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


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*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 1

A large square container with thin transparent vertical walls and filled with water (refractive index 4/3 ) is kept on a horizontal table. A student holds a thin straight wire vertically inside the water 12 cm from one of its corners, as shown schematically in the figure. Looking at the wire from this corner, another student sees two images of the wire, located symmetrically on each side of the line of sight as shown. The separation (in cm) between these images is ____________. 


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 2

A train with cross-sectional area St is moving with speed vt inside a long tunnel of cross-sectional area S0(S0=4St). Assume that almost all the air (density ρ) in front of the train flows back between its side and the walls of the tunnel. Also, the air flow with respect to the train is steady and laminar. Take the ambient pressure and that inside the train to be p0. If the pressure in the region between the sides of the train and the tunnel walls is p, then p0−p= The value of N is ________.


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 3

Two large circular discs separated by a distance of 0.01 m are connected to a battery via a switch as shown in the figure. Charged oil drops of density 900 kg m−3 are released through a tiny hole at the center of the top disc. Once some oil drops achieve terminal velocity, the switch is closed to apply a voltage of 200 V across the discs. As a result, an oil drop of radius 8×10−7 m stops moving vertically and floats between the discs. The number of electrons present in this oil drop is ________. (neglect the buoyancy force, take acceleration due to gravity =10 ms−2 and charge on an electron (e) = 1.6 ×10–19 C)


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 4

A hot air balloon is carrying some passengers, and a few sandbags of mass 1 kg each so that its total mass is 480 kg. Its effective volume giving the balloon its buoyancy is V. The balloon is floating at an equilibrium height of 100 m. When N number of sandbags are thrown out, the balloon rises to a new equilibrium height close to 150 m with its volume V remaining unchanged. If the variation of the density of air with height h from the ground is , where ρ0=1.25 kg m−3 and h0=6000 m, the value of N is _____.


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 5

A point charge q of mass m is suspended vertically by a string of length l. A point dipole of dipole moment is now brought towards q from infinity so that the charge moves away. The final equilibrium position of the system including the direction of the dipole, the angles and distances is shown in the figure below. If the work done in bringing the dipole to this position is N×(mgh), where g is the acceleration due to gravity, then the value of N is _________ . (Note that for three coplanar forces keeping a point mass in equilibrium,  is the same for all forces, where F is any one of the forces and θ is the angle between the other two forces) 


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 6

A thermally isolated cylindrical closed vessel of height 8 m is kept vertically. It is divided into two equal parts by a diathermic (perfect thermal conductor) frictionless partition of mass 8.3 kg. Thus the partition is held initially at a distance of 4 m from the top, as shown in the schematic figure below. Each of the two parts of the vessel contains 0.1 mole of an ideal gas at temperature 300 K. The partition is now released and moves without any gas leaking from one part of the vessel to the other. When equilibrium is reached, the distance of the partition from the top (in m) will be _______ (take the acceleration due to gravity =10 ms−2 and the universal gas constant = 8.3 J mol−1K−1).


*Multiple options can be correct
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 7

A beaker of radius r is filled with water (refractive index 4/3) up to a height H as shown in the figure on the left. The beaker is kept on a horizontal table rotating with angular speed ω. This makes the water surface curved so that the difference in the height of water level at the center and at the circumference of the beaker is ℎ  (h ≪ H, h ≪ r) as shown in the figure on the right. Take this surface to be approximately spherical with a radius of curvature R. Which of the following is/are correct? (g is the acceleration due to gravity) 

*Multiple options can be correct
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 8

A student skates up a ramp that makes an angle 30° with the horizontal. He/she starts (as shown in the figure) at the bottom of the ramp with speed v0 and wants to turn around over a semicircular path xyz of radius R during which he/she reaches a maximum height h (at point y) from the ground as shown in the figure. Assume that the energy loss is negligible and the force required for this turn at the highest point is provided by his/her weight only. Then (g is the acceleration due to gravity)

*Multiple options can be correct
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 9

A rod of mass m and length L pivoted at one of its ends, is hanging vertically. A bullet of the same mass moving at speed v strikes the rod horizontally at a distance x from its pivoted end and gets embedded in it. The combined system now rotates with angular speed ω about the pivot. The maximum angular speed ωM is achieved for x = xM. Then

*Multiple options can be correct
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 10

In an X-ray tube, electrons emitted from a filament (cathode) carrying current I hit a target (anode) at a distance d from the cathode. The target is kept at a potential V higher than the cathode resulting in emission of continuous and characteristic X-rays. If the filament current I is decreased to I/2, the potential difference V is increased to 2V, and the separation distance d is reduced to d/2, then 

*Multiple options can be correct
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 11

Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings is α. The spheres are now immersed in a dielectric liquid of density 800 kg m−3 and dielectric constant 21. If the angle between the strings remains the same after the immersion, then

*Multiple options can be correct
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 12

Starting at time t = 0 from the origin with speed 1 ms−1, a particle follows a two-dimensional trajectory in the x-y plane so that its coordinates are related by the equation  The x and y components of its acceleration are denoted by ax and ay, respectively. Then,

*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 13

A spherical bubble inside water has radius R. Take the pressure inside the bubble and the water pressure to be p0. The bubble now gets compressed radially in an adiabatic manner so that its radius becomes (R-a). For a ≪ R the magnitude of the work done in the process is given by (4πp0Ra2)X, where X is a constant and γ = CP/Cv = 41/30. The value of X is _____.


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 14

In the balanced condition, the values of the resistances of the four arms of a Wheatstone bridge are shown in the figure below. The resistance R3 has temperature coefficient 0.0004 °C-1. If the temperature  of R3 is increased by 100“C the voltage developed between S and T will be _____ volt.


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 15

Two capacitors with capacitance values C1 = 2000 ± 10 pF and C2 = 3000 ± 15 pF are connected in series. The voltage applied across this combination is V = 5.00 ± 0.02 V. The percentage error in the calculation of the energy stored in this combination of capacitors is _______. 


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 16

A cubical solid aluminium (bulk modulus =  block has an edge length of 1 m on the surface of the earth. It is kept on the floor of a 5 km deep ocean. Taking the average density of water and the acceleration due to gravity to be 103 kg m−3 and 10 ms−2, respectively, the change in the edge length of the block in mm is _____. 


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 17

The inductors of two LR circuits are placed next to each other, as shown in the figure. The values of the self-inductance of the indicators, resistance, mutual-inductance and applied voltage are specified in the given circuit. After both the switches are closed simultaneously, the total work done by the batteries against the induced EMF in the inductors by the time the currents reach their steady-state values is________ mJ.


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 18

A container with 1 kg of water in it is kept in sunlight, which causes the water to get warmer than the surroundings. The average energy per unit time per unit area received due to the sunlight is 700Wm−2 and it is absorbed by the water over an effective area of 0.05 m2. Assuming that the heat loss from the water to the surroundings is governed by Newton’s law of cooling, the difference (in °C) in the temperature of water and the surroundings after a long time will be _____. (Ignore effect of the container, and take constant for Newton’s law of cooling = 0.001 s−1, Heat capacity of water = 4200 J kg−1 K−1


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 19

The 1st, 2nd and the 3rd ionization enthalpies I1, I2 and I3, of four atoms with atomic numbers n, n+1, n+2 and n+3 , where n < 10, are tabulated below. What is the value of n? 


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 20

Consider the following compounds in the liquid form : 
O2, HF, H2O, NH3, H2O2, CCl4, CHCl3, C6H6, C6H5Cl.
When a charged comb is brought near their flowing stream, how many of them show deflection as per the following figure? 


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 21

In the chemical reaction between stoichiometric quantities of KMnO4 and KI in weakly basic solution, what is the number of moles of I2 released for 4 moles of KMnO4 consumed?


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 22

An acidified solution of potassium chromate was layered with an equal volume of amyl alcohol. When it was shaken after the addition of 1 mL of 3% H2O2, a blue alcohol layer was obtained. The blue color is due to the formation of a chromium (VI) compound 'X'. What is the number of oxygen atoms bonded to chromium through only single bonds in a molecule of X?


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 23

The structure of a peptide is given below  

If the absolute values of the net charge of the peptide at pH = 2, pH = 6, and pH = 11 are |z1| , |z2| and |z3|, respectively, then what is |z1| + |z2| + |z3|?  


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 24

An organic compound (C8H10O2) rotates plane-polarized light. It produce pink color with neutral FeCl3 solution. What is the total number of all the possible isoemrs for this compound? 


*Multiple options can be correct
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 25

In an experiment, m grams of a compound X (gas/liquid/solid) taken in a container is loaded in a balance as shown in figure I below. In the presence of a magnetic field, the pan with X is either deflected upwards (figure II), or deflected downwards (figure III), depending on the compound X. Identify the correct statement(s)



*Multiple options can be correct
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 26

Which of the following plots is(are) correct for the given reaction?  
([P]0 is the initial concentration of P) 

*Multiple options can be correct
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 27

Which among the following statement(s) is(are) true for the extraction of aluminium from bauxite?

*Multiple options can be correct
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 28

Choose the correct statement(s) among the following. 

*Multiple options can be correct
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 29

Consider the following four compounds I, II, III, and IV.


Choose the correct statement(s).

*Multiple options can be correct
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 30

Consider the following transformations of a compound P.  

Choose the correct option(s).  

*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 31

A solution of 0.1 M weak base (B) is titrated with 0.1 M of a strong acid (HA). The variation of pH of the solution with the volume of HA added is shown in the figure below. What is the pKb of the base? The neutralization reaction is given by B+HA → BH++A.


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 32

Liquids A and B form ideal solution for all compositions of A and B at 25°C. Two such solutions with 0.25 and 0.50 mole fractions of A have the total vapor pressures of 0.3 and 0.4 bar, respectively. What is the vapor pressure of pure liquid B in bar?


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 33

The figure below is the plot of potential energy versus internuclear distance (d) of H2 molecule in the electronic ground state. What is the value of the net potential energy E0 (as indicated in the figure) in kJ mol−1, for d = d0 at which the electron-electron repulsion and the nucleus-nucleus repulsion energies are absent? As reference, the potential energy of H atom is taken as zero when its electron and the nucleus are infinitely far apart. 
Use Avogadro constant as 6.023 × 1023 mol−1


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 34

Consider the reaction sequence from P to Q shown below. The overall yield of the major product Q from P is 75%. What is the amount in grams of Q obtained from 9.3 mL of P? (Use density of P = 1.00 g mL–1, Molar mass of C = 12.0, H = 1.0, O = 16.0 and N = 14.0 g mol–1


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 35

Tin is obtained from cassiterite by reduction with coke. Use the data given below to determine the minimum temperature (in K) at which the reduction of cassiterite by coke would take place. 
At 298 K : ∆fH°(SnO2(s)) = –581.0 kJ mol–1, ∆fHº(CO2(g)) = –394.0 kJ mol–1 
S°(SnO2(s)) = 56.0 J K–1 mol–1, S°(Sn(s)) = 52.0 J K–1 mol–1
Sº(C (s)) = 6.0 J K–1 mol–1 , Sº(CO2(g)) = 210.0 J K–1 mol–1
Assume that the enthalpies and the entropies are temperature independent.


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 36

An acidified solution of 0.05 M Zn2+ is saturated with 0.1 M H2S. What is the minimum molar concentration (M) of H+ required to prevent the precipitation of ZnS? 
Use Ksp (ZnS) = 1.25 × 10–22 and  
Overall dissociation constant of H2S, KNET = K1K2 = 1 × 10–21


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 37

For a complex number z, let Re(z) denote the real part of z. Let S be the set of all complex numbers z satisfying z4-|z|4 = 4iz2, where i = √-1. Then the minimum possible value of |z1 - z2|2, where z1, z2 ∈ S with Re (z1) > 0 and Re(z2) < 0, is ____


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 38

The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of completely destroying the target is NOT less than 0.95, is _____


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 39

Let O be the centre of the circle x2 + y2 = r2, where r > √5/2. Suppose PQ chord of this circle and the equation of the line passing through P and Q is 2x + 4y = 5. If the centre of the circumcircle of the triangle OPQ lies on the line x + 2y = 4, then the value of r is _____


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 40

The trace of a square matrix is defined to be the sum of its diagonal entries. If A is a 2 × 2 matrix such that the trace of A is 3 and the trace of A3 is −18, then the value of the determinant of A is ____


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 41

Let the functions: (−1, 1)→ and g : (-1, 1) → (-1, 1) be defined by
ƒ(x) = |2x-1|+|2x+1|and g(x) = x[x],
where [x] denotes the greatest integer less than or equal to x. Let  be the composite function defiend by  Suppose c is the number of points in the interval (-1, 1) at which fºg is NOT continuous, and suppose d is the number of points in the interval (-1, 1) at which fºg is NOT differentiable. Then the value of c + d is ____


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 42

The value of the limit

is_______


*Multiple options can be correct
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 43

Let b be a nonzero real number. Suppose  is a differentiable function such that (0) = 1. If the derivative f' of f satisfies the equation f'x =  
for all  then which of the following statement is/are True?

*Multiple options can be correct
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 44

Let a and b be positive real numbers such that a > 1 and b < a. Let P be a point in the first quadrant that lies on the hyperbola  Suppose the tangent to the hyperbola at P passes through the point (1,0), and suppose the normal to the hyperbola at P cuts off equal intercepts on the coordinate axes. Let Δ denote the area of the triangle formed by the tangent at P, the normal at P and the x-axis. If e denotes the eccentricity of the hyperbola, then which of the following statements is/are TRUE? 

*Multiple options can be correct
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 45

Let  be functions satisfying f(x+y) = f(x)+f(y)+f(x)f(y) and f(x)=xg(x) for all  If  then which of the following statement is/are TRUE?

*Multiple options can be correct
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 46

Let α, β, γ, δ be real numbers such that α222≠0 and α+γ=1. Suppose the point (3,2,-1) is the mirror image of the point (1,0,-1) with respect to the plane αx+βy+γz=δ. Then which of the following statements is/are TRUE?

*Multiple options can be correct
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 47

Let a and b be positive real numbers. Suppose  are adjacent sides of a parallelogram PQRS. Let  be the projection vectors of  along  respectively. If  and if the area of the parallelogram PQRS is 8, then which of the following statements is/are TRUE?

*Multiple options can be correct
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 48

For non-negative integers s and r, let 

For positive integers m and n, let 

where for any nonnegative integer p,

Then which of the following statements is/are TRUE?

*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 49

An engineer is required to visit a factory for exactly four days during the first 15 days of every month and it is mandatory that no two visits take place on consecutive days. Then the number of all  possible ways in which such visits to the factory can be made by the engineer during 1-15 June 2021 is ___


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 50

In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two persons. Then the  number of all possible ways in which this can be done is ____


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 51

Two fair dice, each with faces numbered 1,2,3,4,5 and 6, are rolled together and the sum of the  numbers on the faces is observed. This process is repeated till the sum is either a prime number or a perfect square. Suppose the sum turns out to be a perfect square before it turns out to be a prime number. If p is the probability that this perfect square is an odd number, then the value of 14p is ____


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 52

Let the function  be defined by 
Then the value of  is_____


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 53

Let  be a differentiable function such that its derivative f' is continuous and f(π) = -6. If  is defiend by , and if
 
then the value of f(0) is ______


*Answer can only contain numeric values
JEE Main 2020 Question Paper with Solution (27th September - Evening) - Question 54

Let the function:  be defined by
(θ) = (sinθ + cosθ)2 + (sinθ - cosθ)4
Suppose the function f has a local minimum at θ precisely when θ ∈ {λ1π,....,λrπ},
where 0 < λ1 < ... < λr < 1. Then the value of λ1 + ... + λr is ____


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