gate test 01 website

fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES

Website: www.physicsbyfiziks.com Email: [email protected] 1

Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498

Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16

PH: PHYSICS

2014

GATE Test Paper

Duration: Three Hours Maximum Marks: 100 Q. 1 Q. 25 carry one mark each.

Q1. Consider an anti-symmetric tensor Pij with indices i and j running from 1 to 5. The

number of independent components of the tensor is

(A) 3 (B) 10 (C) 9 (D) 6

Q2. The value of the integral 2 2Cos sx

dxk x

, is

(A) 2

2kse

k (B) 2

ksek (C) kse

k (D) kse

k

Q3. The eigenvalues of the matrix

100023032

are

(A) 5, 2, -2 (B) -5, -1, -1 (C) 5, 1, -1 (D) -5, 1, 1

Q4. Which of the following is correct expression of probability current density in one

dimension .

(A) *

*. .2xi d dJm dx dx

(B) *

*. .2xi d dJm dx dx

(C) *

*. .2xi d dJm dx dx

(D) *

*. .2xi d dJm dx dx

Q.5 Three fermions of spin 32

is adjusted in one dimensional harmonic oscillator of

frequency what is energy of ground state configuration .

(A) 2 (B) 3

2 (C) 5

2 (D) 7

2





Q6. Which of the following potential will give not give bound state for energy 0 E .

(A) 2( )V x kx (B) ( ) kV rr

in three dimensional

(C) ( )V x k x (D) 0 0( ) coshV x V x V

Q7. Consider Maxwells equations in vacuum in the absence of sources. If the solutions to

these equations are of the form trkitr .exp, 0 , trkitrB .exp, 0 where 00 , and k are constant vectors, then

(A) 0. 00 k (B) 000 k (C) 0dkd (D) ck

Q8. Consider an electric field existing in the interface between a conductor and free space.

Then the electric field is

(A) external to the conductor and normal to the conductors surface

(B) internal to the conductor and normal to the conductors surface

(C) external to the conductor and tangential to the conductors surface

(D) both external and internal to the conductor and normal to the conductors surface

Q9. The xoy plane carries a uniform surface current of density x50 A/m. The magnetic

field (in Wb) at the point z = - 0.5 m is

(A) 10106 Wb (B) 1 106 Wb (C) 106 Wb (D) 10 106 Wb

Q10. A planet of mass m is moving in a circular orbit of radius a under central force around

the sun of mass M, such that m





Q11. A bead of mass m is slide down smoothly on a wire of shape z = x2 in the (z, x) plane.

The Lagrangian of the bead is .

(A) 222 121 mgxxxm (B) 222 41

21 mgxxxm

(C) 222 121 mgxxxm (D) 222 41

21 mgxxxm

Q.12 The Lagrangian for a particle in cylindrical coordinates is given to be

)(/(1/21 22222 VzmL

where m is the mass of the particle and is a constant. Then which of the following is not

a conserved quantity?

(A) m (B) 2m

(C) 2/1/ zm (D) )(/(1/21 22222 Vzm

Q.13 Consider the Fermi-Dirac distribution function Ef at room temperature (300K) where

E refers to energy. If FE is the Fermi energy, which of the following is true?

(A) Ef is a step function

(B) FEf has a value

(C) States with FEE are filled completely

(D) Ef is large and tends to infinity as E decreases much below FE

Q.14 Find the average value of 2

x yv iv for ideal gas at temperature T

(A) 0 (B) kTm

(C) 2kTm

(D) 32kTm

Q15. ensemble of N three level systems with energies 1,0, 1 is in thermal equilibrium at

temperature T. Let 1kT .

The partition function is given by

(A) (1+cosh2 ) (B) (1+cos2 ) (C) (1+2cosh2 ) (D) (1+cosh2)





Q16. For a cubic crystal the diffraction line from the planes with (h2+k2+l2) = 8 is observed at

an angle of diffraction 10.230. If only one line is observed at an angle lower than this, the

crystal structure is?

(A) Simple Cubic

(B) Body Centered Cubic

(C) Face Centered Cubic

(D) Diamond Cubic Lattice

Q17. Consider an ideal Fermi gas, with energy spectrum (p is momentum), contained in

a box of volume V in space of 3 dimension. Which of the following is correct PV relation

for this system?

(A) (B)

(C) (D)

Q18. Which of the following statement about superconductor is not correct?

(A) With appearance of Meisner effect, resistivity disappear

(B) When superconductivity is destroyed with magnetic field, the material will heat.

(C) Superconductivity occurs in material having high electrical resistivity

(D) Critical temperature (Tc) decreases with isotopic mass

Q19. In a He-Ne laser, the laser transition takes place in:

(A) He only (B) Ne only

(C) Ne first, then in He (D) He first, then in Ne

Q20. All vibrations producing a change in the electric dipole moment of a molecule yield

(A) Raman spectra (B) Infrared spectra

(C) Ultra-violet spectra (D) X-ray spectra





Q21. Pick the WRONG statement.

(A) The nuclear force is independent of electric charge

(B) The Yukawa potential is proportional to

rh

mcr exp1 , where r is the separation

between two nucleons.

(C) The range of nuclear force is of the order of 10-15 m 10-14m

(D) The nucleons interact among each other by the exchange of mesons.

Q.22 In the circuit shown in the figure the Thevenin voltage THV and Thevenin resistance THR

as seen by the load between point A and B are respectively

(A) 2,4V (B) 3,8V (C) 3,12V (D) 2,16V

Q.23 How many maximum number of electrons can be adjusted in d orbital of hydrogen atom ..

Q24. An amplifier has a voltage gain of 500 and input impedance 20 K, without any

feedback. Now a negative feedback with = 0.1 is applied. Its gain and input impedance

(K ohms) with feedback will respectively be ..

Q25. If the nuclear radius of 27Al is 3.6 Fermi, the approximate nuclear radius of 64Cu in Fermi

is ..

2

34

A

B

A12

THR A

B

THV





Q. 26 Q. 55 carry two marks each.

Q.26 The solution of the differential equation for2

2 2 101 10.4xd y dy y e

dx dx , subject to the

initial conditions 0 1.1y and0

0.9x

dydt

, is

(A) ( cos10 sin10 )xe A x B x (B) ( cos sin )xe A x B x

(C) ( cos10 sin10 )xe A x B x (D) ( cos10 sin10 )xe A x B x

Q.27 A binary star system consists of two stars S1 and S2, with masses m and 2m respectively

separated by a distance r. If both S1 and S2 individually follow circular orbits around the

centre of mass with instantaneous speeds v1 and v2 respectively, the speeds ratio v1/v2 is

.

Q.28 A particle of unit mass moves along the x-axis under the influence of a potential,

24V x x x . The particle is found to be in stable equilibrium at the point . The time

period of oscillation of the particle is

(A) 2 (B) (C)

23 (D) 2

Q.29 A parallel plate capacitor has circular plates of radius R. It is being charged by a current I.

Then the magnetic induction B at a point between the plates at a distance R/2 from the

axis of the capacitor is:

(a) 2

0

RIB (b)

4

0

RIB (c)

6

0

RIB (d)

8

0

RIB

Q30. Consider a system in the unperturbed state described by the Hamiltonian, 01 00 1

H

.

The system is subjected to a perturbation of the form0

'0

H

, when





(C) (1+2 ) and (1 - ) (D) (1+ ) and (1 - 2)

Q31. Consider a two level quantum system with energies 01 and 1 . The specific heat

of the system is given by

(A) 2/

/

1 Tk

Tk

B B

B

ee

Tk

(B) Tk

Tk

BB

B

ee

Tk //

2

2

1

(C) 2/

/2

1 Tk

Tk

B

B

ee

(D)

2//

2

2

1 Tk

Tk

B B

B

ee

Tk

Q32. The internal energy of n moles of a gas is given by 32

aE nRTV

, where V is the

volume of the gas at temperature T and a is a positive constant. One mole of the gas in

state (T1, V1) is allowed to expand adiabatically into vacuum to a final state (T2, V2). The

temperature T2 is

(A) 12 1

1 1aR V V

(B) 12 1

2 1 13

aR V V

(C) 12 1

2 1 13

aR V V

(D) 12 1

1 1 13

aR V V

Q33. Consider the following circuit in which the current gain dc of the transistor is 100

and VVBE 7.0 . Which one of the following correctly represents the collector current IC

and collector-emitter voltage VCE?

(A) VmA 5.0,12

(B) VmA 1,14

(C) VmA 2,16

(D) VmA 3,18

900

V 15

100

k 100





Q.34 For the given circuit the frequency above which the gain will decrease by 20 dB per

decade is

(A) kHz12

(B) kHz16

(C) kHz18

(D) kHz20

Q.35 In the circuit shown, the ports Q1 and Q2 are in the state Q1 = 1, Q2 = 0. The circuit is

now subjected to three complete clock pulses. The state of these ports now becomes

(A) Q2 = 1, Q1 = 0

(B) Q2 = 0, Q1 = 1

(C) Q2 = 1, Q1 = 1

(D) Q2 = 0, Q1 = 0

Q.36 There are only three bound states for a particle of mass m in a one-dimensional potential

well of the form shown in the figure. The depth V0 of the

potential satisfies

(a) 222

02

22

292

maV

ma

(b) 222

02

22 2ma

Vma

(c) 222

02

22 82ma

Vma

(d) 2

22

02

22 502ma

Vma

0V

x

V2/a 2/a

inVk10

1000pF

k1

k2

outV

J Q

CLK

K Q

J Q

CLK

K Q 1

1

2Q

1

1

1Q





Q.37 The equation of a surface of revolution is 2223

23 yxz

The unit normal to the surface at the point

1,0,

32A is

(A) ki 102

53

(B) ki 102

53

(C) ki 5

253

(D) ki 102

103

Q.38 If

3for 3,3for 0

xxx

xf then the Laplace transform of f(x) is

(A) s-2e3s (B) s2e-3s (C) s-2 (D) s-2e-3s

Q.39 A hypothetical semiconductor has a conduction band that can be described by

Ecb = E1 E2 cos (Ka)

and valence band that can be described by :

Evb = E3 E4 sin2 (Ka/2)

Where E3 < (E1 E2) and Ka a

The band gap of the material is

(A) E1-E2-E3+E4 (B) E1+E2- E3

(C) E1-E2+E4 (D) 2(E2-E4)

Q.40 The electron concentration in the conduction band of Ge at 77K is 1012 cm-3. At this

temperature the electron and hole nobilities are equal, = 0.5 x 104 cm2 /V-sec. The

dielectric constant of Ge is 16.

If 100 volts is applied across a 1 cm cube of crystal, the current (mA) flowing in the

sample is ..





Q.41. Assuming a dispersion relation under long wavelength approximation for elastic

wave in one dimensional lattice of ferromagnetic system. The lattice specific heat at low

temperature varies as

(A) (B) (C) (D)

Q.42 According to the single particles nuclear shell model, the spin-parity of the ground state

of O178 is

(A)

21 (B)

23 (C)

23 (D)

25

Q.43 The disintegration energy is defined to be the difference in the rest energy between the

initial and final states. Consider the following process: He U Pu 42236

9224094

The emitted particle has a kinetic energy 5.17 MeV. The value of the disintegration

energy in MeV is ..

Q44. Which of the following fusion reaction give more energy? The nuclear mass of the different

nuclei is as follows

M ( ) = 1.00783amu, M ( ) = 2.01410amu, M ( ) = 3.01605amu,

M ( ) = 3.01603amu, M ( ) = 4.02603amu, M ( ) = 6.01512amu and

M(e) = 0.00055amu

(A) +

(B)

(C)

(D)

Q.45 If B and p is the wavelength of the series limit of Bracket and Pfund series respectively.

The ratio of B and p will be

(A) 2516 (B)

3625 (C)

259 (D)

169





Q.46 A pure rotational Raman spectrum of a linear diatomic molecule is recorded using

electromagnetic radiation of frequency ve. The frequency of two consecutive stokes

(A) ve 10 B, ve 14 B (B) ve 2 B, ve 4 B

(C) ve + 10 B, ve + 14 B (D) ve + 2 B, ve + 4 B

Q.47 The first excited state of nucleus has spin parity 2+ and decays to 1+ ground state by

emitting gamma rays. The possible multipole radiation for the above transition are?

(A) E1, E2, E3 (B) M1, M2, M3

(C) M1, E2, M3 (D) E1, M2, E3.

Common Data Questions

Common Data for Questions 48 and 49

A hydrogen beam is prepared in the state

31 21 2 31 2 3, exp exp exp

14 7 14E tE t E tr t i r i r i r

where E1, E2, E3 are the energies of the ground state and the first excited state of the

hydrogen atom and rrr 321 ,, are their normalized wave functions respectively.

The beam is incident on a detector which measures their energy. Let E0 be the ionization

energy of the hydrogen atom.

Q48. what will be probability such that energy is 0E and 09E

respectively .

(A) 114

, 314

(B) 114

, 914

(C) 114

, 114

(D) 314

, 314

Q49. The average energy measured by the detector is given by

(A) E0 (B) 0143 E (C) 0E (D) 0

314

E





Common Data for Questions 50 and 51

Consider a hetero nuclear diatomic molecule with moment of inertia I .

Q50. If N no of such molecule kept at equilibrium temperature T with j total angular

orbital quantum no then write the partition fuction at low temperature .

a)2

exp( )ZIkT

b)

2

1 exp( )ZIkT

c)

2

1 3exp( )ZIkT

221 3exp( )ZIkT

Q51. what will average energy per molecule at higher temperature T

(A) kT (B) 2kT (C) 32kT (D)3 kT

Linked Answer Questions

Statement for Linked Answer Questions 52 and 53:

Three particles of equal mass m are connected by two identical mass less springs of

stiffness constant k as shown in the figure:

Q.52 If 1 2x , x and 3x denote the horizontal displacements of the masses from their

respective equilibrium positions, the potential energy of the system is

(A) 23222121 xxxk (B) 3122322212

1 xxxxxxk

(C) 312232221 2221 xxxxxxk (D) 312232221 222

1 xxxxxxk

Q.53 The normal mode of frequency is given by

(A) ,k km m

(B) 2,k km m

(C) 3,k km m

(D) , 2k km m

.

k k

mmm





Statement for Linked Answer Questions 54 and 55:

A long solenoid, of radius a, is driven by alternating current, so that the field inside is

sinusoidal: 0 cosB t B t z

. A circular loop of wire, of radius 2a and resistance R,

is placed inside the solenoid, and coaxial with it.

Q54. The Magnetic flux through the loop is,

(A) 2 01 sin4

a B t (B) 2 0 sina B t

(C) 2 0 cosa B t (D) 2 01 cos4

a B t

Q55. Then the amplitude of current induced in the loop is

(A) 2

0

2a B

R

(B) 2

0

3a B

R

(C) 2

0

4a B

R

(D) 2

0

5a B

R





General Aptitude (GA) Questions

Q.56 Q.60 carry one mark each

Q.56 Choose the grammatically INCORRECT sentence:

(a) They gave us the money back less the service charges of Three Hundred rupees.

(b) This countrys expenditure is not less than that of Bangladesh.

(c) The committee initially asked for a funding of Fifty Lakh rupees, but later settled for a

lesser sum.

(d) This countrys expenditure on educational reforms is very less.

Q.57. Which one of the following options is the closest in meaning to the word given below?

Mitigate

(a) Diminish (b) Divulge (c) Dedicate (d) Denote

Q.58 Choose the most appropriate alternative from the options given below to complete the

following sentence:

Despite several the mission succeeded in its attempt to resolve the conflict.

(a) attempts (b) setbacks (c) meetings (d) delegations

Q.59 T he cost function for a product in a firm is given by 5q2, where q is the amount of

production. The firm can sell the product at a market price of Rs50 per unit. The number

of units to be produced by the firm such that the profit is maximized is

(a) 5 (b) 10 (c) 15 (d) 25

Q.60 Choose the most appropriate alternative from the options given below to complete the

following sentence:

Sureshs dog is the one was hurt in the stampede.

(a) that (b) which (c) who (d) whom





Q.61 Q.65 carry two marks each.

Q.61 Which of the following assertions are CORRECT?

P: Adding 7 to each entry in a list adds 7 to the mean of the list

Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list

R: Doubling each entry in a list doubles the mean of the list

S: Doubling each entry in a list leaves the standard deviation of the list unchanged

(a) P, Q (b) Q, R (c) P, R (d) R, S

Q.62 An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X

supplies

60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a

quality test. The ones that pass the quality test are considered reliable. Of Xs shock

absorbers, 96% are reliable. Of Ys shock absorbers, 72% are reliable.

The probability that a randomly chosen shock absorber, which is found to be reliable, is

made by Y is

(a) 0.288 (b) 0.334 (c) 0.667 (d) 0.720

Q.63 A political party orders an arch for the entrance to the ground in which the annual

convention is

being held. The profile of the arch follows the equation y = 2x 0.1x2 where y is the

height of the

arch in meters. The maximum possible height of the arch is

(a) 8 meters (b) 10 meters (c) 12 meters (d) 14 meters





Q.64 Wanted Temporary, Part-time persons for the post of Field Interviewer to conduct

personal interviews to collect and collate economic data. Requirements: High School-

pass, must be available for Day, Evening and Saturday work. Transportation paid,

expenses reimbursed.

Which one of the following is the best inference from the above advertisement?

(a) Gender-discriminatory

(b) Xenophobic

(c) Not designed to make the post attractive

(d) Not gender-discriminatory

Q.65 Given the sequence of terms, AD CG FK JP, the next term is

(a) OV (b) OW (c) PV (d) PW

gate test 01 website

Documents