1

PHYSICS DL -2012

1. the following bond is known as fairly strong a) Covalent bond b) molecular bond c) ionic bond d) metallic bond

2. The lattice constant of cubic lattice is a the spacing between (0 1 1), (101) and (112) planes are

a).2

a ,2

a ,3

a b) 2

a ,3

a ,6

a c) 2

a ,2

a ,6

a d) 3

a ,3

a ,2

a

. 3. The number of atoms per unit cell for a face entered cubic (FCC) lattice of copper crystal is Nearly (given a=3.60 Ao .ext. wt. of copper = 63.6, density of copper = 8.86) a) 3 b) 4 c) 5 d) 2 4. If the unit cells have following characteristics a=10.8Ao, b=9.47 Ao, ,41.41 0=α 00 93,83 == γβ Identify which type of crystal structure

a) Hexa gonal b) Rhombic c) cubic d) Triclinic 5. The primitives of a crystal are 1.2 A0, 1.8 A0 and 2 A0 along whose miller indices (2 3 1) cut intercept 1.2 A0 along x-axis .the lengths of intercept along y and z-axis are respectively. a)1.2 A0 ,1.2 A0 b)1.4 A0 ,1.6 A0 c)1.2 A0 ,1.4 A0 d)1.3 A0 ,1.4 A0

6. A substance with B.C.C lattice has density 6250 kg/m3 and molecular weight 60.2. The lattice a is (Given 261002.6 ×=N kg mol-1) a) 4 A0 b) 6 A0 c) 2 A0 d) 8 A0

7. If the ionic radii of Na+and Cl- are 0.98 A0 ,1.33 A0 and 1.81 A0 respectively , then NaCl has the inter ionic distance a) 0.83 A0 b) 2.79 A0 c) 2.3 A0 d) 0.35 A0 8. Where an electron is considered to belong to the crystal as a whole than to the particular atom, which of the following approaches are applicable. a)Heitler-London theory b) Bloch approach c) Bragg’s law d) none 9. Example for semiconductors a) Iron b) copper c) germanium d) lead 10. Majority carries in p-type semiconductors a) Electrons b) holes c) ions d) voltage

2

11. What is the donor concentration in n type germanium of 1 ohm-cm. resistivity at 300k . given electron mobility =3900vcm/volt.sec a) cm/1060.1 15× b) cm/1020.1 15× c) cm/1035.2 15× d) cm/10012.3 15× 12. The impurities that capture electrons from the valance band in a semiconductor are called a)donors b)Acceptors c)intrinsic d)Extrinsic 13. If a positive charge q moving with velocity v through a point p in a magnetic field experiences a deflective force F

r , then magnetic induction B at P is defined by the relation

a) BVqF

rr×= 0 b) BVqF

rrr•= 0 c) VqFB

rrr0×= d) FVqB

rrr•= 0

14. The unit for magnetic induction Br

a)weber b)weber/meter2 c)Weber. meter d)weber.sec.meter2

15. A long straight copper tube having an inside radius of 1 cm and outside radius of 2cms carries a current of 200 Amp. The magnetic field at a distance of 4 cm from the axis is a) 0 b) 3101.1 −× web/m c) 310− wb/sq.mt d) 3105.2 −× web/sq.mt 16. Mono atomic gases give a) Bands composed of closely spaced lines b) Continuous lines c) Distinct bright emission lines d) None 17. When a single particle emits light of wave number 1 cm-1 , which is equal to a) 1610986.1 −× erg/molecule b) 1810678.1 −× erg/molecule c) 1410524.1 −× erg/molecule d) 1610678.2 −× erg/molecule 18. A line spectrum of an excited atom of an element has wavelengths a) Equal for all elements b) Are found through out the spectrum c) Are different for dark line spectrum d) Are characteristics of given element 19. For paschen series, lower orbit of quantum number n f is a) 1 b)2 c) 3 d)4 20.According to quantum theorem , the frequency of radiation υ is related with energy between two States as

3

a) h

EE fi + b) h

EE fi − c)FI EE

h−

d) FI EE

h+

21.The series limit wavelength of the Balmer series in hydrogen spectrum is 3646 Ao. the Rydberg constant is a) 510063.1 × cm-1 b) 510467.1 × cm-1 c) 510097.1 × cm-1 d) 510536.2 × cm-1 22. A voltage amplifier use a tube having anode slope resistance of 15 kilo ohms. The voltage gain of this amplifier remains unaltered if the tube is replaced by another tube having amplification factor 2 times as large. The anode slope resistance of this second tube is a)20 kilo ohms b)25 kilo ohms c)35 kilo ohms d)15 kilo ohms 23. State which of the following statements is false a) In class B amplifier output current flows for half cycle of the input signal b) Voltage gain of each stage of an amplifier using resistive load can never exceed of the tube c) R.C. coupled amplifier has maximum gain in the middle range. d) Load line is a characteristic of the amplifying device alone 24. In R.C coupled amplifier, the voltage gain in the low frequency range drops due to a) The presence of shunt capacitance b) The presence of coupling capacitance C) The presence of both shunt and coupling capacitance. d) Increasing the shunt capacitance 25. A sweep speed is defined as a) Rate of change of sweep voltage with time. b) Molecule of the difference between the voltage ramp values c) Rate of change of input voltage d) None 26. How many ways of connecting the feed back signal? a) 2 b) 4 c) 1 d) 3 27. In voltage series feedback, the gain with feedback is the amplifier gain reduced by the factor. a) Aβ−1 b) Aβ+1 c) 1−Aβ d) Aβ 28. The voltage gain, for voltage series feed back A= -100, ki 10=α , R0=2k with 05.0−=β is a) 05.5− b) 09.9− c) 86.2− d) 76.6−

4

29. The relation between the charge density and the electric field provided by a)Couloumb’s law b)Ampere’s law c)Faraday’s law d)Gauss’s law 30. Propagation velocity of electromagnetic wave is given by

a) µε b)µε1 c)

εµ d)

µε

31. When the order parameter changes discontinuously at the transition a) The transition is second order b) Transition is first order c) May be either first order or second order d) None of the above 32. Pauli’s spin matrices are

a) ∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛=

0110

x , ∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛ −=

00i

iy , ∑ ⎟⎟

⎠

⎞⎜⎜⎝

⎛−

=10

01z

b) ∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛=

0110

x , ∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛−

=0110

y , ∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛−

=10

01z

c) ∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛=

0110

x , ∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛−

=0

0i

iy , ∑ ⎟⎟

⎠

⎞⎜⎜⎝

⎛−

=10

01z

d) ∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛=

0110

x , ∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛−

=0

0i

iy , ∑ ⎟⎟

⎠

⎞⎜⎜⎝

⎛=

1001

z

33. The first order energy correction in the non degenerate perturbation theory when the perturbed Hamiltonian H1 is a) τψψ dHE mm

0101 ∫ ∗=

b) τψψ dHE nm010

1 ∫ ∗=

c) τψψ dHHE mm01

00

1 )(∫ += ∗

d) τψψ dHE mm0

00

1 ∫ ∗= 34. Stark effect is a) Splitting of energy levels when the atom is placed in magnetic field b) Splitting of energy levels when the atom is placed in electric field c) Splitting of energy levels when the atom is placed in strong magnetic field d) Splitting of energy levels when the atom is placed in weak electric field 35. Hydrogen atom problem with one electron moving around the nucleus can be treated as a) Gravitational interaction

5

b) Central force problem c) Harmonic oscillator d) Square well potential problem 36. The primitive transition vectors of a simple cubic lattice be taken as

a) zyx ccbbaa∧∧∧

=== ::

b) zyx cccbca∧∧∧

=== ::

c) yyx acabaa∧∧∧

=== ::

d) zyx acabaa∧∧∧

=== :: 37. In a simple cubic lattice the six planes bond a cube of edge an of volume as

a) aπ2 and

32⎟⎠⎞

⎜⎝⎛

aπ

b) aπ2 and

32⎟⎠⎞

⎜⎝⎛

aπ

c) aπ2 and ⎟

⎠⎞

⎜⎝⎛

32aπ

d) aπ2 and ⎟

⎠⎞

⎜⎝⎛

aπ2

38. The miller indices of the plane parallel to y and Z axes are a) (010) b) (111) c) (001) d) (100) 39. The wave function for the motion of the particle in one dimensional potential box of length L is

Given by ⎟⎠⎞

⎜⎝⎛=

LxnAnπψ sin where A is normalization constant. The value of A is

a) L1 b)

L2 c)L d)

2L

40. The Eigen values of the Hamiltonian operator of the harmonic oscillator are given by a) ,.......3,2,1,0, == nnEn ωh b) ,.......3,2,1,0,)1( =+= nnEn ωh

c) ,.......3,2,1,)21( =+= nnEn ωh

6

d) ,.......3,2,1,0,)21( =+= nnEn ωh

41. The vibrational bands in an electronic spectrum are violet degraded if a) 111

VV BB < b) 111VV BB > c) 111

VV BB = d)none 42. The separation between consecutive lines is given by a) 2B b)4B 3)6B 4)12B 43. When alternate lines in rotational spectrum is missing the nuclear spin I is a) I=0 b) I=1/2 c) I=1 d) I=3/2 44. The following molecule exhibits rotational Raman spectrum a) C2 b) CH4 C) CF4 d) CCL4

45. The symmetry of (2, 0, 0) vibrational state of CO2 is

a) 1∑+

g b) 3∑−

g c) A1 d) B1

46. The number of IR bands expected in Formaldehyde is a) one b) two c) four d) six 47. Strong evidence for the existence of shell structure was obtained from a) γ-ray b) β-emission spectroscopy c) Existence of magic numbers d) Existence of magnetic moment 48. In shell model the weak interaction paradox has been resolved by the following a) Pauli’s Exclusion principle B) Existance of nuclear forces principle c) Observation of nuclear scattering d) Large nuclear mean path 49. Without use of spin –orbit coupling magic numbers could be explained up to a) 20 b) 40 c) 50 d) 28 50. The number of nucleons in a state with quantum number j is a) (2l+1) b) 2(2l+1) c) (2j+1) d) 2 (2j+1) 51. When nucleus undergoes β decay, the following are formed in the ground state a) Isotopes b) isotones c) isobars d) isomers 52. The neutrino and anti neutrino differ in this property a) Spin b) Linear momentum c) Helicity d) velocity 53. In Cowan and Reines experiment for the detection of neutrino, vp +1 gives a) n1

0 and −e b) +e and −e c) n10 and +e d) p1

0 and +e 54. The energy released in the fission of a uranium nucleus is nearly

7

a)200 Mev b) 100 Mev c) 300 Mev d) 400 Mev 55. The nuclei undergo spontaneous fission if the following condition is satisfied

a) 472

≥Az b) 47

2

≤Az c) 3

2

≥Az d) 3

2

≤Az

56. Negative feed back amplifier has a signal corrupted by the noise as its input. The amplifier will a) Amplify the noise as much as the signal b) Reduce the noise c) Increase the noise and noise figure d) Decrease the noise figure 57. Frequency stability in an oscillator can be achieved by a) Adjusting the phase shift b) Controlling its gain c) Incorporating a tuned circuit d) Controlling its feedback 58. An oscillator is basically an amplifier with a) Zero gain b) Very large gain c) Very low gain d) Infinite Gain 59. To generate a 1 MHZ signal, the most suitable oscillator is a) Phase shift b) wein bridge c) colpitts d) clapp 60. In an electronic circuit, matching means a) Connecting a high impedance directly to low impedance b) Transferring maximum amount of signal between different kinds of circuits c) Selection of components which are compatible d) RC coupled stages

61. Ampere’s law inconsistent with a) Momentum conservation b) Energy conservation c) Charge conservation d) None 62. The net magnetic flux passing through any closed surface is a) finite b) Infinite c) less than zero d) Zero 63. The direction of propagation of electromagnetic wave is given by the direction of a) HE × B) EH × C) E.H D) H.E 64. In An Isotropic Crystal Medium , Properties Are a) Dependent of direction

8

b) Dependent of planes c) Independent of direction d) Independent of planes 65. In an isotropic medium permittivity is a) Vector b) scalar c) Tensor d) None 66. Melting point of a following substance rise with increase in pressure a) Gallium b) Bismuth c) Wax d) Ice 67. Relationship between the magnetic vector potential and scalar potential

a) tV

cA

∂∂

=∇ 2

1. b) tV

cA

∂∂

=∇ 2

1. c) tVcA∂∂

−=∇ 2. d) tVcA∂∂

=∇ 2.

68. Unit of magnetic flux is a) Gauss b) Weber c) Ampere /m d)Ampere-m2

69. Fundamental laws governing electromagnetism are known as a) Newton’s laws b) Maxwell equations c) Lorentz transformations d) Laws of electromagnetic induction 70. Electromagnetic field tensor is tensor of rank a) Zero b) one c) two d) three 71. Vector potential is given by =uA

a) ⎟⎠⎞

⎜⎝⎛

ciA φ, b) ⎟

⎠⎞

⎜⎝⎛

cAi φ, c) ⎟

⎠⎞

⎜⎝⎛

ciAi φ, d) ⎟

⎠⎞

⎜⎝⎛

ciA φ,

72. A steady magnetic field in a current carrying conductor is a) Solenoidal and irrotational b) Solenoidal but not irrotational c) irrotational but not Solenoidal d) Neither solenoidal nor irrotational 73. The electric field intensity of a dipole is inversely (R is the distance )

a) R b) R2 c)R3 d) 21

R 74. According to micro canonical ensemble

a) Probability, sePr

αε= when )( EEEE r δ+<<

b) Probability, 1

1+

=+ re

Pr βεα when )( EEEE r δ+<<

9

c) cPr = When )( EEEE r δ+<< d) None of the above 75. According to canonical ensemble

a) rEr ceP β= b)

2rE

r ceP α= c) ∑ −=

r

E

E

r r

r

eeP β

β 2

d) rE

r ceP β−=

76. According to grand canonical ensemble.

a)rr NE

r eP βα −=

b) rr EN

r eP βα +=

c) rr NE

r eP αβ −−∝

d) None of the above 77. The mean energy according to grand canonical ensemble

a)rNeE α−=

b) rEeE β=

c) rr ENeE βα −−=

d) ∑∑

−−

−−

=

r

NE

rNE

rrr

rr

e

EeE αβ

αβ

10

78. Quantum mechanically the partition function

a)

rEez β−∫= c)

sE

sez β∑=

b)

rE

rez β−∑=

d)

rr NE

sez αβ −−∑=

79. Another name for partition function a) Sum over states c) Subtraction of states b) Addition of states d) Multiplication of states 80. Equipartition theorem says

a) kTi 23

=ε b) nTi 23

=ε c) kTi 21

=ε d) kTi 32

=ε

81. Entropy which avoids Gibb’s paradox difficulties

a) ⎥⎦⎤

⎢⎣⎡ ++= 0ln

23ln σβ

NVKRS

b) ⎥⎦⎤

⎢⎣⎡ ++= βσln

23ln

NVKNS

c) ⎥⎦⎤

⎢⎣⎡ ++= 0ln

25ln σβ

NVKRS

d) ⎥⎦⎤

⎢⎣⎡ ++= 0ln

23ln σT

NVKRS

82. In Maxwell-Boltzmann statistics a) Particles are distinguishable b) Particles are Indistinguishable c) Particles are photons d) Particles are electrons

11

83. In Bose-Einstein Statistics a) Particles are distinguishable b) Particles are Indistinguishable c) Particles are Fermions d) None of the Above. 84. Fermions have a)No spin b) Integral Spin c)1/2 integral spin d)None of the above. 85. Bose Einstein distribution

a) 11−

= + senS βεα

b) 11+

= + senS βεα

c) 11

+= −− se

nS βεα

d) 11

−= +− se

nS βεα

86. If heat is absorbed or evolved in a phase transition a) It is a phase transition of second order b) A phase transition of first order c) It is special case of both orders d) Such transitions occur very rarely , so they do not fall either 1st or 2nd order 87. In the P_T diagram, the state in which three phases coexist will be represented on the phase boundary line by a point called a) Critical point b)Melting Point c) Boiling Point d)Triple Point 88. Magnitude of the specific heat discontinuity in Curie-Weiss theory is a) 2/3NK b) 2/NK c) 4NK/3 d)None of the Above. 89. Specific heat is discontinuous at the phase point of the second order phase transition .This statement a) Violates Landau theory of the order parameter b) Is shown clearly by the Landau theoryof the order parameters c) Is obtained from hypothesis of university of critical behaviour d) None of the Above.

12

90. Which of the following is a first order phase transition? a) Solid – Liquid Transition b) Transition of iron to paramagnetic state at the curie point c) Transition between different crystal modifications d) All the above. 91. A wave is specified by a) Frequency and phase velocity only b) Frequency and Amplitude only c) Frequency only d) Frequency, phase velocity and Amplitude 92. Einstein’s energy relation is

a)0ν

hE = b) h

E 0ν= c) 0νhE = d) 02 νhE =

93.Heisenberg’s uncertainity relation

a) h≤∆∆ xPx b) h≥∆∆ xPx c) 0=∆∆ xPx d) 1=∆∆ xPx 94. The value of Planck’s constant h is

a)26106.6 −× erg.sec

b) 27106.6 −× erg.sec

c) 34106.6 −× erg.sec

d) 31106.6 −× erg.sec

95. The value of the wave function at the surface of an infinite potential is a)∞ b)0 c)2 d)-1 96. If a beam of electrons of energy 0.04 ev impinges on any energy barrier of height 0.03 ev and of Infinite width, then the fraction of electrons reflected is nearly a) 0.2 b) 0.1 c) 0 d) 0.9 97. the total energy of normal helium atom after first order energy is

a) HzEE ⎟⎠⎞

⎜⎝⎛=

45

b) ( ) HEzzE 4/52 2 +=

c) ( ) HEzzE 4/52 2 −=

d) ( ) HEzzE 4/52 2 −−= 98. For the ground state of Hydrozen atom , the first order stark effect is

13

a) Unity b) Zero c) Infinity d)-3E 99. Degeneracy means a) Same energy different wave functions b) Different energies same wave function c) Different energies different wave functions d) None 100. Fermi’s Golden rule states that the transition Probability per unit time is a) non-zero only between continuous states of the same energy. b) Proportional to square of meH ψ of the perturbation connecting the states c) Proportional to the density of the final state d) All the above three 101. In Dirac’s theory, which particle is considered as an unoccupied state of negative energy? a) Electron b) Proton c) Positron d) molecule 102. One Barn is equal to a) 10-20 cm2 b) 10-22cm2 c) 10-24 cm2 d) 10-26 cm2 103. The velocity of Barn’s approximation in high energy limit

a) 12

20 ≥h

aVµ

b) 12

20 ≤h

aVµ

c) 10 ≤vaV

h

µ

d) 10 >>vaV

h

µ

104. Two particles come towards each other with speed 0.8c with respect to the Laboratory, their relative speed is a) 0.852c b)0.976 c)1.256c d)0.506c

105. The half life of a particle in the laboratory is 8104 −× sec, when its speed is 0.8c. What half life will be measured in the laboratory if the speed of the particle is reduced 0.6?

a) sec102 8−× b) sec103 8−× c) sec101 8−× d) sec1075.0 8−× 106. Two particles are traveling in opposite direction with speed 0.9c relative to the Laboratory . What is The relative speed? a)0.948c b)0 c)c d)0.995c 107. What is the total energy of an electron when its momentum is ten times its rest mass multiplied by light velocity (rest mass of electron = 9 3110−× kg)? a) 6.1404 j1310−× b) j13101404.8 −× c) j1310502.4 −× d) j35101404.8 −×

14

108. The relativistic mass of a photon of wave length 050000A=λ

a) kg361054.3 −× b) 36104.4 −× kg c) 35104.4 −× kg d) 351045.3 −× kg

109. By what factor does the density of an object change when its move with speed v?

a)

2

2

1

1

cv

−

b)

2

2

1

1

cv

−

c)cv d)

vc

110. At what velocity will the mass of a particle be doubleof its rest mass

a) 2c b) c

23 c)

3c d)

2c

111. Change in rest mass m∆ is equal to

a) cE∆ b) 2c

E∆ c) CE.∆ d)

Ec∆

112. In a medium of dielectric constant ∈ and permittivityε , the velocity of a plane electromagnetic wave is a) Less than c b) More than c c) equal to c d) None 113. Which field does contribute to the increase in the energy of the moving charge? a) only electric field b)Electric and Magnetic field c)Only Electric field d) Static field 114. What is the nature of four-vector { }µK for electromagnetic fields ? a) Space- like b) Time-like c) light-like d) space time-like 115. At what velocity along its length will a rod contract 50%

a)2

c b) c23 c)

2c d)2c

116. Every clock appears to go at its fastest rate, relative to an observer, when it is a) Slow b) Moving with velocity C c) At rest d) None 117. Which of the following is correct?

a)

2

2

11

1cv

vtxx

−

−= b)

2

2

11

1cv

vtxx

+

−= c)

2

2

11

1cv

vtxx

+

+= d)

2

2

11

1cv

vtxx

−

+=

118. The formula for relativistic longitudinal Doppler’s effect for light waves in medium is

a)vcvcvv

+−

+ 0 b) vcvcvv

+−

= 0

c) 2

2

0 1cvvv −= d) 2

2

0 1cvvv +=

119. 1 ev is equal to a) Joules17106.1 −× b) Joules19106.1 −×

15

c) Joules20106.1 −× d) Joules18106.1 −× 120. Binding energy of a) 7.8 ev b) 6.9 ev c) 8.3 ev d)9.2 ev 121. The curl of yxjyix ++ /ˆˆ is a) ( ) ( )22/ˆ yxiyx +− b) ( ) ( )22/ˆ yxkyx −+ c) ( ) ( )2/ yxkyx +− d) ( ) ( )2/ˆ yxjyx +− 122. Div curl v is equal to a) Grad v b) Laplacian c) Zero d) None 123. The unit vector normal to the surface 08 222 =+−= zyxφ at the point (8, 1, 4) Is

a)3

ˆ32ˆ

32 kji +−

b) 3

ˆ32ˆ

32 kji ++

c) 3

ˆ32ˆ

32 kji −−

d) 3

ˆ32ˆ

32 kji −+

124. Using Green’s theorem in the plane , the value of the integral cφ ( )[ ],22 dyxdxyxy ++ where c is the closed curve of the region bounded by y=x and y=x is a)-19/20 b)-1/20 c)-7/20 d)+19/20 125. A matrix is called a null matrix if a) Upper diagonal elements are zero b) Every element is zero. c) Lower diagonal elements are zero d) Every element is zero 126. The complex conjugate of the sum of two matrices is a) The product of their conjugate in reverse order b) Difference of their complex conjugates c) Sum of their complex conjugates d) Transpose of the Conjugates 127. A square matrix A is said to be unitary if a)all elements are unity b) Its inverse is equal to its conjugate transpose c) Its inverse is equal to transpose d) its transpose is equal to its inverse

16

128. If one of the Eigen vectors of ⎟⎟⎠

⎞⎜⎜⎝

⎛3005

is ⎟⎟⎠

⎞⎜⎜⎝

⎛01

what is another basic given vector

a) ⎥⎦

⎤⎢⎣

⎡11

b) ⎥⎦

⎤⎢⎣

⎡−11

c) ⎥⎦

⎤⎢⎣

⎡−10

d) ⎥⎦

⎤⎢⎣

⎡10

129. The Eigen value of ⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

101011101

a)(1,1,1) b) (1,0,1) c) (0,1,1) d) (0,1,2) 130. What is the number algebraically independent components of the covariant curvature tensor in four Dimensional space a) 20 b)256 c)21 d)15 131. The isotropic tensor of second rank is necessarily a) controvariant b)Diagonal c)Mixed d)Covariant 135. Which of the following is the unit of radioactivity? a) Roentgen b) Curie c)Fermi d) Covariant 137. Lagrange’s equation of motion (of the second kind )for conservative system

a) 0=∂∂

−⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂

jj qL

qL

dtd

& b) 0=∂∂

−⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂

jj qL

qL

dtd

&&

c) 0=∂∂

−⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂

jj qL

qL

dtd

& d) 0=∂∂

−⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂

jj qL

qL

dtd

140. The equation of motion of one dimensional Harmonic oscillator using Hamilton’s principle is given By a) 0=+ kxxm && b) 0=+ krnxm && c) 0=+ mxxk && d) 0=− kxxm && 141. The equation of motion of simple pendulum, using Hamilton’s equation of motion is

a) 0=+θθ&&lg b) 0=+ θθ

gl&& c) 0=+ θθ

lg&& d) 0=− θθ

lg&&

142. The principle of least action for conservative system is expressed as

a)0

2

1

=∆∫∑ dtqPt

t jjj & b)

02

1

=∆∫∑ dtqPt

t jjj &

&

17

c) 0

2

1

=∆∫∑ dtqPt

t jjj d)

02

1

=∆∫∑ dtqPt

t jjj

&

143. The eccentricity Σ of a conic is 24

2221zme

Eα+=∑ , then for E<0 the particle is

a) Circle b) Parabola c) Hyperbola d) Ellipse

144. If [ ]ψ,Φ be the Poisson bracket of Φ and ψ then [ ]ψφ,t∂∂ is equal to

a) ⎥⎦⎤

⎢⎣⎡

∂∂

+∂∂

ttψφ

b) ⎥⎦⎤

⎢⎣⎡

∂∂

+∂∂

ttφψψφ

c) ⎥⎦⎤

⎢⎣⎡

∂∂

+∂∂

ttψφψφ ,

d) ⎥⎦⎤

⎢⎣⎡

∂∂

−∂∂

ttψφψφ

145. The poisson bracket of two constants of motion is itself a) a conservative b)a constant motion c)a constraint d)a canonical 146. The equation of motion of a charged particle in an electromagnetic field is given by

a) )ˆ.(ˆ Avcqqp ∇∇−= φ&

b) )ˆ.(ˆ Avcqqp ∇+∇= φ&

c) )ˆ.(ˆ Avcqqp ∇−∇= φ&&

d) )ˆ.(ˆ Avcqqp ∇−∇−= φ&

147. The motion of a particle moving under the influence of a central force takes place in a) Spheroid b)a plane c)a cone d)3-dimensional curve 148. According to Kepler’s third law of planetary motion, the time period T of revolution of the planet around the sun is expressed

a) T α the semi major or axis of the ellipse b) T α square of the semi major or axis of the ellipse c) T α square of the semi major or axis of the ellipse

18

d) T α cube of the semi major or axis of the ellipse

149. A free particle traveling in one dimension is represented by the wave ( )[ ]wtkxie −=ψ

a) u=2g b)u=g/4 c)u=g/2 d)u=g 150.A particle is placed between two impenetrable potential walls at =-a/2 and x=a/2 , then the eigen values for n=1 is

a) 2

2

2mah b) 2

2

2maah c) 22ma

πh d) 2

2

2 am

πh