FINAL JEE–M AIN EXA MINATION –...

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Final JEE -Main Exam April,2019/12-04-2019/Morning Session

1. The value of numerical aperature of theobjective lens of a microscope is 1.25. If lightof wavelength 5000 Å is used, the minimumseparation between two points, to be seen asdistinct, will be :(1) 0.24 mm (2) 0.48 mm(3) 0.12 mm (4) 0.38 mm

Official Ans. by NTA (1)2. A progressive wave travelling along the positive

x-direction is represented by y(x, t) = A sin(kx – wt + f). Its snapshot at t = 0 is given in thefigure:

A

y

x

For this wave, the phase f is :

(1) 0 (2) 2p

- (3) p (4) 2p

Official Ans. by NTA (3)3. A circular disc of radius b has a hole of radius a

at its centre (see figure). If the mass per unit area

of the disc varies as 0

rsæ ö

ç ÷è ø

, then the radius of

gyration of the disc about its axis passing throughthe centre is :

a

b

(1) a b

2+

(2) a b

3+

(3) 2 2a b ab

2+ +

(4) 2 2a b ab

3+ +

Official Ans. by NTA (4)

FINAL JEE–MAIN EXAMINATION – APRIL,2019(Held On Friday 12th APRIL, 2019) TIME : 9 : 30 AM To 12 : 30 PM

PHYSICS TEST PAPER WITH ANSWER

4. Shown in the figure is a shell made of aconductor. It has inner radius a and outer radiusb, and carries charge Q. At its centre is a dipole

pr

as shown. In this case :

p

(1) Electric field outside the shell is the sameas that of a point charge at the centre of theshell.

(2) Surface charge density on the inner surfaceof the shell is zero everywhere.

(3) Surface charge density on the inner surface

is uniform and equal to 2

(Q/ 2)4 ap

.

(4) Surface charge density on the outer surface

depends on pr


5. A person of mass M is, sitting on a swing oflength L and swinging with an angularamplitude q0. If the person stands up when theswing passes through its lowest point, the workdone by him, assuming that his centre of massmoves by a distance l (l < < L), is close to :

(1) Mgl

(2) Mgl (1 + q02)

(3) Mgl (1 – q02)

(4) Mgl 201

2

æ öq+ç ÷

è ø


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6. A concave mirror has radius of curvature of40 cm. It is at the bottom of a glass that haswater filled up to 5 cm (see figure). If a smallparticle is floating on the surface of water, itsimage as seen, from directly above the glass,is at a distance d from the surface of water. Thevalue of d is close to : (Refractive index of water= 1.33)

5cm

particle

(1) 8.8 cm (2) 11.7 cm(3) 6.7 cm (4) 13.4 cm

Official Ans. by NTA (1)7. Two identical parallel plate capacitors, of

capacitance C each, have plates of area A,separated by a distance d. The space between theplates of the two capacitors, is filled with threedielectrics, of equal thickness and dielectricconstants K1, K2 and K3. The first capacitor isfilled as shown in fig. I, and the second one is filledas shown in fig. II.If these two modified capacitors are charged bythe same potential V, the ratio of the energy storedin the two, would be (E1 refers to capacitor (I) andE2 to capacitor (II)) :

K1

K1K2K2

K3

K3

(I) (II)

(1) 1 2 31

2 1 2 3 2 3 3 1 1 2

9K K KEE (K K K ) (K K K K K K )

=+ + + +

(2) 1 2 31

2 1 2 3 2 3 3 1 1 2

K K KEE (K K K ) (K K K K K K )

=+ + + +

(3) 1 2 3 2 3 3 1 1 21

2 1 2 3

(K K K ) (K K K K K K )EE K K K

+ + + +=

(4) 1 2 3 2 3 3 1 1 21

2 1 2 3

(K K K ) (K K K K K K )EE 9K K K

+ + + +=


8. A point dipole 0 ˆp p x= -r

is kept at the origin.

The potential and electric field due to this dipoleon the y-axis at a distance d are, respectively:(Take V = 0 at infinity) :

(1) 2 30 0

| p | p,

4 d 4 d-

pe pe

r r

(2) 30

p0,

4 dpe

r

(3) 2 30 0

| p | p,

4 d 4 dpe pe

r r

(4) 30

p0,

4 d-

pe

r

Official Ans. by NTA (4)9. When M1 gram of ice at –10ºC (specific heat

= 0.5 cal g–1ºC–1) is added to M2 gram of waterat 50ºC, finally no ice is left and the water is at0ºC. The value of latent heat of ice, in cal g–1 is:

(1) 1

2

5M50

M- (2)

2

1

50MM

(3) 2

1

50M5

M- (4)

2

1

5M5

M-

Official Ans. by NTA (3)10. The trajectory of a projectile near the surface of

the earth is given as y = 2x – 9x2. If it werelaunched at an angle q0 with speed n0 then(g = 10 ms–2) :

(1) 1

0

1cos

5- æ öq = ç ÷

è ø and 1

0

5ms

3-n =

(2) 1

0

1sin

5- æ öq = ç ÷

è ø and 1

0

5ms

3-n =

(3) 1

0

2sin

5- æ öq = ç ÷

è ø and 1

0

3ms

5-n =

(4) 1

0

2cos

5- æ öq = ç ÷

è ø and 1

0

3ms

5-n =


3


11. The truth table for the circuit given in the fig.is:

AB

Y

(1)

A B Y

0 0 1

0 1 1

1 0 0

1 1 0

(2)

A B Y

0 0 0

0 1 0

1 0 1

1 1 1

(3)

A B Y

0 0 1

0 1 0

1 0 0

1 1 0

(4)

A B Y

0 0 1

0 1 1

1 0 1

1 1 1


12. A shell is fired from a fixed artillery gun withan initial speed u such that it hits the target onthe ground at a distance R from it. If t1 and t2are the values of the time taken by it to hit thetarget in two possible ways, the product t1t2 is:

(1) R/g (2) R/4g

(3) 2R/g (4) R/2g


13. A submarine (A) travelling at 18 km/hr is beingchased along the line of its velocity by anothersubmarine (B) travelling at 27 km/hr. B sendsa sonar signal of 500 Hz to detect A andreceives a reflected sound of frequency n. Thevalue of n is close to :

(Speed of sound in water = 1500 ms–1)

(1) 499 Hz (2) 502 Hz

(3) 507 Hz (4) 504 Hz


14. Two moles of helium gas is mixed with threemoles of hydrogen molecules (taken to berigid). What is the molar specific heat ofmixture at constant volume ? (R = 8.3 J/mol K)

(1) 21.6 J/mol K

(2) 19.7 J/mol K

(3) 17.4 J/mol K

(4) 15.7 J/mol K


15. The stopping potential V0 (in volt) as a functionof frequency (n) for a sodium emitter, is shownin the figure. The work function of sodium,from the data plotted in the figure, will be :

(Given : Planck's constant

(h) = 6.63 × 10–34 Js, electron

charge e = 1.6 × 10–19 C)

2

1.0

2.0

3.0

4 6 8 10

V0

n(10 Hz)14

(1) 1.95 eV (2) 1.82 eV

(3) 1.66 eV (4) 2.12 eV


16. At 40ºC, a brass wire of 1 mm radius is hungfrom the ceiling. A small mass, M is hung fromthe free end of the wire. When the wire is cooleddown from 40ºC to 20ºC it regains its originallength of 0.2 m. The value of M is close to :

(Coefficient of linear expansion and Young'smodulus of brass are 10–5/ºC and 1011 N/m2,respectively; g = 10 ms–2)

(1) 1.5 kg (2) 9 kg

(3) 0.9 kg (4) 0.5 kg


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17. A uniform rod of length l is being rotated ina horizontal plane with a constant angular speedabout an axis passing through one of its ends. Ifthe tension generated in the rod due to rotationis T(x) at a distance x from the axis, then whichof the following graphs depicts it most closely?

(1)

lx

T(x)

(2)

lx

T(x)

(3)

lx

T(x)

(4)

lx

T(x)

Official Ans. by NTA (4)18. Which of the following combinations has the

dimension of electrical resistance (e0 is thepermittivity of vacuum and m0 is the permeabilityof vacuum) ?

(1) 0

0

em (2)

0

0

me

(3) 0

0

me (4)

0

0

em


19. In a double slit experiment, when a thin filmof thickness t having refractive index m isintroduced in front of one of the slits, themaximum at the centre of the fringe patternshifts by one fringe width. The value of t is (lis the wavelength of the light used) :

(1) 2( 1)l

m - (2) (2 1)l

m -

(3) 2

( 1)l

m - (4) ( 1)l

m -

Official Ans. by NTA (4)20. An electromagnetic wave is represented by the

electric field

0 ˆE E nsin[ t (6y 8z)]= w + -r

. Taking unit vectors in

x, y and z directions to be ˆ ˆ ˆi, j,k , the direction of

propogation s , is :

(1) ˆ ˆ4 j 3k

s5-

= (2) ˆ ˆ3i 4 j

s5-

=

(3) ˆ ˆ3j 4k

s5

æ ö- += ç ÷ç ÷

è ø(4)

ˆ ˆ4k 3js

5- +

=

Official Ans. by NTA (3)21. The figure shows a square loop L of side 5 cm

which is connected to a network of resistances.The whole setup is moving towards right with aconstant speed of 1 cms–1. At some instant, a partof L is in a uniform magnetic field of 1T,perpendicular to the plane of the loop. If theresistance of L is 1.7 W, the current in the loop atthat instant will be close to :

5cm

L

n=1cm/sec

1W

1W

2W

2W

3W

D

BB

A C

(1) 115 mA (2) 170 mA(3) 60 mA (4) 150 mA


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22. The transfer characteristic curve of a transistor,having input and output resistance 100 W and100 kW respectively, is shown in the figure. TheVoltage and Power gain, are respectively :

I ( A)b m

I(mA)

C

(100, 5)

(200, 10)

(300, 15)

(400, 20)

(1) 5 × 104, 5 × 105

(2) 5 × 104, 5 × 106

(3) 5 × 104, 2.5 × 106

(4) 2.5 × 104, 2.5 × 106

Official Ans. by NTA (3)23. A galvanometer of resistance 100W has

50 divisions on its scale and has sensitivity of20 mA/division. It is to be converted to avoltmeter with three ranges, of 0–2 V, 0–10 Vand 0–20 V. The appropriate circuit to do sois :

(1)

GR1 R2 R3

2V 10V 20V

R = 1900 1 WR = 9900 2 WR = 19900 3 W

(2)

GR1 R2 R3

2V 10V 20V

R = 2000 1 WR = 8000 2 WR = 10000 3 W

(3)

GR1 R2 R3

20V 10V 2V

R = 19900 1 WR = 9900 2 WR = 1900 3 W

(4)

GR1 R2 R3

2V 10V 20V

R = 1900 1 WR = 8000 2 WR = 10000 3 W


24. To verify Ohm's law, a student connects thevoltmeter across the battery as, shown in thefigure. The measured voltage is plotted as afunction of the current, and the following graphis obtained:

internalResistance Ammeter

R

V

1.5V

V0I 1000 mA

V

If V0 is almost zero, identify the correctstatement:

(1) The value of the resistance R is 1.5 W

(2) The emf of the battery is 1.5 V and the valueof R is 1.5 W

(3) The emf of the battery is 1.5 V and itsinternal resistance is 1.5 W

(4) The potential difference across the batteryis 1.5 V when it sends a current of 1000mA.


25. An excited He+ ion emits two photons insuccession, with wavelengths 108.5 nm and30.4 nm, in making a transition to ground state.The quantum number n, corresponding to itsinitial excited state is (for photon of wavelength

l, energy 1240eV

E(in nm)

=l

) :

(1) n = 5 (2) n = 4

(3) n = 6 (4) n = 7


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26. A sample of an ideal gas is taken through thecyclic process abca as shown in the figure. Thechange in the internal energy of the gas alongthe path ca is –180J. The gas absorbs 250 J ofheat along the path ab and 60 J along the pathbc. The work done by the gas along the pathabc is :

P

V

a b

c

(1) 100 J (2) 120 J

(3) 140 J (4) 130 J


27. A thin ring of 10 cm radius carries a uniformlydistributed charge. The ring rotates at a constantangular speed of 40 p rad s–1 about its axis,perpendicular to its plane. If the magnetic fieldat its centre is 3.8 × 10–9 T, then the chargecarried by the ring is close to (m0 = 4p × 10–7

N/A2) :

(1) 2 × 10–6 C (2) 3 × 10–5 C

(3) 4 × 10–5 C (4) 7 × 10–6 C


28. A magnetic compass needle oscillates 30 timesper minute at a place where the dip is 45º, and40 times per minute where the dip is 30º. If B1

and B2 are respectively the total magnetic fielddue to the earth at the two places, then the ratioB1/B2 is best given by :(1) 2.2 (2) 1.8 (3) 0.7 (4) 3.6

Official Ans. by NTA (3)29. A man (mass = 50 kg) and his son (mass = 20

kg) are standing on a frictionless surface facingeach other. The man pushes his son so that hestarts moving at a speed of 0.70 ms–1 withrespect to the man. The speed of the man withrespect to the surface is :(1) 0.20 ms–1 (2) 0.14 ms–1

(3) 0.47 ms–1 (4) 0.28 ms–1

Official Ans. by NTA (1)30. The resistive network shown below is connected

to a D.C. source of 16V. The power consumedby the network is 4 Watt. The value of R is :

e = 16V

RR

4 R

4 R 12 R

6 R

(1) 8W (2) 6W (3) 1W (4) 16W


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