a car. When the car is at rest, the string hangs vertically. The angle made by the string
with the vertical when the car has a constant acceleration a = 1:2 m=s2 is approximately
a) 1_
b) 7_
c) 15_
d) 90_
44. Consider the di_erential equation
dG(x)
dx
+ k G(x) = _(x);
where k is a constant. Which of the following statements is true?
a) Both G(x) and G0(x) are continuous at x = 0.
b) G(x) is continuous at x = 0 but G0(x) is not.
c) G(x) is discontinuous at x = 0.
d) The continuity properties of G(x) and G0(x) at x = 0 depend on the value of k.
45. 238U decays with a half life of 4:51 _ 109 years, the decay series eventually ending at 206Pb, which is
stable. A rock sample analysis shows that the ratio of the numbers of atoms of 206Pb to 238U is 0:0058.
Assuming that all the 206Pb has been produced by the decay of 238U and that all other half-lives in
the chain are negligible, the age of the rock sample is
a) 38 _ 106 years
b) 48 _ 106 years
c) 38 _ 107 years
d) 48 _ 107 years
46. A metal bullet comes to rest after hitting its target with a velocity of 80 m/s. If 50% of the heat
generated remains in the bullet, what is the increase in its temperature? (The speci_c heat of the
bullet = 160 Joule per Kg per degree C)
a) 14_ C
b) 12:5_ C
c) 10_ C
d) 8:2_ C
10
47. If the Poisson bracket fx; pg = _1, then the Poisson bracket fx2 + p; pg is
a) _2x
b) 2x
c) 1
d) _1
48. The electric and magnetic _elds caused by an accelerated charged particle are found to scale as E / r_n
and B / r_m at large distances. What are the values of n and m?
a) n = 1;m = 2
b) n = 2;m = 1
c) n = 1;m = 1
d) n = 2;m = 2
49. The binding energy of the k-shell electron in a Uranium atom (Z = 92; A = 238) will be modi_ed due
to (i) screening caused by other electrons and (ii) the _nite extent of the nucleus as follows:
a) increases due to (i), remains unchanged due to (ii).
b) decreases due to (i), decreases due to (ii).
c) increases due to (i), increases due to (ii).
d) decreases due to (i), remains unchanged due to (ii).
50. The period of a simple pendulum inside a stationary lift is T. If the lift accelerates downwards with
an acceleration g=4, the period of the pendulum will be
a) T
b) T=4
c) 2T=p3
d) 2T=p5
Space for rough work
11

JEST Exam Physics Question paper 2

Both the question papers will be fully of objective type. It will contain 50 multiple-choice
questions and the answers are to be given in an OMR sheet. Sample questions for the
M.Sc. level paper follow (B.Sc. level paper will have similar pattern).
1. Black-body radiation, at temperature Ti, fills a volume V. The system expands
adiabatically and reversibly to a volume 8V. The final temperature Tf = xTi, where
the factor x is equal to
(a) 0.5 (b) 2.8 (c) 0.25 (d) 1
2. A particle of mass m, constrained to move along the x-axis. The potential energy is
given by, V(x) = a + bx + cx2, where a, b, c are positive constants. If the particle is
disturbed slightly from its equilibrium position, then it follows that
(a) it performs simple harmonic motion with period 2m/2c
(b) it performs simple harmonic motion with period 2ma/2b2
(c) it moves with constant velocity
(d) it moves with constant acceleration
3. Consider a square ABCD, of a side a, with charges +q, –q, +q, –q placed at the vertices, A,
B, C, D respectively in a clockwise manner. The electrostatic potential at some point
located at distances r (where r > > a) is proportional to
(a) a constant (b) 1/r (c) 1/r2 (d) 1/r3
4. The general solution of dy/dx - y = 2ex
is (C is an arbitrary constant)
(a) e2x + Cex (b) 2xex + Cex
(c) 2xex + C (d) ex2 + C
5. As 0, lim 




q
q
sin
) sin 1 ln( is
(a) (b) (c) 1 (d) 0
6. If P^ is the momentum operator, and s^ are the three Pauli spin matrices, the
eigenvalues of (s^.P^) are
(a) px and pz (b) px ipy (c) | p | (d) (px + py + pz)
7. Two parallel infinitely long wires separated by a distance D carry steady currents I1
and I2 (I1> I2) flowing in the same direction. A positive point charge moves between
the wires parallel to the currents with a speed v at a distance D/2 from either wire.
The magnitude of an electric field that must be turned on to maintain the trajectory of
the particle is proportional to
(a) (I1 - I2)v/D (b) (I1 + I2)v/D
(c) (I1 - I2)v2/D2 (d) (I1 + I2)v2/D2
8. An ideal gas of non-relativistic fermions in three dimensions is at a temperature of 0
K. When both the mass of the particles and the number density are doubled, the
energy per particle is multiplied by a factor,
(a) 2 (b) 1 (c) 21/3 (d) 1/21/3
9. The rotational part of the Hamiltonian of a diatomic molecule is (1/2 1)(Lx
2 + Ly
2)
+ (1/2 2) Lz
2 where 1 and 2 are moments of inertia. If 1 = 22, the three
lowest energy levels (in units of h2/4 2) are given by
(a) 0, 2, 3 (b) 0, 1, 2 (c) 1, 2, 3 (d) 0, 2, 4
10. A particle of mass 1 gm starts from rest and moves under the action of a force of 30
Newtons defined in the rest frame. It will reach 99% the velocity of light in time
(a) 9.9 x 103 sec (b) 7 x 104 sec
(c) 0.999 sec (d) 0.7 sec
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