GATE-PH 2003 QUESTION PAPER 1

PHYSICS-PH
Q.1 – Q.30 : Carry ONE mark each.

1. The two vectors P  i, q  (i  j ) / 2 are

(a) related by a rotation (b) related by a reflection through the xy-plane
(c) related by an inversion (d) not linearly independent
2. A 3 × 3 matrix has eigenvalues 0, 2  i and 2  i . Which one of the following statements is correct?
(a) The matrix is Hermitian (b) The matrix is unitary
(c) The inverse of the matrix exists (d) The determinant of the matrix is zero
2
3. The value of the integral  dz / z , where z is a complex variable and C is the unit circle with the origin
C

as its centre, is
(a) 0 (b) 2i (c) 4i (d) 4i
4. A particle with an initial velocity v0 iˆ enters a region with an electric field E0 ˆj and a magnetic field B0 ˆj .
The trajectory of the particle will
(a) be an ellipse (b) be a cycloid
(c) be a helix with constant pitch (d) not be confined to any plane
5. An object of mass m rests on a surface with coefficient of static friction  . Which of the following is NOT
correct?
(a) The force of friction is exactly mg
(b) The maximum force of friction is mg
(c) The force of friction is along the surface
(d) The force of friction opposes any effort to move the object
6. The Lagrangian of a particle of mass m moving in a plane is given by L = (1/2) m[vx2  v y2 ]  a ( xv y  yvx ),
where vx and vy are velocity components and a is a constant. The canonical momenta of the particle are
given by
(a) px  mvx and p y  mv y (b) px  mvx  ay and p y  mv y  ax

(c) px  mvx  ay and p y  mv y  ax (d) px  mvx  ay and p y  mv y  ax

7. Two events are separated by a distance of 6 × 105 km and the first event occurs 1sec before the second
event. The interval between the two events
(a) is time-like (b) is light-like (null)
(c) is space-like (d) cannot be determined from the information given
8. An electric charge, +Q is placed on the surface of a solid, conducting sphere of radius a. The distance
measured from the centre of the sphere is denoted as r. Then
(a) the charge gets distributed uniformly through the volume of the sphere
(b) the electrostatic potential has the same value for r  a
(c) an equal and opposite charge gets induced in the bottom half of the sphere
(d) the electric field is given by 1 / (40 r 2 ) for r  a
GATE-PH 2003 QUESTION PAPER 2

9. An electric field applied along the length of a long cylinder produces a polarization P. The depolarization
field produced in this configuration is
(a) 4P / 3 (b) 4P / 3 (c) 2P (d) 0
10. Which one of the following Maxwell’s equations implies the absence of magnetic monopoles?
(a)   E   /  0 (b)   B  0

(c)   E  B / t (d)   B  (1 / c 2 )B / t   0 J

11. An electromagnetic wave is propagating in free space in the z-direction. If the electric field is given by
E  cos(t  kz )i, where t  ck , then the magnetic field is given by
(a) B  (1 / c) cos(t  kz ) j (b) B  (1/ c) sin(t  kz ) j
(c) B  (1/ c) cos(t  kz )i (d) B  (1 / c) cos(t  kz ) j
12. Given a wave with the dispersion relation   ck  m for k  0 and m  0, which one of the following
is true?
(a) The group velocity is greater than the phase velocity
(b) The group velocity is less than the phase velocity
(c) The group velocity and the phase velocity are equal
(d) There is no definite relation between the group velocity and the phase velocity
13. Which of the following is a valid normalized wave function for a particle in a one dimensional infinite potential
well of width L centered at x  0 ?
(a) (2 / L)[cos(2x / L)  sin(2 x / L)] (b) (2 / L)1/ 2 sin[nx / L] for odd n

(c) (2 / L)1/ 2 cos[nx / L] for odd n (d) (2 / L) cos(x / L)

14. The commutator [ x, P 2 ], where x and P are position and momentum operators respectively, is
(a) 2iP (b) iP (c) 2ixP (d) 2ixP

15. A spin half particle is in the state S z   / 2 . The expectation values of S x , S x2 , S y , S y2 are given by

(b) 0,  / 4,  / 4,0
2 2
(a) 0, 0, 2 / 4,  2 / 4

(c) 0,  2 / 4, 0,  2 / 4 (d) 2 / 4,  2 / 4,0, 0

16. The spectral term for the atom with 70% filled subshell and only S = 3/2 is
3 4
(a) P0 (b) F9/ 2 (c) 3 F1/ 2 (d) 4 P1/ 2
17. The hyperfine splitting of the spectral lines of an atom is due to
(a) the coupling between the spins of two or more electrons
(b) the coupling between the spins and the orbital angular momenta of the electrons
(c) the coupling between the electron spins and the nuclear spin
(d) the effect of external electromagnetic fields
GATE-PH 2003 QUESTION PAPER 3
18. A piston containing an ideal gas is originally in the state X (see figure). The gas is taken through a thermal
cycle X  Y  X as shown. The work done by the gas is positive if the direction of the thermal cycle is

X
(a) clockwise
(b) counter-clockwise P
(c) neither clockwise nor counter-clockwise Y
(d) clockwise from X  Y and counter-clockwise from Y  X
V
19. A second order phase transition is one in which
(a) the plot of entropy as a function of temperature shows a discontinuity
(b) the plot of specific heat as a function of temperature shows a discontinuity
(c) the plot of volume as a function of pressure shows a discontinuity
(d) the plot of comprehensibility as a function of temperature is continuous
20. Consider the Fermi-Dirac distribution function f(E) at room temperature (300 K) where E refers to energy.
If EF is the Fermi energy, which of the following is true?
(a) f(E) is a step function
(b) f(EF) has a value of 1/2
(c) States with E < EF are filled completely
(d) f(E) is large and tends to infinity as E decreases much below EF
21. If the ionic radii of Mn and S are 0.80 and 0.184 nm respectively, the structure of MnS will be
(a) cubic closed packed (b) body centered cubic
(c) NaCl type (d) primitive cubic cell
22. A cubic cell consists of two atoms of masses m1 and m2 (m1 > m2) with m1 and m2 atoms situated on
alternate planes. Assuming only nearest neighbor interactions, the centre of mass of the two atoms
(a) moves with the atoms in the optical mode and remains fixed in the acoustic mode
(b) remains fixed in the optical mode and moves with the atoms in the acoustic mode
(c) remains fixed in both optical and acoustic modes
(d) moves with the atoms in both optical and acoustic modes
23. In simple metals the phonon contribution to the electrical resistivity at temperature T is
(a) directly proportional to T above Debye temperature and to T3 below it
(b) inversely proportional to T for all temperatures
(c) independent of T for all temperatures
(d) directly proportional to T above Debye temperature and to T5 below it
24. The effective mass of an electron in a semiconductor can be
(a) negative near the bottom of the band (b) a scalar quantity with a small magnitude
(c) zero at the center of the band (d) negative near the top of the band
25. The dielectric constant of water is 80. However its refractive index is 1.75 invalidating the expression
n  1/ 2 . This is because
(a) the water molecule has a permanent dipole moment
(b) the boiling point of water is 100ºC
(c) the two quantities are measured in different experiments
(d) water is transparent to visible light
GATE-PH 2003 QUESTION PAPER 4
26. The nucleus of the atom 9Be4 consists of
(a) 13 up quarks and 13 down quarks (b) 13 up quarks and 14 down quarks
(c) 14 up quarks and 13 down quarks (d) 14 up quarks and 14 down quarks
27. Which one of the following nuclear reactions is possible?
(a) 14
N 7  13C6    vc (b) 13 N 7  13C6    vc

(c) 13
N 7  13C6   (d) 13 N 7  13C7     vc
28. Suppose that a neutron at rest in free space decays into a proton and an electron. This process would
violate
(a) conservation of charge (b) conservation of energy
(c) conservation of linear momentum (d) conservation of angular momentum
29. Which one of the following is TRUE for a semiconductor pn junction with no external bias?
(a) The total charge in the junction is not conserved (b) The p side of the junction is positively charged
(c) The p side of the junction is negative charged (d) No charge develops anywhere in the junction
30. Which one of the set of values given below does NOT satisfy the Boolean relation R  PQ (where Q
denotes NOT Q)?
(a) P  1, Q  1, R  0 (b) P  1, Q  1, R  1
(c) P  0, Q  0, R  0 (d) P  0, Q  1, R  1

Q.31 – Q.90 : Carry ONE mark each.

31. The curl of the vector A  zi  xj  yk is given by
(a) i  j  k (b) i  j  k (c) i  j  k (d) i  j  k
32. Consider the differential equation d 2 x / dt 2  2dx / dt  x  0 . At time t  0, it is given that x  1 and
dx / dt  0 . At t  1, the value of x is given by
(a) 1/ e (b) 2 / e (c) 1 (d) 3 / e
33. Sij and Aij represent a symmetric and an antisymmetric real-valued tensor respectively in three dimensions.
The number of independent components of Sij and Aij are
(a) 3 and 6 respectively (b) 6 and 3 respectively
(c) 6 and 6 respectively (d) 9 and 6 respectively
34. Consider the four statements given below about the function f ( x )  x 4  x 2 in the range   x   .
Which one of the following statements is correct?
P the plot of f ( x) versus x has two maxima and two minima
Q the plot of f(x) versus x cuts the x axis at four points
R the plot of f(x) versus x has three extrema
S no part of the plot f(x) versus x lies in the fourth quadrant
Pick the right combination of correct choices from those given below
(a) P and R (b) R only (c) R and S (d) P and Q
35. The Fourier transform of the function f ( x ) is F (k )   eikx f ( x )dx . The Fourier transform of df ( x) / dx
is
(a) dF ( k ) / dk (b)  F (k ) / dk (c) ikF (k ) (d) ikF (k )
GATE-PH 2003 QUESTION PAPER 5

36. A particle of mass m is moving in a potential of the form V ( x, y , z )  (1/ 2)m2 (3 x 2  3 y 2  2 z 2  2 xy ) .

The oscillation frequencies of the three normal modes of the particle are given by

(a) , 3 and 3 (b) 2, 3 and 3

(c) 2, 2 and 2 (d) 2, 2 and 2

37. The speed of a particle whose kinetic energy is equal to its rest mass energy is given by (c is the speed
of light in vacuum)

3
(a) c / 3 (b) 2c / 3 (c) c / 2 (d) c
2
38. Electromagnetic waves are propagating along a hollow, metallic waveguide whose cross-section is a square
of side W. The minimum frequency of the electromagnetic waves is
(a) c / W (b) 2c / W (c) c / W (d) 2c / W
39. Consider the given statements about E(r, t) and B ( r , t ), the electric and magnetic vectors respectively in
a region of free space
P Both E and B are conservative vector fields
Q Both E and B are central force fields
R E and B are mutually perpendicular in the region
S Work done by B on a moving charge in the region is zero
Choose the right combination of correct statements from the following
(a) P and R (b) R and S (c) S only (d) P and Q
40. An infinite conducting sheet in the x-y plane carries a surface current density K along the y-axis. The
magnetic field B for z  0 is
(a) B  0 (b) B   0 Kkˆ / 2 (c) B   0 Kiˆ / 2 (d) B   0 Kjˆ / ( x 2  z 2 )0.5
41. A parallel beam of infrared radiation of wavelength of 1.01 × 10–6 m is incident normally on a screen with
two slits 5 × 10–6 m apart and the resulting interference pattern is observed on a distant screen. What is
the largest number of maxima that can be observed on the screen?
(a) 4 (b) 9 (c) 13 (d) infinitely many
42. A parallel beam of electrons of a given momentum pass through a screen S1 containing a slit and then
produces a diffraction pattern on a screen S2 placed behind it. The width of the central maximum observed
on the screen S2 can be increased by
(a) decreasing the distance between the screens S1 and S2
(b) increasing the width of the slit in screen S1
(c) decreasing the momentum of the electrons
(d) increasing the momentum of the electrons
43. An electron in a time independent potential is in a state which is the superposition of the ground state
(E0 = 11eV) and the first excited state (E1 = 1eV). The wave function of the electron will repeat itself with
a period of
(a) 3.1 × 10–18 s (b) 2.1 × 10–15 s
(c) 1.2 × 10–12 s (d) 1.0 × 10–9 s
GATE-PH 2003 QUESTION PAPER 6

44. A particle has the wave function  ( x, t )  A exp(it ) cos( kx) . Which one of the following is correct?
(a) This is an eigenstate of both energy and momentum
(b) This is an eigenstate of momentum and not energy
(c) This is an eigenstate of energy and not momentum
(d) This is not an eigenstate of energy of momentum
45. A free particle with energy E whose wave-function is a plane wave with wavelength  enters a region of
constant potential V  0 where the wavelength of the particle is 2 . The ratio (V/E) is
(a) 1/2 (b) 2/3 (c) 3/4 (d) 4/5
46. The vibrational spectrum of a molecule exhibits a strong line with P and R branches at a frequency v1 and
a weaker line at a frequency v2. The frequency v3 is not shown up. Its vibrational Raman spectrum shows
a strongly polarized line at frequency v3 and no feature at v1 and v2.
(a) the molecule could be linear
(b) the molecule lacks a center of inversion
(c) v1 arises from a symmetric stretching mode
(d) v3 arises from a bending mode
47. Three values of rotational energies of molecules are given below in different units
P 10 cm–1
Q 10–23 J
R 104 MHz
Choose the correct arrangement in the increasing order of energy
(a) P, Q, R (b) R, Q, P (c) R, P, Q (d) Q, R, P
48. The short wavelength cut off of the continuous X-ray spectrum from a nickel target is 0.0825 nm. The
voltage required to be applied to an X-ray tube is
(a) 0.15 KV (b) 1.5 KV (c) 15 KV (d) 150 KV
49. The spin-orbit coupling constant for the upper state of sodium atom which emits D lines of wave numbers
16956.2 and 16973.4 cm–1 is
(a) 15 cm–1 (b) 11.4 cm–1 (c) 12.5 cm–1 (d) 15.1 cm–1
50. Consider the following statements about molecular spectra
P CH4 does not give pure rotational Raman lines
Q SF6 could be studied by rotational Raman spectroscopy
R N2 shows infrared absorption spectrum
S CH3CH3 shows vibrational Raman and infrared absorption lines
T H2O2 shows pure rotational spectrum
Choose the right combination of correct statements
(a) P and Q (b) P, R and T (c) P, S and T (d) Q and R
51. The temperature of a cavity of fixed volume is doubled. Which of the following is true for the black-body
radiation inside the cavity?
(a) its energy and the number of photons both increase 8 times
(b) its energy increases 8 times and the number of photons increases 16 times
(c) its energy increases 16 times and the number of photons increases 8 times
(d) its energy and the number of photons both increase 16 times
GATE-PH 2003 QUESTION PAPER 7
52. A sample of ideal gas with initial pressure P and volume V is taken through an isothermal expansion proceed
during which the change in entropy is found to be S . The universal gas constant is R. Then the work done
by the gas is given by
(a) ( PV S ) / (nR ) (b) nRS (c) PV (d) ( PS ) / ( nRV )
53. Hydrogen molecules (mass m) are in thermal equilibrium at a temperature T. Assuming classical distribution
of velocity, the most probable speed at room temperature is
(a) (k BT ) / m (b) 2k BT / m (c) ( 2k BT / m ) (d) m / ( 2k BT )
54. Consider the energy E in the first Brillouin zone as a function of the magnitude of the wave vector k for
a crystal of lattice constant a. Then
(a) the slope of E versus k is proportional to the group velocity
(b) the slope of E versus k has its maximum value at | k |   / a
(c) the plot of E versus k will be parabolic in the interval (  / a )  k  ( / a )
(d) the slope of E versus k is non-zero for all k the interval (  / a)  k  (  / a)
55. An external magnetic field of magnitude H is applied to a Type-I superconductor at a temperature below
the transition point. Then which one of the following statements is NOT true for H less than the critical field
HC?
(a) the sample is diamagnetic
(b) it magnetization varies linearly with H
(c) the lines of magnetic induction are pushed out from the sample
(d) the sample exhibits mixed states of magnetization near HC
56. A ferromagnetic material has a Curie temperature 100K. Then
(a) its susceptibility is doubled when it is cooled from 300K to 200K
(b) all the atomic magnets in it get oriented in the same direction above 100K
(c) the plot of inverse susceptibility versus temperature is linear with a slope TC
(d) the plot of its susceptibility versus temperature is linear with an intercept TC
57. The point group symmetrics of the three molecules shown in Figs. 1–3 are respectively
H H Cl Cl H Cl
C C C C C C
H H H H Cl H
Fig. 1 Fig. 2 Fig. 3
[notation : C 2v = 2mm; C 2h = 2/m; D2h = mmm]

(a) C2h, C2v, C2h (b) C2v, C2h, C2h

(c) D2h, C2v, C2h (d) C2v, D2h, C2h
58. The energy density of states of an electron in a one dimensional potential well of infinitely high walls is (the
symbols have their usual meaning)
(a) L m / [ (2 E )] (b) Lm / (  E )

(c) Lm / [ (2 E )] (d) L m / (2E )

59. Which one of the following statements concerning the Compton effect is NOT correct?
(a) The wavelength of the scattered photon is greater than or equal to the wavelength of the incident photon
(b) The electron can acquire a kinetic energy equal to the energy of the incident photon
(c) The energy of the incident photon equals to the kinetic energy of the electron plus the energy of the
scattered photon
(d) The kinetic energy acquired by the electron in the largest when the incident and scattered photons move
in opposite directions
GATE-PH 2003 QUESTION PAPER 8
60. If the photon were to have a finite mass, then the Coulomb potential between two stationary charges
separated by a distance r would
(a) be strictly zero beyond some distance (b) fall off exponentially for large values of r
(c) fall off as 1 / r 3 for large values of r (d) fall off as 1/ r for large values of r
61. A stationary particle in free space is observed to spontaneously decay into two photons. This implies that
(a) the particle carries electric charge
(b) the spin of the particle must be greater than or equal to 2
(c) the particle is a boson
(d) the mass of the particle must be greater than or equal to the mass of the hydrogen atom
62. The masses of a hydrogen atom, neutron and 238U92 are given by 1.0078, 1.0087 and 238.0508 respectively.
The binding energy of 238U92 is therefore approximately equal to (taking 1 a.m.u. = 931.64 MeV)
(a) 120 MeV (b) 1500 MeV (c) 1600 MeV (d) 1800 MeV
63. A bistable multivibrator with a saturation voltage 5V is shown in the diagram. The positive and negative
threshold at the inverting terminal for which the multivibrator will switch to the other state are
2M

–
+ O

2M
0.01F
200k

(a) 5 / 11V (b) 10 / 11V (c) 5V (d) 11V

64. An avalanche effect is observed in a diode when
(a) the forward voltage is less than the breakdown voltage
(b) the forward voltage exceeds the breakdown voltage
(c) the reverse voltage exceeds the breakdown voltage
(d) the diode is heavily doped and forward biased
65. Which of the given relations between the Boolean variables P and Q is NOT correct? (In the notation used
here, P  denotes NOT P and Q denotes NOT Q)
(a) PQ  PQ  P (b) ( PQ)  P  Q
(c) PQ  ( P  Q) (d) PQ  Q  P

Data for Q. No. 66 to 67

Consider the vector V  r / r 3
66. The surface integral of this vector over the surface of a cube of size a and centered at the origin
(a) 0 (b) 2 (c) 2a 3 (d) 4
67. Which one of the following is NOT correct?
(a) Value of the line integral of this vector around any closed curve is zero
(b) This vector can be written as the gradient of some scalar function
(c) The line integral of this vector from point P to point Q is independent of the path taken
(d) This vector can represent the magnetic field of some current distribution
GATE-PH 2003 QUESTION PAPER 9
Data for Q. No. 68 to 69
Consider the motion of a particle in the potential V ( x) shown in the figure.

V1

V(x)

P Q R S T
x
68. Suppose the particle has a total energy E = V1 in the figure. Then the speed of the particle is zero when
it is at
(a) point P (b) point Q (c) point S (d) point T
69. Which one of the following statements is NOT correct about the particle?
(a) It experience no force when its position corresponds to the point Q on the curve
(b) It experience no force when its position corresponds to the point R on the curve
(c) Its speed is the largest when it is at S
(d) It will be in a closed orbit between P and R if E < V1
Data for Q. No. 70 to 71
A particle of mass m moving with speed v collides with a stationary particle of equal mass. After the
collision, both the particles move. Let  be the angle between the two velocity vectors
70. If the collision is elastic, then
(a)  is always less than 90º (b)  is always equal to 90º
(c)  is always greater than 90º (d)  cannot be deduced from the given data
71. If the collision is inelastic, then
(a)  is always less than 90º
(b)  is always equal to 90º
(c)  is always greater than 90º
(d)  could assume any value in the range 0º to 180º

Data for Q. No. 72 to 73

Consider two conducting plates of infinite extent, one plate at z  0 and the other at z  L, both parallel
to the xy plane. The vector and scalar potential in the region between the plates is given by
A(r , t )  A0iˆ cos(kz   ) cos(kct );
( r , t )  0
72. For this to represent a standing wave in the empty region between the plates
(a) k   / L and   0 (b) k  2 / L and    / 2
(c) k   / (2 L) and    / 2 (d) k   / 2 L and   0
GATE-PH 2003 QUESTION PAPER 10

73. The energy density at z  0 and t  0 is

2 2 2
(a) 0 (b) 0 c k A0

(c) (1 / 2) 0 A0 2 k 2 (d) (1 / 2) 0 A0 2 k 2  (1 / 2) 0 c 2 k 2 A0 2

Data for Q. No. 74 to 75

A particle is located in a three dimensional cubic well of width L with impenetrable walls.
74. The sum of the energies of the third and the fourth levels is
(a) 102  2 / mL2 (b) 10 2  2 / 3mL2
(c) 11 2  2 / 2mL2 (d) 152  2 / 2mL2
75. The degeneracy of the fourth level is given by
(a) 1 (b) 2 (c) 3 (d) 4

Data for Q. No. 76 to 77

The normalized wave functions 1 and  2 correspond to the ground state and the first excited state of
a particle in a potential. You are given the information that the operator  acts on the wave functions as
Â1   2 and Â 2  1 .

76. The expectation value of A for the state   (31  4 2 ) / 5 is

(a) –0.32 (b) 0.0 (c) 0.75 (d) 0.96
77. Which of the following are eigenfunctions of Â2 ?
(a) 1 and  2 (b)  2 and not 1

(c) 1 and not  2 (d) neither 1 nor  2

Data for Q. No. 78 to 79

In the presence of an inhomogeneous weak magnetic field, spectral lines due to transitions between two sets
of states were observed.
(1) 5l5  5 H 4 and (2) 2 D5/ 2  2 P3/ 2
78. The types of Zeeman effect observed in (1) and (2) respectively are
(a) normal, normal (b) anomalous, anomalous
(c) anomalous, normal (d) normal, anomalous
79. The number of levels into which each of the above four terms split into respectively is
(a) 6, 4, 10, 8 (b) 4, 6, 10, 12 (c) 11, 9, 6, 4 (d) 9, 5, 12, 10

Data for Q. No. 80 to 82

A system consists of three spin-half particles, the z components of whose spins S z (1), S z (2) and S z (3)
can take value +1/2 and –1/2. The total spin of the system is S z  S z (1)  S z (2)  S z (3) .
80. The total number of possible micro-states of this system is
(a) 3 (b) 6 (c) 7 (d) 8
GATE-PH 2003 QUESTION PAPER 11

81. The total number of micro-states with S z  1/ 2 is

(a) 3 (b) 5 (c) 6 (d) 7
82. Consider an ensemble of systems where each microstate has equal probability. The ensemble average of
Sz is
(a) –1/2 (b) 0 (c) 1/2 (d) 3/2

Data for Q. No. 83 to 84

A gas of N particles is enclosed in a volume V at a temperature T. The logarithm of the partition function
is given by ln Z  N ln{(V  bN ) (k BT )3/ 2 } where b is a constant with appropriate dimensions
83. If P is the pressure of the gas, the equation of state is given by
(a) P(V  bN )  Nk BT (b) P(V  bN )  k BT

(c) P(V  b)  Nk BT (d) P(V  b)  Nk BT

84. The interval energy of the gas is given by
(a) U  (1/ 2)k BT (b) U  Nk BT

(c) U  (3 / 2) Nk BT (d) U  2 Nk BT

Data for Q. No. 85 to 86

A crystal belongs to a face centered cubic lattice with four atoms in the unit cell. The size of the crystal
is 1 cm and its unit cell dimension is 1 nm. f is the scattering factor of the atom.
85. The number of atoms in the crystal is
(a) 2 × 1021 (b) 4 × 1021
(c) 2 × 1023 (d) 4 × 1024
86. The structure factors for (0 1 0) and (2 0 0) reflections respectively are
(a) 2f and zero (b) zero and 4f
(c) 2f and 2f (d) zero and zero

Data for Q. No. 87 to 88

An atomic bomb consisting of 235U explodes and releases an energy of 1014 J. It is known that each 235U
which undergoes fission releases 3 neutrons and about 200 MeV of energy. Further, only 20% of the 235U
atoms in the bomb undergo fission.
87. The total number of neutrons released is about
(a) 4.7 × 1024 (b) 9.7 × 1024
(c) 1.9 × 1025 (d) 3.7 × 1025
88. The mass of 235U in the bomb is about
(a) 1.5 kg (b) 3.0 kg (c) 6.1 kg (d) 12 kg
GATE-PH 2003 QUESTION PAPER 12
Data for Q. No. 89 to 90
The circuit below represents a non-inverting integrator

R
–
V1 + V0
R
C

89. For high frequencies (   ) the input impedance is

(a) 0 (b) R (c) R / (1  RC ) (d) 
90. For low frequencies (   ) the input impedance is

(a) V0  (1/ RC )  V1dt

(b) The voltages at the inverting and non-inverting terminals of the op-amp are nearly
(c) The voltage at the non-inverting terminal of the op-amp and the current in the resistor attached to it
are  / 2 out of phase
(d) The current in the two resistors are in phase