JEE Main 2021 (Online) 25th February Evening Shift

Paper was held on
Thu, Feb 25, 2021 9:30 AM

## Chemistry

The correct sequence of reagents used in the preparation of 4-bromo-2-nitroethyl benzene from benzene is :

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What is 'X' in the given reaction?

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Water does not produce CO on reacting with :

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The solubility of Ca(OH)2 in water is :[Given : The solubility product of Ca(OH)2 in water = 5.5 $$\times$$ 10$$-$$6]

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Given below are two statements :Statement I : The pH of rain water is normally 5.6.Statement II : If the pH of rain wate

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Given below are two statements :Statement I : $$\alpha$$ and $$\beta$$ forms of sulphur can change reversibly between th

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Which among the following species has unequal bond lengths?

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In which of the following order the given complex ions are arranged correctly with respect to their decreasing spin only

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The major components of German Silver are :

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The correct order of acid character of the following compounds is :

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The major product of the following reaction is :

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The method used for the purification of Indium is :

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Correct statement about the given chemical reaction is :

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Given below are two statements :Statement I : The identification of Ni2+ is carried out by dimethyl glyoxime in the pres

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

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Carbylamine test is used to detect the presence of primary amino group in an organic compound. Which of the following co

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Which of the following is correct structure of $$\alpha$$-anomer of maltose?

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Which of the following compound is added to the sodium extract before addition of silver nitrate for testing of halogens

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The major product of the following reaction is :

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The correct order of bond dissociation enthalpy of halogens is :

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The unit cell of copper corresponds to a face centered cube of edge length 3.596 $$\mathop A\limits^o $$ with one copper

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Copper reduces NO$$_3^ - $$ into NO and NO2 depending upon the concentration of HNO3 in solution. (Assuming fixed [Cu2+]

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The spin only magnetic moment of a divalent ion in aqueous solution (atomic number 29) is _________ BM.

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If a compound AB dissociates to the extent of 75% in an aqueous solution, the molality of the solution which shows a 2.5

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Electromagnetic radiation of wavelength 663 nm is just sufficient to ionise the atom of metal A. The ionization enegy of

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Consider titration of NaOH solution versus 1.25 M oxalic acid solution. At the end point following burette readings were

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Five moles of an ideal gas at 293 K is expanded isothermally from an initial pressure of 2.1 MPa to 1.3 MPa against at c

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The number of compound/s given below which contain/s -COOH group is __________. (Integer answer)(A) Sulphanilic acid(B)

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The rate constant of a reaction increases by five times on increase in temperature from 27$$^\circ$$C to 52$$^\circ$$C.

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Among the following, number of metal/s which can be used as electrodes in the photoelectric cell is _________. (Integer

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## Mathematics

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

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The shortest distance between the line x $$-$$ y = 1 and the curve x2 = 2y is :

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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), the

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A function f(x) is given by $$f(x) = {{{5^x}} \over {{5^x} + 5}}$$, then the sum of the series $$f\left( {{1 \over {20}}

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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

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The integral $$\int {{{{e^{3{{\log }_e}2x}} + 5{e^{2{{\log }_e}2x}}} \over {{e^{4{{\log }_e}x}} + 5{e^{3{{\log }_e}x}} -

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Let A be a set of all 4-digit natural numbers whose exactly one digit is 7. Then the probability that a randomly chosen

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Let $$\alpha$$ and $$\beta$$ be the roots of x2 $$-$$ 6x $$-$$ 2 = 0. If an = $$\alpha$$n $$-$$ $$\beta$$n for n $$ \ge

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If 0 < x, y < $$\pi$$ and cosx + cosy $$-$$ cos(x + y) = $${3 \over 2}$$, then sinx + cosy is equal to :

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cosec$$\left[ {2{{\cot }^{ - 1}}(5) + {{\cos }^{ - 1}}\left( {{4 \over 5}} \right)} \right]$$ is equal to :

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Let A be a 3 $$\times$$ 3 matrix with det(A) = 4. Let Ri denote the ith row of A. If a matrix B is obtained by performin

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If $$\alpha$$, $$\beta$$ $$\in$$ R are such that 1 $$-$$ 2i (here i2 = $$-$$1) is a root of z2 + $$\alpha$$z + $$\beta$$

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

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If $${I_n} = \int\limits_{{\pi \over 4}}^{{\pi \over 2}} {{{\cot }^n}x\,dx} $$, then :

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In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are n

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If for the matrix, $$A = \left[ {\matrix{
1 & { - \alpha } \cr
\alpha & \beta \cr
} } \right]$$, $

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If the curve x2 + 2y2 = 2 intersects the line x + y = 1 at two points P and Q, then the angle subtended by the line segm

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The following system of linear equations2x + 3y + 2z = 93x + 2y + 2z = 9x $$-$$ y + 4z = 8

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A hyperbola passes through the foci of the ellipse $${{{x^2}} \over {25}} + {{{y^2}} \over {16}} = 1$$ and its transvers

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$$\mathop {\lim }\limits_{n \to \infty } \left[ {{1 \over n} + {n \over {{{(n + 1)}^2}}} + {n \over {{{(n + 2)}^2}}} + .

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A line is a common tangent to the circle (x $$-$$ 3)2 + y2 = 9 and the parabola y2 = 4x. If the two points of contact (a

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If the remainder when x is divided by 4 is 3, then the remainder when (2020 + x)2022 is divided by 8 is __________.

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The total number of two digit numbers 'n', such that 3n + 7n is a multiple of 10, is __________.

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The value of $$\int\limits_{ - 2}^2 {|3{x^2} - 3x - 6|dx} $$ is ___________.

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A line 'l' passing through origin is perpendicular to the lines$${l_1}:\overrightarrow r = (3 + t)\widehat i + ( - 1 +

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A function f is defined on [$$-$$3, 3] as$$f(x) = \left\{ {\matrix{
{\min \{ |x|,2 - {x^2}\} ,} & { - 2 \le x \le

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Let $$\overrightarrow a = \widehat i + \alpha \widehat j + 3\widehat k$$ and $$\overrightarrow b = 3\widehat i - \alph

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If the curves x = y4 and xy = k cut at right angles, then (4k)6 is equal to __________.

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If $$\mathop {\lim }\limits_{x \to 0} {{ax - ({e^{4x}} - 1)} \over {ax({e^{4x}} - 1)}}$$ exists and is equal to b, then

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If the curve, y = y(x) represented by the solution of the differential equation (2xy2 $$-$$ y)dx + xdy = 0, passes throu

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## Physics

If a message signal of frequency 'fm' is amplitude modulated with a carrier signal of frequency 'fc' and radiated throug

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An LCR circuit contains resistance of 110$$\Omega$$ and a supply of 220 V at 300 rad/s angular frequency. If only capaci

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An electron with kinetic energy K1 enters between parallel plates of a capacitor at an angle '$$\alpha$$' with the plate

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A sphere of radius 'a' and mass 'm' rolls along a horizontal plane with constant speed v0. It encounters an inclined pla

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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 w

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Consider the diffraction pattern obtained from the sunlight incident on a pinhole of diameter 0.1 $$\mu$$m. If the diame

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

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Given below are two statements :Statement I : In a diatomic molecule, the rotational energy at a given temperature obeys

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Match List I with List II.
List I
List II
(a)
Rectifier
(i)
Used either fo

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A charge 'q' is placed at one corner of a cube as shown in figure. The flux of electrostatic field $$\overrightarrow E $

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Thermodynamic process is shown below on a P-V diagram for one mole of an ideal gas. If V2 = 2V1 then the ratio of temper

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

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Y = A sin($$\omega$$t + $$\phi$$0) is the time-displacement equation of a SHM. At t = 0 the displacement of the particle

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Two identical springs of spring constant '2k' are attached to a block of mass m and to fixed support (see figure). When

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The point A moves with a uniform speed along the circumference of a circle of radius 0.36 m and covers 30$$^\circ$$ in 0

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If e is the electronic charge, c is the speed of light in free space and h is Planck's constant, the quantity $${1 \over

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For extrinsic semiconductors; when doping level is increased;

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The truth table for the following logic circuit is :

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A stone is dropped from the top of a building. When it crosses a point 5 m below the top, another stone starts to fall f

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The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength 491 nm is

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A reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is reduced by

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If $$\overrightarrow P \times \overrightarrow Q = \overrightarrow Q \times \overrightarrow P $$, the angle between $$

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

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The initial velocity vi required to project a body vertically upward from the surface of the earth to reach a height of

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The peak electric field produced by the radiation coming from the 8W bulb at a distance of 10 m is $${x \over {10}}\sqrt

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Two identical conducting spheres with negligible volume have 2.1 nC and $$-$$0.1 nC charges, respectively. They are brou

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The wavelength of an X-ray beam is 10$$\mathop A\limits^o $$. The mass of a fictitious particle having the same energy a

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Two small spheres each of mass 10 mg are suspended from a point by threads 0.5 m long. They are equally charged and repe

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Two particles having masses 4 g and 16 g respectively are moving with equal kinetic energies. The ratio of the magnitude

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A current of 6A enters one corner P of an equilateral triangle PQR having 3 wires of resistance 2$$\Omega$$ each and lea

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