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JEE Main 2020 Question Paper with Solution (9th January - Evening) - JEE MCQ


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30 Questions MCQ Test - JEE Main 2020 Question Paper with Solution (9th January - Evening)

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JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 1

A mass m attached to spring of natural lengthand spring constant k.One end of string is attached to centre of disc in horizontal plane which is being rotated by constant angular speed ω. Find extension per unit length in spring (given k >> mω2) :

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 1



JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 2

A loop of radius R and mass m is placed in a uniform magnetic field B with its plane perpendicular to the field. Current I is flowing in it. Now loop is slightly rotated about its diameter and released. Find time period of oscillation.

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 2

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JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 3

A string of mass per unit length μ = 6 × 10–3 kg/m is fixed at both ends under the tension 540 N. If the string is in resonance with consecutive frequencies 420 Hz and 490 Hz. Then find the length of the string? 

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 3

Fundamental frequency = 490 – 420
= 70 Hz

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 4

Ratio of energy density of two steel rods is 1 : 4 when same mass is suspended from the rods. If length of both rods is same then ratio of diameter of rods will be.

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 4

stress x 


 

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 5

A particle is projected from the ground with speed u at angle 60° from horizontal. It collides with a second particle of same mass moving with horizontal speed u in same direction at highest point of its trajectory. If collision is perfectly inelastic then find horizontal distance travelled by them after collision when they reached at ground

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 5



so horizontal range after collision

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 6

H-like atom with ionization energy of 9R. Find the wavelength of light emitted (in nm) when electron jumps from second excited state to ground state. (R is Rydberg constant) 

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 6


wavelength = nm
λ = 11.39 nm

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 7

Two planets of masses M and M/2 have radii R and R/2 respectively. If ratio of escape velocities from their surfaces v1/v2 is n/4, then find n :    

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JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 8

Find centre of mass of given rod of linear mass density λ = , x is distance from one of its end. Length of the rod is l. 

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JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 9

If a point source is placed at a depth h in a liquid of refractive index 4/3. Find percentage of energy of light that escapes from liquid. (assuming 100% transmission of emerging light)

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 9



Solid angle dΩ = 2pR2 (1 - cos β)
Percentage of light = 

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 10

System is released from rest. Moment of inertia of pulley 'I'. Find angular speed of pulley when m1 block falls by 'h'. (Given m1 > m2 and assume no slipping between string and pulley).

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 10

k1+ U1 = k1 + k2

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 11

Find the current supplied by the battery?

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 11

Both diodes are in reverse biased

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 12

An AC source is connected to the LC series circuit with V = 10 sin (314t). Find the current in the circuit as function of time ? (L = 40 mH, C = 100 μF) 

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JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 13

There is a long solenoid of radius ‘R’ having ‘n’ turns per unit length with current i flowing in it. A particle having charge ‘q’ and mass ‘m’ is projected with speed 'v' in the perpendicular direction of axis from a Point on its axis  Find maximum value of 'v' so that it  will not collide with the solenoid.

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 13


 

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 14

A Capacitor C and resister R are connected to a battery of 5V in series. Now battery is disconnected and a diode is connected as shown in figure (a) and (b) respectively. Then charge on the capacitor after time RC in (a) and (b) respectively is QA and QB. Their value are

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 14

Maximum charge on capacitor = 5CV
(a) is forward biased and
(b) is reverse biased for case (a)

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 15

A sphere of density ρ is half submerged in a liquid of density σ and surface tension T. The sphere remains in equilibrium. Find radius of the sphere (assume the force due to surface tension acts tangentially to surface of sphere)

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 15


JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 16

An EM wave is travelling in  direction. Axis of polarization of EM wave is found to be  Then equation of magnetic field will be

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 16

EM wave is in direction 
Electric field is in direction ---> kˆ
--> direction of propagation of EM wave

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 17

Different value of a, b and c are given and their sum is d. Arrange the value of d in increasing order

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JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 18

Two gases Ar (40) and Xe (131) at same temperature have same number density. Their diameters are 0.07 nm and 0.10 nm respectively. Find the ratio of their mean free time

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 18

Mean free time = 

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 19

A particle starts moving from origin with velocityfrom origin and acceleration . Find x-coordinate at the instant when y-coordinate of the particle is 32 m.

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 19


t =  4 sec

= 60 m.

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 20

An electron is released in Electric field E from rest. Rate of change of de-Broglie wavelength with time will be.  

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 20


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 21

In YDSE pattern with light of wavelength λ1 = 500nm, 15 fringes are obtained on a certain segment of screen. If number of fringes for light of wavelength λ2 on same segment of screen is 10, then the value of λ2 (in nm) is-


Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 21

*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 22

If in a meter bridge experiment, the balancing length ' l ' was 25 cm for the situation shown in the figure. If the length and diameter of the of wire of resistance R is made half, then find the new balancing length in centimetre is


Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 22



l = 40.00 cm

*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 23

Find the power loss in each diode (in mW), if potential drop across the zener diode is 8V.


Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 23


Power loss in each diode = (4)(10–2) W = 40 mW

*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 24

An ideal gas at initial temperature 300 K is compressed adiabatically of its initial volume. The gas is then expanded isobarically to double its volume. Then final temperature of gas round to nearest integer is:
 


Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 24


PVy = constant
TVy–1 = constant 

TB = 300 × 28/5
Now for BC process


Tc = 1819 K

*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 25

If electric field in the space is given by  and electric flux through ABCD is φ1 and electric flux through BCEF is φ2 , then find (φ1 - φ2)


Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 25

Flux via ABCD

Flux via BCEF


JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 26

5 g of Zn reacts with
(I) Excess of NaOH  (II) Dilute HCl, then volume ratio of H2 gas evolved in (I) and (II) is

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 26

Zn + 2NaOH ---> Na2ZnO2 + H2
Zn + 2HCl ---> ZnCl2 + H2
According to stoichiometry in both the reactions, equal number of moles of H2 are evolved.

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 27

Given Ksp for Cr(OH)3 is 6 × 10–31 then determine [OH].
(Neglect the contribution of OH ions from H2O)

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 27



 

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 28

Select the correct statements among the followings
(A) LiCl does not dissolve in pyridine
(B) Li does not react ethyne to form ethynide.
(C) Li and Mg react slowly with water.
(D) Among alkali metals Li has highest hydration tendency.

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 28

Theory based

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 29

​Given an element having following ionisation enthalpies IE1 = 496 and IE2 = 4562 one mole 
hydroxide of this element is treated separated with HCl and H2SO4 respectiv ely. Moles of HCl and H2SO4  reacted respectively is

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 29

According to the given data of I.E, This element must belong to group 1 and thus is monovalent & form hydroxide of the type M(OH).
MOH + HCl --> MCl + H2O
1 mole 1 mole
2MOH + H2SO4 ---> M2SO4 + H2O
1 mole 1/2 mole

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 30

Reactant A represented by square is in equilibrium with product B represented by circles. Then value of equilibrium constant is

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