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# JEE Main Question Paper 2020 With Solutions (9th January - Morning)

## 75 Questions MCQ Test JEE Main Mock Test Series 2020 & Previous Year Papers | JEE Main Question Paper 2020 With Solutions (9th January - Morning)

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This mock test of JEE Main Question Paper 2020 With Solutions (9th January - Morning) for JEE helps you for every JEE entrance exam. This contains 75 Multiple Choice Questions for JEE JEE Main Question Paper 2020 With Solutions (9th January - Morning) (mcq) to study with solutions a complete question bank. The solved questions answers in this JEE Main Question Paper 2020 With Solutions (9th January - Morning) quiz give you a good mix of easy questions and tough questions. JEE students definitely take this JEE Main Question Paper 2020 With Solutions (9th January - Morning) exercise for a better result in the exam. You can find other JEE Main Question Paper 2020 With Solutions (9th January - Morning) extra questions, long questions & short questions for JEE on EduRev as well by searching above.
QUESTION: 1

Solution:

QUESTION: 2

Solution:

QUESTION: 3

### Two immiscible liquids of refractive index √2 and 2√2 are filled with equal height h in a vessel. Then apparent depth of bottom surface of the container given that outside medium is air:

Solution:

QUESTION: 4

Three identical solid spheres each having mass 'm' and diameter 'd' are touching each other as shown in figure. Calculate ratio of moment of inertia about an axis (perpendicular to plane of paper) passing through point P and B as shown in figure. Given P is centroid of triangle ABC.

Solution:

Now ratio = 13 / 23

QUESTION: 5

A solid sphere having radius R and Uniform charge density ρ has a cavity of radius R/2 as shown in figure. Find the ratio of magnitude of electric field at point A and B i.e.

Solution:

For a solid sphere

Electric field at point B = EB = E1A + E2A
E1A = Electric Field Due to solid sphere of radius R at point B =
E2A = Electric Field Due to solid sphere of radius R/2 (which having charge density –ρ)
E2A = R/2

EB =  E1A + E2A  =

QUESTION: 6

Consider an infinitely long current carrying cylindrical straight wire having radius 'a'. Then the ratio of magnetic field at distance a/3 and 2a from axis of wire is.

Solution:

QUESTION: 7

Find current in the wire BC.

Solution:

QUESTION: 8

Two electromagnetic waves are moving in free space whose electric field vectors are given by  . A charge q is moving with velocity .Find the
net Lorentz force on this charge at t = 0 and when it is at origin.

Solution:

Magnetic field vectors associated with this electromagnetic wave are given by

by putting the value of
The net Lorentz force on the charged particle is
at t = 0 and at x = y = 0
t = 0 , x = y = 0

QUESTION: 9

Two ideal di-atomic gases A and B. A is rigid, B has an extra degree of freedom due to vibration. Mass of A is m and mass of B is m/4. The ratio of molar specific heat of A to B at constant volume is :

Solution:

Molar heat capacity of A at constant volume = 5R/2
Molar heat capacity of B at constant volume = 7R/2
Dividing both

QUESTION: 10

An ideal liquid (water) flowing through a tube of non uniform cross section area at A and B are 40 cm2 and 20 cm2 respectively. If  pressure difference between A & B is 700 N/m2 then volume flow rate is :

Solution:

using equation of continuity
40 VA = 20 VB
2VA =  VB
Using Bernoullies equation

Volume flow rate = 20 × 100 × VB = 2732 cm3/s

QUESTION: 11

A screw gauge adv ances by 3mm in 6 rotations. There are 50 divisions on circular scale. Find least  count of screw gauge ?

Solution:

Pitch = 3/6 = 0.5 mm
L.C. = =  = 0.01 mm = 0.001 cm

QUESTION: 12

A telescope of aperture diameter 5m is used to observe the moon from the earth. Distance between the moon and earth is 4 × 105 km. Determine the minimum distance between two points on the moon's surface which can be resolved using this telescope. (Wave length of light is 5893 Å).

Solution:

distance = O1O2 = dθ

distance = O1O2≈ 57.5 m
∴ answer from options = 60m
(minimum distance)

QUESTION: 13

A particle of mass m is revolving around a planet in a circular orbit of radius R. At the instant the particle has velocity another particle of mass m/2 moving at velocity collides perfectly in-elastically with the first particle. The new path of the combined body will take is

Solution:

Conserving momentum

vf < vorb (= v) thus the combined mass will go on to an elliptical path.

QUESTION: 14

Two particles of same mass 'm' moving with velocities and  collide in-elastically. Find the loss in kinetic energy.

Solution:

Conserving momentum
on solving

Change in K.E

QUESTION: 15

Three wav es of same intensity (I0) having initial phases rad respectively interfere at a point.Find the resultant Intensity

Solution:

QUESTION: 16

Particle moves from point A to point B along the line shown in figure under the action of force. . Determine the work done on the particle by in moving the particle from point A to point B

Solution:

QUESTION: 17

For the given P-V graph for an ideal gas, chose the correct V- T graph. Process BC is adiabatic.

Solution:

For process A – B Volume is constant
PV = nRT ; as P increases T increases
For process B – C
PVγ = Constant
TVγ-1 = Constant
For process C – A pressure is constant
V = kT

QUESTION: 18

Given. Find vector parallel to electric field at position
[Note that ]

Solution:

Since
must be antiparallel to
So ,
where λ is a arbitrary positive constant
Now

so

QUESTION: 19

Which of the following statements are correct for moving charge as shown in figure.

Solution:

QUESTION: 20

Photons of wav elength 6556 Å falls on a metal surface. If ejected electrons with maximum K.E. moves in magnetic field of 3 × 10–4 T in circular orbit of radius 10–2m, then work function of metal surface is

Solution:

= 1.1 eV

*Answer can only contain numeric values
QUESTION: 21

A rod of length 1 m is released from rest as shown in the figure below.

If ω of rod is √n at the moment it hits the ground, then find n.

Solution:

*Answer can only contain numeric values
QUESTION: 22

If reversible voltage of 100 V is applied across an inductor, current in it reduces from 0.25A to 0A in 0.025ms. Find inductance of inductor (in mH).

Solution:

∴ L = 100 × 10–4 H
= 10 mH

*Answer can only contain numeric values
QUESTION: 23

A wire of length l = 3m and area of cross section 10–2cm2 and breaking stress 48×107N/m2 is attached with block of mass 10kg. Find the maximum possible value of angular velocity with which block can be moved in circle with string fixed at one end.

Solution:

Solving

*Answer can only contain numeric values
QUESTION: 24

Position of a particle as a function of time is given as x2 = at2 + 2bt + c, where a, b, c are constants. Acceleration of particle varies with x–n then value of n is.

Solution:

*Answer can only contain numeric values
QUESTION: 25

In the given circuit both diodes having zero forward resistance and built-in potential of 0.7 V. Find the potential of point E in volts.

Solution:

Let VB = 0
Right diode is reversed biased and left diode is forward biased
∴ VE = 12.7 – 0.7
= 12 Volt

QUESTION: 26

Determine wavelength of electron in 4th Bohr's orbit ?

Solution:

QUESTION: 27

Which of the following species have one unpaired electron each?

Solution:

QUESTION: 28

For Br2(l) Enthalpy of atomisation = x kJ/mol Bond dissociation enthalpy of bromine = y kJ/mole
then

Solution:

ΔHatomisation = ΔHvap + Bond energy
Hence x > y

QUESTION: 29

Which of the following oxides are acidic, Basic Amphoteric Respectively.

Solution:

Non-metal oxides are acidic in nature alkali metal oxides are basic in nature Al2O3 is amphoteric.

QUESTION: 30

Complex Cr(H2O)6Cln shows geometrical isomerism and also reacts with AgNO3 solution.
Given : Spin only magnetic moment = 3.8 B.M.
What is the IUPAC name of the complex.

Solution:

Cr(H2O)6Clncomplex)spin = 3.8 B.M.
From data of magnetic moment oxidation number of Cr should be +3
Hence complex is Cr(H2O)6Cl3.
Complex shows geometrical isomerism therefore formula of complex is [Cr(H2O)4Cl2]Cl . 2H2O.
It's IUPAC Name: Tetraaquadichloridochromium(III) chloride dihydrate.

QUESTION: 31

The electronic configuration of bivalent Europium and trivalent cerium respectively is:  (Atomic Number : Xe = 54, Ce = 58, Eu = 63)

Solution:

Eu2+ : [Xe]4f7
Ce3+ : [Xe]4f1

QUESTION: 32

Ksp of PbCl2 = 1.6 × 10–5
On mixing 300 mL, 0.134M Pb(NO3)2(aq.) + 100 mL, 0.4 M NaCl(aq.)

Solution:

= 0.105 × 10–2
=1.005 ×10–3
Q > Ksp

QUESTION: 33

Which of the following can not act as both oxidising and reducing agent ?

Solution:

As in H3PO4 Phosphorous is present it's maximum oxidation number state hence it cannot act as reducing agent.

QUESTION: 34

​First Ionisation energy of Be is higher than that of Boron.
Select the correct statements regarding this
(i) It is easier to extract electron from 2p orbital than 2s orbital
(ii) Penetration power of 2s orbital is greater than 2p orbital
(iii) Shielding of 2p electron by 2s electron
(iv) Radius of Boron atom is larger than that of Be

Solution:

Theory Based

QUESTION: 35

[PdFClBrI]2– Number of Geometrical Isomers = n. For [Fe(CN)6]n–6, Determine the spin only magnetic moment and CFSE (Ignore the pairing energy)

Solution:

Number of Geometrical Isomers in square planar [PdFClBrI]2– are = 3
Hence, n = 3

Fe3+ = 3d5,
According to CFT configuration is

CFSE = - 0 .4 Δ0 x nt2g + 0 .6 Δ0 x neg = -0.4 Δ0 × 5 = -2.0Δ0

QUESTION: 36

A can reduce BO2 under which conditions.

Solution:

A + BO---> B + AO2
ΔG = -ve
Only above 1400°C

QUESTION: 37

Rate of reaction in absence of catalyst at 700 K is same as in presence of catalyst at 500 K. If catalyst decreases activation energy barrier by 30 kJ/mole, determine activation energy in presence of catalyst. (Assume 'A' factor to be same in both cases)

Solution:

Activation energy of the catalysed reaction = 105 – 30 = 75 kJ/mole

QUESTION: 38

A substance 'X' having low melting point, does not conduct electricity in both solid and liquid state. 'X' can be :

Solution:

CCl4 ---> Non-conductor in solid and liquid phase.

QUESTION: 39

The major product for above sequence of reaction is :

Solution:

QUESTION: 40

Which of the following can give highest yield in Friedel craft reaction?

Solution:

Aniline form anilinium complex with lewis acid so phenol is most reactive among the given compounds for electrophilic substitution reaction.

QUESTION: 41

What will be the major product ?

Solution:

QUESTION: 42

Which of the following is correct order for heat of combustion?

Solution:

In isomers of hydrocarbon heat of combustion depends upon their stabilities. As the stability increases heat of combustion decreases.
Stability order

QUESTION: 43

Write the correct order of basicity.

Solution:

Basicity is inversely proportional to electronegativity.

QUESTION: 44

A, B, C, and D are four artificial sweetners.
(i) A & D give positive test with ninhydrin.
(ii) C  form precipitate with AgNO3 in the lassaigne extract of the sugar.
(iii) B & D give positive test with sodium nitroprusside.
Correct option is :`

Solution:

A – Aspartame

B – Saccharine

C – Sucralose

D – Alitame

(i) A & D give positive test with ninhydrin because both have free carboxylic and amine groups.
(ii) C form precipitate with AgNO3 in the lassaigne extract of the sugar because it has chlorine atoms.
(iii) B & D give positive test with sodium nitroprusside because both have sulphur atoms.

QUESTION: 45

Predict the compound (P) on the basis of above sequence of the reactions?
Where compound (P) gives positive Iodoform test.

Solution:

*Answer can only contain numeric values
QUESTION: 46

Given a solution of HNO3 of density 1.4 g/mL and 63% w/w. Determine molarity of HNO3 solution.

Solution:

*Answer can only contain numeric values
QUESTION: 47

Determine degree of hardness in term of ppm of CaCO3 of 10–3 molar MgSO4 (aq).

Solution:

10–3 molar MgSO4 = 10–3 moles of MgSO4 present in 1 L solutions.

*Answer can only contain numeric values
QUESTION: 48

Determine the amount of NaCl to be dissolved in 600g H2O to decrease the freezing point by 0.2°C
Given : kf of H2O = 2 k-m–1 density of H2O(l) = 1 g/ml

Solution:

*Answer can only contain numeric values
QUESTION: 49

On passing a particular amount of electricity in AgNO3 solution, 108 g of Ag is deposited. What will be the volume of O2(g) in litre liberated at 1 bar, 273K by same quantity of electricity?

Solution:

1F charge is required to deposit 1 mole of Ag

2F charge deposit → 1/2 mole
1F charge will deposit → 1/4 mole

*Answer can only contain numeric values
QUESTION: 50

Find percentage nitrogen by mass in Histamine ?

Solution:

Structure of Histamine is
Molecular formula of Histamine is C5H9N3
Molecular mass of Histamine is 111
Percentage nitrogen by mass in Histamine =

QUESTION: 51

Find the number of solution of log1/2 |sinx| = 2 – log1/2 |cosx| , x ∈ [0,2π]

Solution:

log1/2 |sinx| = 2 – log1/2 |cosx|
log1/2 |sinx cosx| = 2
|sinx cosx| = 1/4
sin2x = ± 1/2

Number of solution = 8

QUESTION: 52

If e1 and e2 are eccentricities of and , respectively and if the point (e1, e2) lies on ellipse 15x2 + 3y2 = k. Then find value of k

Solution:

∴ k = 16

QUESTION: 53

Find integration

Solution:

QUESTION: 54

If  = 1, |z| = 5/2 then value of |z + 3i| is

Solution:

QUESTION: 55

Solution:

QUESTION: 56

Value of is

Solution:

QUESTION: 57

Find the value of

Solution:

QUESTION: 58

If f(x) = a + bx + cx2 where a, b, c ∈ R then is

Solution:

f(1) = a + b + c
f(0) = a

Now

QUESTION: 59

If number of 5 digit numbers which can be formed without repeating any digit while tenth place of all of the numbers must be 2 is 336 k find value of k

Solution:

Number of numbers
= 8 x 8 x 7 x 6 = 2688 = 336k => k = 8

QUESTION: 60

A (3,–1), B(1,3), C(2,4) are vertices of ΔABC if  D is centroid of ΔABC and P is point of intersection of lines x + 3y - 1 = 0 and 3x - y + 1 = 0 then which of the following points lies on line joining D and P

Solution:

D (2,2)
Point of intersection P
and equation of line DP
8x – 11y + 6 = 0

QUESTION: 61

If f(x) is twice differentiable and continuous function in x ∈ [a,b] also f'(x) > 0 and f ''(x)  < 0 and c ∈ (a,b)
then is greater than

Solution:

QUESTION: 62

If plane
x + 4y – 2z = 1
x + 7y – 5z = β
x + 5y + αz = 5
intersects in a line (R × R × R) then α + β is equal to

Solution:

(7α + 25) - (4α + 10) + (-20 + 14) = 0
3α + 9 = 0
α = - 3
Also Dz = 0  = 0
1(35 – 5β) - (15) + 1 (4β - 7) = 0
β = 13

QUESTION: 63

For observations xi given and . If mean and variance of observations is λ & μ respectively then ordered pair (λ, μ) is

Solution:

Mean
∴ λ = {Mean (xi – 5)} + 2 = 3
μ = var (xi – 5) =

QUESTION: 64

In a bag there are 20 cards 10 names A and another 10 names B. Cards are drawn randomly one by one with replacement then find probability that second A comes before third B.

Solution:

AA + ABA + BAA + ABBA + BBAA + BABA

QUESTION: 65

The negation of ‘ √5 is an integer or 5 is an irrational number’ is

Solution:

√5 is not an integer and 5 is not an irrational Number ~ (p v q) = ~ p ∧ ~ q

QUESTION: 66

If a circle touches y-axis at (0, 4) and passes through (2, 0) then which of the following can not be the tangent to the circle

Solution:

equation of family of circle
(x – 0)2 + (y – 4)2 + λx = 0
passes (2, 0)
4 + 16 + 2λ = 0
λ= - 10
x2 + y2 – 10x – 8y + 16 = 0
centre (5, 4). R = = 5

QUESTION: 67

If f'(x) = tan–1 (secx + tanx), x ∈ and f(0) = 0 then the value of f(1) is

Solution:

f'(x) = tan–1 (secx + tanx) =
tan–1

= tan–1

QUESTION: 68

A sphere of 10cm radius has a uniform thickness of ice around it. Ice is melting at rate 50cm3/min when thickness is 5cm then rate of change of thickness

Solution:

Let thickness = x cm
Total volume v = 4/3 π(10 + x)3

Given dv/dt = 50cm3/min
At x = 5cm
50 = 4π (10 + 5)2dx/dt

QUESTION: 69

Find number of real roots of equation e4x + e3x – 4e2x + ex + 1 = 0 is

Solution:

Let ex = t ∈ (0, ∞)
Given equation t4 + t3 – 4t2 + t + 1 = 0

QUESTION: 70

If A = B = adj(A) and C = 3A then is

Solution:

= 13 + 1 – 8 = 6

*Answer can only contain numeric values
QUESTION: 71

Solution:

∴ at   x = 2,  y = 0
∴ 0 = 3 (2+1+c) => c = -3
at x = 3 , y = 3

*Answer can only contain numeric values
QUESTION: 72

Function is continuous at x = 0, find a + 2b.

Solution:

LHL = a + 3
f(0) = b
RHL =
∴ a = -2   b = 1 ∴ a + 2b = 0

*Answer can only contain numeric values
QUESTION: 73

Find the coefficient of x4 in (1 + x + x2)10

Solution:

General term
for coefficient of  x4
=> β + 2γ = 4
γ = 0, β = 4 , α = 6

γ = 1, β = 2 , α = 7

γ = 2, β = 0 , α = 8

Total = 615

*Answer can only contain numeric values
QUESTION: 74

and are coplanar vectors and then value of λ is

Solution:

= 0
a + 1 + a + a = 0 => a =

*Answer can only contain numeric values
QUESTION: 75

If points A (2, 4, 0), B(3, 1, 8), C(3, 1, –3), D(7, –3, 4) are four points then projection of line segment AB on line CD.

Solution: