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# JEE Mains 2019 Question Paper with Solutions- 9 Jan P1

This blog contains quality solutions for JEE Mains 2019 9th January shift 1. Download Kunduz app to get solutions to all your doubts. Kunduz solves first five questions for free

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Posted by Mahak Jain, 13/2/2021 Hesap Oluştur

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Attempting question papers is best way to practice. In this blog you have JEE Mains 2019 question paper with solutions for 9th January shift 1.

Before starting with JEE Mains 2019 question paper with solutions, let me tell you some tips to prepare better and score higher.

1. Before seeing JEE Mains 2019 question paper you should know the syllabus and exam paper pattern. Click here to know the same.

2. One should be aware of previous year chapter wise weightage. Click here to know the chapter wise weightage of JEE Mains previous year paper.

3. Make a proper schedule. While planning out a schedule for JEE Mains preparation, it will be beneficial for you to have a properly structured schedule. Click here to read a short article on time management.

4. List down all equations and formulas. Physics requires practice. This blog of JEE Mains 2019 solved question paper will help you in same.

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## JEE Mains 2019 Question Paper with Solutions- 9 January Shift 1

### Physics

Question 1

A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of 10 A. The magnetic field at point O will be close to:

1. 1.0 ⨯ 10-7 T
2. 1.5 ⨯ 10-7 T
3. 1.5 ⨯ 10-5 T
4. 1.0 ⨯ 10-5 T

Question 2

A gas can be taken from A to B via two different processes ACB and ADB.

When path ACB is used 60 J of heat flows into the system and 30 J of work is done by the system. If path ADB is used work done by the system is 10 J. The heat Flow (in J) into the system in path ADB is:

1. 80 J
2. 20 J
3. 100 J
4. 40 J

#### Question 3

A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive x – direction. At a particular point in space and time, E=6.3j V/m. The corresponding magnetic field B, at that point will be:

1. 1.89⨯10-8 kT
2. 6.3⨯10-8 kT
3. 2.1⨯10-8 kT
4. 18.9⨯10-8 kT

Question 4

Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is 16. The intensity of the waves are in the ratio:

1. 4:1
2. 25:9
3. 16:9
4. 5:3

#### Question 5

An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in the figure. If AB= BC, and the angle made by AB with downward vertical is θ, then:

1. tan θ = 2/√3

2. tan θ = 1/3

3. tan θ = 1/2

4. tan θ = 1/2√3

Question 6

A mixture of 2 moles of helium gas (atomic mass =4 u), and 1 mole of argon gas (atomic mass = 40 u) is kept at 300 K in a container. The ratio of their rms speeds

is close to:

1. 2.24
2. 0.45
3. 0.32
4. 3.16

Question 7

When the switch S, in the circuit shown, is closed, then the value of current i (in amperes)  will be:

1. 3 A
2. 5 A
3. 4 A
4. 2 A

Question 8

A resistance is shown in the figure. Its value and tolerance are given respectively by:

1. 27 kΩ, 20%
2. 270 kΩ, 5%
3. 270 kΩ, 10%
4. 27 kΩ, 10%

Question 9

A bar magnet is demagnetized by inserting it inside a solenoid of length 0.2 m, 100 turns, and carrying a current of 5.2 A. The coercivity of the bar magnet is:

1. 1200 A/m
2. 2600 A/m
3. 520 A/m
4. 285 A/m

#### Question 10

A rod, of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion α/℃. It is observed that an external copressive force F, is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by △TK. Young’s modulus, Y , for this metal is:

1. F / (Aα△T)

2. F / (Aα (△T-273))

3. F / (2Aα△T)

4. 2F / (Aα△T)

Question 11

A block of mass m, lying on a smooth horizontal surface, is attached to a spring (of negligible mass), as shown in the figure. The block is initially at rest in its equilibrium position. If now the block is pulled with a constant force F, the maximum speed of the block is:

1. πF / √(mk)
2. 2F / √(mk)
3. F / √(mk)
4. F / √(πmk)

#### Question 12

Three charges +Q, q, +Q are placed respectively, at distance,0,d/2 and d from the origin, on the x-axis. If the net force experienced by +Q. placed at x=0, is zero, then value of q is:

1. +Q/2
2. -Q/2
3. -Q/4
4. +Q/4

Question 13

A conducting circular loop made of a thin wire, has area 3.5⨯10-3 m2 and resistance 10Ω. It is placed perpendicular to a time dependent magnetic field B(t) = (0.4T)sin(50πT). The field is uniform in space. Then the net charge flowing through the loop during t=0s and t=10ms is close to:

1. 0.14 mC
2. 21 mC
3. 6 mC
4. 7 mC

Question 14

Two masses m and m/2 are connected at the two ends of a massless rigid rod of length l. The rod is suspended by a thin wire of torsional constant k at the centre of mass of the rod-mass system (see figure). Because of torsional constant k, the restoring torque is τ=kθ for angular displacement θ. If rod is rotated by θo and  released, the tension in it when it passes through its mean position will be:

1. 3kθo2 / l
2. o2 / 2l
3. 2kθo2 / l
4. o2 / l

#### Question 15

A copper wire is stretched to make it 0.5 % longer. The percentage change (in % ) in its electrical resistance if its volume remains unchanged is:

1. 2.5%
2. 0.5%
3. 1.0%
4. 2.0%

Question 16

A parallel plate capacitor is made of two square plates of side ‘a’ , separated by a distance d (d<<a). The lower triangular portion is filled with a dielectric of dielectric constant K, as shown in the figure. Capacitance of this capacitor is :

1. kε0a2 / (2d)

2. (kε0a2 lnK) / d

3. (kε0a2 lnK) / (d(K-1))

4. (kε0a2 ) / (2d(K+1))

Question 17

Mobility of electrons in a semiconductor is defined as the ratio of their drift velocity to the applied electric field. If , for an n-type semiconductor, the density of electrons is 1019 m -3 and their mobility is 1.6 m2/(V.s) then the resistivity of the semiconductor (since it is an n-type semiconductor contribution of holes is ignored ) is close to :

1. 2 Ωm
2. 0.4 Ωm
3. 4 Ωm
4. 0.2 Ωm

Question 18

If the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L, about the center of the Sun, its areal velocity is

1. 4L / m
2. L / m
3. L / 2m
4. 2L / m

Question 19

A block of mass 10 Kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P (in N), such that the block doesnot move downward ? (take g =10ms-2)

1. 32 N
2. 25 N
3. 23 N
4. 18 N

#### Question 20

Temperature difference of 120℃ is maintained between two ends of a uniform rod AB of length 2L. Another bent rod PQ, of same cross-section as AB and length 3L/2, is connected across AB (See figure). In steady state, temperature(in ℃) difference between P and Q will be close to:

1. 60 ℃
2. 75 ℃
3. 35 ℃
4. 45 ℃

Question 21

A heavy ball of mass M is suspended from the ceiling of a car by a light string of mass m (m<<M). When the car is at rest, the speed of transverse waves in the string is 60 ms-1. When the car has acceleration a, the wave-speed increases to 60.5 ms-1.The value of a , in terms of gravitational acceleration g, is closest to:

1. g/5
2. g/20
3. g/10
4. g/30

Question 22

A sample of radioactive material A, that has an activity of 10 mCi (1 Ci = 3.7 x 1010 decays/s), has twice the number of nuclei as another sample of a different radioactive material B which has an activity of 20 mCi. The correct choices for half-lives of A and B would then by respectively:

1. 20 days and 5 days
2. 20 days and 10 days
3. 5 days and 10 days
4. 10 days and 40 days

#### Question 23

Consider a tank made of glass (refractive index 1.5) with a thick bottom. It is filled with a liquid of refractive index μ. A student finds that, irrespective of what the incident angle i (see figure) is for a beam of light entering the liquid,the light reflected from the liquid glass interface is never completely polarized. For this to happen,the minimum value of μ is:

1. 3/√5
2. 5/√3
3. √(5/3)
4. 4/3

Question 24

An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is a and distance of its centre from the wire is d (d>>a). If the loop applies a force F on the wire then:

1. F ∝ (a2/d3)

2. F ∝ (a/d)

3. F ∝ (a/d)2

4. F = 0

#### Question 25

Surface of certain metal is first illuminated with light of wavelength λ1=350nm and then, by light of wavelength λ2=540nm. It is found that the maximum speed of the photo-electrons in the two cases differ by a factor of 2. The work function of the metal (in eV) is close to:

1. 1.8
2. 1.4
3. 2.5
4. 5.6

Question 26

A particle is moving with a velocity

where K is a constant. The general equation for its path is:

1. xy = constant

2. y2 = x2 + constant

3. y = x2 + constant

4. y2 = x + constant

Question 27

A convex lens is put 10cm from a light source and it makes sharp images on a screen, kept 10 cm from the lens. Now a glass block (refractive index 1.5) of 1.5 cm thickness is placed in contact with the light source. To get the sharp image again, the screen is shifted by a distance d. Then d is:

1. 0.55 cm away from the lens
2. 1.1 cm away from the lens
3. 0.55 cm towards the lens
4. 0

#### Question 28

For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its centre. Then value of h is:

1. R/√5
2. R
3. R/√2
4. R√2

Question 29

Three blocks A, B and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, m while C has mass M. Block A is given an inital speed ν towards B due to which it collides with B perfectly inelastically. The combined mass collides with C, also perfectly inelastically and 5/6 of the initial kinetic energy is lost in whole process. What is value of M/m?

1. 4
2. 5
3. 3
4. 2

#### Question 30

Drift speed of electrons, when 1.5 A of current flows in a copper wire of cross-section 5 mm2 , is ν. If the electron density in copper is 9⨯1028/m3 the value of ν in mm/s  is close to (Take charge of an electron to be = 1.6⨯10-19 C)

1. 0.2
2. 3
3. 2
4. 0.02

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