Attempting question papers is best way to practice. In this blog you have JEE Main 2019 question paper with solutions for 10^{th} January shift 1.

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## JEE Main 2019 Question Paper with Solutions- 10 January Shift 1

### Physics

**Question 1 **

A uniform metallic wire has a resistance of 18 Ω and is bent into an equilateral triangle. Then, the resistance (in Ω) between any two vertices of the triangle is:

- 8 Ω
- 12 Ω
- 4 Ω
- 2 Ω

Correct answer: 3

**Question 2 **

A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass ‘m’ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is:

- 1.5 mv
^{2} - mv
^{2} - 2 mv
^{2} - 0.5 mv
^{2}

Correct answer: 2

**Question 3 **

A solid metal cube of edge length 2 cm is moving in a positive y-direction at a constant speed of 6m/s. There is a uniform magnetic field of 0.1 T in the positive z-direction. The potential difference between the two faces of the cube perpendicular to the x-axis, is:

- 6 mV
- 1 mV
- 12 mV
- 2 mV

Correct answer: 3

**Question 4 **

A Parallel plate capacitor is of area 6 cm^{2} and separation 3 mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants K_{1}=10 and K_{2}=12 and K_{3}=14. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be:

- 12
- 4
- 36
- 14

Correct answer: 1

**Question 5 **

A 2 W carbon resistor is color-coded with green, black, red and brown respectively. The maximum current (in mA) which can be passed through this resistor is :

- 63 mA
- 0.4 mA
- 100 mA
- 20 mA

Correct answer: 4

**Question 6 **

In a young’s double slit experiment with slit separation 0.1mm, one observes a bright fringe at angle 1/40 rad by using light of wavelength λ_{1}. When the light of wavelength λ_{2} is used a bright fringe is seen at the same angle in the same set up. Given that λ_{1} and λ_{2} are in visible range (380nm to 740nm), their values are:

- 380 nm, 500 nm
- 625 nm, 500 nm
- 380 nm, 525 nm
- 400 nm, 500 nm

Correct answer: 2

**Question 7 **

A magnet of total magnetic moment 10^{-2}i Am^{2} is placed in a time-varying magnetic field, B(cosωt)î where B=1 Tesla and w=0.125 rad/s. The work done for reversing the direction of the magnetic moment at t=1 second, is:

- 0.01 J
- 0.007 J
- 0.028 J
- 0.014 J

Correct answer: d

**Question 8 **

To mop – clean a floor, a cleaning machine presses a circular mop of radius R vertically down with a total force F and rotates it with a constant angular speed about its axis. If the force F is distributed uniformly over the mop and if coefficient of friction between the mop and if coefficent of friction between the mop and the floor is μ, the torque, applied by the machine on the mop is:

- 2μFR/3
- μFR/3
- μFR/2
- μFR/6

Correct answer: 1

**Question 9 **

Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600 counts per second and t=8 seconds it was 100 counts per second. The count rate observed, as counts per second, at t=6 seconds is close to:

- 150
- 360
- 200
- 400

Correct answer: 3

**Question 10 **

If the magnetic field of a plane electromagnetic wave is given by (The speed of light=3⨯10^{8}m/s).

B=100⨯10^{-4} sin[2π⨯2⨯10^{15}(t – x/c)] then the maximum electric field associated with it is:

- 4⨯10
^{4}N/C - 4.5⨯10
^{4}N/C - 6⨯10
^{4}N/C - 3⨯10
^{4}N/C

Correct answer: 4

**Question 11**

A charge Q is distributed over three concentric spherical shells of radii a,b,c (a<b<c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r<a, would be:

1. | |

2. | |

3. | |

4. |

Correct answer: 4

**Question 12 **

Water flows into a large tank with flat bottom at the rate of 10^{-4}m^{3}s^{-1} . Water is also leaking out of a hole of area 1cm^{2} at its bottom. If the height of the water in the tank remains steady, then this height (in cm) is:

- 4cm
- 2.9cm
- 1.7cm
- 5.1cm

Correct answer: 4

**Question 13 **

A piece of wood of mass 0.03 kg is dropped from the top of a 100m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upward, with a velocity 100m/s from the ground. The bullet gets embedded in the wood. Then the maximum height ( in meter) to which the combined system reaches above the top of the building before falling below is: (g=10m/s^{2})

- 30m
- 10m
- 40m
- 20m

Correct answer: 3

**Question 14 **

The density of material in SI unit is 128kg m^{-3}. In certain units in which the unit of length is 25 cm and the unit of mass is 50g, the numerical value of density of the material is:

- 410
- 640
- 16
- 40

Correct answer: 4

**Question 15 **

To get output ‘1’ at R, for the given logic gate circuit the input values must be:

- X=0 ,Y=1
- X=1, Y=1
- X=0, Y=0
- X=1, Y=0

Correct answer: 4

**Question 16 **

A block of mass m is kept on a platform which starts from rest with constant acceleration g/2 upward, as shown in the figure. Work done by normal reaction on block in time t is:

- 0
- 3mg
^{2}t^{2}/ 8 - -mg
^{2}t^{2}/ 8 - mg
^{2}t^{2}/ 8

Correct answer: 2

**Question 17 **

A heat source at T=10^{3} K is connected to another heat heat reservoir at T=10^{2} K by a copper slab which is 1m thick. Given that the thermal conductivity of copper is 0.1WK^{-1}m^{-1}, the energy flux (Wm^{-2}) through it in the steady state is:

- 90
- 200
- 65
- 120

Correct answer: 1

**Question 18 **

A TV transmission tower has height of 140m and the height of receiving antenna is 40m. What is the maximum distance up to which signals can be broadcasted from this tower in LOS(line of sight) mode?

(Given : radius of earth = 6.4 X 10^{6} m)

- 80 km
- 48 km
- 40 km
- 65 km

Correct answer: 4

**Question 19 **

A potentiometer wire AB having length L and resistance 12r is joined to a cell D of emf ε and internal resistance r. A cell C having emf ε/2 and internal resistance 3r is connected. The length AJ is connected with the galvanometer as shown in the fig. shows no deflection is:

- 5L/12
- 11L/24
- 11L/12
- 13L/24

Correct answer: 4

**Question 20 **

An insulating thin rod of length l has a linear charge density λ(x)=ρ_{0}x/l on it. The rod is rotated about an axis passing through the origin (x=0) and perpendicular to the rod. If the rod makes n rotations per second, then the time-averaged magnetic moment of the rod is

- πnρl
^{3}/4 - nρl
^{3} - πnρl
^{3} - πnρl
^{3}/3

Correct answer: 1

**Question 21 **

Two guns A and B can fire bullets at speeds 1km/s and 2km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by two guns , on the ground is:

- 1:2
- 1:4
- 1:8
- 1:16

Correct answer: 4

**Question 22 **

A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0N. The string is set into vibration using an external vibrator of frequency 100 Hz. The separation(in cm) between successive nodes on the string is close to:

- 16.6
- 20.0
- 10.0
- 33.3

Correct answer: 2

**Question 23 **

A train moves towards a stationary observer with speed 34 m/s. The train sounds a whistle and its frequency registered by the observer is f_{1}. If the speed of the train is reduced to 17 m/s, the frequency registered is f_{2}. If the speed of sound is 340 m/s, then the ratio f_{1}/f_{2} is:

- 18/17
- 19/18
- 20/19
- 21/20

Correct answer: 2

**Question 24 **

In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of 7.5 X 10^{-12} m, the minimum electron energy required is close to:

- 100 keV
- 500 keV
- 25 keV
- 1 keV

Correct answer: 3

**Question 25 **

A homogenous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is:

- 3F/(2MR)
- F/(3MR)
- 2F/(3MR)
- F/(2MR)

Correct answer: 3

**Question 26 **

A plano convex lens of refractive index μ_{1} and focal length f_{1}, is kept in contact with another plano concave lens of refractive index μ_{2} and focal length f_{2}. If the radius of curvature of their spherical faces is R each and f_{1}=2f_{2}, then μ_{1} and μ_{2} are related as:

- μ
_{1}+μ_{2}=3 - 2μ
_{1}-μ_{2}=1 - 2μ
_{2}-μ_{1}=1 - 3μ
_{2}-2μ_{1}=1

Correct answer: 2

**Question 27 **

Two electric dipoles, A, B with respective dipole moments are placed on the x-axis with a separation R, as shown in the figure

The distance from A at which both of them production the same potentials is:

- R√2 / (1+√2)
- R / (1+√2)
- R√2 / (√2 – 1)
- R / (√2 – 1)

Correct answer: 3

**Question 28 **

In the given circuit the cells have zero internal resistance. The currents (in Amperes ) Passing through resistance R_{1} and R_{2} respectively, are :

- 2, 2
- 0, 1
- 1, 2
- 0.5, 0

Correct answer: 4

**Question 29 **

In the cube of side ‘a’ shown in the figure , the vector from the central point of the face ABOD to the central point of the face BEFO will be:

1. 0.5 a (î-k)

2. 0.5 a (j-î)

3. 0.5 a (k-î)

4. 0.5 a (j-k)

Correct answer: 2

**Question 30 **

Three Carnot engines operate in series between a heat source at a temperature T_{1} and a heat sink at temperature T_{4} (see figure). There are two other reservoirs at temperature T_{2} and T_{3}, as shown, with T_{1}>T_{2}>T_{3}>T_{4}. The three engines are equally efficient if:

1. T_{2}=(T_{1}T_{4})^{1/2}; T_{3}=(T_{1}^{2}T_{4})^{1/3}

2. T_{2}=(T_{1}^{2}T_{4})^{1/3}; T_{3}=(T_{1}T_{4}^{2})^{1/3}

3. T_{2}=(T_{1}T_{4}^{2})^{1/3}; T_{3}=(T_{1}^{2}T_{4})^{1/3}

4. T_{2}=(T_{1}^{3}T_{42})^{1/4}; T_{3}=(T_{1}T_{4}^{3})^{1/4}

Correct answer: 2

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