MAHA SET 2015 Question Paper 3 Physics

Test Booklet No.
M
PHYSICAL SCIENCE
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2

PHYSICAL SCIENCE
Paper III
Time Allowed : 2½ Hours] [Maximum Marks : 150
Note : This Paper contains Seventy Five (75) multiple choice questions, each
question carrying Two (2) marks. Attempt All questions.

1. The area of the triangle whose base 3. The eigenvalues of the matrix :
is given by a 5 iˆ 3 ˆj 4 kˆ and
1 2 3
b ˆj kˆ is another side is :
0 4 7
(A) 50 / 2
0 0 3
(B) 61 / 2
are :
(C) 14 / 2
(A) 1, 4, 3
(D) 51 / 2
(B) 3, 7, 3
2. The value of the integral (C) 7, 3, 2

x2 (D) 1, 2, 3
e
dx
x
2
a
2 4. Linearly independent solution of the
0

differential equation
is :
d2y dy
2 2
3 2y 0
(A) ea dx dx
2a
are :
2
a
(B) e (A) e x , e 2 x
2a
2 2 (B) e x , e2 x
(C) e a
a
(C) e 2 x , e x
2 a
(D) e (D) e2 x , e x
a
3 [P.T.O.

7. A wheel of mass 60 kg and radius
5. The centre of the circle
of gyration 40 cm is rotating at 300

zz (2 3 i) z (2 3i) z 1 0 rpm. Its kinetic energy is :

(A) 470 J
is :
(B) 47 J
(A) (2, 3)
(C) 4.7 J

(B) (3, 2) (D) 0.47 J

(C) (–2, –3) 8. Ideal Atwood machine is nothing but
an inextensible string of negligible
(D) (4, 0) mass going around the fixed pulley
with masses m1 and m2 attached to
6. Fourier transform of the function
the ends of the string. If m1 > m2,

f (x) exp ( | x | ) then the magnitude of acceleration

of mass m1 is............... .
is :

m1 g
1 2 (A) (m
(A) 1 m2 )
2 1 k2
m2g
(B) 0 (B) (m m2 )
1

1 1 (m 1 m 2 ) g
(C) 2 (C)
k (m 1 m 2 )

1 1 (D) g
(D)
2 1 k2

4

9. A one-dimensional simple harmonic 10. A planet moves around the sun in

an elliptic orbit with length of major
oscillator with generalised
axis equal to 1.524 times that of the
coordinate q is subjected to an
Earth. The time of revolution of the
additional potential energy of the
planet about the Sun is................. .

form (A) 1 year

(B) 10.24 year
2 2
V(t ) q t qqt
(C) 0.5315 year

The Lagrange’s equation of motion (D) 1.8814 year

of the oscillator due to the extra 11. A particle is released from a large

height h, at a location with latitude
potential will contain :
. At the time of striking the ground,
(A) an extra term proportional to t
the horizontal deflection that occurs

due to Coriolis force, is proportional
(B) an extra term proportional to t2
to................. .
(C) an extra term proportional to
(A) sin

(t + t2) (B) cos

(C) sec
(D) no extra term
(D) cosec

5 [P.T.O.

12. A n el ect r on w i t h r est m ass m0 is 14. Two equal charges each of

accelerated. Its relativistic mass is magnitude ‘q’ are kept ‘d’ distance

2m0 when its speed is.................. . apart along X-axis. Now, the electric

(A) c field at a distance z(z >> d) above

c 3 the midpoint between two charges
(B)
2
is given by :
(C) c 3

(D) 2c | E|

13. Twelve equal charges of magnitude

q are kept at the corners of a regular

12-sided polygon one at each of the

corner. What is the net force on a

test charge Q at the center of the

polygon at distance r ?
1 2q
(A) Ez = 4 .
(A) Zero 0 z2
2
1 12 q Q 1 q
(B) 4 (B) Ez = 2
r2 4 0 z
0

1 6 qQ 1 2q
(C) 4 2 (C) Ez = 4 3 /2
0 r 0 r

1 qQ 1 2q
(D) Ez = 4 .
(D) 4 r )2
0 r2 0 (2

6

16. A plane wave of electric and
15. Poynting’s vector represents which

magnetic fields E 0 , B0 and
of the following quantities ?
frequency enters in a conducting

(A) Current density vector bar of conductivity along z-axis.

Which of the following pairs of
producing electrostatic field
equations best represents the

(B) Power density vector producing propagating wave ? ( k wave

number)
electromagnetic field
(A) E( z, t ) E 0 e ik z · ei ( k z t ) . x̂ and

(C) Current density vector k
B( z, t ) E 0 e ik z . ei ( k z t )
yˆ

producing electromagnetic (B) E( z, t ) E 0 . e k z ei ( k z t)
x̂ and

k
B( z, t ) E 0 e k z xˆ ei ( k z t )
. yˆ
field
k kz i ( kz t)
(C) E( z , t ) E0 e e xˆ and
(D) Power density vector producing
k
B( z, t ) E 0 e ik z ei ( k z t )
yˆ

electrostatic and magnetostatic k
(D) E( z, t ) E 0 e k z e i( k z t)
xˆ and

fields
B( z, t ) E 0 e k z e i ( kz t )
yˆ

7 [P.T.O.

18. An electric dipole of moment P and
17. The magnetic field due to the TE11

length l aligned along the z-axis is
mode in a rectangular wave guide
used to generate electromagnetic

aligned along Z-axis is given by
waves. Initially it was operated at

frequency 10 MHz and its power
Hz = H1cos(0.5 x) cos (0.6 y)
along the equatorial plane at certain

where x and y are in cm. Then
distance d (d >> l) was measured as

dimensions of the rectangular wave P 1. Later, the same dipole was

operated at frequency 40 MHz and
guide a and b , respectively,
power P2 was measured at the same

are :
point. How do you compare the two

powers ?
(A) 2.00 cm and 1.66 cm

(A) P2 = 256 P1
(B) 1.66 cm and 2.66 cm
(B) P2 = 64 P1

(C) 2.54 cm and 1.66 cm
(C) P2 = 128 P1

(D) 1.66 cm and 1.25 cm (D) P2 = 16 P1

8

19. The anomalous dispersion of light 20. For attractive one-dimensional delta

observed in gases is well represented potential situated at x = 0, the wave

function of the bound state is given
by the Cauchy’s formula. The
by :
refractive index of the medium in
(A) (x) = e– x
such case is given as n =
(B) (x) = e– |x|
AB
1 A+ . ( wavelength of 2
(x) = e– x
2
(C)

light in air) (D) (x) = sin x

What does the terms A and B where is positive constant of

respectively represent ? appropriate dimensions.

21. The spin part of two electron wave
(A) Coefficients of refraction and
function is described as a triplet
dispersion
state. The space part of the wave
(B) Coefficients of dispersion and
fu n ct i on i s gi ven by ( 1 and 2 are
refraction
two different functions) :
(C) Coefficients of dispersion and
(A) 1(r1) 2(r2)
polarization
(B) 1(r1) 2(r2) – 2(r1) 1(r1)

(D) Coefficients of refraction and (C) 1(r1) 2(r2) + 2(r1) 1(r2)

scattering (D) 1(r1) 1(r2) + 2(r1) 1(r2)

9 [P.T.O.

22. A state of a system with spherically
23. The wave function for identical

symmetric potential has zero
fermions is antisymmetric under
uncertainty in simultaneous

particle exchange. Which of the
measurement of operators Lx and

L y. Which of the following following is a consequence of this

statements is true ?
property ?

(A) The state must be l = 0 state
(A) Heisenberg’s uncertainty

(B) Such a state can never exist as

principle
operators L x and Ly do not

commute (B) Bohr correspondence principle

(C) The state has l = 1 with m = 0
(C) Bose-Einstein condensation

(D) The state cannot be an
(D) Pauli exclusion principle
eigenstate of L2 operator

10

24. A system is known to be in a state 25. A transition, in which one photon

is radiated by an electron in an
described by the wave function
Hydrogen atom, when the electron

wave function changes from 1 to
1 0 0 3
( , ) = {5 Y4 Y6 2Y6 }
30
2, is forbidden if 1 and 2 :

(A) have opposite parity
where Ylm are spherical harmonics.
(B) are both spherically symmetric

The probability of finding the system (C) are orthogonal to one another

(D) are zero at the center of the
in a state with m = 0 is :
atom

26. In 3S state of the Helium atom, the
(A) zero
possible values of the total electronic

6 angular momentum quantum
(B)
30
numbers are :

6 (A) 0(zero) only
(C)
30
(B) 1 only
13
(D) (C) 0, 1 and 2
15

(D) 0 and 1 only

11 [P.T.O.

27. Five electrons (Fermions with spin
29. In a counting experiment to
1/2 ) are kept in a one-dimensional
infinite potential well with width a.
determine the statistics obeyed by
(Ground state energy of single
2 2

electron in well = 2 ) the particles emitted by a
2ma
The first absorption line corresponds
to energy : radioactive substance, the number

2 2 2 2
5
(A) (B) of particles counted in 50 seconds
2m a 2 2m a 2

7 2 2 11
2 2
(C) (D) time interval was repeatedly
2 m a2 2m a 2
28. Using the Clausius-Clapeyron
measured 100 times. The statistical
equation, the change in melting

point of ice for 1 atmosphere rise in ensemble in this case consists of the

pressure is :
following number of members :
(Given : The latent heat of fusion

for water at 0°C is 3·35 × 10 5 J/kg,
(A) 50
the volume of ice is 1.09070 cc/g and

the volume of water is 1.00013
(B) 100
cc/gm) :

(A) –0·0075°C
(C) 5000
(B) 0·0075°C

(C) 0·075°C
(D) 2
(D) –0·075°C

12

30. Consider a system of N linear 31. The partition function z(T) of a linear

quantum mechanical harmonic
polyatomic molecules. Each molecule

oscillator in thermal equilibrium
consists of n atoms. At high

with a heat reservoir at temperature
temperatures the vibrational

T is given by :
contribution to the specific heat

e
is : (A)
1 e

e
(A) (3 n 5) k N (B)
1 e

kN /2
e
(B) (3 n 5) (C)
2 1 e

/2
(C) (3 n 6) k N e
(D)
1 e

kN
(D) (3 n 6)
2 where kT

13 [P.T.O.

32. A set of 15 distinguishable particles 34. For a face centred cubic crystalline

are placed in 3 energy states such structure the following diffraction

that 2 particles are in the first state, peaks may be observed in the X-ray

diffraction experiment :
12 in the second state and 1 in the

third state. The number of district (A) (110), (330)

arrangements are : (B) (111), (321)

(A) 1365 (C) (100), (321)

(B) 15 (D) (111), (331)

(C) 455 35. NaI(Tl) scintillation detector is used

only for the detection of gamma
(D) 3 15
radiation because :
33. The critical temperature for the
(A) it has large scattering cross-
Bose-Einstein condensation depends
section
on the density of particles as :
(B) it has small Compton scattering
(A) n 1/3
(C) it has small absorption cross-
(B) n 2/3
section

(C) n
(D) it has large absorption cross-

(D) n 1/2 section

14

37. In the X-ray diffraction of a set of
36. The output of a laser has a pulse
crystal planes having ‘d’ equal to

0.18 nm, a first order reflection is
width of 30 ms and average output
found to be at an angle of 12°. The

power of 0.6 watt per pulse. If the wavelength of X-ray used is [Given :

sin 12° = 0.2079]
wavelength of the laser light is 640
(A) 0·1543 nm

(B) 0·0749 nm
nm. How many photon does each
(C) 0·0374 nm

(D) 0·749 nm
pulse contain ?
38. Load regulation is determined by :

(A) Changes in load current and
(A) 2.9 × 1018
output voltage

(B) Changes in load current and
(B) 3.5 × 1018
input voltage

(C) Changes in load resistance and
(C) 5.8 × 1015
input voltage

(D) Changes in zener current and
(D) 6.5 × 1016
load current

15 [P.T.O.

40. Sum of all the three inputs will
39. In the circuit given below what is
appear as output from :

(A) A 3-input NAND gate followed
the approximate ac voltage across
by an inverter

the output resistor : (B) A 3-input XOR gate followed by

an inverter

(C) A 3-input NOR gate followed by

an inverter

(D) An inverter followed by 3-input

NOR gate

41. In the following circuit the current

through the load resistance is :

(A) 15 mV

(B) 150 mV
(A) 10 mA

(C) 150 µV (B) 1 mA

(C) 5 mA
(D) 15 V
(D) 0.5 mA

16

42. Merit of a solar cell or fill factor is 44. In the following clipping circuit, the

clipping level is :
defined as :

(A) I mVm/IscVoc

(B) ImVoc/VmIsc

(C) IscVoc/ImVm

(A) + 25 V
(D) IscVm/ImVoc
(B) – 25 V

(C) – 5 V
43. The resonant frequency of a Hartley
(D) + 5 V

oscillator with L1 = 12 µH, L2 = 45. In an open loop differential

operational amplifier having a gain
8 µH and C = 1000 PF is :
of A = 2 × 105 receives inputs as

(A) 1.12 MHz at non-inverting terminal 5 µV and

at inverting terminal –7 µV, then

(B) 11.2 MHz the output is :

(A) 2.4 V
(C) 11.2 kHz
(B) 0.24 V

(C) 2.4 mV
(D) 112 kHz
(D) 2.4 µV

17 [P.T.O.

46. The number of Full-adders and Half- 48. The L, S and J quantum numbers

corresponding to the ground state
adders required to add 16-bit
electronic configuration of Boron
numbers is :
(z = 5) are :

(A) 1 HA and 15 FA
(A) L = 1, S = 1/2, J = 3/2

(B) 8 HA and 08 FA (B) L = 1, S = 1/2, J = 1/2

(C) 16 HA and 0 FA (C) L = 1, S = 3/2, J = 1/2

(D) L = 0, S = 3/2, J = 3/2
(D) 4 HA and 12 FA

49. The number of fundamental
47. A carrier is simultaneously
vibrational modes of CO2 molecule
modulated by two sine waves with
is :
modulation indices of 0.3 and 0.4;
(A) 4 : 2 Raman active and 2 IR
then the total modulation index active

is :
(B) 4 : 1 Raman active and 3 IR

(A) 1 active

(C) 3 : 1 Raman active and 2 IR
(B) 0.1
active
(C) 0.5
(D) 3 : 2 Raman active and 1 IR

(D) 0.35 active

18

50. Consider a nuclear F19. When it is 51. The outer electron configuration of

divalent Manganese ion is 3d54s0.
placed in a magnetic field of 1.0 tesla,
The ground state of this ion is
the resonance frequency (in units of
characterized by the spectroscopic

MHz) of the signal observed for this term :

nucleus in the NMR spectrometer (A) 6S 5/2

(B) 2D5/2
is :

(C) 2F 5/2
(Given : gN = 5.256, µN = 5.0504 ×
(D) 6H5/2
10–27 J/T; the subscript N refers to
52. The 623.8 nm radiation emitted by
the nuclear factors)
a He-Ne laser is due to the transition

between :
(A) 30 MHz

(A) 3s and 2p levels of Ne
(B) 90 MHz
(B) 3s and 3p levels of Ne

(C) 40 MHz
(C) 2p and 2s levels of Ne

(D) 5.0 MHz (D) 2p and 1s levels of Ne

19 [P.T.O.

55. The number of photons emitted per
53. In the Stern-Gerlach experiment,
second from a 1 watt Ar-ion laser
the number of components in which
operating at 488 nm is
the atomic beam splits depends upon
approximately :

the value of :
(A) 10.23 × 1019

(A) l (B) 2.46 × 1018

(B) s (C) 10.23 × 1017

(D) 2.46 × 1015
(C) j

56. The “Normal” and “Anomalous”
(D) m l
Zeeman effects are observed when

54. The Lande’s splitting factor for the (here S' is the total spin angular

momentum due to the coupling of
atomic state 2P3/2 is :
individual spin angular momenta).
(A) 1/3
(A) S' = 0 and S' 0, respectively

(B) 2/3
(B) S' = 0 and S' 0, respectively

(C) 1 (C) S' 0 and S' 0, respectively

(D) 4/3 (D) S' 0 and S' 0, respectively

20

58. van der Waals attractive interaction
57. Metallic nickel crystallizes in fcc-

between inert gas atoms varies with

type structure with lattice
interatomic separation (R) as :

1
(A) 2
R
constant a. The interplanar
1
(B)
R3

distance between the diffracting 1
(C)
R6
1
(D)
R 12
planes (220) in this material is :

59. If the concentration of Schottky

(A)
a defects in a fcc crystal is 1 in 1010
2 2
at 300°K, the energy of formation in

a eV of Schottky defects will be :
(B)
2

(A) 0.60
3
(C) .a
2 (B) 0.50

(C) 0.40
a
(D)
2
(D) 1.0

21 [P.T.O.

61. If the Debye characteristic
60. Consider the elastic vibrations of a
frequency for copper is 6.55 × 1012

crystal with two atoms per primitive Hz, the Debye temperature for

copper is :

cell having masses m and M (M > m). (A) 200 K

(B) 314.5 K
Using dispersion relation between

(C) 405 K
the angular frequency ( ) and wave
(D) 150 K

vector (K), find the frequency for 62. The energy of an electron in an

energy band as a function of its wave

acoustic branch at K = 0 : vector k is given by

1 /2
E( k ) E0 B(cos k x a cos k y a cos k z a );
2C
(A) Ka
m M where E0, B and a are constants.

The effective mass of the electron
1 /2
2C
(B) 2K a near the bottom of the band is :
m M
(A) 2 2 / 3Ba 2
1 /2
1 2C
(C) Ka (B) 2
2 m M / 3Ba 2

(C) 2
/ 2Ba 2
1/2
1 2C
(D) Ka
2 M (D) 2
/ Ba 2

22

63. An elemental dielectric has a 65. If the critical magnetic field for

dielectric constant = 12 and it aluminium is 7.9 × 103 A/m, the

contains 5 × 1018 atoms/m3. Its critical current which can flow

electronic polarizability in units of through long thin superconducting

FM2 is : wire of aluminium of diameter

(A) 4.17 × 10–30 is :

(B) 8.34 × 10–30 (A) 5.1 A

(C) 6.32 × 10–30 (B) 1.6 A

(D) 12.64 × 10–30 (C) 4.0 A

64. Magnetite (Fe 3 O 4 ) has a cubic (D) 2.48 A

structure with a lattice constant of
66. Deviation from Rutherford
8.4 Å. The saturation magnetization
scattering formula for -particle
in this material in units of A/m
scattering gives an estimate of :
is :
(A) size of an atom
(A) 6.2 × 105
(B) thickness of target
(B) 6.2 × 106
(C) size of a nucleus
(C) 12.4 × 106

(D) half life of -emitter
(D) 12.4 × 105

23 [P.T.O.

67. Binding energy difference in mirror 69. A satisfactory quenching gas in G.M.

nuclei can be understood using
tube must have the following
Coulomb energy difference. This
property :
indicates that :

(A) Nuclear force is spin dependent (A) Ionisation potential should be

(B) Nuclear force is strong force equal to the main counting gas

(C) Nuclear force is as strong as in the tube

Coulomb force
(B) Ionisation potential should be

(D) Nuclear force is charge
higher than that of the main
independent
counting gas in the tube
68. Find the half value thickness in

aluminium for beta particle of (C) It must have very narrow

energy 1.17 MeV : ultraviolet absorption bands

(A) 0.014 m
(D) When in an excited state it

(B) 0.016 m
must prefer to dissociate rather

(C) 0.020 m
than to de-excite by the

(D) 0.025 m
emission of photon

24

71. What are the expected types of
70. State the following decay mode in
gamma ray transitions between the
the category of allowed, forbidden following states of odd ‘A’ nuclei :

and Fermi or Gammow-Teller g9 /2 P1/ 2

(A) M4 and E5
transition :

(B) M1 and E2

(C) M3 and E4

(D) M6 and E7

72. According to the liquid drop model,

the occurrence of fission is due to

competition between :

(A) Fermi transition and allowed (A) Surface energy term and

symmetry energy term
(B) Fermi transition and second
(B) Surface energy term and
forbidden
Coulomb energy term

(C) G-T transition and allowed (C) Volume energy term and

surface energy term
(D) G-T transition and third
(D) Volume energy term and

forbidden Coulomb energy term

25 [P.T.O.

74. Give the approximate values for the
73. Based on the additive quantum
corresponding lifetimes of hadronic
numbers such as Lepton number,
decay, electromagnetic decay and

Baryon number, charge of the weak decay :

(A) 10–9 sec, 10–6 sec, 10–3 sec
Particle and Isospin, indicate the
(B) 10–12 sec, 10–9 sec, 10–6 sec
following nuclear reaction cannot be
(C) 10–15 sec, 10–13 sec, 10–6 sec
induced with the following
(D) 10–23 sec, 10–18 sec, 10–10 sec
combination :
75. Parity non-conservation was

n p e !e established in -decay when it was
observed that from polarised Co60
(A) Q, B are conserved, but I3, L nuclei :

are not conserved (A) Electrons were emitted equally
in all directions
(B) Q, B, L are conserved, but I 3
(B) More electrons were emitted in
is not conserved direction opposite to that of
magnetic field
(C) Q, B, I3 are conserved, but L
(C) Electrons were not emitted in
is not conserved
any direction

(D) B, I3, L are conserved, but Q (D) More electrons were emitted
perpendicular to the direction of
is not conserved
magnetic field
26

ROUGH WORK

27 [P.T.O.

ROUGH WORK

28