gate physics test series

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Q.1-Q.25 carry one mark each.1. The inverse Laplace’s transform of 1 is:

(a) 1 (b) (t) (c) (t–1) (d) t

2. Two of the eigen values of a 3×3 matrix, whose determinant equals 4, are –1 & +2, the third eigenvalue of thematrix is equal to:(a) –2 (b) –1 (c) 1 (d) 2

3. The differential equation 3 5 3y" x sin x.y ' y cos x is

(a) Second order, homogeneous (b) Second order, non-linear(c) Second order, linear(d) Second order, non-homogeneous with constant co-efficients.

4. First order phase transition is an:(a) isothermal and isobaric process (b) isothermal and adiabatic process(c) adiabatic process (d) isothermal and isochoric process

5. When a system is held at constant temperature and pressure in a state of equilibrium, then it attains a minimumvalue of:(a) Internal energy (b) Enthalpy (c) Helmholtz energy (d) Gibb’s free energy

6. The partition function of a single gas molecule is Z . The partition function of N such non-interacting gas-molecules is given by

(a) NZN! (b) nZ (c) N Z (d) NZ

N

7. The Lagrangian for a particle is given by 2 2 212

L m x y z mgz , then

(a) z - compoennt of linear momentum is conserved(b) x - component of linear momentum is conserved(c) y - component of linear momentum is conserved(d) x & y component of linear momentum are conserved

8. In a straight coaxial cable, the central conductor and the outer one carry equal current in opposite directions.The magnetic field will be zero.(a) inside the conductor (b) inside the outer conductor(c) in between the two conductors (d) outside the cable

9. The hyperfine structure arises due to:(a) interaction between nuclear spin angular momentum & internal magnetic field produced by the

surrounding electrons in the atom only.(b) is due to the presence of different of isotopic species in the element under consideration only.(c) the interaction between nuclear spin angular momentum & internal magnetic field produced by the

surrounding electrons in the atom & due to isotope effect both(d) spin-orbit interaction of electron & relativistic correction both



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10. The diffuse series in emission spectrum of Cs arises due to the transition:(a) 2p 3s (b) 2d 3s (c) 4f 3d (d) 3d 3s

11. About the superconductors which option is correct?(a) Specific heat shows the discontinuity at T = Tc, & having large value at T > Tc for superconductor(b) Entropy & thermal conductivity increases in superconducting state(c) Superconductors have negative magnetic susceptibility(d) All are correct

12. If nuclear forces are long range forces, then:(a) binding energy will be independent of number of nucleons in the nucleus(b) binding energy will be proportional to number of nucleons in the nucleus(c) binding energy will be proportional to square number of nucleons in the nucleus(d) the forces between n–n, n–p, p–p will be different

13. A free neutron decays to a proton but a free proton does not decay to a neutron. This is because:(a) neutron is a composite particle made of a proton and an electron wheras proton is a fundamental

particle.(b) neutron is an uncharged particle whereas proton is a charged particle(c) neutron has large rest mass than the proton(d) weak forces can operate in a neutron but not in a proton

14. About FET correct option is:(a) The minimum current occurs at VGS = pinch of voltage(b) The maximum current for JFET occurs at VGS = 0V(c) JFET is non-linear voltage controlled device(d) All above are correct

15. In an n–p–n transistor circuit, the collector current is 10mA, If 90% the electrons emitted, reach the collectorthen:(a) the emitter current will be 9 mA (b) the emitter current will be 11 mA(c) the base current will be –1 mA (d) the collector current will be 9 mA

16. Four point charges are placed in a plane at following positions

Q 1,0 , Q 1, 0 , Q 0,1 and Q 0, –1 .At large distances, the electrostatic potential due to this charge distribution will be dominated by(a) Monopole moment (b) Dipole moment(c) Quadrapole moment (d) Octapolemoment.

17. The S.I. Unit of probability current density in 3 dimensional position space:(a) sec–1 (b) m–2sec–1 (c) m–1sec–1 (d) dimensionless

18. State of a particle in a infinite potential well is given to be

2sin cos where 0x xx A x LL L

Which of the following values will the energy measurement give?

(a) 2 2 2 2

2 2

9,2 2mL mL

(b) 2 2 2 2

2 2

2 9,2mL mL

(c)

2 2 2 2

2 2

2,mL mL

(d) 2 2 2 2

2 2

8 2,mL mL

19. The number of zeeman levels for the term 2D5/2 in strong magnetic field is:(a) 10 (b) 4 (c) 6 (d) 8



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20. Let A be a hermitian operator and B be an anti-hermitian operator and the two commute. Eigenvalues of

product ˆ ˆAB are,(a) real (b) either real or imaginary (c) imaginary or zero (d) only zero

21. The ratio between the kinetic energies of an electron in a two-dimensional square lattice which has akk yx

and an electron has akx

and ky = 0, is:

(a) 4 (b) 21

(c) 1 (d) 2

22. Among the following reactions in which reaction(s), the interaction is weak.(a) ° p + – (b) – ° + – (c) ep (d) all above

23. If a is a constant vector, r position vector and p is momentum value of poisson bracket 2a.r , p is :

(a) 2 r.a r (b) 2 r.a a

(c) 2a (d) 2r

24. The degeneracy of the ground state of the positronium atom is(a) 1 (b) 2 (c) 3 (d) 4

25. A metal rod AB rotate clockwise in the plane of the paper about the end B with an angular velocity inuniform magnetic field emerging out of the plane of the paper normally, the end B about which rod rotates willbe(a) Positive with respect to end A.(b) Negative with respect to end A(c) Having same potential as remaining part of the rod.(d) Having same potential as end A, but the centre will be at higher potential.

Q.26-Q.55 carry two marks each.

26. An infinite cylindrical region of radius R and axis along z-direction has a uniform increasing magnetic induction

ˆB B t k

. Direction of induced electric field E t

and poynting vector S at the point on the surface of the

cylinder will be, respectively?(a) ˆ ˆ, r (b) ˆ ˆ, r (c) ˆ ˆ, r (d) ˆr,

27. An unmagnetised sample of iron is placed in a magnetic field H which varies with as shown in the plot below.

The magnetisation M of this iron sample is continuously measured and also plotted as a function of time. Theappearance of this plot will be closest to



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(a) (b)

(c) (d)

28.

Which one of the following gives the output F for the logic diagram show above?(a) A B A C B C (b) CBCAAB

(c) ACCBBA (d) A + B + C

29. In the R-2R ladder type DAC is shown in figure. For S0 = 5V, S1 = 5V, S2 = 5V, find the output of DAC.

2R 2R 2R 2R

R R

0V 5V 5V

V0

(a) 5/4 V (b) 15/4 V (c) 12.5/4 V (d) 17.5/4 V

30. A current I flows in the loop having circular arc of radius ‘r’ (shown in figure). The magnetic field at point ‘O’is equal to

Or

(a) 0I2r

(b) 03 I8r

(c) 03 I4r

(d) 0I4r



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31.30V 24V

A

B

3

Thevenin voltage and current through the 3 load is:(a) 27V, 3A (b) 28V, 4A (c) 12V, 3A (d) 24V, 4A

32. The one-dimensional quantum mechanical potential energy of a particle of mass m is given by

0 ,, ,

V x V x a xx a

At t = 0, the wave function of the particle is completely confined to region –a < x < 0. The normalized wavefunction of the particle at time t = 0 is

(a)

2 sin , ,

0,

n x a xa a

x a

(b)

0,

2 sin ,

a x

n x x aa a

(c) 2 sin

,

0,

na x a a x

ax a

(d) 0, everywhere

33. Consider a system of spin ½ .The eigenvalues of the operator ˆ ˆ ˆy zO A S B S ,where A and B are constant,

are

(a) 0 and 1 (b) 1 (c) 2 2

2A B

(d) 2

A B

34. The number of fission per second ina 100-MW reactor is

(a) 610 (b) 1210 (c) 1810 (d) 2410

35. The value of the complex integral c zzd ,tan where C is the closed curve 22z is:

(a) 2i (b) –i (c) 0 (d) –2i

36. The matrix A =

5i21i3i212i32i3i321

is:

(a) Hermitian (b) Skew Hermitian(c) Unitary (d) Hermitian & Unitary

37. The fourier sine transform of the function f(x) = e–ax is:

(a)

2221

sas

(b)

22 saa

21

(c)

22 asa2

(d)

22 ass2



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38. For the force rkrrF 4 , the relation between the average kinetic energy & potential energy is:

(a) 0VT2 (b) 0V3T2 (c) 0VT (d) 0V2T3

39. The Hamiltonian of a system is given by:

mgzzb1a1m2

pH 222

2z

Then the Langrangian of the system is:

(a) mgzzb1a1m2

pL 222

2z

(b) mgzzb1a1

zm21L 222

2o

(c) mgzzbam

pL z 112

2222

(d) mgz1zb1azm21L 222

2o

40. The uncertainty in momentum for two particles represented by the wavefunctions:

01 xxAx & pxi

2 e2Ax

respectively are:(a) p1 = 0, p2 = 0 (b) p1 = , p2 = (c) p1 = 0, p2 = (d) p1 = , p2 = 0

41. For a particle described by the wave function 2reiyxA where r2 = x2 + y2 + z2, the z – component ofthe angular momentum is:(a) 0 (b) (c) 2 (d) 2

42. A particle of mass ‘m’ is moving in a potential of the form 2 2 2 21V x, y, z m 3x 3y 2z 2xy2

. The

oscillation frequencies of 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

43. A particle of mass m is moving in a potential weil of the type:V(x) =0 it 0 < x < 2L otherwiseIf we perturb the system simply by raising the floor of the well by a constant amount V0 only half way across thewell. The first order correction in energy is:

(a) 0 (b) 2V0 (c) V0 (d) 2V0

44. A carnot engine has a efficiency of 1/6 on reducing the sink temperature by 65°C, the efficiency becomes 31

.

What is the source temperature?(a) 265 K (b) 350 K (c) 390 K (d) 400 K

45. The J 0 J 1 rotational absorption line occurs at 111.153 10 cycles / sec in n 16C O and at111.102 10 cycles / sec in 12 16C O . The mass number of unknown carbon isotope is equal to

(a) 13 (b) 11 (c) 10 (d) 14



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46. The phase of diagram of a free particle of mass ‘m’ and kinetic energy E, moving in 1-D box with perfectlyelastic walls at x = 0 and x = 2L is given by

(a)

2mE

2mEL

xO

px

(b)

2mE

2mE2L

xO

px

(c)

2mE

2mE

Lx

px

–L O (d) 2mE

x

px

2LO

47. The magnetic field at a distance r above the centre of a circular loop of radius R placed in YZ plane and carriesa steady current I is given by:

(a) zrR

IRo ˆ2 2322

2

(b) y

rR2IR

2322

20

(c) yrR2

IR322

20

(d) x

rR2IR

2322

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Common Data QuestionsCommon data for Q. 48Q. 49.We consider a gas of N diatomic non-interacting diatomic molecule in thermal equilibrium at temprature T.

48. The rotational partition function of gas is:

(a) 3 23 2N

NN

V mkTh

(b) 2

28 IkT

h

(c) 3 23 2V mkT

h (d)

2

28

NIkT

h

49. The entropy of the gas is:

(a) 23 2 32 2

mkT VNK n NKNh

(b) 23 2 32 2

mkTK n Kh

(c) 2

28 IkTNK n NK

h

(d) 2

28 IkTNKT n

h

Common data for Q. 50Q. 51Consider the scattering of two particles of equal mass. Let 1 & be the scattering angle of projectile in Lab &CM system respectively. 2 be the angle of scattering of target & consider that scattering is elastic.

50. The angle of scattering of target in Lab system is:

(a) 2

(b) (c) 2

+1 (d) 2

–1

51. The relation between the differential cross-sections in Lab & C-M systems for projectile is:

(a) cos

4CMLab d

ddd

(b) 2cos

dd4

dd

Lab

(a) sin

4CMLab d

ddd

(b) 2sin

dd4

dd

Lab



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Linked Answer QuestionsLinked Answer Q.52Q.53.

52. The electric field of an e.m. wave propagating through vacuum is given by

0ˆE r , t z E cos 100 3 x 100 y t , wave vector and type of wave will be, respectively..

(a) 3 1 ˆˆ200 x y , TE

2 2

(b) 3 1ˆ ˆ50 x y , TM

2 2

(c) 3 1ˆ ˆ100 x y , TEM

2 2

(d) 3 1ˆ ˆ200 x y , TM

2 2

53. Direction of magnetic field B r, t

and poynting vector S r , t

are given by, respectively..

(a) 3 1 3 1ˆ ˆ ˆ ˆy x and x y

2 2 2 2

(b) 3 1 3 1ˆ ˆ ˆ ˆy x and x y

2 2 2 2

(c) 3 1 3 1ˆ ˆ ˆ ˆy x and x y

2 2 2 2

(d) 3 1 3 1ˆ ˆ ˆ ˆy x and x y

2 2 2 2

Linked Answer Q.54 Q.55.54. The density of copper is 8.94×103 kg/m3, and its atomic mass is 63.5 amu. If resistivity of the copper at

20ºC is: 81.72 10 m . What is relaxation time of electron? Each copper atom contributes onefree electron to the metal.(a) 162.5 10 sec. (b) 152.5 10 sec.

(c) 142.5 10 sec. (d) 132.5 10 sec.55. Estimate mean free path between collisions of the free electrons in copper at 20ºC?

(a) 84 10 m (b) 94 10 m (c) 104 10 m (d) 72 10 mGeneral Aptitude(GA) Questions

Q.56-Q.60 carry one mark each.

56. Which is the correct form of incorrect sentence: The speed of this car is greater than the old one.(a) Correct: The speed of this car is greater than that a old one.(b) Correct: The speed of this car is greater than that the old one.(c) Correct: The speed of this car is greater than that old one.(d) Correct: The speed of this car is greater than that of old one.

57. Which is the correct form of incorrect sentence: Neither his brother nor any member of the family helped him.(a) Correct: Neither his brother nor other member of the family helped him.(b) Correct: Neither his brother nor any other member of the family helped him.(c) Correct: Neither his brother nor any member of the family helped him.(d) Correct: Neither his brother or any other member of the family helped him.

58. Two numbers X and Y are 20% and 28% less than a third number Z. Find by what percentage is the numberY less than the number X?(a) 8% (b) 12% (c) 10% (d) 9%

59. What is the antonyms of word advent?(a) Arrival (b) Runaway (c) Departure (d) Discover.



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60. What is the synonym of word skirmish?(a) Minor fight (b) Discussion (c) Killing (d) High expectation

Q.61-Q.65 carry two marks each.

61. The Geology/Geography department of Dabbawara university has 100 student applicants. 10 of these studenthave never traken a course in geology/geography. 63 of the students have taken at least one geology course.81 has taken at least one geography courseThe probability that of the 100 applicants any student-selected at random has taken only one course in eithergeology or geography course is

(a) 925 (b)

563 (c)

990 (d)

81100

62. If the operation, A is defined by the equation 2 x y x y the value of a in 2 3 a a given by(a) –1 (b) 0 (c) 1 (d) 2

63. In the Andman Islands the natives trade (barter) 2 spears as worth 3 fishooks and one knife. They will give 25coconuts for 3 spears, 2 knives and a fishook together. How many coconuts will they give for only one fishook(a) 2 (b) 4 (c) 5 (d) 8

64. A man returns after shooting and catching birds in his bag. He was asked how many birds he had in his bag. Hesaid, “they are all house sparrows, but six, all pigeons but six and all parrots but six.” The number of birds hehad in all were(a) 18 (b) 36 (c) 9 (d) 27

65. What is the last digit of 254?(a) 2 (b) 4 (c) 6 (d) 8

*****END OF THE QUESTION PAPER



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GATE TEST SERIES -IANSWER SHEET

1. (b) 2. (a) 3. (c) 4. (a) 5. (d) 6. (b) 7. (d)

8. (d) 9. (c) 10. (d) 11. (c) 12. (c) 13. (c) 14. (d)

15. (b) 16. (b) 17. (c) 18. (a) 19. (c) 20. (c) 21. (d)

22. (d) 23. (b) 24. (d) 25. (a) 26. (c) 27. (b) 28. (a)

29. (b) 30. (b) 31. (b) 32. (a) 33. (c) 34. (c) 35. (d)

36. (a) 37. (d) 38. (b) 39. (d) 40. (d) 41. (b) 42. (c)

43. (b) 44. (c) 45. (b) 46. (b) 47. (d) 48. (d) 49. (c)

50. (d) 51. (b) 52. (a) 53. (c) 54. (a) 55. (a) 56. (d)

57. (b) 58. (c) 59. (c) 60. (a) 61. (a) 62. (c) 63. (a)

64. (c) 65. (b)

Date: 04-01-2014

gate physics test series

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