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# 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

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 :

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

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.

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

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)

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

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

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

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

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 31

Given following complexes
(I) Na4[Fe(CN)6]
(II) [Cr(H2O)6] Cl2
(III) (NEt4)2 [CoCl4]
(IV) Na3[Fe(C2O4)3] (Δ0 > P)
Correct order of spin only magnetic moment for the above complexes  is.

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 31

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 32

Select the correct option :

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 32

Entropy is function of temperature and also entropy change is function of temperature.
ΔS = ∫dq/T
ST = ∫0T ncdT/T

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 33

A compound (A ; B3N3H3Cl3) reacts with LiBH4 to form inorganic benzene (B). (A) reacts with (C) to form B3N3H3(CH3)3. (B) and (C) are respectively.

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 33

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 34

In a box a mixture containing H2, O2 and CO along with charcoal is present then variation of pressure with the time will be as follows :

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 34

Theory based.

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 35

Given complex [Co(NH3)4Cl2]. In it if Cl – Co – Cl bond angle is 90º then it is :

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 35

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 36

Amongst the following which has minimum conductivity.

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 36

Theory based.

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 37

Number of sp2 hybrid orbitals in Benzene is :

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 37

In benzene total six sp2 hybrid carbon atoms are present. Each carbon atom has 3 sp2 hybrid orbitals.
Therefore total sp2 hybrid orbitals are 18 in benzene.

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 38

Which of the following reaction will not form racemic mixture as product?

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 38

(CH3)2CH–CH=CH2 --HCl----> ---Hybride shift--->

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 39

In which compound C–Cl bond length is shortest?

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 39

Resonance form of Cl–CH=CH–NO2 is more stable than resonance form of any other given compounds. Hence, double bond character in carbon-chlorine bond is maximum and bond length is shortest.

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 40

Biochemical oxygen demand (BOD) is defined as ............ in ppm of O2.

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 40

The amount of oxygen required by bacteria to break down the organic matter present in a certain volume of a sample of water, is called Biochemical Oxygen Demand (BOD).

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 41

Monomer(s) of which of the given polymer is chiral?

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 41

In PHBV, both monomers have chiral centre.

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 42

Which of the following options is correct ?

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 43

​The order of basic character is :
(I)          (II)      (III)     (IV)

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 43

Basic strength depends upon availability of lone pairs. Greater the resonance of lone pairs lesser the basic strength.

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 44

Compound A Compound A will be :

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 44

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 45

Compound X

Compound X will be :

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 45

*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 46

Total number of Cr–O bonds in Chromate ion and dichromate ion is.

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 46

Chromate ion --->
Dichromate ion --->
=> Total number of Cr and O bonds is 12.

*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 47

Lacto bacillus has generation time 60 min. at 300 K and 40 min. at 400 K. Determine activation energy in (given wrong in paper)

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 47

ln(3/2) × 8.3 × 1200 = Ea
=> Ea = 0.4 × 8.3 × 1200
=> Ea = 3984 J/mol.
=> Ea = 3.984 kJ/mol.

*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 48

One litre sea water (d = 1.03g/cm3) contains 10.3 mg O2 gas. Determine concentration of O2 in ppm.

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 48

*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 49

0.1 ml of an ideal gas has volume 1 dm3 in a locked box with friction less piston. The gas is in thermal equilibrium with excess of 0.5 m aqueous ethylene glycol at its freezing point. If piston is released all of a sudden at 1 atm then determine the final volume of gas in dm3 (R = 0.08 atm L mol–1 K–1 Kf = 2.0 K molal–1).

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 49

Kf = 2.0
m = 0.5 m
ΔTf = Kfm = 0.5 × 2
Tinitial = 272 K
n = 0.1 mol
V = 1 dm3

= 2.176 atm
After releasing piston P1V1 = P2V2
2.176 × 1 = 1 × V2
V2 = 2.176 dm3

*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 50

Compound A
Percentage carbon in compound A is:

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 50

Compound A is
Percentage carbon in compound A =

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 51

If f(x) =  g(x) = then find the area bounded by f(x) and g(x) from x = .

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 51

Required area = Area of trapezium ABCD –

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 52

z is a complex number such that |Re(z)| + |Im (z)| = 4 then |z| can't be

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 52

z = x + iy
|x| + |y| = 4
Minimum value of |z| = 2√2
Maximum value of |z| = 4

So |z| can't be √7

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 53

If f(x) =  and a – 2b + c = 1 then

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 53

Apply R1 = R1 + R3 – 2R2

f(x) = 1
f(50) = 1

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 54

Let an is a positive term of a GP and

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 54

Let GP is a, ar, ar2 ……..
= a3 + a5 + ….. a201 = 200
............(1)
= a2 + a4 + ……. a200 = 100
........... (2)
Form (1) and (2) r = 2
a2 + a3 + ……….. a200 + a201 = 300
r(a1 + ………… a200) = 300
= 300/r = 150

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 55

If y(1) = 1 and y(x) = e then x = ?

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 55

Put y = vx

When x = 1, y = 1 then

So x = √3e

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 56

Let probability distribution is

then value of p(x > 2) is

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 56

6k2 + 5k = 1
6k2 + 5k – 1 = 0
6k2 + 6k – k – 1 = 0
(6k – 1) (k + 1) = 0
k = – 1 (rejected); k = 1/6
P(x > 2) = k + 2k + 5k2

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 57

= λtanq + 2log f(x) + c  then ordered pair (λ, f(x)) is

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 57

tanθ = t => sec2θ dθ = dt

= – t + 2 log (1+t) + C
= –tanθ + 2 log (1 + tanθ) + C
= λ = -1 and f(x) = 1 + tanθ

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 58

If p ---> (p ∧ ~ q) is false. Truth value of p & q will be

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 58

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 59

If  = A then the value of x at which f(x) = [x2] sinπx is discontinuous.

(where [.] denotes greatest integer function)

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 59

4 – 0 = A
check when
(A) x = => x = √5 => discontinuous
(B) x = A + 21 => x = 5
=> continuous
(C) x = A => x = 2
=> continuous

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 60

Let one end of focal chord of parabola y2 = 8x is , then equation of tangent at other end of this focal chord is

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 60

Let is (2t2, 4t)
=>
Parameter of other end of focal chord is 2
=> point is (8, 8)
=>equation of tangent is 8y – 4(x+8) = 0
=> 2y - x = 8

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 61

Let x + 6y = 8 is tangent to standard ellipse where minor axis is , then eccentricity of ellipse is

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 61

Equation of tangent ≡ y = mx ±
comparing with
and

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 62

if f(x) and g(x) are continuous functions, fog is identity function, g'(b) = 5 and g(b) = a then f'(a) is

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 62

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 63

If 7x + 6y – 2z = 0
3x + 4y + 2z = 0
x – 2y – 6z = 0 then which option is correct

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 63

= 7(–20) – 6(–20) – 2(–10)
= – 140 + 120 + 20 = 0
so infinite non-trivial solution exist
now equation (1) + 3 equation (3)
10x – 20z = 0
x = 2z

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 64

Let  x = 2sinθ - sin2θ  and
y = 2 cosθ - cos2θ
find at θ = π

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 64

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 65

then correct choice is

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 65

F'(x) = x2g(x)
=> F'(1) = 1.g(1) = 0 ....(1)
(∴ g(1) = 0)
F''(1) = 0 + 1 × 3
=> F''(1) = 3 .....(2)
From (1) and (2) F(x) has local minimum at x = 1

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 66

Let both root of equation ax2 – 2bx + 5 = 0 are α and root of equation x2 - 2bx - 10 = 0 are α and β. Find the value of α2 + β2

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 66

b2 = 5a ..... (i) (a ≠ 0)
α + β  = 2b ..... (ii)
and αβ = – 10 ......(iii)
α = b/a is also root of x2 - 2bx - 10 = 0
b2 – 2ab2 – 10a2 = 0
by (i) 5a – 10a2 – 10a2 = 0
20a2 = 5a
a = 1/4 and b2 = 5/4
α= 20 and β2 = 5
Now α2 + β2
= 5 + 20
= 25

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 67

​Let A = {x : |x| < 2} and B = {x : |x – 2| ≥ 3} then

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 67

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 68

Let x =  and y =  where θ ∈ (0,π/4), then

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 68

y = 1 + cos2θ + cos4θ + .......

= > y (1 – x) = 1

JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 69

Let the distance between plane passing through lines  and and plane  23x – 10y – 2z + 48 = 0 is then k is equal to

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 69

Lines must be intersecting
(2s – 1, 3s + 3, 8s –1)
= (2t – 3, t – 2 , λt + 1)
2s - 1 = 2t - 3,
3s + 3 = t - 2 ,
8s - 1 = λt + 1
=> t = -1, s = -2 , λ = 18
distance of plane contains given lines from given plane is same as distance between point (–3, –2,1) from given plane.
Required distance equal to

k = 3

*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 70

If 25C0 + 5 25C1 + 9 25C2 ……… 101 25C25 = 225 k find k = ?

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 70

So k = 51

*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 71

Let circles (x – 0)2 + (y – 4)2 = k and (x – 3)2 + (y – 0)2 = 12 touches each other than find the maximum value of 'k'

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 71

Two circles touches each other if C1C2 = = |r1 ± r2|
Distance between C2(3, 0) and C1(0, 4) is either √k + 1 or     (C1C2 = 5)
=> √k + 1 = 5 or
=> k = 16 or k = 36
=> maximum value of k is 36

*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 72

Let angle between equal to π/3
If is perpendicular to  then find the value of

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 72

Also

*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 73

Number of common terms in both sequence 3, 7, 11, ………….407 and 2, 9, 16, ……..905 is

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 73

First common term = 23
common difference = 7 × 4 = 28
Last term ≤ 407
=> 23 + (n-1) × 28 ≤ 407
=> (n - 1) × 28 ≤ 384
=> n  ≤ 13.71 + 1
n ≤ 14.71
So n = 14

*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 74

If minimum value of term free from x for is L1 in θ ∈ and L2 in θ ∈  find

Detailed Solution for JEE Main 2020 Question Paper with Solution (9th January - Evening) - Question 74

∵ {Min value of L1 at θ = π/4}

= 16C8 . 28.24 {∵ min value of L2 at θ = π/8]

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