JEE Main - 2018Paper - IPhysicsCODE - C

PHYSICS Analysis

Sl.No. UNIT NAME Q. Nos. Correct Wrong

1. PHYSICS AND MEASUREMENT 64

2. KINEMATICS 81

3. LAWS OF MOTION 67

4. WORK, ENERGY & POWER 68, 78, 83

5. ROTATIONAL MOTION & M.I. 77, 90

6. GRAVITATION

7. PROPERTIES OF SOLIDS AND LIQUIDS 87

8. THERMODYNAMICS 86, 88, 89

9. KINETIC THEORY OF GASES

10. OSCILLATIONS AND WAVES

11. ELECTROSTATICS 66

12. CURRENT ELECTRICITY 76, 82

13. MAGNETIC EFFECTS OF CURRENT AND MAGNETISM 65

14. ELECTROMAGNETIC INDUCTION & ALT. CURRENTS 80, 85

15. ELECTROMAGNETIC WAVES 79

16. OPTICS 61, 75

17. DUAL NATURE OF MATTER AND RADIATION 62, 84

18. ATOMS AND NUCLEI

19. ELECTRONIC DEVICES 63

20. COMMUNICATION SYSTEMS 74

21. EXPERIMENTAL SKILLS

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[CODE - C]

61. The angular width of the central maximum in a single slit diffraction pattern is 60o . The width of theslit is 1 m .The slit is illuminated by monochromatic plane waves.If another slit of same width ismade near it, Young’s fringes can be observed on a screen placed at a distance 50 cm from the slits.If the observed fringe width is 1 cm, what is slit separation distance?

(i.e. distance between the centres of each slit.)

a) 50 m b) 75 m c) 100 m d) 25 m

Sol : D

sin n =

6 110

2 −=

d

∆=

610 1 1

2 2 d

−

= × ×

6210

104d

−−=

410

4d

−

=

425 10−= ×

625 10 m−= ×

25 m=

62. An electron from various excited states of hydrogen atom emit radiation to come to the ground

state. Let 'n g be the de Broglie wavelength of the electron in the thn state and the ground state

respectively. Let nΛ be the wavelength of the emitted photon in the transition from the thn state to

the ground state. For large n, (A, B are constants)

a) n nA BΛ ≈ + b) 2 2n nA BΛ ≈ + c) 2

n Λ ≈ d) 2nn

BA

Λ ≈ +

Sol : D

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2 2

1 1 1

f i

kn n

= −

2 2

1

f i

k k

n n= −

( )2

1... 1

n

kA

n= −

n

mV =

( )... 2n⇒ ∴

2

1

n

BA

= −

1

2n

BA

−

= −

Using binomial approx

2n

BA

≈ +

63. The reading of the ammeter for a silicon diode in the given circuit is:

a) 15 mA b) 11.5 mA c) 13.5 mA d) 0

Sol : B

3 0.7 2.311.5

200 200i mA

−= = =

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64. The density of a material in the shape of cube is determined by measuring three sides of the cube andits mass. If the relative erros in measuring the mass and length are respectively 1.5% and 1%, themaximum error in determining the density is:

a) 3.5% b) 4.5% c) 6% d) 2.5%

Sol : B

1.5, 1m l

m l

∆ ∆= =

3m P m l

PV P m l

∆ ∆ ∆ = ⇒ = +

( )1.5 3 1 4.5%= + =

65. An electron, a proton and an alpha particle having the same kinetic energy are moving in circular

orbits of radii , ,e pr r r respectively in a uniform magnetic field B. The relation between , ,e pr r r is:

a) e pr r r< = b) e pr r r< < c) e pr r r< < d) e pr r r> =

Sol : A

2mKr

Bq=

ee

mr

q=

p

p

mr

q=

mr

e

4

2

mpr

e =

mpr

e⇒ =

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66. Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface

charge densities , and + + − respespectively. The potential of shell B is:

a)2 2

0

a bc

b

− + ∈ b)

2 2

0

b ca

b

− + ∈ c)

2 2

0

b ca

c

− + ∈ d)

2 2

0

a bc

a

− + ∈ Sol : A

b

2 2 2

Bo

a b cV

b b c

= − + ∈

2 2

Bo

a bV c

b

−= + ∈

67. Two masses 1 25 kg and 10m m k= = connected by an inextensible string over frictionless pulley,,

are moving as show in the figure. The coefficient of friction horizontal surface is 0.15. The minimum

weight 2m that should be put on top of m to stop the motion is:

a) 27.3 kg b) 43.3 kg c) 10.3 kg d) 18.3 kg

Sol : A

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1 1m g T m a− =

5 5g T a⇒ − =

( )( ) ( )0.15 10 10T m g m a− + = +

50T n=

23.3m kg=

68. A particle is moving in a circular path of radius a under the action of an attractive potential 2.

2

kU

r= −

Its total energy is:

a) 22

k

ab) Zero c) 2

3

2

k

a− d) 24

k

a−

Sol : B

22

KKE

r=

TE PE KE= +

2 22 2

K K

r r

−= +

= 0

69. A parallel plate capacitor of capacitance 90 pF is connected to a battery of emf 20 V. If a dielectric

material of dielectric constatn5

3K = is inserted between the plates, the magnitude of the induced

charge will be:

a) 0.3 n C b) 2.4 n C c) 0.9 n C d) 1.2 n C

Sol : D

0

5

3q kq cv= =

590

3=

30 1210 20−× ×

1030 10−= ×

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1 11Inq q

k = −

10 330 10 1

5− = × −

30= 10 210

5− ×

1012 10−= ×

91.2 10 c−= ×

1.2nc=

70. A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of1210 / sec. What is the force constatn of the bonds connecting one atom with the other? (Mole wt.

of silver = 108 and Average number 23 16.02 10 gm mole−= × )

a) 7.1 N/m b) 2.2 N/m c) 5.5 N/m d) 6.4 N/m

Sol : A

K

m =

2 K

m =

2 24K

nm

=

2 24 3

23

4 10 108 10

6.02 10K

−× × ×=×

=7.1N/m

71. It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss

of its energy is ;dp while for its similar collision with carbon nucleus at rest, fractional loss of energy

is cp . The value of andd cp p are respectively:

a) (.28, .89) b) (0, 0) c) (0, 1) d) (.89, .28)

Sol : D

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( )1 2

2

1 2

4d

m mKE

m m∆ =

+

( )2

4 1 2

3

× ×=

8.89

9= =

( )1 2

2

1 2

4c

m mKE

m m∆ =

+

( )2

4 1 12

13

× ×=

48.28

169= =

72. The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of

the loop is 1.B When the dipole moment is doubled by keeping the current constant, the magnetic

field at the centre of the loop is 2.B The ratio1

2

B

B is:

a) 3 b) 2 c)1

2d) 2

Sol : B

( )2m iA i R= =

( )( 2

2 2m i R =

1 2oiBR

=

22 2

oiBR

=

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1

2

2B

B=

73. In a potentiometer experiment, it is found that no current passes through the galvanometer when theterminals of the cell are connected across 52 cm of the potentiometer wire. If the cell is shunted bya resistance of 5Ω , a balance is found when the cell is connected across 40 cm of the wire. Find theinternal resistance of the cell.

a) 1.5Ω b) 2Ω c) 2.5Ω d) 1Ω

Sol : A

52

40

R r

V R

+= =

52 51.5

40 5

rr

+= ⇒ = Ω

74. A telephonic communication service is working at carrier frequency of 10 GHz. Only 10% of its isutilized for transmission. How many telephonic channels can be transmitted simultaneously if eachchannel requires a bandwidth of 5 kHz?

a) 42 10× b) 52 10× c) 62 10× d) 32 10×

Sol : B

Bandwidth = 5kHz

310% 5 10c n = × ×

110

10× 9 310 5 10n× = × ×

6 5110 2 10

5n = × ⇒ ×

75. Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer B is

placed behind A. The intensity of light beyond B is found to be .2

I Now another identical polarizer

C is placed between A and B. The intensity beyond B is now found to be .8

I The angle between

polarizer A and C is:

a) 30o b) 45o c) 60o d) 0o

Sol : B

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2 2cos sin2 84o oI I =

2sin 2 1 =

sin 2 1 =

22

=

4

=

76. On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The

resistance of their series combination is 1kΩ . How much was the resistance on the left slot beforeinterchaning the resistances?

a) 505Ω b) 550 Ω c) 910 Ω d) 990 Ω

Sol : B

1

2 100

R x

R x=

−

2

1

10

110

R x

R x

−=−

1 2

1 2

100

100

R R

R R x x

+ =− − +

2 1

2 1

100

2 100

R R

R R x

+ =− −

1 2 1000R R+ = Ω

Solving above equation

1 550R = Ω

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77. From a uniform circular disck of radius R and mass 9 M, a small disc of radius3

R is removed as

shown in the figure. The moment of intia of the remaining disc about an axis perpendicular to theplane of the disc and passing through centre of disck is:

a)240

9MR b) 210MR c)

237

9MR d) 24MR

Sol : D

( )2 2 29 4

2 2 9 9

mR MR RI m

= − +

2 29 9

2 18

mR mR= −2

284

22

mRmR= =

78. In a collinear collision, a particle with an initial speed o strikes a stationary particle of the same

mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude ofthe relative velocity between the two particles, after collision, is:

a) 2 o b)2o c)

2o

d)4o

Sol : A

2 2 20 1 2

1 1 11.5 0

2 2 2mv mv mv

+ = +

( )0 1 2mv m v v= +

2 2 21 2 01.5v v v+ =

1 2 02v v v− =

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( ) ( ) ( )2 2 2 21 2 1 2 1 22v v v v v v+ + − = +

( )2 21 2 02v v v⇒ − =

1 2 02v v v− =

79. An EM wave from air enters a medium. The electric fields are 1 01 ˆ cos 2z

E E x v tc

= −

in air

and ( )2 02 ˆ cos 2E E x k z ct= −

in medium, where the wave their number k and frequency v refer to

their values in air. The medium is non-magnetic. If1 2

andr r∈ ∈ refer to relative permittivities of air

and medium respectively, which of the following options is correct?

a)1

2

2r

r

∈=

∈ b)1

2

1

4r

r

∈=

∈ c)1

2

1

2r

r

∈=

∈ d)1

2

4r

r

∈=

∈

Sol : B

0r

∈∈ =∈

2

2 2 2 22n

c

= =

2 0

1C

=

∈

1 2 2

c

n

= = = =

1v

=

∈

0 0

12

air

med

= = =∈

Solving above equation1

2

1

4r

r

∈=

∈

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80. For an RLC circuit driven with voltage of amplitude m and frequency o

1

LC = the current

exbits resonance. The quality factor, Q is given by:

a) o R

L

=b) ( )o

R

C c)o

CR

d) oL

R

Sol : D

Q = oL

R

81. All the graphs below are intended to represent the same motion. One of them does it incorrectly.Pick it up.

a) b)

c) d)

Sol : A

82. Two batteries with e.m.f. 12 V and 13 V are connected in parallel across a load resistor of 10Ω .

The internal resistances of the two batteries are 1 and 2Ω Ω respectively . The voltage across theload lies between:

a) 11.5 V and 11.6 V b) 11.4 V and 11.5 V

c) 11.7 V and 11.8 V d) 11.6 V and 11.7 V

Sol : A

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12

13 2 Ω

1Ω

10 Ω

( ) ( )12 12 13 1 312.33

3 3emf

+ +∈ = = =

2

3reff =

12.3310 11.559

210

3

RV

× = +

∴ It lies between 11.559V=

83. A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely

proportional to the thn power of R. If the peiod of rotation of the particle is T, then:

a) 12

n

T R+

∝ b) ( )1 / 2nT R +∝

c) / 2nT R∝ d) 3/ 2 for any nT R∝ .

Sol : B

1n

FR

22 nmR RT

−

1

2

nR R+

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84. If the series limit frequency of the Lyman series is ,Lv then the series limit frequency of the Pfund

series is:

a) 16 Lv b) /16Lv c) / 25Lv d) 25 Lv

Sol : C

Ln Lyman

?Ln = Pfund

42 31 5Ly Bal Para Br Pfund

2

1 1

1R n

= =

1 2

1 1

5R f

= =

25

nf =

85. In an a.c. circuit instantaneous e.m.f. and current are given by

100sin30e t=

20sin 304

i t = −

In one cycle of a.c., the average power consumed by the circuit and the walltless current are,respectivly:

a)100

,102

b)50

,02

c) 50, 0 d) 50, 10

Sol : A

( )0 0 cos2

V iP < >=

2000 1

2 2= ×

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1000

2P< >=

0 cos2

watless

ii = ×

10=

86. Two moles of an ideal monoatomic gas occupies a volume V at 27o C . The gas expands adiabaticallyto a volume 2 V. Calculate (a) the final temperature of the gas and (b) change in its internal energy.

a) 1) 195 K 2) 2.7 kJ−

b) 1) 189 K 2) 2.7 kJ−

c) 1) 195 K 2) 2.7 kJ

d) 1) 189 K 2) 2.7 kJ

Sol : B

1constant, constantPV TV −= =

1

12 1

2

189V

T T KV

−

= =

2

fv n R T∆ = ∆

2.7v kJ∆ = −

87. A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in acylindrical container. A masseless piston of area a floats on the surface of the liquid, covering entirecross section of culindrical container. When a mass m is placed on the surface of the piston to

compress the liquid, the fractional decrement in the radius of the sphere, ,dr

r

is:

a) 3

Ka

mg b) 3

mg

Ka c)mg

Kad)

Ka

mg

Sol : B

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mgp

a∆ =

.pVk

V

∆=∆

V p

V k

∆ ∆=

3r mg

r ak

∆× =

3

3

r g

r ak

∆ =

88. A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The

density of granite is 3 32.7 10 /kg m× and its Young’s modules is 109.27 10 .Pa× What will be the

fundamental frequency of the longitudinal vibrations?

a) 2.5 kHz b) 10 kHz c) 7.5 kHz d) 5 kHz

Sol : D

60l cm=

32.7 10p kHz= ×

109.27 10y Pa= ×

?21

vn =

212

l = ⇒ =

2

1

2 60 10

yn

p−=× ×

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10

1 3

1 9.27 10

12 10 2.7 10−

×=× ×

7103.43 10

12

= × ×

41034.3

12=

3 5.8510

12×

4.8 kHz=

89. the mass of a hydrogen molecule is 27 233.32 10 . If 10kg−× hydrogen molecules strike, per sec ond, a

fixed wall of area 22 cm at an angle of 45o to the normal, and rebound elastically with a speed of

310 / ,m s then the pressure on the wall is nearly:

a) 3 24.70 10 /N m× b) 2 22.35 10 /N m×

c) 2 24.70 10 /N m× d) 3 22.35 10 /N m×

Sol : D

273.32 10Hm kg−= ×

2310n

t= 22A cm=

34 10= 45o =

2 sinF mVn

A A

=

27 3 23

4

2 3.32 10 10 10

2 10 2

−

−

× × ×= ××

1 42.34 10− += ×

3 22.35 10 /N m= ×

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90. Seven identical circular planar disks, each of mass M and radius R are welded symmetrically asshown. The moment of inertia of the arrangement about the axis normal to the plane and passingthrough the point P is:

a)255

2MR b)

273

2MR c)

2181

2MR d)

219

2MR

Sol : C

Disck M, R

( )2 2

26

2 2

mR mRm R

+ +

( )27 . 3M R+

9 7×

32 1 6

24 632 2

mR

= + + +

2 190

2mR

= +

2181

2mR=