JEE Main 2021 (Online) 31st August Evening Shift

Paper was held on
Tue, Aug 31, 2021 9:30 AM

## Chemistry

Arrange the following conformational isomers of n-butane in order of their increasing potential energy :

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The Eu2+ ion is a strong reducing agent in spite of its ground state electronic configuration (outermost) : [Atomic numb

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The structures A and B formed in the following reaction are : [Ph = $$-$$C6H5]

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In which one of the following sets all species show disproportionation reaction?

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Match List - I with List - II
List - I(Parmeter)
List - II(Unit)
(a)
Cell constant

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The major products A and B formed in the following reaction sequence are :

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Which of the following is not an example of fibrous protein?

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The deposition of X and Y on ground surfaces is referred as wet and dry depositions, respectively. X and Y are :

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For the reaction given below :-The compound which is not formed as a product in the reaction is a :

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Spin only magnetic moment in BM of [Fe(CO)4(C2O4)]+ is :

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Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A)

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The incorrect expression among the following is :

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Which one of the following statements is incorrect?

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Which among the following is not a polyester?

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Which one of the following correctly represents the order of stability of oxides, X2O; (X = halogen)?

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Match List - I with List - II :
List - I(Metal Ion)
List - II(Group of Qualitative analysis)

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The major product of the following reaction is :

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For the following sequence of reactions, the correct
products are :

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Identify correct A, B and C in the reaction sequence given below :

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The number of S = O bonds present in sulphurous acid, peroxodisulphuric acid and pyrosulphuric acid, respectively are :

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CH4 is absorbed on 1g charcoal at 0$$^\circ$$C following the Freundlich adsorpiton isotherm 10.0 mL of CH4 is adsorbed a

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1.22 g of an organic acid is separately dissolved in 100 g of benzene (Kb = 2.6 K kg mol$$-$$1) and 100 g of acetone (Kb

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The value of magnetic quantum number of the outermost electron of Zn+ ion is ______________.

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The empirical formula for a compound with a cubic close packed arrangement of anions and with cations occupying all the

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In the electrolytic refining of blister copper, the total number of main impurities, from the following, removed as anod

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The pH of a solution obtained by mixing 50 mL of 1 M HCl and 30 mL of 1 M NaOH is x $$\times$$ 10$$-$$4. The value of x

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For the reaction A $$\to$$ B, the rate constant k(in s$$-$$1) is given by$${\log _{10}}k = 20.35 - {{(2.47 \times {{10}^

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Sodium oxide reacts with water to produce sodium hydroxide. 20.0 g of sodium oxide is dissolved in 500 mL of water. Negl

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According to molecular orbital theory, the number of unpaired electron(s) in $$O_2^{2 - }$$ is :

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The transformation occurring in Duma's method is given below :$${C_2}{H_7}N + \left( {2x + {y \over 2}} \right)CuO \to x

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## Mathematics

If $$\alpha$$ + $$\beta$$ + $$\gamma$$ = 2$$\pi$$, then the system of equations x + (cos $$\gamma$$)y + (cos $$\beta$$)z

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Let $$\overrightarrow a ,\overrightarrow b ,\overrightarrow c $$ three vectors mutually perpendicular to each other and

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The domain of the function$$f(x) = {\sin ^{ - 1}}\left( {{{3{x^2} + x - 1} \over {{{(x - 1)}^2}}}} \right) + {\cos ^{ -

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Let S = {1, 2, 3, 4, 5, 6}. Then the probability that a randomly chosen onto function g from S to S satisfies g(3) = 2g(

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Let f : N $$\to$$ N be a function such that f(m + n) = f(m) + f(n) for every m, n$$\in$$N. If f(6) = 18, then f(2) . f(3

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The distance of the point ($$-$$1, 2, $$-$$2) from the line of intersection of the planes 2x + 3y + 2z = 0 and x $$-$$ 2

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Negation of the statement (p $$\vee$$ r) $$\Rightarrow$$ (q $$\vee$$ r) is :

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If $$\alpha = \mathop {\lim }\limits_{x \to {\pi \over 4}} {{{{\tan }^3}x - \tan x} \over {\cos \left( {x + {\pi \ove

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The locus of mid-points of the line segments joining ($$-$$3, $$-$$5) and the points on the ellipse $${{{x^2}} \over 4}

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If $${{dy} \over {dx}} = {{{2^x}y + {2^y}{{.2}^x}} \over {{2^x} + {2^{x + y}}{{\log }_e}2}}$$, y(0) = 0, then for y = 1,

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An angle of intersection of the curves, $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ and x2 + y2 = ab, a &g

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If $$y{{dy} \over {dx}} = x\left[ {{{{y^2}} \over {{x^2}}} + {{\phi \left( {{{{y^2}} \over {{x^2}}}} \right)} \over {\ph

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The sum of the roots of the equation $$x + 1 - 2{\log _2}(3 + {2^x}) + 2{\log _4}(10 - {2^{ - x}}) = 0$$, is :

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If z is a complex number such that $${{z - i} \over {z - 1}}$$ is purely imaginary, then the minimum value of | z $$-$$

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Let a1, a2, a3, ..... be an A.P. If $${{{a_1} + {a_2} + .... + {a_{10}}} \over {{a_1} + {a_2} + .... + {a_p}}} = {{100}

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Let A be the set of all points ($$\alpha$$, $$\beta$$) such that the area of triangle formed by the points (5, 6), (3, 2

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The number of solutions of the equation $${32^{{{\tan }^2}x}} + {32^{{{\sec }^2}x}} = 81,\,0 \le x \le {\pi \over 4}$$

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Let f be any continuous function on [0, 2] and twice differentiable on (0, 2). If f(0) = 0, f(1) = 1 and f(2) = 2, then

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If [x] is the greatest integer $$\le$$ x, then $${\pi ^2}\int\limits_0^2 {\left( {\sin {{\pi x} \over 2}} \right)(x - [x

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The mean and variance of 7 observations are 8 and 16 respectively. If two observations are 6 and 8, then the variance of

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If the coefficient of a7b8 in the expansion of (a + 2b + 4ab)10 is K.216, then K is equal to _____________.

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Suppose, the line $${{x - 2} \over \alpha } = {{y - 2} \over { - 5}} = {{z + 2} \over 2}$$ lies on the plane $$x + 3y -

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The number of 4-digit numbers which are neither multiple of 7 nor multiple of 3 is ____________.

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If $$\int {{{\sin x} \over {{{\sin }^3}x + {{\cos }^3}x}}dx = } $$
$$\alpha {\log _e}|1 + \tan x| + \beta {\log _e}|1 -

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A tangent line L is drawn at the point (2, $$-$$4) on the parabola y2 = 8x. If the line L is also tangent to the circle

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If $$S = {7 \over 5} + {9 \over {{5^2}}} + {{13} \over {{5^3}}} + {{19} \over {{5^4}}} + ....$$, then 160 S is equal to

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The number of elements in the set $$\left\{ {A = \left( {\matrix{
a & b \cr
0 & d \cr
} } \right):a,

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If the line y = mx bisects the area enclosed by the lines x = 0, y = 0, x = $${3 \over 2}$$ and the curve y = 1 + 4x $$-

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Let B be the centre of the circle x2 + y2 $$-$$ 2x + 4y + 1 = 0. Let the tangents at two points P and Q on the circle in

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Let f(x) be a cubic polynomial with f(1) = $$-$$10, f($$-$$1) = 6, and has a local minima at x = 1, and f'(x) has a loca

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## Physics

Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 $$\times$$ 103 kg. The inner

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A current of 1.5 A is flowing through a triangle, of side 9 cm each. The magnetic field at the centroid of the triangle

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A system consists of two identical spheres each of mass 1.5 kg and radius 50 cm at the end of light rod. The distance be

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Statement I :Two forces $$\left( {\overrightarrow P + \overrightarrow Q } \right)$$ and $$\left( {\overrightarrow P -

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A free electron of 2.6 eV energy collides with a H+ ion. This results in the formation of a hydrogen atom in the first e

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Two thin metallic spherical shells of radii r1 and r2 (r1 < r2) are placed with their centres coinciding. A material

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If VA and VB are the input voltages (either 5V or 0V) and V0 is the output voltage then the two gates represented in the

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Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the

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A bob of mass 'm' suspended by a thread of length l undergoes simple harmonic oscillations with time period T. If the bo

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Statement : 1If three forces $${\overrightarrow F _1},{\overrightarrow F _2}$$ and $${\overrightarrow F _3}$$ are repres

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If velocity [V], time [T] and force [F] are chosen as the base quantities, the dimensions of the mass will be :

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The magnetic field vector of an electromagnetic wave is given by $$B = {B_0}{{\widehat i + \widehat j} \over {\sqrt 2 }}

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The equivalent resistance of the given circuit between the terminals A and B is :

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Choose the incorrect statement :(1) The electric lines of force entering into a Gaussian surface provide negative flux.(

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A mixture of hydrogen and oxygen has volume 500 cm3, temperature 300 K, pressure 400 kPa and mass 0.76 g. The ratio of m

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A block moving horizontally on a smooth surface with a speed of 40 m/s splits into two parts with masses in the ratio of

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A coil is placed in a magnetic field $$\overrightarrow B $$ as shown below :A current is induced in the coil because $$\

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For a body executing S.H.M. :(1) Potential energy is always equal to its K.E.(2) Average potential and kinetic energy ov

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Statement - I :To get a steady dc output from the pulsating voltage received from a full wave rectifier we can connect a

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If RE be the radius of Earth, then the ratio between the acceleration due to gravity at a depth 'r' below and a height '

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A bandwidth of 6 MHz is available for A.M. transmission. If the maximum audio signal frequency used for modulating the c

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A parallel plate capacitor of capacitance 200 $$\mu$$F is connected to a battery of 200 V. A dielectric slab of dielectr

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A long solenoid with 1000 turns/m has a core material with relative permeability 500 and volume 103 cm3. If the core mat

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A particle is moving with constant acceleration 'a'. Following graph shows v2 versus x(displacement) plot. The accelerat

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In a Young's double slit experiment, the slits are separated by 0.3 mm and the screen is 1.5 m away from the plane of sl

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The diameter of a spherical bob is measured using a vernier callipers. 9 divisions of the main scale, in the vernier cal

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A sample of gas with $$\gamma$$ = 1.5 is taken through an adiabatic process in which the volume is compressed from 1200

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At very high frequencies, the effective impendence of the given circuit will be ________________ $$\Omega$$.

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Cross-section view of a prism is the equilateral triangle ABC in the figure. The minimum deviation is observed using thi

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A resistor dissipates 192 J of energy in 1s when a current of 4A is passed through it. Now, when the current is doubled,

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