JEE Main 2021 (Online) 16th March Evening Shift

Paper was held on
Tue, Mar 16, 2021 9:30 AM

## Chemistry

Match List - I with List - II :
List - I Test/Reagents/Observation(s)
List - II Species detected

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The structure of X is :

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The INCORRECT statement regarding the structure of C60 is :

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An unsaturated hydrocarbon X on ozonolysis gives A. Compound A when warmed with ammonical silver nitrate forms a bright

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The green house gas/es is (are) :(A) Carbon dioxide(B) Oxygen(C) Water vapour(D) MethaneChoose the most appropriate answ

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The exact volumes of 1 M NaOH solution required to neutralise 50 mL of 1 M H3PO3 solution and 100 mL of 2 M H3PO2 soluti

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The characteristics of elements X, Y and Z with atomic numbers, respectively, 33, 53 and 83 are :

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Which of the following is least basic?

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The correct statements about H2O2 are :(A) used in the treatment of effluents.(B) used as both oxidising and reducing ag

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Ammonolysis of Alkyl halides followed by the treatment with NaOH solution can be used to prepare primary, secondary and

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The secondary structure of protein is stabilised by:

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Which of the following polymer is used in the manufacture of wood laminates?

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Fex2 and Fey3 are known when x and y are :

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Identify the elements X and Y using the ionisation energy values given below :
Ionization energy (kJ/mol)

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In the above reaction, the reagent ''A'' is :

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The INCORRECT statements below regarding colloidal solutions is :

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Arrange the following metal complex/compounds in the increasing order of spin only magnetic moment. Presume all the thre

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Identify the reagent(s) 'A' and condition(s) for the reaction

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Statement I : Sodium hydride can be used as an oxidising agent.Statement II : The lone pair of electrons on nitrogen in

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Which of the following reduction reaction CANNOT be carried out with coke?

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[Ti(H2O)6]3+ absorbs light of wavelength 498 nm during a d $$-$$ d transition. The octahedral splitting energy for the a

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A 5.0 m mol dm$$-$$3 aqueous solution of KCl has a conductance of 0.55 mS when measured in a cell of cell constant 1.3 c

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At 25$$^\circ$$C, 50 g of iron reacts with HCl to form FeCl2. The evolved hydrogen gas expands against a constant pressu

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The number of orbitals with n = 5, m1 = +2 is ___________. (Round off to the Nearest Integer).

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A and B decompose via first order kinetics with half-lives 54.0 min and 18.0 min respectively. Starting from an equimola

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In Duma's method of estimation of nitrogen, 0.1840 g of an organic compound gave 30 mL of nitrogen collected at 287 K an

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Ga (atomic mass 70 u) crystallizes in a hexagonal close packed structure. The total number of voids in 0.581 g of Ga is

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When 35 mL of 0.15 M lead nitrate solution is mixed with 20 mL of 0.12 M chromic sulphate solution, _________ $$\times$$

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Sulphurous acid (H2SO3) has Ka1 = 1.7 $$\times$$ 10$$-$$2 and Ka2 = 6.4 $$\times$$ 10$$-$$8. The pH of 0.588 M H2SO3 is

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At 363 K, the vapour pressure of A is 21 kPa and that of B is 18 kPa. One mole of A and 2 moles of B are mixed. Assuming

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## Mathematics

If y = y(x) is the solution of the differential equation $${{dy} \over {dx}}$$ + (tan x) y = sin x, $$0 \le x \le {\pi

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Let f be a real valued function, defined on R $$-$$ {$$-$$1, 1} and given by f(x) = 3 loge $$\left| {{{x - 1} \over {x +

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Let $$\overrightarrow a $$ = $$\widehat i$$ + 2$$\widehat j$$ $$-$$ 3$$\widehat k$$ and $$\overrightarrow b = 2\widehat

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If the foot of the perpendicular from point (4, 3, 8) on the line $${L_1}:{{x - a} \over l} = {{y - 2} \over 3} = {{z -

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If the points of intersections of the ellipse $${{{x^2}} \over {16}} + {{{y^2}} \over {{b^2}}} = 1$$ and the circle x2 +

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Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA respectively. Let

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Let f : S $$ \to $$ S where S = (0, $$\infty $$) be a twice differentiable function such that f(x + 1) = xf(x). If g : S

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Consider the integral $$I = \int_0^{10} {{{[x]{e^{[x]}}} \over {{e^{x - 1}}}}dx} $$, where [x] denotes the greatest inte

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Let C1 be the curve obtained by the solution of differential equation $$2xy{{dy} \over {dx}} = {y^2} - {x^2},x > 0$$.

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Let P(x) = x2 + bx + c be a quadratic polynomial with real coefficients such that $$\int_0^1 {P(x)dx} $$ = 1 and P(x) le

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Let A = {2, 3, 4, 5, ....., 30} and '$$ \simeq $$' be an equivalence relation on A $$\times$$ A, defined by (a, b) $$ \s

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If (x, y, z) be an arbitrary point lying on a plane P which passes through the points (42, 0, 0), (0, 42, 0) and (0, 0,

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The least value of |z| where z is complex number which satisfies the inequality $$\exp \left( {{{(|z| + 3)(|z| - 1)} \ov

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Let $$\alpha$$ $$\in$$ R be such that the function $$f(x) = \left\{ {\matrix{
{{{{{\cos }^{ - 1}}(1 - {{\{ x\} }^2}){

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Let C be the locus of the mirror image of a point on the parabola y2 = 4x with respect to the line y = x. Then the equat

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Given that the inverse trigonometric functions take principal values only. Then, the number of real values of x which sa

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Let the lengths of intercepts on x-axis and y-axis made by the circle x2 + y2 + ax + 2ay + c = 0, (a < 0) be 2$${\sqr

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Let A($$-$$1, 1), B(3, 4) and C(2, 0) be given three points. A line y = mx, m > 0, intersects lines AC and BC at poin

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Let A denote the event that a 6-digit integer formed by 0, 1, 2, 3, 4, 5, 6 without repetitions, be divisible by 3. Then

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The maximum value of $$f(x) = \left| {\matrix{
{{{\sin }^2}x} & {1 + {{\cos }^2}x} & {\cos 2x} \cr
{1 +

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Sn(x) = loga1/2x + loga1/3x + loga1/6x + loga1/11x + loga1/18x + loga1/27x + ...... up to n-terms, where a > 1. If S2

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If the distance of the point (1, $$-$$2, 3) from the plane x + 2y $$-$$ 3z + 10 = 0 measured parallel to the line, $${{x

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Let $${1 \over {16}}$$, a and b be in G.P. and $${1 \over a}$$, $${1 \over b}$$, 6 be in A.P., where a, b > 0. Then 7

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Let $$\overrightarrow c $$ be a vector perpendicular to the vectors, $$\overrightarrow a $$ = $$\widehat i$$ + $$\wideha

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For real numbers $$\alpha$$, $$\beta$$, $$\gamma$$ and $$\delta $$, if $$\int {{{({x^2} - 1) + {{\tan }^{ - 1}}\left( {{

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In $$\Delta$$ABC, the lengths of sides AC and AB are 12 cm and 5 cm, respectively. If the area of $$\Delta$$ABC is 30 cm

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Let f : R $$ \to $$ R and g : R $$ \to $$ R be defined as $$f(x) = \left\{ {\matrix{
{x + a,} & {x < 0} \cr

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Consider the statistics of two sets of observations as follows :
Size
Mean
Variance
Obs

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Let n be a positive integer. Let $$A = \sum\limits_{k = 0}^n {{{( - 1)}^k}{}^n{C_k}\left[ {{{\left( {{1 \over 2}} \right

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Let $$A = \left[ {\matrix{
{{a_1}} \cr
{{a_2}} \cr
} } \right]$$ and $$B = \left[ {\matrix{
{{b_1}} \cr

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## Physics

What will be the nature of flow of water from a circular tap, when its flow rate increased from 0.18 L/min to 0.48 L/min

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The refractive index of a converging lens is 1.4. What will be the focal length of this lens if it is placed in a medium

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The following logic gate is equivalent to :

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Statement I : A cyclist is moving on an unbanked road with a speed of 7 kmh$$-$$1 and takes a sharp circular turn along

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Two identical antennas mounted on identical towers are separated from each other by a distance of 45 km. What should nea

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A large block of wood of mass M = 5.99 kg is hanging from two long massless cords. A bullet of mass m = 10 g is fired in

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Calculate the time interval between 33% decay and 67% decay if half-life of a substance is 20 minutes.

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A mosquito is moving with a velocity $$\overrightarrow v = 0.5{t^2}\widehat i + 3t\widehat j + 9\widehat k$$ m/s and ac

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Red light differs from blue light as they have :

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The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same pot

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The half-life of Au198 is 2.7 days. The activity of 1.50 mg of Au198 if its atomic weight is 198 g mol$$-$$1 is, (Na = 6

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Calculate the value of mean free path ($$\lambda$$) for oxygen molecules at temperature 27$$^\circ$$C and pressure 1.01

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A charge Q is moving $$\overrightarrow {dl} $$ distance in the magnetic field $$\overrightarrow {B} $$. Find the value o

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In order to determine the Young's Modulus of a wire of radius 0.2 cm (measured using a scale of least count = 0.001 cm)

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A resistor develops 500 J of thermal energy in 20 s when a current of 1.5A is passed through it. If the current is incre

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Find out the surface charge density at the intersection of point x = 3 m plane and x-axis, in the region of uniform line

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The magnetic field in a region is given by $$\overrightarrow B = {B_o}\left( {{x \over a}} \right)\widehat k$$. A squar

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A bimetallic strip consists of metals A and B. It is mounted rigidly as shown. The metal A has higher coefficient of exp

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Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass = 500g, Decay

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For the given circuit, comment on the type of transformer used.

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A solid disc of radius 'a' and mass 'm' rolls down without slipping on an inclined plane making an angle $$\theta$$ with

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The energy dissipated by a resistor is 10 mJ in 1 s when an electric current of 2 mA flows through it. The resistance is

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For an ideal heat engine, the temperature of the source is 127$$^\circ$$C. In order to have 60% efficiency the temperatu

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In a parallel plate capacitor set up, the plate area of capacitor is 2 m2 and the plates are separated by 1 m. If the sp

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If one wants to remove all the mass of the earth to infinity in order to break it up completely.The amount of energy tha

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A body of mass 2 kg moves under a force of $$\left( {2\widehat i + 3\widehat j + 5\widehat k} \right)$$N. It starts from

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A closed organ pipe of length L and an open organ pipe contain gases of densities $$\rho$$1 and $$\rho$$2 respectively.

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A swimmer can swim with velocity of 12 km/h in still water. Water flowing in a river has velocity 6 km/h. The direction

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A deviation of 2$$^\circ$$ is produced in the yellow ray when prism of crown and flint glass are achromatically combined

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A force $$\overrightarrow F $$ = $${4\widehat i + 3\widehat j + 4\widehat k}$$ is applied on an intersection point of x

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