MAHA SET 2015 Question Paper 2 Physics

Test Booklet No.
F
PHYSICAL SCIENCE
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2

Physical Science
Paper II
Time Allowed : 75 Minutes] [Maximum Marks : 100
Note : This Paper contains Fifty (50) multiple choice questions. Each question
carries Two (2) marks. Attempt All questions.

3. The constant term ( a 0 ) in the
1. If a is a constant vector, then
Fourier series expansion of the

· a r is equal to : function f(x) = x2 for – < x <
is :
(A) 2
(A) a
(B) 2/3
(B) 2a
(C) /2
(C) 0 3/3
(D)
(D) a/2 4. Fourier transform of unit step
2. The volume of the parallelepiped function :

with sides : 1 x 0
x
0 x 0
a iˆ 2 ˆj 3 kˆ,
is :
b 4 iˆ 5 ˆj 6 kˆ and
1
(A)
2 k
c 7 iˆ 8 ˆj 10 kˆ is :
1
(A) 2 3 (B) k
2
(B) 2 1 1
(C)
2 k2
(C) 3
1
(D) 3 (D) e k
2 k

3 [P.T.O.

z2
5. The residue of at z = ia 7. y ( x ) satisfies the differential
z2 a2
is : equation :

(A) ia/2 d2y
y cosec x
dx 2
(B) ia
The complementary function part

(C) ia2 yc of y(x) is given by :

(D) ia2/2 (A) yc(x) = c1 sin x + c2 cos x

6. A deck of 5 cards (each carrying a
(B) yc(x) = xeix
distinct number from 1 to 5) is
(C) yc(x) = (c1 sin x + c2 cos x) ex
shuffled thoroughly. Two cards are
(D) yc(x) = c1ex + c2 cos x
then removed one at a time from the

deck. What is the probability that 8. A, B, C, D are (n × n) matrices, each

the two cards are selected with the with non-zero determinant. If :
number on the first card being one
ABCD = I,
higher than the number on the
then B–1 is :
second card ?

(A) D–1C–1A–1
(A) 1/5

(B) 4/25 (B) CDA

(C) 1/4 (C) ADC

(D) 2/5 (D) does not exist

4

11. Which of the following properties of
9. The degrees of freedom for a particle
the Lagrangian is due to “space is
falling under gravity (without air isotropic” characteristic of the
inertial frame of reference ?
resistance) are : (A) Invariant to translation
(B) Invariant to time
(A) Zero
(C) Invariant to rotation
(D) Explicit function of time
(B) One
12. For a given system, Hamiltonian
H(q, p) is defined as :
(C) Two
H(q, p) = p + 1 p 2 · sin q |p| 1.
The Hamilton’s equations of motion
(D) Three
are :
p sin q
10. A particle of mass m is released from (A) q 1 ,
1 p2
height h. Its velocity at the position p 1 p 2 cos q

when it has covered a distance equal p cos q
(B) q 1 ,
1 p2
to (h/2) is :
p 1 p 2 cos q

2g 2 p cos q
(A) v = (C) q 1 ,
h 1 p2

2g p 1 p 2 cos q
(B) v =
h
p sin q
(D) q 1 ,
(C) v = g. h 1 p2

(D) v = g.h p 1 p 2 cos q

5 [P.T.O.

13. For a particle under the action of 15. The plane of oscillation of Focoult
central force, which of the following pendulum rotates with infinite
quantities is invariant ? period, when it is located at ( is the

(A) Linear velocity lattitude of location) :

(B) Angular velocity (A) = 90°N

(C) Linear momentum (B) = 60°N

(D) Angular momentum (C) = 30°N

14. Which of the following statements (D) = 0°
holds true for a rigid rotator (or
16. An observer is moving with
rotor) ?
relativistic speed u . His length
(A) All the three principal moments
measurements along the direction
of inertia are different
of velocity are half of the
(B) All the three principal moments measurements made when he
of inertia are equal
was at rest. His time measurement
(C) Two of the three principal of 1 hr. when he was at rest, now
moments of inertia are equal becomes :
and the third one is non-zero
(A) 30 minutes
and different
(B) 01 hour
(D) Two of the three principal

moments of inertia are equal (C) 02 hours

and the third one is zero (D) Infinite hours
6

18. A cubical box of sides 5 cm encloses
17. The magnetic induction B at point
100 electric dipoles of unit moments.
O in the figure is given as : What would be the flux of electric

field emanating from the cube ?

20
(A) V cm
0

100
(B) V cm
30 0

(C) Zero V cm

200
(D) V cm
0

19. A uniform current 20 A flows

0
I 1 1 through a copper pipe of inner
(A) 4 R1 R2 radius 10 cm. Which of the following
statements is valid ?

(A) The magnetic field is non-zero
0I except along the axial points of
(B) R1 R 2
4 the pipe.

(B) The magnetic field everywhere
inside the pipe is zero.
0
I 1 1
(C) 4 R1 R2 (C) The magnetic field everywhere
inside the pipe is constant and
non-zero.

0I (D) The magnetic field is non-
(D) R1 + R 2
4 uniform inside the pipe.

7 [P.T.O.

20. An uncharged sphere of 21. In electrodynamics, the curling
homogeneous linear dielectric magnetic field is more appropriately
material is placed in an uniform expressed as :

electric field E 0 . The resultant (A) a bound magnetization current

density J
electric field E inside the dielectric M

sphere is : (B) a free current density J

(C) stationary electric charges

(D) a free current density J and a

time-varying electric field D

22. The continuity equation for charges

and currents is not explicitly written

in the Maxwell’s equations. This is

because :

(A) It is not a universal law and
(A) Zero
holds good in certain cases only
(B) Uniform non-zero and parallel
(B) It is difficult to prove the
to E 0 continuity equation rigorously

(C) Uniform non-zero and anti- (C) It is not required for time-

varying electromagnetic fields
parallel to E 0
(D) It is already included implicitly
(D) Non-uniform but along E 0 in the Maxwell’s equations

8

24. A plane polarized EM wave is
23. If A and V are the vector and
propagating in certain medium

such that the ratio of the electric
scalar potentials, respectively,
energy density to the magnetic

energy density is 0.01. Which of the

then the Lorentz gauge in time- following statements is valid for

this medium ?

varying electromagnetic case is
(A) Conduction current is about

100 times larger than the

given by : displacement current

(B) Conduction and displacement
V
(A) A 0 0 currents are of the same
t
magnitude

V
(B) ·A 0 0 (C) Displacement current is about
t
100 times larger than the

A conduction current
(C) ·V 0 0
t
(D) The medium through which the

V EM wave is propagating is a
(D) ·A 0 0
t
dielectric

9 [P.T.O.

26. If two operators  and B̂ have
25. A proton of mass m and charge Q

a common eigenfunction . What
is moving in counter-clockwise
is the value of the commutator

direction in a crossed uniform
[ Â , B̂ ] ?

magnetic field of induction B (A) 1

pointed into the plane of the paper. (B) i

If v and R are the velocity and (C) Â – B̂

(D) Zero
radius of the orbit, then angular

27. Standing wave with wave function
momentum p acquired by the
(x) = A sin kx, (corresponding to
particle is given by :
particles of mass m) gives rise to

current density equal to :
(A) p = QBR

(A) | A| 2 k / m
QB
(B) p =
R
(B) | A| 2 k
QB
(C) p =
mR (C) | A| 2 sin k x cos k x m

QBR
(D) p = (D) Zero
m
10

28. A particle moves in one-dimensional 29. The wave function of a particle

potential V(x). At x = a, if V has a
moving in one-dimensional time

finite discontinuity (jump), then
independent potential V( x ) is

which of the following is true for its
r ep r esen t ed b y ( x ) = e –iax + b

wave function ! and its first
where a and b are real constants.

derivative !" at x = a ?
This means that the potential V(x)

(A) Both ! and !" are discontinuous
is of the form :

(B) Both ! and !" are continuous
(A) V(x) # x

(C) ! is continuous and !" must be

(B) V(x) # x2
discontinuous

(C) V(x) = constant
(D) ! is discontinuous and !" must

(D) V(x) = e–ax + b
be continuous

11 [P.T.O.

30. In a quantum mechanical
31. Which of the following is an
one-dimensional system, the

Hamiltonian is : eigenfunction of linear momentum

p 2x
H = + ½m$2x2 + %x = H0 + %x
2m operator , such that the
i x
where % is very small. The
eigenfunction describes a particle
eigenvalues of H0 are $ n ½

with (0) x as eigenfunctions.
n moving in free space in the

Which of the following is correct ?
direction of positive x -axis, with
(A) The energy levels are not

changed since all eigen- zero uncertainty in the linear

functions (0) x have definite
n
momentum ?
parity

(B) All energy levels are shifted (A) e–kx

by a constant amount
(B) eikx
(C) Only n = odd energy

eigenvalues are shifted
(C) cos kx

(D) Only n = even energy
(D) sin kx
eigenvalues are shifted

12

33. The expectation value of momentum
32. A system in one-dimension is in a

for a bound state of finite square
state described by :
well potential (width a and depth

V0) is :
(x, t) = A exp{i(px – Et)/ } +

(A) Zero
B exp{–i(px + Et)/ }
(B) Depends on V0

A and B are complex numbers, p
(C) Depends on a

and E are real. The probability (D) Depends on V0a2

34. L is quantum mechanical operator
current density is given by :

of orbital angular momentum.

(A) p/m L × L is equal to :

(A) 0
(B) (|A| – |B|) p/m

(B) i L
(C) (|A|2 + |B|2) p/m
(C) l(l + 1) 2

(D) (|A|2 – |B|2) p/m (D) L 2

13 [P.T.O.

35. A constant volume ideal gas 36. Consider a process in which a system

thermometer in thermal equilibrium
is in thermal equilibrium with a

with system A at temperature TA
heat reservoir at temperature T.
measures a pressure pA. When the

The pressure of the system remains
same thermometer is brought in

constant at the pressure of the
thermal equilibrium with another

system B at temperature TA/3, the reservoir p . Such a process is

pressure in the thermometer will
called :

now be :
(A) Isothermal process

(A) pA/3

(B) Adiabatic and isochoric process
(B) 2
pA 3

(C) Isochoric process
(C) 3pA

(D) p A 3 (D) Isobaric and isothermal process

14

37. A Carnot engine operates between 38. A gas is contained in a box of volume
V at pressure P and temperature T.
two temperatures T 1 and T 2 as
One wall of the box is moved at a
shown in the diagram. very high speed so that the volume
is doubled. Which of the following
is true ?

(A) P, T both increase

(B) P, T both decrease

(C) P increases, T decreases

(D) P decreases, T increases

39. A thermodynamic system is
characterized by independent
variables entropy S and volume V
The maximum efficiency of the
and dependent variables pressure P
and temperature T. Then which of
engine &max is given by :
the following is true ?

T1 P T
(A) &max = 1 – (A)
T2 S V S
V

T2 P T
(B) &max = (B)
T1 S V V S

T2 P T
(C) &max = 1 + (C)
T1 T V V S

T2 P T
(D) &max = 1 – (D)
T1 T V V S

15 [P.T.O.

40. A system consists of 3 independent 42. In the Debye model of specific heat
particles. Each particle can occupy
of solids, the specific heat at low
any of the two energy states with

energy 0 and . The system is in temperature has the following

thermal equilibrium with a heat temperature dependence :
reservoir at temperature T. Its
(A) T 3/2
partition function will be :

(A) Z = 1 + 3e–' + 3e–2' + e–3' (B) T 2

(B) Z = 1 + e–'
(C) T 3
(C) Z = 1 + e–3'
(D) T 1/2
(D) Z = 1 + e–' + e–2' + e–3'

41. Considering the Maxwell-Boltzmann 43. In Signal generators :

distribution of speeds of molecules,
(A) Energy is created
the average speed of the molecule

of mass m at temperature T is : (B) Energy is generated

3k T (C) Energy is converted from a
(A)
m
simple d.c. source into a.c.
8k T
(B)
m energy at some specific

(C) 0
frequency
2k T
(D) (D) Energy is maintained
m

16

44. In an experiment, the voltage 45. When two rotary pumps are

connected in series to a vacuum
across a 10 k( resistor is applied to
chamber, the ultimate pressure can
CRO. The screen shows a sinusoidal
be achieved is closest to :

signal of total vertical occupancy
(A) 1 × 10–6 Torr

3 cm and total horizontal occupancy
(B) 1 × 10–5 Torr

of 2 cm. The front-panel controls of
(C) 1 × 10–3 Torr

V/div and time/div are on 2 V/div
(D) 1 × 10–9 Torr

and 2 ms/div respectively. Find out
46. Which of the following noise can be

the frequency of the waveform : reduced by integration of the

signal ?
(A) 250 kHz

(A) White noise
(B) 250 Hz
(B) Shot noise

(C) 2.5 kHz
(C) Flicker noise

(D) 25 kHz (D) Environmental noise

17 [P.T.O.

47. In which of the following detector 49. A McLead gauge has a volume of
100 ml and a capillary of 0.5 mm
P-N junction diode is used ?
diameter. The pressure indicated by

(A) G.M. counter a reading of 25 cm of mercury
corresponds to :
(B) Scintillation counter
(A) 24.54 × 10–9
(C) Lithium drifted detector
(B) 12.27 × 10–10

(D) Ionisation chamber (C) 1.227 × 10–3

48. An oil drop has a weight of (D) 2.454 × 10–8

50. A transparent film of glass of
3.2 × 10–13 N. With an electric field
refractive index 1.5 is introduced
of 5 × 105 V/m between the plates
normally in the path of one of the
of Millikan’s oil-drop apparatus, this interfering beams of Michelson’s

drop is observed to be essentially interferometer which is illuminated
with light of wavelength 4800 Å.
balanced. The charge on the drop in
This causes 500 dark fringes to
electron charge units is : sweep across the field of view. The
thickness of the film is :
(A) 2 electrons
(A) 0.012 cm
(B) 4 electrons
(B) 0.024 cm
(C) 3 electrons
(C) 0.005 cm

(D) 6 electrons (D) 0.015 cm

18

ROUGH WORK

19 [P.T.O.

ROUGH WORK

20