MAHA SET 2018 Question Paper 2 Physical Science

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A
PHYSICAL SCIENCE
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JAN - 32218 (To be filled by the Candidate)
Time Allowed : 1¼ Hours] [Maximum Marks : 100
Number of Pages in this Booklet : 16 Number of Questions in this Booklet : 50
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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.

dz 3. Two unbiased dice are thrown. The
1. Value of , c : | z | = 1
c ( z 2) probability that both dice show the
is : same number is :

1
(A) i (A)
3

(B) zero 11
(B)
36
(C) 2 i
1
(C)
6
(D) –2 i
1
2. The inverse Fourier transform of (D)
36
e–|k| is :
4. Eigen values of a nilpotent matrix

1 1 A, i.e., a matrix satisfying AK = 0
(A)
1 x2 for some integer K are :

(B) e– x2 (A) Real and distinct

(B) Zero
(C) e–|x|
(C) Purely imaginary
1
(D)
1 x (D) Real and negative

3 [P.T.O.

5. Residue of cot (z) at z = 0 is : 8. The average of function f(x) = sin x

1 in the interval 0 to is :
(A)
2
(A) 1/2
(B) 0
(B) 2/
(C) 2
(C) 1/
(D) 1
(D) 4/

6. Trace of a 3 × 3 matrix is 6. Two 9. If r2 = x2 + y2 + z2, grad rn is :
of its eigen values are 1 and 2. The
(A) 0
third eigen value is :
(B) r n –1 r

(A) 1 (C) nr n –2 r

(B) 2 (D) n(n – 2)r n r

(C) 3 10. A simple pendulum of mass m and
length l oscillates with a frequency
(D) 6
0 . A piece breaks off from the
d2 f
7. 2 sech2 x f – f 0. pendulum and the mass is reduced
dx2
to m/2. The frequency of oscillation
One of the solution is :
then becomes :
(A) sech x
(A) = 2 0
(B) sech2 x
(B) = 0/2
(C) tanh x
(C) = 0

(D) sech3 x (D) 0 = 2 0
4

11. A propagating wave is reflected at 13. Time-order of two events can be
a barrier. The phase of the wave
changed by making a Lorentz
changes in the act of reflection by :
transformation only if they occur in :
(A) /2

(B) zero (A) Time-like region

(C) (B) Space-like region

(D) – /2
(C) Light-like region
12. Two particles of mass m1 and m2 and

charge q1 and q2 respectively are (D) Speed of light can be exceeded

constrained to move in a straight
14. A satellite is moving around the
line along x-axis. The Lagrangian
earth in a circular orbit at a height
of the system (in esu) is :
1 . 1 . of 2R, from the earth surface. R is
(A) m1 x12 m2 x22
2 2
+ q1q2/|x1 – x2| the radius of the earth. The speed

1 . 1 .
(B) m1 x12 m2 x22 of satellite is :
2 2
– q1q2/|x1 – x2| (A) gR/3
1 . 1 .
(C) – m1 x12 – m2 x22
2 2 (B) (gR/2)1/2
– q1q2/|x1 – x2|
1 . 1 . (C) (gR/3)1/2
(D) – m1 x12 – m2 x22
2 2
+ q1q2/|x1 – x2| (D) gR/2

5 [P.T.O.

15. Virial theorem is expressed as 17. As shown in the figure a ball of mass

m suspended by an inextensible
. .
p · = – p · massless string is released from

height h and collides elastically
The theorem is valid, if : when it is at its lowest point with

a block of mass 2m at rest on a
(A) is bounded (remain finite
frictionless surface. After the
over all values of time)
collision the ball will rise to a total
(B) p is bounded height equal to :

(C) both and p are bounded

(D) is unbounded

16. Electron and positron annihilate and

produce a single photon only when :

(A) Electron and positron are at rest

(A) h/9
(B) Electron is at rest

(B) h/8
(C) Positron is at rest

(C) h/3
(D) At least one particle is in a

bound state (D) 2h/3

6

18. Uniformly charged solid sphere of
radius R has a volume charge 20. Points P and Q are at a distance of
density . The strength of electric
field, at a distance r, (r > R), from 10 cm and 20 cm respectively from
its centre is :
the ideal magnetic dipole. The ratio
r3
(A)
3 0 R2 of magnitude of vector potential at

R3 point P to that at point Q is :
(B)
3 0 r2
(A) 4
R3
(C)
3 0r
(B) 8
r3
(D) (C) 1/4
3 0R
19. Consider the figure shown. AB is an
infinite, uniform line charge (D) 1/8
distribution ‘ ’. P and Q are two
points as shown in the figure. The 21. A circular loop of radius r is placed
ratio of strength of electric fields at
P and Q; i.e., EP/EQ is : in a magnetic field B(t) = B0 e– t z,

B0 is constant. If the loop is in xy

plane, then the induced emf in the

loop is :

(A) Zero

(fig. not to the scale) (B) r 2 B0e – t
(A) 3 : 1
(B) 1 : 3 (C) 2 rB0e – t
(C) 4 : 1
(D) 1 : 4 (D) 2 r B0e – t
7 [P.T.O.

22. Plane monochromatic electromagnetic 24. A point charge ‘q’ having mass ‘m’

wave is propagating through a follows a circular trajectory of radius

conducting material of refractive ‘R’ under the action of magnetic field

index n + ik. The phase difference B . The magnitude of the angular

between the fields E and B momentum of the particle is :

associated with the wave is : (A) Zero

(A) tan–1 (n) (B) Bq 2R 2

(B) tan–1 (k) (C) Bmq 2R2

(C) tan–1 (nk) (D) Bq R 2

(D) tan–1 (n/k) 25. If ‘A1’ and ‘A2’ are the amplitudes

23. Under the Lorentz gauge condition, of two electromagnetic waves (same

frequency) coming from two slits in
the electric potential V, is related to
Young’s double slit experiment, then
magnetic vector potential A as :
the maximum intensity of
V
(A) ·A (1 / 0 0 ) 0
t interference fringe is :

V (A) A1 + A2
(B) ·A 0 0 0
t
(B) A12 + A22
2V
(C) – ·A – (1 / 0 0 ) 0
t2 (C) (A1+ A2)2

V (D) A12 A 22
(D) ·A – 0 0 0
t
8

28. The electron in a hydrogen atom is
26. Given [xi, pj] = i ij , i, j = 1, 2, 3,
in a superposition state described by

[x1, p13] is : the wave function

1
(r) [4 100 ( r ) – 2 211 ( r )
(A) (i )3 p1 6

6 210 ( r ) – 10 21–1 ( r )],
(B) i 2 p1

where nem ( r ) is a normalized
(C) 3i p12 eigenstate. The expectation value of
Lz is :
(D) Zero (A) – / 6

(B) /6
27. Which of the following is not an
(C) 6

(D) –6
eigenstate of linear momentum
29. Two coherent light sources of

operator px ? intensities I and 9I are used in an
interference experiment. The
resultant intensity at points where
(A) Aeikx the waves from the two sources
superpose with a phase difference
(B) Ae–ikx zero is :

(A) 16I

(C) Ae–x (B) 9I

(C) I
(D) A sin kx (D) Zero

9 [P.T.O.

30. The number of distinct (n, l, ml) states 32. Addition of angular momentum
of hydrogen atom with n = 3 is :
states j1 = 1/2 and j2 = 1/2 will

(A) 5 result in 4 states, of which number

(B) 9 of linearly dependent states with

magnetic quantum number m = 0
(C) 3
is :
(D) 2
(A) Zero
31. The condition for two distinct
(B) 1
quantum mechanical states,

represented by wave functions (C) 2

1(x) and 2(x) respectively, to be
(D) 4
orthogonal is :

33. In the Born approximation, the
(A)
– 1 * ( x) 2 ( x) dx 1
effective cross-section of scattering

depends :
(B)
– 1 * ( x) 2 ( x) dx 0

(A) L inear ly on scat t er ing angle
(C)
– 1 * ( x) 2 ( x) dx
(B) on p sin2

(D) [ 1 * ( x) 2 ( x)
– (C) on p sin /2

2 * ( x) 1 ( x)] dx 1 (D) only on the momentum p

10

34. A system consists of two indistin- 36. Let f(T, l) be the tension in a rubber
band of length l , T being the
guishable fermions. Each particle absolute temperature. Let F denote
can occupy only two energy levels Helmholtz free energy and S the
entropy. Then :
E1 = and E2 = 2 . The canonical
F F
partition function is : (A) S, f
l T T l

(A) Z = e– + e–2
F F
(B) f, –S
l T T l
(B) Z = e–3
F F
(C) Z = 3e– (C) Sl, fl
l T T l

(D) Z = e– + 2e–2 F F
(D) 0, f
l T T l
35. Consider 5 independent magnetic
37. An insulated chamber is divided into
moments. Each moment has only two two halves of volume. The left half
directions +m and – m. Hamiltonian contains an ideal gas at temperature
T0 and the right half is evacuated.
of such system is given by A small hole is opened between the
5
two halves, allowing the gas to flow
x= mi . If the total magnetization through and the system comes to
i 1 equilibrium. No heat is exchanged
of the system is equal to m, the with walls. What is the final
temperature of the system :
entropy is equal to :
(A) 2T 0
(A) k ln(10) 3
(B) T
2 0
(B) Zero
(C) T 0
(C) k ln(20)
1
(D) T
(D) k ln(5) 2 0

11 [P.T.O.

38. Consider a mixture of equal number
40. What play the role of thermo-
of non-interacting single atomic gas

and diatomic gas. The internal dynamic potential in micro-
energy per particle is given by :
canonical ensemble ?
(A) 2 kT

(B) 4kT (A) Entropy

3
(C) kT
2 (B) Enthalpy

5
(D) kT
2 (C) Gibbs potential

39. Consider an ensemble of systems
(D) Internal energy
having only two energy levels

having energies 0 and respectively.
41. For a metal CV = T + T3 at low
The average energy of the system

at temperature T is : temperatures. The entropy is :

(A)
e– / kT 1 (A) + 3 T2

(B)
e / kT 1 (B) T + 3 T2

(C) T3
e– / kT – 1 (C) T +
3

(D) T3
e / kT – 1 (D)
3
12

42. In which of the following detectors
44. Air Ballast valve in a rotary pump
P-N junction diode is used ?
is used for :
(A) G.M. Counter

(B) Scintillation detector (A) Reducing the noise

(C) Surface Barrier detector
(B) Removing the condensable
(D) Proportional counter
vapors
43. The X-rays emitted by a target
consist of continuous range of (C) Reducing the back streaming
wavelengths superimposed by
(D) Increasing the ultimate vacuum
characteristic X-rays named K , K
etc. It is found that : to 10–5 Torr

(A) K has high intensity and lower
45. A signal of one V is burried under
wavelength compared to that of
K . 1V RMS noise. Which of the

(B) K has low intensity and lower following devices is suitable to detect
wavelength as compared to that
it ?
of K .

(C) K has high intensity and (A) High gain linear amplifier
higher wavelength compared to
that of K . (B) Band pass filter

(D) K has lower intensity and (C) Notch filter
higher wavelength compared to
that of K . (D) Phase sensitive amplifier

13 [P.T.O.

46. Steady state response of an electric 48. Frequency Bandwidth of CRO is
decided by :
circuit is generally tested by giving
(A) Horizontal amplifier
following waveform at the input :
(B) Vertical amplifier
(A) Sinusoidal
(C) Delay line

(B) Square (D) Triggering circuit

(C) Triangular 49. Resolving power of a 2 cm2 site
grating having a rulings of 600 l/
(D) Swatooth mm in order one is approximately :

47. An inductance ‘L’, resistance ‘R’ and (A) 10

capacitance ‘C’ are connected in (B) 102

series to resonate to frequency ‘‘fs’’. (C) 103

(D) 104
When they are connected in parallel,
50. A dual slope digital voltmeter has
the resonance frequency is ‘‘fp’’.
a gate time of 400 ms reflecting the
(A) fp < fs measurement cycle. The frequency
bandwidth of this instrument is :
(B) fp > fs
(A) 2·5 Hz
(C) fp = fs
(B) 1·25 Hz

(D) There is no relation between the (C) 0·8 Hz

two (D) 0·6 Hz

14

ROUGH WORK

15 [P.T.O.

ROUGH WORK

16