3. iit-jam full-length-test 03_17-1-2016.pdf

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fiziksInstituteforCSIRUGCJRF/NET,GATE,IITJAM,GREinPHYSICALSCIENCES

Website:http://www.physicsbyfiziks.com

Email:[email protected]

Headoffice:

fiziks,H.No.23,G.F,JiaSarai,

NearIIT,HauzKhas,NewDelhi16

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28B/6,JiaSarai,NearIIT

HauzKhas,NewDelhi16

ALL INDIA TEST SERIES

IIT - JAM - 2016

Full Length Test 03

PHYSICS (PH)

TIME: 3 HOURS MAXIMUM MARKS. 100

Section A: This section contains a total of 30 Multiple Choice Questions (MCQ)

carrying one or two marks each. Each MCQ type question has four choices out of which

only one choice is the correct answer.

There will be negative marking @1

3

rdfor one marks MCQ and

2

3

rdnegative marks

for two marks MCQ for each wrong answer.

Section B:This section contains a total of 10 Multiple Select Questions (MSQ)carrying

two marks each. Each MSQ type question is similar to MCQ but with a difference that

there may be one or more than one choice(s) that are correct out of the four given choices.The candidate gets full credit if he/she selects all the correct answers only and no wrong

answers.

Section C:This section contains a total of 20 Numerical Answer Type (NAT)questions

carrying one or two marks each. For these NAT type questions, the answer is a signed

real number which needs to be entered using the virtual keyboard on the monitor. No

choices will be shown for these types of questions.

Note: There will be no negative marking for Section B and Section C.


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SECTION A

Q1 Q10 (Multiple Choice Questions: One mark each)

There will be

1

3

rd

negative marks for each wrong answerQ1. If Eis energy and n is number density of the ideal gas, then pressure Pis given by

(a)

1

3P n E= (b)

2

3P n E= (c) P n E= (d)

3

2P n E=

Q2. In the figure shown all the strings are mass less, and friction is absent everywhere. If

210 / sg m= , then tension 1 2,T T and 3T are respectively:

(a) 1 2 310 , 10 , 10T N T N T N = = =

(b) 1 2 310 , 20 , 30T N T N T N = = =

(c) 1 2 310 , 30 , 20T N T N T N = = =

(d) 1 2 310 , 20 , 10T N T N T N = = =

Q3. The wave function of free particle is given by ( ) 4 5ikx ikxx e e = + then current density

associated with wave function ( )x is

(a)k

m

(b)k

m

(c)

9 k

m

(d)

9 k

m

Q4. An electron is accelerated though a potential difference V . If de Broglie wavelength is

given byV

= for nonrelativistic speeds. If and V represent numerical values in

angstrom and volt, then the value of is

(a) 1.25 (b) 12.25 (c) 2.50 (d) 22.25

Q5. The smallest value of integer n for which1

11

ni

i

+ =

is

(a) 2 (b) 3 (c) 4 (d) 8

3T

2 kg 1kg1T

2 kg1kg

2T


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Q6. An object is 30cm from a spherical mirror, along the central axis. The absolute value of

lateral magnification is1

2. The image produced is inverted. The focal length of the

mirror is

(a) 10cm (b) 10cm+ (c) 15cm (d) 30cm+

Q7. In a crystallography notation the vector P

in the unit cell shown in the figure is

(a) [ ]221

(b) [ ]212

(c) 212

(d) 212

Q8. The particular integral of the differential equation ( ) xexyDD 232 44 =+ is:

(a) xex 24

20

1 (b) xex 25

20

1 (c) xex 24

10

1 (d) xex 25

10

1

Q9. The magnetic field at a distance R from a long straight wire carrying a steady current Iis

proportional to

(a) IR (b) 2/I R (c) 2 2/I R (d) /I R

Q10. The group velocity of electromagnetic waves moving with phase velocity c in a

dispersive medium of refractive index is given by

(a)c

d

d

+

(b)c

d

d

+

(c)c

d

d

+

(d)c

d

d

+

y

P / 2a

o

z

x

a


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Q11 Q30 (Multiple Choice Questions: Two marks each)

There will be2

3

rdnegative marks for each wrong answer

Q11. The Van der Waal gas2

RT aP

V b V=

with specific heat at constant volume VC

undergoes adiabatic change then value ofdT

dVfor large volume V is given by

(a)( )V

RT

C V b (b)

( )V

RT

C b V (c)

( )VC V b

RT

(d)

( )VC b V

RT

Q12. For two phase system in equilibrium,P

is a function of temperature T . Ifs

is adiabatic

Compressibility then value of specific heat at constant volume VC is given by

(a)

2

V s

dPC TV

dT

=

(b)

2

V

s

TV dP C

dT

=

(c)

2

V s

dTC TV

dP

=

(d)

2

V

s

TV dT C

dP

=

Q13. A planet of mass m moves in a circular orbit of radius 0r in the gravitational potential

( )r

krV = , where kis a positive constant. The orbital angular momentum of the planet is

(a) kmr02 (b) kmr02 (c) kmr0 (d) 0r km

Q14. A thin uniform circular disc of mass and radius R is rotating in a horizontal plane

about an axis passing through its centre and perpendicular to its plane with an angular

velocity . Another disc of the same dimensions but of mass 4/M is placed gently on

the first disc coaxially. The angular velocity of the system now is

(a) / 5 (b) 5/2 (c)2

5

(d)

4

5


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Q15. There are two stationary fields of force 1F ayi=

and 2

F axi byj= +

, where i and j are

the unit vectors of the and y axes, and a and b are constants.

(a) 1F

is conservative field

(b) 2F


(c) Both 1F

and 2F


(d) Neither 1F

or 2F


Q16. A particle with rest mass is at rest and decays into two particles of equal rest masses

3

10which move along the zaxis. Their velocities are given by

(a) ( )zcvv 8.021 ==

(b) ( )zcvv 8.021 ==

(c) ( )zcvv 6.021 ==

(d) ( ) ( )zcvzcv 8.0;6.0 21 ==

Q17.

1 1 1

1 1 1

1 1 1

A

=

, then which of the following is NOT correct?

(a) The sum of Eigen values are 3

(b) The product of Eigen value is zero

(c) All Eigen values are non degenerate.

(d) The Eigen values of the given matrices are real.

Q18. 2 2 , 2 ,u x y v xy= = cos , sinx r y r = = , then( , )

( , )

u v

r

(a) 2r (b) 24r (c) 3r (d) 34r

Q19. A half wave plate is introduced between two cross polaroid 1 2&P P . The optic axis

makes an angle of 030 with the pass axis of 1P. If unpolarized light of intensity 0I is

normally incident on 1P, then the intensity of light after polaroid 2P is

(a) 0

8

I (b) 0

4

I (c) 0

2

I (d) 0

3

8

I


6/15




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Q20. If the quality factor of an underdamped harmonic oscillator of frequency 512Hzbe

48 10 . The number of oscillation does the oscillator make in time in which its energy

reduced to 1e

of its energy in the absence of damping is

(a) 12840 (b) 12740 (c) 12640 (d) 12540

Q21. Consider the digital circuit shown below in which the input C is always low (0).

The truth table for the circuit can be written as

A B Z

0 0

0 1

1 0

1 1

The entries in the Z column (vertically) are

(a) 1010 (b) 0101 (c) 1111 (d) 1011

Q22. Atoms are arranged in a three dimensional simple hexagonal structure. If

atomic radius is r, then packing fraction of this structure is

(a) 3 2

(b) 3 3

(c)

3

16

(d)

2

3 3

C

B

A

Z

(Low)


7/15




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Q23. A periodic function

( ) { [ ]21 , 1,1f t t t=

is defined as an expansion in a series of sines and cosines as

( ) ( ) ( )01 1

cos sin2

k k

k k

af t a k t b k t

= =

= + +

The coefficient ka is

(a)4

3 (b) ( ) 2 2

41

k

k

(c) 0 (d) ( )1

2 2

41

k

k

+

Q24. Which one of the following curves gives the solution of the differential

equation 321 KxKdt

dxK =+ , where 21 ,KK and 3K are positive constants with initial

conditions 0=x at t= ?

t

)(a

t

)(c

x

t

)(d

)(b

t


8/15




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Phone:01126865455/+919871145498

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Q25. The equation of a surface of revolution is 2 23 3

2 22

zx y= + . The unit normal to the

surface at the point

2

,0,23A

is

(a) ki

10

25

3+ (b) ki

10

25

3

(c)3 4 5 10

i k (d) ki 10

210

3+

Q26. In deep inelastic scattering electrons are scattered off protons to determine if a proton has

any internal structure. The energy of the electron for this must be at least of the order of

(a) 610 eV (b) 810 eV (c) 910 eV (d) 1210 eV

Q27. The electrostatic potential V(x, y) in free space in a region where the charge density is

zero is given by ( ) ( ) 22 34, yxfeyxV x += . Given that the x-component of the electric

field Ex, and Vare zero at the origin, f(x)is

(a) xex x 843 22 + (b) xex x 1643 22 +

(c) 84 2 xe (d) xex 22 43

Q28. The vector potential due to a magnetic moment m at a point ris given by3

r

rmA

= .

If m is directed along the positive z-axis, the x-component of the magnetic field, at the

point r, is

(a)5

3

r

myz (b)

5

3

r

mxy (c)

5

3

r

mxz (d)

( )5

23

r

xyzm

Q29. Consider the interference of two coherent electromagnetic waves whose electric field

vectors are given by tEiE cos 01 =

and ( ) += tEjE cos 02

where is the phase

difference. The intensity of the resulting wave is given by 20

2E , where 2E is the

time average ofE2. The total intensity is

(a) 0 (b) 200E (c) 22

00 sinE (d) 22

00 cosE


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Q30. Consider the Op-Amp circuit shown in figure. If ( )1 siniV V t= and ( )2 sinoV V t = + ,

then the minimum and maximum values of (in radians) are respectively

(a) and2 2 +

(b) 0 and 2

+

(c) and 0

(d) and 02

Q31 Q40 (Multiple Select Type Questions: Two marks each) No negative marking:

Q31. m gram water at 00 C is mixed with an equal amount of water at 080 C , then which of

the following statements are correct?

(a) The final temperature at equilibrium is 313K

(b) Increase in entropy when temperature of m gram of cold water rises from 273K to

313K

is 1 10.1367 calm g K

(c) Decrease in entropy when temperature of m gram of hot water drops from from

353Kto 313K

is 1 10.1367 calm g K

(d) Total change in entropy is equal to zero.

Q32. A sphere of mass and radius rshown in figure below slips on

a rough horizontal plane. At some instant it has translational

velocity 0v and rotational velocity about the centre0

2

v

r. Then

which of the following statements are correct?

(a) Angular momentum of the system about center of the sphere is conserved.

(b) Initial Angular momentum of the system about point is 015

rv

(c) Initial Angular momentum of the system is 06

5rv

(d) The velocity when sphere is just starting pure rolling is0

6

7v

0

2

v

r=

0vr

A

oVi

V1R

1R

R

C

+


10/15




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Q33. Which of the following statements are INCORRECT?

(a) Electrons are fermions and photons are bosons and both are distinguishable particle.

(b) In any particular quantum state only one indistinguishable particle can be adjusted.

(c) The Fermi Dirac distribution at equilibrium temperature T is1

( )

exp 1

f EE

kT

=

+

(d) The Bose Einstein distribution at equilibrium temperature T is

1( )

exp 1

f EE

kT

=

Q34. Light from a discharge tube containing hydrogen atoms falls on the surface of a piece of

sodium. The kinetic energy of the fastest photoelectrons emitted from sodium is eV73.0 .

The workfunction for sodium is eV82.1 , then which of the following statements are

correct?

(a) The energy of the photons causing the photoelectric emission eVE 55.2=

(b) The quantum numbers of the two levels involved in the emission of these photons are

4 to 2

(c) The change in the angular momentum of the electron in the hydrogen atom in the

above transition is2

hL

=

(d) The recoil speed of the emitting atom assuming it to be at rest before the transition is

smv /814.0=

(Ionization potential of hydrogen is eV6.13 )

Q35. If ( )2x

exf = and ( )

2xexxg = , then which of the following statements are correct?

(a) fand gare continuous

(b) fis differentiable everywhere but gis not

(c) gis differentiable everywhere but fis not

(d) fand gare differentiable


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R

100TV V=

C

6.7

L 203 H

500pF

Q36. A grating with 15000 lines per inch is illuminated by sodium light having 1D and 2D

lines of wavelength0

5890A and0

5896A . The grating spectrum is observed on the focal

plane of a convex lens of focal length 10cm . Choose the correct statements for 2 inch

wide grating with slit width of 0.0001cm .

(a) Grating is unable to resolve first order peak

(b) Grating can resolve 2ndorder peaks

(c) To resolve 1storder peak minimum grating width required is 2.5 inch

(d) Can resolve 3rd

order peaks

Q37. A plastic sphere floats in water with 50 percent of its volume submerged. This same

sphere floats in glycerin with 40 percent of its volume submerged. Which of the

following statements are correct for the density of glycerin ( )gl and density of sphere

( )sp ?

(a) 31250 /gl kg m = (b)3500 /gl kg m =

(c) 3250 /sp kg m = (d)3500 /sp kg m =

Q38. For the circuit shown in figure, which of the

following statements are correct?

(a) The resonant frequency is 500kHz

(b) The resonant frequency is 400kHz

(c) Impedance at resonance is 61k

(d) Total r.m.s current at resonance is1.65 mA

Q39. At a surface current, which one of the

magnetostatic boundary conditions are correct?

(a) Normal component of the magnetic field is continuous.

(b) Normal component of the magnetic vector potential is continuous.

(c) Tangential component of the magnetic vector potential is continuous.

(d) Tangential component of the magnetic vector potential is not continuous.


12/15




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Q40. Consider the circuits shown in figures (a) and (b) below

If the transistors in figures (a) and (b) have current gain ( )dc of 40 and 10 respectively.

Then which of the following statements are true?

(a) Circuit (a) in active region

(b) Circuit (a) in saturation region

(c) Circuit (b) in active region

(d) Circuit (b) in saturation region

Q41Q50 (Numerical Answer Type Questions: One mark each) No negative

marking:

Q41. The front tyre of Car have pressure 2 atm at 0300 K . If tyre suddenly brusts and 1.40 = ,

then final temperature is 0K

Q42. Two radioactive materials 1X and 2X have decay constants 10 and respectively. If

initially they have the same number of nuclei, then the ratio of the number of nuclei of

1X to that of 2X will be e/1 after a time1

. Then the value of is

Q43. An amplifier has a voltage gain of 500 and input impedance k20 , without any feedback.

Now a negative feedback with 1.0= is applied. Its input impedance with feedback will

be.............k

Q44. The Jupiters period of revolution around the Sun is 12 times that of the Earth. Assuming

the planetary orbits to be circular, then the ratio of distance between Jupiter and Sun and

that between Earth and Sun is .

100K

10.7V

2K

10V

(a)

4V

5V

10K

1K

(b)


13/15




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Q45. The energy dependence of the density of states for a two dimensional non-relativistic

electron gas is given by, ( ) nCEEg = , where Cis constant. The value of n is.

Q46. Theratio of mobility ( ) and diffusion coefficient ( )D for electrons in a semiconductor attemperature 0127T C= is ..Volts

Q47. In the Expansion of Maclaurins series expand of tanx the coefficient of 3x is given

by

Q48. A simple pendulum of length 2.0m is oscillating in an elevator accelerating upward at a

rate of 22 / secm . The frequency of pendulum is .Hz

Q49. The lattice constant of( )

Cu FCC is0

2.5A . Then the volume of its primitive cell

is.

30

A

Q50. The RCseries circuit is shown in figure below. The capacitor is initially uncharged. At

time 0t= , the switch S is closed. The voltage across resistor 1sec after the circuit is

closed isvolts

1000C F=

2R k=

110V

0=t

S


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Q51Q60 (Numerical Answer Type Questions: Two marks each) No negative

marking:

Q51. The two particles of mass m and 2m undergoes uniform circular motion about each other

at a separation R under the influence of their mutual attraction F . The angular velocity

is radian per second. If 2F

Rm

= , then value of is given by ..

Q52. If potential in one dimension is given by2 4

( )2 4

x xV x = then stable equilibrium point is

at x= .

Q53. In a Young double slit experiment with 50D cm= and 0.1d cm= , mica sheets of

thickness 6cm and 7 cm is introduced after 1stand 2ndslit. The refractive index of mica

sheet is 1.58 . Due to introduction of mica sheet, the central fringe get shifted by .

Q54. A horizontal pipe 10 cm in diameter has a smooth reduction to a pipe 5 cm in diameter. If

the pressure of the water in the larger pipe is 48 10 aP and the pressure in the smaller

pipe is 46 10 aP , the rate at which water flow through the pipes is .. /seckg .

Q55. The entropy of a gas containing Nparticles enclosed in a volume V is given by

= 2/5

2/3

ln N

aVENkS B , where E is the total energy, a is a constant and Bk is the

Boltzmann constant. The chemical potential of the system at a temperature T is given

by

3

2

5

2

lnBaVE

k T

N

where value of

is given by

Q56. Consider a system of eight non-interacting, identical quantum particles of spin3

2

in a one

dimensional box of length L . The minimum excitation energy of the system is2 2

22mL

.

Then the value of is..


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Q57. Liquid 4He has a normal boiling point of 4.2K . However, at a pressure of 1mm of Hg ,

it boils at 1.2K . The average latent heat of vaporization of 4He in this temperature

range is 1

J mol

. Take1 1

8.314R J mol K

= .

Q58. A plane electromagnetic wave of intensity 29 /W m is incident normally on the surface

of a material is partially reflected. Measurements on the standing wave in the region in

front of the interface show that the ratio of the electric field amplitude at the maxima and

the minima is 5. Then the intensity of the reflected wave is 2............. /W m

Q59. For the given zener diode network, the maximum value of load resistance LR that will

maintain output voltage to 15V is ( 15ZV V= , mAIZM 32= )

Q60. A unit vector n on the y -plane is at an angle of o120 with respect to i . If 2/ab= then

angle between the vectors nbiau +=

and ibnav +=

will be...........degree .

------------------------------------------------------------------------------------------------------------

+

ZI

LI

I

LR

k1

VVi 50=

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