JEE Main 31 August 2021 Shift 1 Question Paper

Question 1

Let $*, \square \in \{\wedge, \vee\}$ be such that the Boolean expression $(p * \sim q) \Rightarrow (p \square q)$ is a tautology. Then :

Accepted Answer

(C) $* = \wedge,\ \square = \vee$

Answer

(A) $* = \vee,\ \square = \vee$

Answer

(B) $* = \wedge,\ \square = \wedge$

Answer

(D) $* = \vee,\ \square = \wedge$

Question 2

The number of real roots of the equation $e^{4x} + 2e^{3x} - e^{x} - 6 = 0$ is :

Accepted Answer

(C) 1

Answer

(A) 2

Answer

(B) 4

Answer

(D) 0

Question 3

The sum of 10 terms of the series $\frac{3}{1^{2} 	imes 2^{2}} + \frac{5}{2^{2} 	imes 3^{2}} + \frac{7}{3^{2} 	imes 4^{2}} + ....$ is :

Accepted Answer

(B) $\frac{120}{121}$

Answer

(A) 1

Answer

(C) $\frac{99}{100}$

Answer

(D) $\frac{143}{144}$

Question 4

Let the equation of the plane, that passes through the point $(1, 4, -3)$ and contains the line of intersection of the planes $3x - 2y + 4z - 7 = 0$ and $x + 5y - 2z + 9 = 0$, be $\alpha x + \beta y + \gamma z + 3 = 0$, then $\alpha + \beta + \gamma$ is equal to :

Accepted Answer

(A) $-23$

Answer

(B) $-15$

Answer

(C) 23

Answer

(D) 15

Question 5

Let f be a non-negative function in $[0, 1]$ and twice differentiable in $(0, 1)$. If $\int_{0}^{x} \sqrt{1 - \left(f'(t)ight)^{2}}\, dt = \int_{0}^{x} f(t)\, dt$, $0 \le x \le 1$ and $f(0) = 0$, then $\lim_{x 	o 0} \frac{1}{x^{2}} \int_{0}^{x} f(t)\, dt$ :

Accepted Answer

(D) equals $\frac{1}{2}$

Answer

(A) equals 0

Answer

(B) equals 1

Answer

(C) does not exist

Question 6

Let $\vec{a}$ and $\vec{b}$ be two vectors such that $\left|2\vec{a} + 3\vec{b}\right| = \left|3\vec{a} + \vec{b}\right|$ and the angle between $\vec{a}$ and $\vec{b}$ is $60^{\circ}$. If $\frac{1}{8}\vec{a}$ is a unit vector, then $\left|\vec{b}\right|$ is equal to :

Accepted Answer

(C) 5

Answer

(A) 4

Answer

(B) 6

Answer

(D) 8

Question 7

The function $f(x) = \left|x^{2} - 2x - 3\right| \cdot e^{\left|9x^{2} - 12x + 4\right|}$ is not differentiable at exactly :

Accepted Answer

(C) two points

Answer

(A) four points

Answer

(B) three points

Answer

(D) one point

Question 8

Three numbers are in an increasing geometric progression with common ratio r. If the middle number is doubled, then the new numbers are in an arithmetic progression with common difference d. If the fourth term of GP is $3r^{2}$, then $r^{2} - d$ is equal to :

Accepted Answer

(B) $7 + \sqrt{3}$

Answer

(A) $7 - 7\sqrt{3}$

Answer

(C) $7 - \sqrt{3}$

Answer

(D) $7 + 3\sqrt{3}$

Question 9

Which of the following is not correct for relation R on the set of real numbers ?

Accepted Answer

(B) $(x, y) \in R \Leftrightarrow 0 < |x - y| \le 1$ is symmetric and transitive.

Answer

(A) $(x, y) \in R \Leftrightarrow 0 < |x| - |y| \le 1$ is neither transitive nor symmetric.

Answer

(C) $(x, y) \in R \Leftrightarrow |x| - |y| \le 1$ is reflexive but not symmetric.

Answer

(D) $(x, y) \in R \Leftrightarrow |x - y| \le 1$ is reflexive and symmetric.

Question 10

The integral $\int \frac{1}{\sqrt[4]{(x - 1)^{3} (x + 2)^{5}}} dx$ is equal to : (where C is a constant of integration)

Accepted Answer

(C) $\frac{4}{3}\left(\frac{x - 1}{x + 2}\right)^{\frac{1}{4}} + C$

Answer

(A) $\frac{3}{4}\left(\frac{x + 2}{x - 1}\right)^{\frac{1}{4}} + C$

Answer

(B) $\frac{3}{4}\left(\frac{x + 2}{x - 1}\right)^{\frac{5}{4}} + C$

Answer

(D) $\frac{4}{3}\left(\frac{x - 1}{x + 2}\right)^{\frac{5}{4}} + C$

Question 11

If p and q are the lengths of the perpendiculars from the origin on the lines,
$x \operatorname{cosec} \alpha - y \sec \alpha = k \cot 2\alpha$ and
$x \sin \alpha + y \cos \alpha = k \sin 2\alpha$
respectively, then $k^{2}$ is equal to :

Accepted Answer

(A) $4p^{2} + q^{2}$

Answer

(B) $2p^{2} + q^{2}$

Answer

(C) $p^{2} + 2q^{2}$

Answer

(D) $p^{2} + 4q^{2}$

Question 12

$\operatorname{cosec} 18^{\circ}$ is a root of the equation :

Accepted Answer

(D) $x^{2} - 2x - 4 = 0$

Answer

(A) $x^{2} + 2x - 4 = 0$

Answer

(B) $4x^{2} + 2x - 1 = 0$

Answer

(C) $x^{2} - 2x + 4 = 0$

Question 13

If the following system of linear equations
$2x + y + z = 5$
$x - y + z = 3$
$x + y + az = b$
has no solution, then :

Accepted Answer

(D) $a = \frac{1}{3},\ b 
e \frac{7}{3}$

Answer

(A) $a = -\frac{1}{3},\ b 
e \frac{7}{3}$

Answer

(B) $a 
e \frac{1}{3},\ b = \frac{7}{3}$

Answer

(C) $a 
e -\frac{1}{3},\ b = \frac{7}{3}$

Question 14

The length of the latus rectum of a parabola, whose vertex and focus are on the positive x-axis at a distance R and S $(> R)$ respectively from the origin, is :

Accepted Answer

(C) $4(S - R)$

Answer

(A) $4(S + R)$

Answer

(B) $2(S - R)$

Answer

(D) $2(S + R)$

Question 15

If the function $f(x) = \begin{cases} \frac{1}{x} \log_{e}\left(\frac{1 + \frac{x}{a}}{1 - \frac{x}{b}}ight), & x < 0 \ k, & x = 0 \ \frac{\cos^{2} x - \sin^{2} x - 1}{\sqrt{x^{2} + 1} - 1}, & x > 0 \end{cases}$ is continuous at $x = 0$, then $\frac{1}{a} + \frac{1}{b} + \frac{4}{k}$ is equal to :

Accepted Answer

(A) $-5$

Answer

(B) 5

Answer

(C) $-4$

Answer

(D) 4

Question 16

If $\frac{dy}{dx} = \frac{2^{x+y} - 2^{x}}{2^{y}}$, $y(0) = 1$, then $y(1)$ is equal to :

Accepted Answer

(B) $\log_{2}(1 + e)$

Answer

(A) $\log_{2}(2 + e)$

Answer

(C) $\log_{2}(2e)$

Answer

(D) $\log_{2}(1 + e^{2})$

Question 17

$\lim_{x 	o 0} \frac{\sin^{2}\left(\pi \cos^{4} xight)}{x^{4}}$ is equal to :

Accepted Answer

(C) $4\pi^{2}$

Answer

(A) $\pi^{2}$

Answer

(B) $2\pi^{2}$

Answer

(D) $4\pi$

Question 18

A vertical pole fixed to the horizontal ground is divided in the ratio $3 : 7$ by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a point on the ground 18 m away from the base of the pole, then the height of the pole (in meters) is :

Accepted Answer

(B) $12\sqrt{10}$

Answer

(A) $12\sqrt{15}$

Answer

(C) $8\sqrt{10}$

Answer

(D) $6\sqrt{10}$

Question 19

If $a_{r} = \cos\frac{2r\pi}{9} + i \sin\frac{2r\pi}{9}$, $r = 1, 2, 3, \ldots$, $i = \sqrt{-1}$, then the determinant $\begin{vmatrix} a_{1} & a_{2} & a_{3} \ a_{4} & a_{5} & a_{6} \ a_{7} & a_{8} & a_{9} \end{vmatrix}$ is equal to :

Accepted Answer

(C) $a_{1}a_{9} - a_{3}a_{7}$

Answer

(A) $a_{2}a_{6} - a_{4}a_{8}$

Answer

(B) $a_{9}$

Answer

(D) $a_{5}$

Question 20

The line $12x \cos	heta + 5y \sin	heta = 60$ is tangent to which of the following curves?

Accepted Answer

(B) $144x^{2} + 25y^{2} = 3600$

Answer

(A) $x^{2} + y^{2} = 169$

Answer

(C) $25x^{2} + 12y^{2} = 3600$

Answer

(D) $x^{2} + y^{2} = 60$

Question 21

Let [t] denote the greatest integer $\le t$. Then the value of $8 \cdot \int_{-\frac{1}{2}}^{1} \left( [2x] + |x| \right) dx$ is ______.

Accepted Answer

5

Question 22

A point z moves in the complex plane such that $\arg\left( \frac{z-2}{z+2} \right) = \frac{\pi}{4}$, then the minimum value of $\left| z - 9\sqrt{2} - 2i \right|^{2}$ is equal to ______.

Accepted Answer

98

Question 23

The square of the distance of the point of intersection of the line $\frac{x-1}{2} = \frac{y-2}{3} = \frac{z+1}{6}$ and the plane $2x - y + z = 6$ from the point $(-1, -1, 2)$ is ______.

Accepted Answer

61

Question 24

If 'R' is the least value of 'a' such that the function $f(x) = x^{2} + ax + 1$ is increasing on $[1, 2]$ and 'S' is the greatest value of 'a' such that the function $f(x) = x^{2} + ax + 1$ is decreasing on $[1, 2]$, then the value of $\left| R - S \right|$ is ______.

Accepted Answer

2

Question 25

The mean of 10 numbers $7 	imes 8,\ 10 	imes 10,\ 13 	imes 12,\ 16 	imes 14,\ \ldots.$ is ______.

Accepted Answer

398

Question 26

If the variable line $3x + 4y = \alpha$ lies between the two circles $(x - 1)^{2} + (y - 1)^{2} = 1$ and $(x - 9)^{2} + (y - 1)^{2} = 4$, without intercepting a chord on either circle, then the sum of all the integral values of $\alpha$ is ______.

Accepted Answer

165

Question 27

The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together, is ______.

Accepted Answer

576

Question 28

If $x\,\phi(x) = \int_{5}^{x} \left( 3t^{2} - 2\phi'(t) \right) dt$, $x > -2$, and $\phi(0) = 4$, then $\phi(2)$ is ______.

Accepted Answer

4

Question 29

If $\left( \frac{3^{6}}{4^{4}} \right) k$ is the term, independent of x, in the binomial expansion of $\left( \frac{x}{4} - \frac{12}{x^{2}} \right)^{12}$, then k is equal to ______.

Accepted Answer

55

Question 30

An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit functions is 0.9 and that of the second unit is 0.8. The instrument is switched on and it fails to operate. If the probability that only the first unit failed and second unit is functioning is p, then 98 p is equal to ______.

Accepted Answer

28

Question 31

A helicopter is flying horizontally with a speed 'v' at an altitude 'h' has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped?

Accepted Answer

(C) $\sqrt{\frac{2v^{2}h}{g}+h^{2}}$

Answer

(A) $\sqrt{\frac{2ghv^{2}+1}{h^{2}}}$

Answer

(B) $\sqrt{2ghv^{2}+h^{2}}$

Answer

(D) $\sqrt{\frac{2gh}{v^{2}}+h^{2}}$

Question 32

In the following logic circuit the sequence of the inputs A, B are (0, 0), (0,1), (1, 0) and (1, 1). The output Y for this sequence will be :

Accepted Answer

(C) 1, 1, 1, 0

Answer

(A) 1, 0, 1, 0

Answer

(B) 0, 1, 0, 1

Answer

(D) 0, 0, 1, 1

Question 33

Two particles A and B having charges 20 $\mu$C and $-5$ $\mu$C respectively are held fixed with a separation of 5 cm. At what position a third charged particle should be placed so that it does not experience a net electric force?

Accepted Answer

(B) At 5 cm from $-$ 5 $\mu$C on the right side

Answer

(A) At 5 cm from 20 $\mu$C on the left side of system

Answer

(C) At 1.25 cm from $-$ 5 $\mu$C between two charges

Answer

(D) At midpoint between two charges

Question 34

An object is placed at the focus of concave lens having focal length $f$. What is the magnification and distance of the image from the optical centre of the lens?

Accepted Answer

(C) $\frac{1}{2},\frac{f}{2}$

Answer

(A) 1, $\infty$

Answer

(B) Very high, $\infty$

Answer

(D) $\frac{1}{4},\frac{f}{4}$

Question 35

A sample of a radioactive nucleus A disintegrates to another radioactive nucleus B, which in turn disintegrates to some other stable nucleus C. Plot of a graph showing the variation of number of atoms of nucleus B vesus time is :
(Assume that at t = 0, there are no B atoms in the sample)

Accepted Answer

(B) (2)

Answer

(A) (1)

Answer

(C) (3)

Answer

(D) (4)

Question 36

A coil having N turns is wound tightly in the form of a spiral with inner and outer radii 'a' and 'b' respectively. Find the magnetic field at centre, when a current I passes through coil :

Accepted Answer

(A) $\frac{\mu_{0}\,IN}{2(b-a)}\log_{e}\left(\frac{b}{a}\right)$

Answer

(B) $\frac{\mu_{0}I}{8}\left[\frac{a+b}{a-b}\right]$

Answer

(C) $\frac{\mu_{0}I}{4(a-b)}\left[\frac{1}{a}-\frac{1}{b}\right]$

Answer

(D) $\frac{\mu_{0}I}{8}\left(\frac{a-b}{a+b}\right)$

Question 37

A body of mass M moving at speed $V_{0}$ collides elastically with a mass 'm' at rest. After the collision, the two masses move at angles $	heta_{1}$ and $	heta_{2}$ with respect to the initial direction of motion of the body of mass M. The largest possible value of the ratio M/m, for which the angles $	heta_{1}$ and $	heta_{2}$ will be equal, is :

Accepted Answer

(C) 3

Answer

(A) 4

Answer

(B) 1

Answer

(D) 2

Question 38

The masses and radii of the earth and moon are ($M_{1}$, $R_{1}$) and ($M_{2}$, $R_{2}$) respectively. Their centres are at a distance 'r' apart. Find the minimum escape velocity for a particle of mass 'm' to be projected from the middle of these two masses:

Accepted Answer

(B) $V=\sqrt{\frac{4G(M_{1}+M_{2})}{r}}$

Answer

(A) $V=\frac{1}{2}\sqrt{\frac{4G(M_{1}+M_{2})}{r}}$

Answer

(C) $V=\frac{1}{2}\sqrt{\frac{2G(M_{1}+M_{2})}{r}}$

Answer

(D) $V=\frac{\sqrt{2G}\,(M_{1}+M_{2})}{r}$

Question 39

A small square loop of side 'a' and one turn is placed inside a larger square loop of side b and one turn (b >> a). The two loops are coplanar with their centres coinciding. If a current I is passed in the square loop of side 'b', then the coefficient of mutual inductance between the two loops is :

Accepted Answer

(A) $\frac{\mu_{0}}{4\pi}8\sqrt{2}\,\frac{a^{2}}{b}$

Answer

(B) $\frac{\mu_{0}}{4\pi}\frac{8\sqrt{2}}{a}$

Answer

(C) $\frac{\mu_{0}}{4\pi}8\sqrt{2}\,\frac{b^{2}}{a}$

Answer

(D) $\frac{\mu_{0}}{4\pi}\frac{8\sqrt{2}}{b}$

Question 40

A uniform heavy rod of weight 10 kg ms$^{-2}$, cross-sectional area 100 cm$^{2}$ and length 20 cm is hanging from a fixed support. Young modulus of the material of the rod is $2	imes10^{11}$ Nm$^{-2}$. Neglecting the lateral contraction, find the elongation of rod due to its own weight.

Accepted Answer

(D) $5	imes10^{-10}$ m

Answer

(A) $2	imes10^{-9}$ m

Answer

(B) $5	imes10^{-8}$ m

Answer

(C) $4	imes10^{-8}$ m

Question 41

Two plane mirrors $M_{1}$ and $M_{2}$ are at right angle to each other shown. A point source 'P' is placed at 'a' and '2a' meter away from $M_{1}$ and $M_{2}$ respectively. The shortest distance between the images thus formed is : (Take $\sqrt{5}$ = 2.3)

Accepted Answer

(B) 4.6 a

Answer

(A) 3a

Answer

(C) 2.3 a

Answer

(D) $2\sqrt{10}$ a

Question 42

Match List-I with List-II.
List-I
(a) Torque
(b) Impulse
(c) Tension
(d) Surface Tension
List-II
(i) $MLT^{-1}$
(ii) $MT^{-2}$
(iii) $ML^{2}T^{-2}$
(iv) $MLT^{-2}$
Choose the most appropriate answer from the option given below :

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 43

For an ideal gas the instantaneous change in pressure 'p' with volume 'v' is given by the equation $\frac{dp}{dv}=-ap$. If p = $p_{0}$ at v = 0 is the given boundary condition, then the maximum temperature one mole of gas can attain is :
(Here R is the gas constant)

Accepted Answer

(A) $\frac{p_{0}}{a\,e\,R}$

Answer

(B) $\frac{ap_{0}}{e\,R}$

Answer

(C) infinity

Answer

(D) 0$^\circ$C

Question 44

Which of the following equations is dimensionally incorrect ?
Where t = time, h = height, s = surface tension, $	heta$ = angle, $ho$ = density, a, r = radius, g = acceleration due to gravity, v = volume , p = pressure, W = work done, $\Gamma$ = torque, $\in$ = permittivity, E = electric field, J = current density, L = length.

Accepted Answer

(A) $v=\frac{\pi\,p\,a^{4}}{8\eta\,L}$

Answer

(B) $h=\frac{2s\cos	heta}{ho\,r\,g}$

Answer

(C) $J=\in\frac{\partial E}{\partial t}$

Answer

(D) $W=\Gamma	heta$

Question 45

Angular momentum of a single particle moving with constant speed along circular path :

Accepted Answer

(B) remains same in magnitude and direction

Answer

(A) changes in magnitude but remains same in the direction

Answer

(C) remains same in magnitude but changes in the direction

Answer

(D) is zero

Question 46

In an ac circuit, an inductor, a capacitor and a resistor are connected in series with $X_{L}=R=X_{C}$. Impedance of this circuit is :

Accepted Answer

(C) R

Answer

(A) $2R^{2}$

Answer

(B) Zero

Answer

(D) $R\sqrt{2}$

Question 47

A moving proton and electron have the same de-Broglie wavelength. If K and P denote the K.E. and momentum respectively. Then choose the correct option :

Accepted Answer

(A) $K_{p}<K_{e}$ and $P_{p}=P_{e}$

Answer

(B) $K_{p}=K_{e}$ and $P_{p}=P_{e}$

Answer

(C) $K_{p}<K_{e}$ and $P_{p}<P_{e}$

Answer

(D) $K_{p}>K_{e}$ and $P_{p}=P_{e}$

Question 48

Consider a galvanometer shunted with 5$\Omega$ resistance and 2% of current passes through it. What is the resistance of the given galvanometer ?

Accepted Answer

(C) 245 $\Omega$

Answer

(A) 300 $\Omega$

Answer

(B) 344 $\Omega$

Answer

(D) 226 $\Omega$

Question 49

When a rubber ball is taken to a depth of ______ m in deep sea, its volume decreases by 0.5%.
(The bulk modulus of rubber = 9.8 $	imes$ 10$^{8}$ Nm$^{-2}$
Density of sea water = 10$^{3}$ kgm$^{-3}$
g = 9.8 m/s$^{2}$)

Accepted Answer

500

Question 50

A particle of mass 1 kg is hanging from a spring of force constant 100 Nm$^{-1}$. The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period T. The time when the kinetic energy and potential energy of the system will become equal, is $\frac{T}{x}$ .The value of x is ____.

Accepted Answer

8

Question 51

If the sum of the heights of transmitting and receiving antennas in the line of sight of communication is fixed at 160 m, then the maximum range of LOS communication is _ km.
(Take radius of Earth = 6400 km)

Accepted Answer

64

Question 52

A square shaped wire with resistance of each side 3$\Omega$ is bent to form a complete circle. The resistance between two diametrically opposite points of the circle in unit of $\Omega$ will be ___.

Accepted Answer

3

Question 53

A wire having a linear mass density 9.0 $	imes$ 10$^{-4}$ kg/m is stretched between two rigid supports with a tension of 900 N. The wire resonates at a frequency of 500 Hz. The next higher frequency at which the same wire resonates is 550 Hz. The length of the wire is ___ m.

Accepted Answer

10

Question 54

The voltage drop across 15$\Omega$ resistance in the given figure will be_______V.

Accepted Answer

6

Question 55

A block moving horizontally on a smooth surface with a speed of 40 ms$^{-1}$ splits into two equal parts. If one of the parts moves at 60 ms$^{-1}$ in the same direction, then the fractional change in the kinetic energy will be x : 4 where x = _______.

Accepted Answer

1

Question 56

The electric field in an electromagnetic wave is given by E = (50 NC$^{-1}$) sin$\omega$ (t$-$x/c)
The energy contained in a cylinder of volume V is 5.5 $	imes$ 10$^{-12}$ J. The value of V is ______ cm$^{3}$.
$\left(	ext{given } \in_0 = 8.8	imes10^{-12}\ 	ext{C}^2	ext{N}^{-1}	ext{m}^{-2}ight)$

Accepted Answer

500

Question 57

A capacitor of 50 $\mu$F is connected in a circuit as shown in figure. The charge on the upper plate of the capacitor is ______ $\mu$C.

Accepted Answer

100

Question 58

A car is moving on a plane inclined at 30$^\circ$ to the horizontal with an acceleration of 10 ms$^{-2}$ parallel to the plane upward. A bob is suspended by a string from the roof of the car.The angle in degrees which the string makes with the vertical is_______.
(Take g = 10 ms$^{-2}$)

Accepted Answer

30

Question 59

The correct order of reactivity of the given chlorides with acetate in acetic acid is :

Accepted Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Answer

(D) (4)

Question 60

Select the graph that correctly describes the adsorption isotherms at two temperatures $\mathrm{T_1}$ and $\mathrm{T_2}$ ($\mathrm{T_1} > \mathrm{T_2}$) for a gas :
(x – mass of the gas adsorbed ; m – mass of adsorbent ; P – pressure)

Accepted Answer

(D) (4)

Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Question 61

The major component/ingredient of Portland Cement is :

Accepted Answer

(B) tricalcium silicate

Answer

(A) tricalcium aluminate

Answer

(C) dicalcium aluminate

Answer

(D) dicalcium silicate

Question 62

In the structure of the dichromate ion, there is a :

Accepted Answer

(B) non-linear symmetrical Cr–O–Cr bond.

Answer

(A) linear symmetrical Cr–O–Cr bond.

Answer

(C) linear unsymmetrical Cr–O–Cr bond.

Answer

(D) non-linear unsymmetrical Cr–O–Cr bond.

Question 63

Which one of the following compounds contains $\beta	ext{-}\mathrm{C_1}	ext{-}\mathrm{C_4}$ glycosidic linkage ?

Accepted Answer

(A) Lactose

Answer

(B) Sucrose

Answer

(C) Maltose

Answer

(D) Amylose

Question 64

The major products A and B in the following set of reactions are :

Accepted Answer

(C) (3)

Answer

(A) (1)

Answer

(B) (2)

Answer

(D) (4)

JEE Main 31 August 2021 Shift 1 Question Paper with Answers

Physics — JEE Main 31 August 2021 Shift 1

Chemistry — JEE Main 31 August 2021 Shift 1

Mathematics — JEE Main 31 August 2021 Shift 1

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