final jee–m ain exa mination –...

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Final JEE -Main Exam April,2019/09-04-2019/Morning Session

1. In the density measurement of a cube, the mass andedge length are measured as (10.00 ± 0.10) kg and(0.10 ± 0.01) m, respectively. The error in themeasurement of density is :

(1) 0.10 kg/m3 (2) 0.31 kg/m3

(3) 0.07 kg/m3 (4) 0.01 kg/m3

Official Ans. by NTA (2)

2. An HCl molecule has rotational, translationaland vibrational motions. If the rms velocity ofHCl molecules in its gaseous phase is v , m is

its mass and kB is Boltzmann constant, then itstemperature will be :

(1) 2

B

mv6k (2)

2

B

mv5k

(3) 2

B

mv3k (4)

2

B

mv7k


3. Following figure shows two processes A andB for a gas. If DQA and DQB are the amount ofheat absorbed by the system in two cases, andDUA and DUB are changes in internal energies,respectively, then :

iB

Af

P

V

(1) DQA = DQB ; DUA = DUB

(2) DQA > DQB ; DUA = DUB

(3) DQA > DQB ; DUA > DUB

(4) DQA < DQB ; DUA < DUB


FINAL JEE–MAIN EXAMINATION – APRIL,2019(Held On Tuesday 09th APRIL, 2019) TIME : 9 : 30 AM To 12 : 30 PM

PHYSICS TEST PAPER WITH ANSWER

4. A wire of resistance R is bent to form a squareABCD as shown in the figure. The effectiveresistance between E and C is :(E is mid-point of arm CD)

A B

D CE

(1) R (2) 1

16R

(3) 764

R (4) 34

R

Official Ans. by NTA (3)5. The total number of turns and cross-section area

in a solenoid is fixed. However, its length L is variedby adjusting the separation between windings. Theinductance of solenoid will be proportional to :(1) 1/L2 (2)1/L(3) L (4) L2

Official Ans. by NTA (2)6. A simple pendulum oscillating in air has period

T. The bob of the pendulum is completelyimmersed in a non-viscous liquid. The density

of the liquid is 1

16th of the material of the bob.

If the bob is inside liquid all the time, its periodof oscillation in this liquid is :

(1)14T

15 (2) 12T

10

(3) 14T

14(4)

12T14


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7. Determine the charge on the capacitor in thefollowing circuit :

(1) 2µC (2) 60µC (3) 200µC (4) 10µC

Official Ans. by NTA (3)8. A system of three charges are placed as shown

in the figure :

+q d –q Q

D

If D >> d, the potential energy of the system isbest given by :

(1) 2

20

1 q qQd–4 d 2D

é ù-ê úpe ë û

(2) 2

20

1 q qQd4 d D

é ù+ +ê úpe ë û

(3) 2

20

1 q 2qQd–4 d D

é ù+ê úpe ë û

(4) 2

20

1 q qQd– –4 d D

é ùê úpe ë û

Official Ans. by NTA (4)9. The stream of a river is flowing with a speed

of 2km/h. A swimmer can swim at a speed of4km/h. What should be the direction of theswimmer with respect to the flow of the river tocross the river straight ?(1) 60° (2) 150° (3) 90° (4) 120°

Official Ans. by NTA (4)10. A body of mass 2 kg makes an eleastic collision

with a second body at rest and continues to movein the original direction but with one fourth of itsoriginal speed. What is the mass of the secondbody ?(1) 1.8 kg (2) 1.2 kg(3) 1.5 kg (4) 1.0 kg


11. A solid sphere of mass 'M' and radius 'a' issurrounded by a uniform concentric sphericalshell of thickness 2a and mass 2M. Thegravitational field at distance '3a' from thecentre will be :

(1) 22GM9a

(2) 2GM3a

(3) 2GM9a

(4) 22GM3a


12. The pressure wave, P = 0.01 sin [1000t – 3x] Nm–2,corresponds to the sound produced by a vibrating bladeon a day when atmospheric temperature is 0°C. Onsome other day, when temperature is T, the speed ofsound produced by the same blade and at the samefrequency is found to be 336 ms–1 . Approximate valueof T is :

(1) 15°C (2) 12°C

(3) 4°C (4) 11°C


13. An NPN transistor is used in common emitterconfiguration as an amplifier with 1 kW loadresistance. Signal voltage of 10 mV is appliedacross the base-emitter. This produces a 3 mAchange in the collector current and 15µAchange in the base current of the amplifier. Theinput resistance and voltage gain are :

(1) 0.33 kW, 1.5

(2) 0.67 kW, 200

(3) 0.33 kW, 300

(4) 0.67 kW, 300


14. A moving coil galvanometer has resistance 50Wand it indicates full deflection at 4mA current.A voltmeter is made using this galvanometerand a 5 kW resistance. The maximum voltage,that can be measured using this voltmeter, willbe close to :

(1) 10 V (2) 20 V

(3) 40 V (4) 15 V


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15. The electric field of light wave is given as

–3 14–7

2 x NˆE 10 cos – 2 6 10 t x5 10 C

pæ ö= p´ ´ç ÷´è ø

r.This

light falls on a metal plate of work function2eV. The stopping potential of the photo-electrons is :

Given, E (in eV) = 12375(in Å)l

(1) 0.48 V (2) 2.0 V

(3) 2.48 V (4) 0.72 V


16. A ball is thrown vertically up (taken as +z-axis)from the ground. The correct momentum-height(p-h) diagram is :

(1) O h

p

(2) O h

p

(3) O h

p

(4) O h

p


17. A capacitor with capacitance 5µF is charged to5µC. If the plates are pulled apart to reduce thecapacitance to 2µF, how much work is done ?

(1) 3.75 × 10–6 J

(2) 2.55 × 10–6 J

(3) 2.16 × 10–6 J

(4) 6.25 × 10–6 J


18. A rigid square loop of side 'a' and carryingcurrent I2 is lying on a horizontal surface neara long current I1 carrying wire in the same planeas shown in figure. The net force on the loopdue to wire will be :

BI2I1

a

a

(1) Attractive and equal to 0 1 2µ I I3p

(2) Repulsive and equal to 0 1 2µ I I4p

(3) Repulsive and equal to 0 1 2µ I I2p

(4) Zero


19. The figure shows a Young's double slitexperimental setup. It is observed that when athin transparent sheet of thickness t andrefractive index µ is put in front of one of theslits, the central maximum gest shifted by adistance equal to n fringe widths. If thewavelength of light used is l, t will be :

a Screen

D

(1) 2D

a(µ –1)l

(2) D

a(µ –1)l

(3) 2nD

a(µ –1)l

(4) nD

a(µ –1)l


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20. A string is clamped at both the ends and it isvibrating in its 4th harmonic. The equation of thestationary wave is Y = 0.3 sin(0.157x) cos(200pt).The length of the string is : (All quantities arein SI units.)(1) 20 m (2) 80 m (3) 60 m (4) 40 m

Official Ans. by NTA (2)21. The following bodies are made to roll up

(without slipping) the same inclined plane froma horizontal plane. : (i) a ring of radius R, (ii)

a solid cylinder of radius R2

and (iii) a solid

sphere of radius R4

. If in each case, the speed

of the centre of mass at the bottom of the inclineis same, the ratio of the maximum heights theyclimb is :(1) 4 : 3 : 2 (2) 14 : 15 : 20(3) 10 : 15 : 7 (4) 2 : 3 : 4

Official Ans. by NTA (3)22. A stationary horizontal disc is free to rotate

about its axis. When a torque is applied on it,its kinetic energy as a function of q, where qis the angle by which it has rotated, is given askq2. If its moment of inertia is I then theangular acceleration of the disc is :

(1) k2I

q (2) kI

q (3) k4I

q (4) 2kI

q

Official Ans. by NTA (4)23. A uniform cable of mass 'M' and length 'L' is

placed on a horizontal surface such that its

th1n

æ öç ÷è ø

part is hanging below the edge of the

surface. To lift the hanging part of the cable uptothe surface, the work done should be :

(1) 2MgL

n(2) 2

MgL2n

(3) 22MgL

n(4) nMgL


24. If 'M' is the mass of water that rises in a capillarytube of radius 'r', then mass of water which willrise in a capillary tube of radius '2r' is :

(1) 4M (2) M

(3) 2M (4) M2


25. Taking the wavelength of first Balmer line inhydrogen spectrum (n = 3 to n = 2) as 660 nm,the wavelength of the 2nd Balmer line (n = 4 ton = 2) will be :

(1) 889.2 nm (2) 642.7 nm

(3) 488.9 nm (4) 388.9 nm


26. The magnetic field of a plane electromagneticwave is given by :

[ ]0 1ˆ ˆB B i cos(kz – t) B jcos(kz t)= w + + w

ur where

B0 = 3 × 10–5 T and B1 = 2 × 10–6 T. The rmsvalue of the force experienced by a stationarycharge Q = 10–4 C at z = 0 is closest to :

(1) 0.9 N (2) 0.1 N

(3) 3 × 10–2 N (4) 0.6 N


27. A rectangular coil (Dimension 5 cm × 2.5 cm)with 100 turns, carrying a current of 3 A in theclock-wise direction is kept centered at theorigin and in the X-Z plane. A magnetic fieldof 1 T is applied along X-axis. If the coil is tiltedthrough 45° about Z-axis, then the torque onthe coil is :

(1) 0.55 Nm (2) 0.27Nm

(3) 0.38 Nm (4) 0.42 Nm


28. A concave mirror for face viewing has focallength of 0.4 m. The distance at which you holdthe mirror from your face in order to see yourimage upright with a magnification of 5 is :

(1) 1.60 m (2) 0.24 m

(3) 0.16 m (4) 0.32 m


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29. A signal Acoswt is transmitted using n0 sin w0tas carrier wave. The correct amplitudemodulated (AM) signal is :

(1) 0 0sin t A cos tn w + w

(2) 0 0 0 0A Asin t sin( – )t sin( )t2 2

n w + w w + w + w

(3) 0 0( A)cos t sin tn + w w

(4) 0 0sin[ (1 0.01Asin t)t]n w + w


30. For a given gas at 1 atm pressure, rms speedof the molecule is 200 m/s at 127°C. At 2 atmpressure and at 227°C, the rms speed of themolecules will be :

(1) 80 m/s (2) 100 5 m/s

(3) 80 5 m/s (4) 100 m/s


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