B PHYSICAL SCIENCE TEST SEREIS # 7 FULL … 2015...1. This test paper has a total of 75 questions carrying 150 marks. All Questions are compulsory. 2. Each question of part A are 2mark

H.O: 27-G 2ND FLOOR, JIA SARAI, NEAR IIT, NEW DELHI- 110016 South Campus Centre: 297, GROUND FLOOR, OPP. VENKY COLLEGE, SATYA NIKETEN Tel: 011-26521410, 26855515 Mobs: 09654680505, 07503646974 E-mail: [email protected] Website: www.ugcpoint.in |

UGC POINT LEADING INSTITUE FOR CSIR-JRF/NET,GATE & JAM

BOOKLET CODE SUBJECT CODE

B PHYSICAL SCIENCE 05

FULL LENGTH # 2

Date: 12/06/2015 Timing: 3:00 H Maximum Marks: 150

Instructions

1. This test paper has a total of 75 questions carrying 150 marks. All Questions are

compulsory.

2. Each question of part A are 2mark marks , part B 3.5 Marks, Part C 5 Marks’s

3. Read the Questions carefully and mark your appropriate response to the OMR sheet.

4. There is Negative marking of 1/4 for each wrong answer.

5. Mark the response by Black or Blue Ball Pen only.

6. Any other belongings like Book/ Notes / Electronic device etc are not permitted in

the examination hall.

7. Submit your answer sheet (OMR Sheet) to the invigilator before leaving the

examination hall.

TEST SEREIS # 7


PART-‘A’

1. Out of 200 musicians in a club 5% can play all the three instruments. I.e. guitar, violin and flute. Each

musician can play at least one among three instruments. Number of musicians who can play exactly two

instruments is 70. The number of musicians who can play the guitar alone is 90. What is the total

number of musicians who can play exactly one instrument out of violin and flute?

(1) 48 (2) 36 (3) 44 (4) 30

2. ‘X’, ‘Y’ and ‘Z’ are 3 runners who start running simultaneously around a square track ABCD of

perimeter 70 meters from the point ‘A’. ‘X’ and ‘Y’ run anti-clockwise at speeds of 5 m/sec and 7

m/sec, respectively, whereas ‘Z’ runs clockwise at a speed of 9 m/sec. The ratio of the time taken by

them to meet for the first time at the starting point to that of their first meeting anywhere on the track is:

(1) 2:1 (2) 3:1 (3) 3:2 (4) 1:9

3. How many 5 digit numbers can be formed by using the first 9 natural numbers, such that all the 5 digit

of the numbers are formed in ascending order and at the hundredth place, the digit in ‘5’?

(1) 31 (2) 34 (3) 36 (4) 37

4. Arjun started a business by investing Rs. 2 lakh for 3 months after which he invested Rs. 4 lakh more

and after 5 more months, he withdraw Rs. 5 lakh from the business. Pandit joined Arjun’s business 4

months after Arjun had started it and he invested Rs. 5 lakh initially. After 3 more months he added Rs.

5 lakh more in the business. Khan joined few months after Pandit and invested Rs. 12 lakh but after 2

more months he withdraw Rs. 5 lakh from the business. If at the end of the year they divide the profit in

ratio 8:13:9, then how many months after Arjun and started the business did Khan join it?

(1) 6 months (2) 7 months (3) 5 months (4) 4 months

5. There are 17 coins in a bag numbered from 1 to 17. Raju picks up a coin at random and puts it back in

the bag. He continues this process until he gets a coin which shows an odd number. What is the

probability that the coin shows a prime number when he stops?

(1) 1

2 (2)

1

3 (3)

2

3 (4)

4

5

6. A point is randomly selected inside a rectangle and perpendiculars are drawn on each of the each of the

4 sides of the rectangle from this point. The sum of the length of these perpendiculars in 24 cm. What is

the perimeter of the rectangle?

(1) 24 cm (2) 48 cm (3) 12 cm (4) cannot be determined

7. Jackie is twice as good a workman (i.e. twice as efficient) as Chan and takes 20 days less than Chan to

complete a job. Find the time in which they can complete the job while working together.

(1) 2

6 days3

(2) 1

13 days3

(3) 2

15 days3

(4) 1

16 days3

8. Equation of a straight line ‘L’ is 4 7 28 0x y out of the points (1,4) and (4,1)

(1) Both lie on the same side of the straight line L

(2) Both lie on the opposite sides of the straight line L

(3) Both lie on the straight line L

(4) Exactly one of the points lies on the straight line L

9. Sajid’s and Ankit’s present ages are in the ratio 5:6. Three years ago their ages were in ratio 9:11. What

will be the ratio of their ages after 6 years from now?

(1) 1:2 (2) 3:4 (3) 6:7 (4) 7:8

10. Rahul had scored twice the marks the scored in an exam, his percentage score would have gone up by

30 % points. Rahul had scored 12 marks less than what he got how, he would have scored 3% less

marks. What is Rahul’s score?

(1) 90 (2) 108 (3) 120 (4) 140


11. A carpenter designs a table such that the shape of the table is a right angled triangle whose hypotenuse is

10 m more than one of the sides. If the area of this table is 150 m2 and the length of each side (in meters)

of the table is an integer, then what is the perimeter of this table?

(1) 45 meters (2) 50 meters (3) 60 meters (4) 75 meters

12. There are M people in the group 13M .Out of these M people, 40% are from India and the

remaining are from Pakistan. What is the minimum number of people in the group from Pakistan?

(1) 3 (2) 6 (3) 9 (4) 12

13. If 321 137 623 743 221123 371 326 347 112A . Find the unit digit of A

(1) 2 (2) 4 (3) 8 (4) 6

14. Which of the following is the largest?

(1) 3

1

7 (2)

2

1

6 (3)

4

1

8 (4)

6

1

5

15. What is the ratio of a b to ?a b

(1) (a-b):(a+b) (2) a2 : b

2

(3) a:b (4) b:a

Directions for question 36 to 38

Study the given pie chart carefully and answer the following questions.

Editing18%

Proofreading12%

Printing36%

Papercost 16%

Miscellaneous

8%

Royalty10%

The pie chart represents the cost analysis of book (Managing Radical Charges)

16. Which of the following is the central angle (in degrees) for paper cost?

(1) 42.8o (2) 32.6

o (3) 36.8

o (4) 57.6

o

17. If the cost of printing is Rs. 23,400, what would the cost of ‘Royalty’ be?

(1) Rs. 6,500 (2) Rs. 2,340 (3) Rs. 4,680 (4) Rs. 7,840

18. If Miscellaneous expenditure amounts is Rs. 18,000 then what is the expenditure on ‘Editing’

(1) Rs. 8,000 (2) Rs. 14,400 (3) Rs. 46,800 (4) None of these

19. Two scooters are sold at Rs. 20,000 each. One of the scooters is sold at a profit of 10% while the other is

sold at a loss of 10%. What is the overall profit or loss?

(1) Loss of Rs. 404 (2) Profit of Rs. 202

(3) Loss of Rs. 202 (4) No profit, No loss

20. What is the value of: 2 5 6 4 8

of5 3 7 13 13

=?

(1) 169

56 (2)

8

7 (3)

28

15 (4)

22

13


PART-‘B’

21. Let 3

sinz zf z

z

be a complex valued function

Then

(1) Pole of order 3 at z =0

(2) Pole of order 2 at z = 0

(3) Pole of order 1 at z =0

(4) Removable singularity

22.

2

2 4C

dz

z where : 2c z i is

(1) 2

4

(2)

2

16

(3)

4

(4)

16

23. Let ijn n

A a

be a real symmetric & unitary matrix then eigen values of A are

(1) 1 or -1 (2) 1 only (3) -1 only (4) i or -i

24. Let

4 4

0

0 0

0 0 0

a b c d

a b cA

a b

a

be a square matrix

Where ‘a’ in 4th root of i then find tr 4( ) ?A

(1) 4i (2) 4 (3) -4 (4) None

25. Let 1 2& 1/y x y x are two linearly independent solution of

2 " ' , 0x y xy y x x

Then the particular integral of the D.E. is

(1) ln2 4

x xx (2) ln

2

xx (3)

4

x (4) None

26. Operator B satisfy , 1B B

and a Hamiltonian is H B B B B

When is real no. It Eigen values are

(1) 2 ,N N takes up values 0, 1, 2, 3 …

(2) 2 ,N N takes up values 1, 2, 3 …

(3) 2 ,N N takes up values 0, 1, 2, 3 …

(4) 2 ,N N takes up values 1, 2, 3 …

27. An electron moves in the z-direction in an uniform magnetic field along z-axis ˆB Bz , the energy

eigen value for the system 2 2 21

2x y zH

m

Where e

p Ac

(1) 2 2

0,1,2,.....2

Kn

m (2)

2 2 10,1,2,.....

2 2

K eBn n

m mc

(3) 1

0,1,2,.....2

n n

(4) 1

0,1,2,.....2

eBn n

mc


28. A particle of mass m is trapped in a square well of width L and infinitely deep. Its normalised wave

function within the well for the nth state is 1/2

2sinn

n x

L L

The x in I excited state is

(1) 2

2

31

12

L

(2)

2

2

31

12 2

L

(3) 2

2

31

6 2

L

(4) None of these

29. In SR flip flop (modify) the resultant flip flop truth table is

30. The phenomenon known as early effect in a bipolar transistor refers to a reduction of the effective

base-width caused by (1) Electron hole recombination at the base (2) The reverse biasing of the base-collector junction (3) The forward biasing of emitter base junction (4) The early removed of stored base charged during saturation to cut off switching

31. Consider three immobile charges a proton at (a, 0, 0), an electron at 3

, ,02 2

a a

and other

electron at 3

, ,02 2

a a

we place a mobile electron at the origin. Find the acceleration of this

mobile electron

(1) 2

204 e

e

a m (2)

2

20

3

2 e

e

a m

(3) 2

202 e

e

m a (4) None of these

32. A magnetic field

00

ˆt

B B zt

Find the vector potential

(1) 00

1

2

tA rB

t (2) 0

0

1

2

tA B

t

(3) 20

0

1

2

tA B r

t (4) 0

1

2A B rt


33. In the above problem assuming that electrostatic potential is zero. Find induced electric field

(1) 0

0

1 ˆ2

BE r

t (2)

20

0

1 ˆ2

B rE

t

(3) 0

1 ˆ2

E B r (4) 20 0

1 ˆ2

E B r t

34. Find the magnetic moment of triangular loop

(1) 2ˆˆ ˆ6 2i j k Am

(2) 2ˆˆ ˆ8 i j k Am

(3) 2ˆˆ ˆ10 2i j k Am

(4) 2ˆˆ ˆ12 2 3i j k Am

35. The motion of a particle of mass m is given by Lagrange’s equations with Lagrangian

Where a is a constant,

is the kinetic energy and V = V(x,y,z). Then which

one is correct

(1) This motion represents a motion under conservative and non-conservative force.

(2) This motion represents a motion under only conservative force.

(3) This motion represents a motion under only non-conservative force.

(4) T+V = H (Hamiltonian) and H is conserved.

36. Two gravitationally bound stars with equal masses m, separated by a distance d, revolve about

their center of mass in circular orbits. The period is proportional to

(1) d3/2 (2) d (3) d1/2 (4) 1/d2

37. A particle moves in a circular orbit in a force field given by

If k suddenly decreased to half its original value, the particle’s orbit become

(1) Parabola (2) Ellipse (3) remains circular (4) None

38. The correct relation is (E = internal energy)

(1) ,N S

EP

V

(2)

,EN

SP T

V

(3)

T,N

EP

V

(4)

,EN

SP T

V

39. Consider a system of N non-interacting spin ½ particles each fixed in position and carrying a

magnetic moment . The system is immersed in uniform magnetic field B. The number of spin up

particle for which the entropy of the system will be minimum is:

(1) N (2) N/2 (3) 0 (4) N or 0


40. The circular loop conductor in the z =0 plane, has a radius of 0.10 m and a resistance of 5.0 .

Given 3 ˆ0.20sin10B t z , determine the current

(1) 30.4 cos10 t

(2) 30.4 sin10 t

(3) 30.8 cos10 t

(4) 30.8 sin10 t

41. The kinetic energy of a relativistic particle is twice of its rest mass energy, the speed of the particle

is

(1) 2 2

3c (2)

2

3c (3)

2

c (4)

4

3c

42. A particle is moving under the influence of the potential

nV r kr

The bound motion is possible for (1) 0, 0k n (2) 0, 0k n

(3) 0, 0k n (4) 0, 0 0, 0k n or k n

43. A uniform plane rectangular sheet has mass m and dimensions as shown

The moment of inertia about an axis passing through a corner and perpendicular to the plane of

the sheet is

(1) 2 2

4

ma b (2) 2 2

3

ma b

(3) 2 2

12

ma b (4) 2 2

2

ma b

44. A particle can occupy any one of the two available energy levels of energies 0 and . The average

energy of the system is

(1) /

/1

kT

kT

e

e

(2)

/

/1

kT

kT

e

e

(3) /1 kTe

(4) /1 kTe

45. An n-type Si bar is 2cm long and has a cross section of 2 2mm mm when 1V battery is connected

across it a current of 8mA flows. The doping level is: (mobility of electrons 21300 /e cm Vs )

(1) 18 31.92 10 / cm (2) 17 31.92 10 / cm

(3) 16 31.92 10 / cm (4) 15 31.92 10 / cm


PART- ‘C’

46. Find 2Re (z )dz

C

I

Where C is the curve from 0 to 2i along the parabola 2y x

(1) 56 40

13

i (2)

56 40

13 3

i (3)

56 40

13 3

i (4)

56 40

13

i

47. The series expansion of

2

1

1 2f z

z z

about the point 1z & valid for the region | 1| 3z

is

(1)

1 2

0

2 3 3 11

1 1

n n nn

n nn

n

z z

(2)

2

0

3 11

1

nn

nn

n

z

(3)

1 2

0

3 121

1 1

nnn

n nn

n

z z

(4)

1

10

3 11

1

nn

nn

n

z

48. Let

3 3

1 2 0

1 1 2

1 2 1

A

then 1A is

(1)

1 2 / 3 4 / 3

1 1/ 3 2 / 3

1 0 1

(2)

1/ 3 2 / 3 4 / 3

1/ 3 1/ 3 2 / 3

1/ 3 0 1/ 3

(3)

1 2 4

1 1 2

1 0 1

(4) None

49. Select the incorrect statement. If is an eigen value of A then

(1) 100 is an eigen value of 100A

(2) | | /A is an eigen value of adjA

(3) 5

2 is an eigen value of 5

2A I

(4) 1/ is an eigen value of A adjA

50. The general solution of 23 '' 108IVy y x Is

(1) 4 2cos 3 sin 3 3 12A Bx C x D x x x

(2) 3 3 4 23 12x xA Bx Ce De x x

(3) 2 3 3 43 12x xA Bx Ce De x x

(4) None

51. Using a trial function of the form

2

2traid

x

Ae

the ground state energy of the system

24

02

pH V x

m

(1)

1/34

02

63

8

V

m

(2)

1/34

02

52

3

V

m

(3)

2/34

02

52

3 2

V

m

(4) None of these


52. Considering the scattering from a hard sphere of radius a such that only S and p-wave are involved

the potential being

0

for r aV r

for r a

The total scattering cross section is

(1) 24 a (2)

224 1

3

Kaa

(3)

224 1

9

Kaa

(4)

224 1

6

Kaa

53. In the operational amplifier circuit the input is applied at t =0 the O/P V0(t) is

54. In the circuit shown below, assume that the voltage drop across a forward biased diode in 0.7V.

The thermal voltage 25t

KTV mV

q

The small signal input cosi pV V t where 100pV mV . The biased current DCI through the diode

is

(1) 1 mA

(2) 1.28 mA

(3) 1.5 mA

(4) 2 mA


55. 0

0

c tF rE E

r

represents a spherical electromagnetic wave emanting from the origin find the

wave energy density and total wave energy as the wave spreads out

(1) 2

2 220 00 0 0 02

c t 4 c tE

F r and E F rr

(2) 2

0 00 0 0 02

c t 4 c tE

F r and E F rr

(3) 220 0

0 0 0 02c t 4 c t

EF r and E F r

r

(4) 2

20 00 0 0 02

c t 4 c tE

F r and E F rr

56. One particle of charge 1q is held at rest at the origin another particle of charge 2q , approaches

along the x-axis in hyperbolic motion

22x t b ct

It reaches the closest point b, at time t=0 and they returns out to infinity. What total impulse

2 2I F dt

is delivered by 2q to 1q

(1) 1 2

04

q q

bc

(2) 1 2

04

q qbc

(3) 1

0 2

1

4

q

q bc

(4) 1 2

0

1

2

q q

bc

57. A straight wire carries a constant electric current I in the positive z-direction which E.M gauge is

applicable here (1) Lorentz Gauze (2) Coulomb Gauze (3) Both Lorentz Gauze and Coulomb Gauze (4) Neither coulomb gauze nor Lorentz gauze

58. Suppose the (electrically neutral) yz plane carries a time dependent but uniform surface current

ˆK t z . Find the electric field at height x above the plane .If a constant current is turned on at t=0

0

0 0

0

tK t

K t

(1) 0 0 cˆ,

2t x

0

K CE x t z for

for ct x

(2)

20 0 ct x ˆ

0

,2

K C

E x t z for

for ct x

(3) 0 0 ct x ˆ

2

0

,K

E for

for ct x

x t z

(4) 0 0 cˆ,

2t x

0

KE x t z

Cfor

for ct x

59. The motion of a particle repelled by a force center according to the law F(r) = kr. The orbit can

(1) Only be hyperbolic

(2) Only be parabolic

(3) Hyperbolic or parabolic depending on energy of the particle.

(4) Unbound but neither parabolic nor hyperbolic.

60. A satellite is moving in circular orbit of radius R about Earth. By what fraction must its velocity v

be increased for the satellite to be in an elliptical orbit with rmin = R and rmax = 2R.

(1) (4/3)1/2 (2) (4/3)2 (3) (4/3)1/3 (4) 4/3


61. A simple pendulum of length b and bob with mass m is attached to a massless support moving (i)

horizontally (ii) vertically upward, with constant acceleration a. The equation of motion in case (i)

& (ii) :-

(1)

, respectively

(2)

, respectively

(3)

, respectively

(4)

62. Energy expression for a crystal under tight binding is given by

0 2 cos cosx yE K E K a K a eV

Find the effective mass at the top of the band

(1) 2

22 a (2)

2

22 a (3)

2

2

2

a (4)

2

2

2

a

63. Consider the Brownian motion of a gas molecules in one dimension. A particular molecule collides

with other molecules in average interval ‘ ’ and after each collision; it may cover distance ‘l ’ in positive or negative direction (with equal probability) before colliding again. The root-mean-square displacement of the molecules is related to time ‘t’ as

(1)

1

3s t (2)

1

2s t (3) s t (4) 2s t

64. In an ideal Fermi gas, there are n particle per unit volume. The pressure ‘P’ of the gas at 0K

temperature is:

(1) 0P (2) 2/5P n (3) 5/3P n (4) 3/5P n

65. Two systems A and B, of identical composition are brought together and allowed to exchange both energy and particles keeping volumes AV and BV constant. The minimum value of the quantity

A

A

dE

dNis given by (symbols have their usual meaning)

(1) A B B A

B A

T T

T T

(2) A B B A

B A

T T

T T

(3) A A B B

A B

T T

T T

(4) A A B B

A B

T T

T T

66. The sodium yellow line 5893o

A arises from the transition 3 3p s . The 3p level is splited by spin-

orbit interaction into two components separated by 32.1 10 eV . The separation between the two components of yellow line is

(1) 5.88o

A (2) 5.68o

A (3) 6.08o

A (4) 6.18o

A

67. The spread of sodium line of wave length 5890o

A is 0.0194o

A . The coherence length is (1) 0.0179m (2) 0.179m (3) 1.79m (4) 2m

68. A given superconductor has critical fields 51.4 10 and 54.2 10 /A m at 14 K and 13 K Calculate its transition temperature (1) 14.47CT K (2) 32.46CT K

(3) 25.76CT K (4) 45.92CT K


69. The nearest neighbour distance in a silver crystal is 2.87o

A silver crystallizes in FCC form. Determine its density

(1) 4 31.068 10 /Kg m (2) 8 32.46 10 /Kg m

(3) 12 32.8 10 /Kg m (4) 24 36.5 10 /Kg m

70. In the laboratory frame two particles each of rest mass m are moving in opposite direction with

equal momenta (of magnitude p). The invariant mass of the system is

(1) 2m (2) 2

2

22

pm

c (3) 2m (4)

22

2

pm

c

71. Consider the decay process

en p e

If the energy of the emitted electron is E, then [the decaying neutron is at rest and2 2 2939.57 / c , 938.28 / c 0.51 / cn p em MeV m MeV m MeV ]

(1) 0.78E MeV (2) 0.51E MeV

(3) 1.29E MeV (4) 0.78E MeV

72. Consider the following reactions involving elementary particles

(A) p n (B) 0 (C)

These process can be classified as: (1) (A):strong (B): weak (C): weak (2) (A): Electromagnetic (B): weak (C): weak (3) (A): Electromagnetic (B): strong (C): weak (4) (A): strong (B): weak (C): Electromagnetic

73. In the ground state of hydrogen atom, the probability for the electron to lie within a sphere of

radius R is : (where 0a is Bohr radius)

(1) 2

20 00

2 2 21 1 exp

R R R

a aa

(2) 2

20 00

2 2 21 1 exp

R R R

a aa

(3) 2

20 00

2 2 21 exp

R R R

a aa

(4) 2

20 00

2 2 21 exp

R R R

a aa

74. The charge distribution in a nucleus is

2

3/2 3

2exp /

rr b

b

Then the form factor F(q):

(1) 2 2

exp2

b qF q

(2) 2 2expF q b q

(3) 2 2

exp8

b qF q

(4) 2 2

exp4

b qF q

75. The ground state wave function of hydrogen atom is

0/

1/230

r ae

a

The expectation value of kinetic energy

(1) 2

02

e

a (2)

2

0

e

a (3)

2

03

e

a (4)

2

04

e

a


Test Series # 7 Full Length #2 (Physics)

Answer Key

1.(4) 2.(1) 3.(3) 4.(2) 5.(3) 6.(2) 7.(2) 8.(4) 9.(3) 10.(3)

11.(3) 12.(3) 13.(3) 14.(2) 15.(1) 16.(4) 17.(1) 18.(4) 19.(1) 20.(2)

21.(4) 22.(4) 23.(1) 24.(1) 25.(1) 26.(1) 27.(2) 28.(2) 29.(2) 30.(2)

31.(3) 32.(1) 33.(1) 34.(2) 35.(1) 36.(1) 37.(1) 38.(4) 39.(4) 40.(1)

41.(1) 42.(4) 43.(2) 44.(4) 45.(2) 46.(2) 47.(1) 48.(1) 49.(4) 50.(1)

51.(1) 52.(2) 53.(3) 54.(1) 55.(1) 56.(1) 57.(2) 58.(1) 59.(1) 60.(1)

61.(1) 62.(1) 63.(2) 64.(3) 65.(1) 66.(1) 67.(2) 68.(1) 69.(1) 70.(2)

71.(3) 72.(4) 73.(2) 74.(4) 75.(1)

Documents

B PHYSICAL SCIENCE TEST SEREIS # 7 FULL … 2015...1. This test paper has a total of 75 questions carrying 150 marks. All Questions are compulsory. 2. Each question of part A are 2mark