JEE Main 25 February 2021 Shift 2 Question Paper

Question 1

A plane passes through the points A(1, 2, 3), B(2, 3, 1) and C(2, 4, 2). If O is the origin and P is (2, –1, 1), then the projection of OP  on this plane is of length:

Accepted Answer

(C) 2 11

Answer

(A) 2 5

Answer

(B) 2 3

Answer

(D) 2 7

Question 2

The contrapositive of the statement “If you will work, you will earn money” is:

Accepted Answer

(A) If you will not earn money, you will not work

Answer

(B) You will earn money, if you will not work

Answer

(C) If you will earn money, you will work

Answer

(D) To earn money, you need to work

Question 3

If α, β∈ R are such that 1 – 2i (here i$^{2}$ = –1) is a root of z$^{2}$ + αz + β = 0, then (α – β) is equal to:

Accepted Answer

(D) –7

Answer

(A) 7

Answer

(B) –3

Answer

(C) 3

Question 4

If In= ∫cot$^{n}$ x dx , then: π/4

Accepted Answer

(B) I$_{2}$1+I$_{4}$, I$_{3}$1+I$_{5}$ , I$_{4}$1+I$_{6}$  are in A.P.

Answer

(A) I$_{2}$1+I$_{4}$, I$_{3}$1+I$_{5}$ , I$_{4}$1+I$_{6}$  are in G.P.

Answer

(C) I2 + I4, I3 + I5, I4 + I6 are in A.P.

Answer

(D) I2 + I4, (I3 + I5)$^{2}$, I4 + I6 are in G.P.

Question 5

If for the matrix, A = [1α–βα], AA$^{T}$ = I2, then the value of α$^{4}$ + β$^{4}$ is:

Accepted Answer

(A) 1

Answer

(B) 3

Answer

(C) 2

Answer

(D) 4

Question 6

Let x denote the total number of one-one functions from a set A with 3 elements to a set B with 5 elements and y denote the total number of one-one functions from the set A to the set A × B. Then:

Accepted Answer

(B) 2y = 91x

Answer

(A) y = 273x

Answer

(C) y = 91x

Answer

(D) 2y = 273x

Question 7

If the curve x$^{2}$ + 2y$^{2}$ = 2 intersects the line x + y = 1 at two points P and Q, then the angle subtended by the line segment PQ at the origin is:

Accepted Answer

(A) 2π+tan$^{–1}$ (14 )

Answer

(B) 2π– tan$^{–1}$ (14 )

Answer

(C) 2π+tan$^{–1}$ (13 )

Answer

(D) 2π– tan$^{–1}$ (13 )

Question 8

The integral ∫e$_{4log}$e$_{e}$ $^{3log}_{x}$+$^{e}$ 5e$^{2x}_{3log}$+5e$_{e}$ $_{x}^{2log}$–7e$^{e}$ $^{2x}_{2log}_{e}$ $_{x}$dx, x > 0, is equal to: (where c is a constant of integration)

Accepted Answer

(C) 4loge|x$^{2}$ + 5x – 7| + c

Answer

(A) loge|x$^{2}$ + 5x – 7| + c

Answer

(B) 14 loge|x$^{2}$ + 5x – 7| + c

Answer

(D) logex$^{2}$+5x –7  + c

Question 9

A hyperbola passes through the foci of the ellipse x$^{2}$+y$^{2}$=1 and its transverse and conjugate 2516 axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities is one, then the equation of the hyperbola is:

Accepted Answer

(B) x$^{2}$–y$^{2}$=1 916

Answer

(A) x$^{2}$–y$^{2}$=1 94

Answer

(C) x$^{2}$ – y$^{2}$ = 9

Answer

(D) x$^{2}$–y$^{2}$=1 925

Question 10

In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are non-smokers and vegetarian. Their chances of getting a particular chest disorder are 35%, 20% and 10% respectively. A person is chosen from the group at random and is found to be suffering from the chest disorder. The probability that the selected person is a smoker and non-vegetarian is:

Accepted Answer

(D) 2845

Answer

(A) 457

Answer

(B) 458

Answer

(C) 1445

Question 11

The following system of linear equations 3x + 3y + 2z = 9 3x + 2y + 2z = 9 x – y + 4z = 8

Accepted Answer

(B) has a unique solution

Answer

(A) does not have any solution

Answer

(C) has a solution (α, β, γ) satisfying α + β$^{2}$ + γ$^{3}$ = 12

Answer

(D) has infinitely many solutions

Question 12

The minimum value of f(x) = a$^{a}^{x}$+a$^{1–a}^{x}$, where a, x ∈ R and a > 0, is equal to:

Accepted Answer

(D) 2 a

Answer

(A) a + 1a

Answer

(B) a + 1

Answer

(C) 2a

Question 13

A function f(x) is given by f(x) = 5$_{x}$5+$^{x}$5, then the sum of the series f (201 ) + f (202 ) + f (203 ) + ...... + f (3920 ) is equal to:

Accepted Answer

(C) 392

Answer

(A) 192

Answer

(B) 492

Answer

(D) 292

Question 14

Let α and β be the roots of x$^{2}$ – 6x – 2 = 0. If an = α$^{n}$ – β$^{n}$ for n ≥ 1, then the value of a$^{10}$– 2a$^{8}$ 3a$_{9}$ is:

Accepted Answer

(C) 2

Answer

(A) 4

Answer

(B) 1

Answer

(D) 3

Question 15

Let A be a 3 × 3 matrix with det(A) = 4. Let Ri denote the i$^{th}$ row of A. If a matrix B is obtained by performing the operation R2→ 2R2 + 5R3 on 2A, then det(B) is equal to:

Accepted Answer

(A) 64

Answer

(B) 16

Answer

(C) 80

Answer

(D) 128

Question 16

The shortest distance between the line x – y = 1 and the curve x$^{2}$ = 2y is:

Accepted Answer

(C) 1 2 2

Answer

(A) 12

Answer

(B) 0

Answer

(D) 1 2

Question 17

Let A be a set of all 4-digit natural numbers whose exactly one digit is 7. Then the probability that a randomly chosen element of A leaves remainder 2 when divided by 5 is:

Accepted Answer

(C) 29797

Answer

(A) 15

Answer

(B) 29

Answer

(D) 122297

Question 18

cosec [2cot$^{–1}$(5)+cos$^{–1}$ (54)] is equal to:

Accepted Answer

(B) 5665

Answer

(A) 5675

Answer

(C) 5633

Answer

(D) 3365

Question 19

If 0 < x, y <π and cosx + cosy – cos(x + y) = 32 , then sinx + cosy is equal to:

Accepted Answer

(A) 1+3 2

Answer

(B) 1–3 2

Answer

(C) 23

Answer

(D) 12

Question 20

If $_{x}$lim$_{→}_{0}$axax− (e(e$_{4x}^{4x}$−−11)) exists and is equal to b, then the value of a – 2b is ______.

Accepted Answer

5

Question 21

A line is a common tangent to the circle (x – 3)$^{2}$+y$^{2}$=9and the parabola y$^{2}$ = 4x. If the two points of contact (a, b) and (c, d) are distinct and lie in the first quadrant, then 2(a+c) is equal to ______.

Accepted Answer

9

Question 22

The value of ∫3x$^{2}$−3x−6  dx is ______. −2

Accepted Answer

19

Question 23

If the remainder when x is divided by 4 is 3, then the remainder when (2020+x)$^{2022}$is divided by 8 is ______.

Accepted Answer

1

Question 24

A line ‘λ’ passing through origin is perpendicular to the lines $_{1}$ :r=(3+t )ˆi+−+(12t )ˆj+(4+2t)kˆ $_{2}$ :r=(3+2s )ˆi+(3+2s )ˆj+(2+s )kˆ If the co-ordinates of the point in the first octant on ‘λ2’  at the distance of 17  from the point of intersection of ‘λ’ and ‘λ1’  are (a, b, c), then 18(a+b+c) is equal to ______.

Accepted Answer

44

Question 25

A function f is defined on [–3,3] as f ()x={min {| x |,2−x$^{2}$}, −2≤x≤2 [| x |],2<| x |≤3 where [x] denotes the greatest integer ≤ x. The number of points, where f is not differentiable in (–3,3) is ______.

Accepted Answer

5

Question 26

If the curves x = y$^{4}$ and xy = k cut at right angles, then (4k)$^{6}$ is equal to ______.

Accepted Answer

4

Question 27

The total number of two digit numbers ‘n’, such that 3$^{n}$+7$^{n}$ is a multiple of 10, is ______.

Accepted Answer

45

Question 28

Let a=ˆi+α+ˆj3kˆ andb=3iˆ−α+ˆjkˆ . If the area of the parallelogram whose adjacent sides are represented by the vectors a  and b  is 8 3  square units, then a·b  is equal to ______.

Accepted Answer

2

Question 29

Match List I with List II. List I    List II (a) Rectifier   (i) Used either for stepping up or stepping down the a.c. Voltage (b) Stabilizer   (ii) Used to convert a.c. voltage into d.c. voltage (c) Transformer   (iii) Used to remove any ripple in the rectified output voltage (d)  Filter    (iv) Used for constant output voltage even when the input voltage or load current change Choose the correct answer form the options given below:

Accepted Answer

(B) (a)-(ii), (b)- (iv), (c)-(i), (d)-(iii)

Answer

(A) (a)-(ii), (b)- (i), (c)-(iv), (d)-(iii)

Answer

(C) (a)-(ii), (b)- (i), (c)-(iii), (d)-(iv)

Answer

(D) (a)-(iii), (b)- (iv), (c)-(i), (d)-(ii)

Question 30

Y = A sin(ωt + φ0) is the time – displacement equation of a SHM, At t = 0 the displacement of A the particle is Y =  and it is moving along negative x-direction. Then the initial phase angle φ0 2 will be.

Accepted Answer

(D) $\dfrac{5\pi}{6}$

Answer

(A) $\dfrac{\pi}{6}$

Answer

(B) $\dfrac{\pi}{3}$

Answer

(C) $\dfrac{2\pi}{3}$

Question 31

Two identical spring of spring constant '2K' are attached to a block of mass m  and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. Then time period of oscillations of this system is: 2km2k mmmm

Accepted Answer

(A) $\pi\sqrt{\dfrac{m}{k}}$

Answer

(B) $\pi\sqrt{\dfrac{m}{2k}}$

Answer

(C) $2\pi\sqrt{\dfrac{m}{k}}$

Answer

(D) $2\pi\sqrt{\dfrac{m}{2k}}$

Question 32

The wavelength of the photon emitted by a hydrogen atom when an electron makes a transition from n = 2 to n = 1 state is:

Accepted Answer

(D) 121.8 nm

Answer

(A) 194.8 nm

Answer

(B) 490.7 nm

Answer

(C) 913.3 nm

Question 33

In a ferromagnetic material, below the curie temperature, a domain is defined as:

Accepted Answer

(C) a macroscopic region with saturation magnetization.

Answer

(A) a macroscopic region with consecutive magnetic diploes oriented in opposite direction.

Answer

(B) a macroscopic region with zero magnetization.

Answer

(D) a macroscopic region with randomly oriented magnetic dipoles.

Question 34

The point A moves with a uniform speed along the circumference of a circle of radius 0.36m and cover 30$^{o}$ in 0.1s. The perpendicular projection 'P' form 'A' on the diameter MN represents the simple harmonic motion of 'P'. The restoration force per unit mass when P touches M will be: A 0.1s 0.36m30$^{o}$ MN OP

Accepted Answer

(C) 9.87 N

Answer

(A) 100 N

Answer

(B) 50 N

Answer

(D) 0.49 N

Question 35

The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength 491 nm is 0.710 V. When the incident wavelength is changed to a new value, the stopping potential is 1.43V. The new wavelength is:

Accepted Answer

(B) 382 nm

Answer

(A) 400 NM

Answer

(C) 309 nm

Answer

(D) 329 nm

Question 36

A charge 'q' is placed at one corner of a cube as shown in figure. The flux of electrostatic field E though the shaded area is: Z qY X qqqq

Accepted Answer

(C) $\dfrac{q}{24\varepsilon_{0}}$

Answer

(A) $\dfrac{q}{48\varepsilon_{0}}$

Answer

(B) $\dfrac{q}{8\varepsilon_{0}}$

Answer

(D) $\dfrac{q}{4\varepsilon_{0}}$

Question 37

Consider the diffraction pattern obtained from the sunlight incident on a pinhole of diameter 0.1 µm. If the diameter of the pinhole is slightly increased, it will affect the diffraction pattern such that:

Accepted Answer

(A) its size decreases, but intensity increases

Answer

(B) its size increases, but intensity decreases

Answer

(C) its size increases, and intensity increases

Answer

(D) its size decreases, and intensity decreases

Question 38

An electron of mass me and a proton of mass mp = 1836 me are moving with the same speed. The ratio of their de Broglie wavelength λ$^{electron}$ will be: λProton 1

Accepted Answer

(B) $1836$

Answer

(A) $918$

Answer

(C) $\dfrac{1}{1836}$

Answer

(D) $1$

Question 39

thermodynamic process is shown below on a P-V diagram for one mole of an ideal gas. If V2 = 2V1 then the ratio of temperature T2/T1 is: P1(P$^{1}$V$^{1}$T$^{1}$)PV$^{1/2}$=constant 2(P2V2T2) V V$_{1}$V$_{2}$

Accepted Answer

(D) $\sqrt{2}$

Answer

(A) $\dfrac{1}{\sqrt{2}}$

Answer

(B) $\dfrac{1}{2}$

Answer

(C) $2$

Question 40

A stone is dropped from the top of a building. When it crosses a point 5m below the top, another stone starts to fall from a point 25m below the top, Both stones reach the bottom of building simultaneously. The height of the building is:

Accepted Answer

(A) 45 m

Answer

(B) 35 m

Answer

(C) 25 m

Answer

(D) 50 m

Question 41

if a message signal of frequency 'ƒm' is amplitude modulated with a carrier signal of frequency 'ƒc' and radiated through an antenna, the wavelength of the corresponding signal in air is: cccc

Accepted Answer

(D) $\dfrac{c}{f_{c}}$

Answer

(A) $\dfrac{c}{f_{c}+f_{m}}$

Answer

(B) $\dfrac{c}{f_{c}-f_{m}}$

Answer

(C) $\dfrac{c}{f_{m}}$

Question 42

Given below are two statements: Statement I: In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution. Statement II: in a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule. In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

(D) Statement I is true but statement II is false.

Answer

(A) Both statement I and statement II are false.

Answer

(B) Both statement I and statement II are true.

Answer

(C) Statement I is false but statement II is true

Question 43

An electron with kinetic energy K1 enters between parallel plates of a capacitor at an angle 'α’ with the plates. It leaves the plates at angle 'β' with kinetic energy K2. Then the ratio of kinetic energies K1 : K2 will be:

Accepted Answer

(B) coscos$^{2}^{2}$αβ

Answer

(A) cossin$^{2}^{2}$βα

Answer

(C) cossinαβ

Answer

(D) coscosαβ

Question 44

An LCR circuit contains resistance of 110Ω and a supply of 220 V at 300 rad/s angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by 45$^{o}$. If on the other hand, only inductor is removed the current leads by 45$^{o}$ with the applied voltage. The rms current flowing in the circuit will be:

Accepted Answer

(B) 2A

Answer

(A) 2.5A

Answer

(C) 1A

Answer

(D) 1.5 A

Question 45

For extrinsic semiconductors: when doping level is increased;

Accepted Answer

(B) Fermi–level of p-type semiconductors will go downward and Fermi–level of n-type semiconductor will go upward.

Answer

(A) Fermi–level of p and n-type semiconductors will not be affected.

Answer

(C) Fermi–level of both p–type and n–type semiconductors will go upward for T > TF K and downward for T< TFK, where TF is Fermi temperature.

Answer

(D) Fermi–level of p-type semiconductor will go upward and Fermi–level of n–type semiconductors will go downward.

Question 46

If e is the electronic charged, c is the speed of light in free space and h is planck's constant, the 1e$^{2}$ quantity  has dimensions of : 4πε$_{0}$hc

Accepted Answer

(B) [M$^{0}$ L$^{0}$ T$^{0}$]

Answer

(A) [ LC$^{-1}$]

Answer

(C) [ M L T$^{0}$]

Answer

(D) [M L T$^{-1}$]

Question 47

The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by 4% will be___________%.

Accepted Answer

2

Question 48

Two small spheres each of mass 10 mg are suspended from a point by threads 0.5 m long. They are equally charged and repel each other to a distance of 0.20 m . Then charge on each of the sphere is a×10$^{-}$ $^{8}$C. The value of 'a' will be________. 21

Accepted Answer

20

Question 49

The peak electric field produced by the radiation coming from the 8 W bulb at a distance of 10 m is xµ$^{0}$ cV. The efficiency of the bulb is 10% and it is a point source. The value of x is ___. 10πm

Accepted Answer

2

Question 50

Two identical conducting spheres with negligible volume have 2.1nC and -0.1nC charges, respectively. They are brought into contact and then separated by a distance of 0.5 m. The electrostatic force acting between the spheres is _______× 10$^{-9}$ N. 1 [Given : 4πε$_{0}$=9×10$_{9}$ SI unit]

Accepted Answer

36

Question 51

The initial velocity υi required to project a body vertically upward from the surface of the earth to reach a height of 10R, where R is the radius of the earth, may be described in terms of x escape velocity υe such that υi = y ×υ$_{e}$. The value of x will be_______.

Accepted Answer

10

Question 52

A current of 6A enters one corner P of an equilateral triangle PQR having 3 wires of resistance 2Ω each and leaves by the corner R. The currents i1 in ampere is______. 6A 2Ω P i$_{1}$i$_{2}$ 2Ω2Ω QR 2Ω

Accepted Answer

2

Question 53

The wavelength of an X-ray beam is 10 Å. The mass of a fictitious particle having the same x energy as that of the X – ray photons is h kg. The value of x is _______. 3

Accepted Answer

10

Question 54

A reversible heat engine converts one- fourth of the heat input into work. When the temperature of the sink is reduced by 52K, its efficiency is doubled. The temperature in Kelvin of the source will be_______.

Accepted Answer

208

Question 55

Two particles having masses 4g and 16g respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is n:2. The value of n will be_____.

Accepted Answer

1

Question 56

If P×Q=Q×P, the angle between P and Q is θ(0$^{o}$ < θ < 360$^{o}$). The value of 'θ' will be____.

Accepted Answer

180

Question 57

Given below are two statements : Statement I : The identification of Ni$^{2+}$ is carried out by dimethyl glyoxime in the presence of NH4OH Statement II : The dimethyl glyoxime is a bidentate neutral ligand. In the light of the above statements, choose the correct answer from the options given below :

Accepted Answer

(D) Statement I is true but statement II is false

Answer

(A) Both statement I and statement II are true

Answer

(B) Both statement I and statement II are false

Answer

(C) Statement I is false but statement II is true

Question 58

Carbylamine test is used to detect the presence of primary amino group in an organic compound. Which of the following compound is formed when this test is performed with aniline ? CONH2NC NHCH$^{3}$CN

Accepted Answer

(B) (B)

Answer

(A) (A)

Answer

(C) (C)

Answer

(D) (D)

Question 59

The correct order of bond dissociation enthalpy of halogen is :

Accepted Answer

(C) Cl2>Br2>F2>I2

Answer

(A) F2>Cl2>Br2>I2

Answer

(B) Cl2>F2>Br2>I2

Answer

(D) I2>Br2>Cl2>F2

Question 60

Which one of the following statements is FALSE for hydrophilic sols ?

Accepted Answer

(D) Their viscosity is of the order of that of H2O

Answer

(A) These sols are reversible in nature

Answer

(B) The sols cannot be easily coagulated

Answer

(C) They do not require electrolytes for stability.

Question 61

Water does not produce CO on reacting with :

Accepted Answer

(D) CO2

Answer

(A) C3H8

Answer

(B) C

Answer

(C) CH4

Question 62

What is ‘X’ in the given reaction ? CH $^{2}$OH+ oxalic acid210$^{0}$Cx (major product) CH2OH CH 2 CH—OHCH$_{2}$OHCHO CH$^{2}$ CH$^{2}$ CHO CHO

Accepted Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Answer

(D) (D)

Question 63

If which of the following order the given complex ions are arranged correctly with respect to their decreasing spin only magnetic moment ? (i) [FeF6]$^{3-}$   (ii) [Co(NH3)6]$^{3+}$ (iii) [NiCl4]$^{2-}$  (iv) [Cu(NH3)4]$^{2+}$

Accepted Answer

(D) (i)>(iii)>(iv)>(ii)

Answer

(A) (ii)>(i)>(iii)>(iv)

Answer

(B) (iii)>(iv)>(ii)>(i)

Answer

(C) (ii)>(iii)>(i)>(iv)

Question 64

The major product of the following reaction is : NO2 H2SO4 NO2

Accepted Answer

(D) (D)

Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

JEE Main 25 February 2021 Shift 2 Question Paper with Answers

Physics — JEE Main 25 February 2021 Shift 2

Chemistry — JEE Main 25 February 2021 Shift 2

Mathematics — JEE Main 25 February 2021 Shift 2

Chapters tested in this paper

Attempt this paper under exam timing.

JEE Main 25 February 2021 Shift 2 Question Paper with Answers

Physics — JEE Main 25 February 2021 Shift 2

Chemistry — JEE Main 25 February 2021 Shift 2

Mathematics — JEE Main 25 February 2021 Shift 2

Chapters tested in this paper

Attempt this paper under exam timing.