JEE Main 27 August 2021 Shift 1 Question Paper

Question 1

If $0 < x < 1$, then $\frac{3}{2}x^2 + \frac{5}{3}x^3 + \frac{7}{4}x^4 + .....$ , is equal to :

Accepted Answer

(A) $x\left(\frac{1+x}{1-x}\right) + \log_e(1-x)$

Answer

(B) $x\left(\frac{1-x}{1+x}\right) + \log_e(1-x)$

Answer

(C) $\frac{1-x}{1+x} + \log_e(1-x)$

Answer

(D) $\frac{1+x}{1-x} + \log_e(1-x)$

Question 2

If for $x, y \in \mathbf{R}$, $x > 0$, $y = \log_{10}x + \log_{10}x^{1/3} + \log_{10}x^{1/9} + .....$ upto $\infty$ terms and $\frac{2+4+6+....+2y}{3+6+9+....+3y} = \frac{4}{\log_{10} x}$ , then the ordered pair $(x, y)$ is equal to :

Accepted Answer

(D) $(10^6, 9)$

Answer

(A) $(10^6, 6)$

Answer

(B) $(10^4, 6)$

Answer

(C) $(10^2, 3)$

Question 3

Let A be a fixed point $(0, 6)$ and B be a moving point $(2t, 0)$. Let M be the mid-point of AB and the perpendicular bisector of AB meets the y-axis at C. The locus of the mid-point P of MC is :

Accepted Answer

(C) $2x^2 + 3y - 9 = 0$

Answer

(A) $3x^2 - 2y - 6 = 0$

Answer

(B) $3x^2 + 2y - 6 = 0$

Answer

(D) $2x^2 - 3y + 9 = 0$

Question 4

If $(\sin^{-1} x)^2 - (\cos^{-1} x)^2 = a$; $0 < x < 1$, $a 
eq 0$, then the value of $2x^2 - 1$ is :

Accepted Answer

(B) $\sin\left(\frac{2a}{\pi}\right)$

Answer

(A) $\cos\left(\frac{4a}{\pi}\right)$

Answer

(C) $\cos\left(\frac{2a}{\pi}\right)$

Answer

(D) $\sin\left(\frac{4a}{\pi}\right)$

Question 5

If the matrix $A = \begin{pmatrix} 0 & 2 \ K & -1 \end{pmatrix}$ satisfies $A(A^3 + 3I) = 2I$, then the value of K is :

Accepted Answer

(A) $\frac{1}{2}$

Answer

(B) $-\frac{1}{2}$

Answer

(C) $-1$

Answer

(D) $1$

Question 6

The distance of the point $(1, -2, 3)$ from the plane $x - y + z = 5$ measured parallel to a line, whose direction ratios are $2, 3, -6$ is :

Accepted Answer

(D) $1$

Answer

(A) $3$

Answer

(B) $5$

Answer

(C) $2$

Question 7

If $S = \left\{ z \in \mathbb{C} : \frac{z-i}{z+2i} \in \mathbb{R} \right\}$, then :

Accepted Answer

(D) S is a straight line in the complex plane

Answer

(A) S contains exactly two elements

Answer

(B) S contains only one element

Answer

(C) S is a circle in the complex plane

Question 8

Let $y = y(x)$ be the solution of the differential equation $\frac{dy}{dx} = 2(y + 2\sin x - 5)\, x - 2\cos x$ such that $y(0) = 7$. Then $y(\pi)$ is equal to :

Accepted Answer

(A) $2e^{\pi^2} + 5$

Answer

(B) $e^{\pi^2} + 5$

Answer

(C) $3e^{\pi^2} + 5$

Answer

(D) $7e^{\pi^2} + 5$

Question 9

Equation of a plane at a distance $\sqrt{\frac{2}{21}}$ from the origin, which contains the line of intersection of the planes $x - y - z - 1 = 0$ and $2x + y - 3z + 4 = 0$, is :

Accepted Answer

(D) $4x - y - 5z + 2 = 0$

Answer

(A) $3x - y - 5z + 2 = 0$

Answer

(B) $3x - 4z + 3 = 0$

Answer

(C) $-x + 2y + 2z - 3 = 0$

Question 10

If $U_n = \left(1 + \frac{1}{n^2}ight)\left(1 + \frac{2^2}{n^2}ight)^2 .... \left(1 + \frac{n^2}{n^2}ight)^n$, then $\lim_{n 	o \infty} (U_n)^{\frac{-4}{n^2}}$ is equal to :

Accepted Answer

(A) $\frac{e^2}{16}$

Answer

(B) $\frac{4}{e}$

Answer

(C) $\frac{16}{e^2}$

Answer

(D) $\frac{4}{e^2}$

Question 11

The statement $(p \wedge (p 	o q) \wedge (q 	o r)) 	o r$ is :

Accepted Answer

(A) a tautology

Answer

(B) equivalent to $p 	o \sim r$

Answer

(C) a fallacy

Answer

(D) equivalent to $q 	o \sim r$

Question 12

Let us consider a curve, $y = f(x)$ passing through the point $(-2, 2)$ and the slope of the tangent to the curve at any point $(x, f(x))$ is given by $f(x) + xf'(x) = x^2$. Then :

Accepted Answer

(C) $x^3 - 3xf(x) - 4 = 0$

Answer

(A) $x^2 + 2xf(x) - 12 = 0$

Answer

(B) $x^3 + xf(x) + 12 = 0$

Answer

(D) $x^2 + 2xf(x) + 4 = 0$

Question 13

$\sum_{k=0}^{20} \left({}^{20}C_k\right)^2$ is equal to :

Accepted Answer

(C) ${}^{40}C_{20}$

Answer

(A) ${}^{40}C_{21}$

Answer

(B) ${}^{40}C_{19}$

Answer

(D) ${}^{41}C_{20}$

Question 14

A tangent and a normal are drawn at the point $P(2, -4)$ on the parabola $y^2 = 8x$, which meet the directrix of the parabola at the points A and B respectively. If $Q(a, b)$ is a point such that AQBP is a square, then $2a + b$ is equal to :

Accepted Answer

(A) $-16$

Answer

(B) $-18$

Answer

(C) $-12$

Answer

(D) $-20$

Question 15

Let $\frac{\sin A}{\sin B} = \frac{\sin(A-C)}{\sin(C-B)}$ , where A, B, C are angles of a triangle ABC. If the lengths of the sides opposite these angles are a, b, c respectively, then :

Accepted Answer

(B) $b^2,\ c^2, a^2$ are in A.P.

Answer

(A) $b^2 - a^2 = a^2 + c^2$

Answer

(C) $c^2, a^2, b^2$ are in A.P.

Answer

(D) $a^2, b^2, c^2$ are in A.P.

Question 16

If $\alpha, \beta$ are the distinct roots of $x^2 + bx + c = 0$, then $\lim_{x 	o \beta} \frac{e^{2\left(x^2+bx+cight)} - 1 - 2\left(x^2 + bx + cight)}{\left(x - \betaight)^2}$ is equal to:

Accepted Answer

(C) $2(b^2 - 4c)$

Answer

(A) $b^2 + 4c$

Answer

(B) $2(b^2 + 4c)$

Answer

(D) $b^2 - 4c$

Question 17

When a certain biased die is rolled, a particular face occurs with probability $\frac{1}{6} - x$ and its opposite face occurs with probability $\frac{1}{6} + x$ . All other faces occur with probability $\frac{1}{6}$ . Note that opposite faces sum to 7 in any die. If $0 < x < \frac{1}{6}$ , and the probability of obtaining total sum $= 7$, when such a die is rolled twice, is $\frac{13}{96}$ , then the value of x is:

Accepted Answer

(B) $\frac{1}{8}$

Answer

(A) $\frac{1}{16}$

Answer

(C) $\frac{1}{9}$

Answer

(D) $\frac{1}{12}$

Question 18

If $x^2 + 9y^2 - 4x + 3 = 0$, $x, y \in \mathbb{R}$ , then x and y respectively lie in the intervals:

Accepted Answer

(D) $[1, 3]$ and $\left[-\frac{1}{3}, \frac{1}{3}\right]$

Answer

(A) $\left[-\frac{1}{3}, \frac{1}{3}\right]$ and $\left[-\frac{1}{3}, \frac{1}{3}\right]$

Answer

(B) $\left[-\frac{1}{3}, \frac{1}{3}\right]$ and $[1, 3]$

Answer

(C) $[1, 3]$ and $[1, 3]$

Question 19

$\int_{6}^{16} \frac{\log_e x^2}{\log_e x^2 + \log_e\left(x^2 - 44x + 484\right)} dx$ is equal to:

Accepted Answer

(C) $5$

Answer

(A) $6$

Answer

(B) $8$

Answer

(D) $10$

Question 20

A wire of length 20 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a regular hexagon. Then the length of the side (in meters) of the hexagon, so that the combined area of the square and the hexagon is minimum, is:

Accepted Answer

(D) $\frac{10}{3+2\sqrt{3}}$

Answer

(A) $\frac{5}{2+\sqrt{3}}$

Answer

(B) $\frac{10}{2+3\sqrt{3}}$

Answer

(C) $\frac{5}{3+\sqrt{3}}$

Question 21

Let $\vec{a} = \hat{i} + 5\hat{j} + \alpha\hat{k}$, $\vec{b} = \hat{i} + 3\hat{j} + \beta\hat{k}$ and $\vec{c} = -\hat{i} + 2\hat{j} - 3\hat{k}$ be three vectors such that, $\left|\vec{b} 	imes \vec{c}ight| = 5\sqrt{3}$ and $\vec{a}$ is perpendicular to $\vec{b}$. Then the greatest amongst the values of $\left|\vec{a}ight|^{2}$ is _______.

Accepted Answer

90

Question 22

The number of distinct real roots of the equation $3x^{4} + 4x^{3} - 12x^{2} + 4 = 0$ is _________.

Accepted Answer

4

Question 23

Let the equation $x^{2} + y^{2} + px + (1 - p)y + 5 = 0$ represent circles of varying radius $r \in (0, 5]$. Then the number of elements in the set $S = \{q : q = p^{2} 	ext{ and } q 	ext{ is an integer}\}$ is _________.

Accepted Answer

61

Question 24

If $A = \{x \in \mathbf{R} : |x - 2| > 1\}$, $B = \left\{x \in \mathbf{R} : \sqrt{x^{2} - 3} > 1\right\}$, $C = \left\{x \in \mathbf{R} : |x - 4| \geq 2\right\}$ and $\mathbf{Z}$ is the set of all integers, then the number of subsets of the set $(A \cap B \cap C)^{c} \cap \mathbf{Z}$ is ___________.

Accepted Answer

256

Question 25

If $\int \frac{dx}{\left(x^{2} + x + 1ight)^{2}} = a	an^{-1}\left(\frac{2x + 1}{\sqrt{3}}ight) + b\left(\frac{2x + 1}{x^{2} + x + 1}ight) + C$, $x > 0$ where $C$ is the constant of integration, then the value of $9\left(\sqrt{3}a + bight)$ is equal to ________.

Accepted Answer

15

Question 26

If the system of linear equations
$2x + y - z = 3$
$x - y - z = \alpha$
$3x + 3y + \beta z = 3$
has infinitely many solution, then $\alpha + \beta - \alpha\beta$ is equal to __________.

Accepted Answer

5

Question 27

Let $n$ be an odd natural number such that the variance of $1, 2, 3, 4, ..., n$ is 14. Then $n$ is equal to ________.

Accepted Answer

13

Question 28

A number is called a palindrome if it reads the same backward as well as forward. For example 285582 is a six digit palindrome. The number of six digit palindromes, which are divisible by 55, is __________.

Accepted Answer

100

Question 29

If $y^{1/4} + y^{-1/4} = 2x$, and $\left(x^{2} - 1\right)\frac{d^{2}y}{dx^{2}} + \alpha x\frac{dy}{dx} + \beta y = 0$, then $|\alpha - \beta|$ is equal to ___________.

Accepted Answer

17

Question 30

A uniformly charged disc of radius R having surface charge density $\sigma$ is placed in the xy plane with its center at the origin. Find the electric field intensity along the z-axis at a distance Z from origin :-

Accepted Answer

(A) $E = \frac{\sigma}{2\varepsilon_0}\left(1 - \frac{Z}{(Z^2 + R^2)^{1/2}}\right)$

Answer

(B) $E = \frac{\sigma}{2\varepsilon_0}\left(1 + \frac{Z}{(Z^2 + R^2)^{1/2}}\right)$

Answer

(C) $E = \frac{2\varepsilon_0}{\sigma}\left(\frac{1}{(Z^2 + R^2)^{1/2}} + Z\right)$

Answer

(D) $E = \frac{\sigma}{2\varepsilon_0}\left(\frac{1}{(Z^2 + R^2)} + \frac{1}{Z^2}\right)$

Question 31

There are $10^{10}$ radioactive nuclei in a given radioactive element, Its half-life time is 1 minute. How many nuclei will remain after 30 seconds ? $\left(\sqrt{2} = 1.414\right)$

Accepted Answer

(B) $7 	imes 10^{9}$

Answer

(A) $2 	imes 10^{10}$

Answer

(C) $10^{5}$

Answer

(D) $4 	imes 10^{10}$

Question 32

Which of the following is not a dimensionless quantity ?

Accepted Answer

(C) Permeability of free space ($\mu_0$)

Answer

(A) Relative magnetic permeability ($\mu_r$)

Answer

(B) Power factor

Answer

(D) Quality factor

Question 33

If E and H represents the intensity of electric field and magnetising field respectively, then the unit of E/H will be :

Accepted Answer

(A) ohm

Answer

(B) mho

Answer

(C) joule

Answer

(D) newton

Question 34

A balloon carries a total load of 185 kg at normal pressure and temperature of 27$^\circ$C. What load will the balloon carry on rising to a height at which the barometric pressure is 45 cm of Hg and the temperature is $-7^\circ$C. Assuming the volume constant ?

Accepted Answer

(D) 123.54 kg

Answer

(A) 181.46 kg

Answer

(B) 214.15 kg.

Answer

(C) 219.07 kg

Question 35

An object is placed beyond the centre of curvature C of the given concave mirror. If the distance of the object is $d_1$ from C and the distance of the image formed is $d_2$ from C, the radius of curvature of this mirror is :

Accepted Answer

(A) $\frac{2d_1d_2}{d_1 - d_2}$

Answer

(B) $\frac{2d_1d_2}{d_1 + d_2}$

Answer

(C) $\frac{d_1d_2}{d_1 + d_2}$

Answer

(D) $\frac{d_1d_2}{d_1 - d_2}$

Question 36

A huge circular arc of length 4.4 ly subtends an angle '4s' at the centre of the circle. How long it would take for a body to complete 4 revolution if its speed is 8 AU per second ? Given : 1 ly = $9.46 	imes 10^{15}$ m $\qquad$ 1 AU = $1.5 	imes 10^{11}$ m

Accepted Answer

(B) $4.5 	imes 10^{10}$ s

Answer

(A) $4.1 	imes 10^{8}$ s

Answer

(C) $3.5 	imes 10^{6}$ s

Answer

(D) $7.2 	imes 10^{8}$ s

Question 37

Calculate the amount of charge on capacitor of 4 $\mu$F. The internal resistance of battery is 1$\Omega$ :

Accepted Answer

(A) 8 $\mu$C

Answer

(B) zero

Answer

(C) 16 $\mu$C

Answer

(D) 4 $\mu$C

Question 38

Moment of inertia of a square plate of side $l$ about the axis passing through one of the corner and perpendicular to the plane of square plate is given by :

Accepted Answer

(D) $\frac{2}{3}Ml^2$

Answer

(A) $\frac{Ml^2}{6}$

Answer

(B) $Ml^2$

Answer

(C) $\frac{Ml^2}{12}$

Question 39

For a transistor in CE mode to be used as an amplifier, it must be operated in :

Accepted Answer

(D) The active region only

Answer

(A) Both cut-off and Saturation

Answer

(B) Saturation region only

Answer

(C) Cut-off region only

Question 40

An ideal gas is expanding such that $PT^3$ = constant. The coefficient of volume expansion of the gas is :

Accepted Answer

(C) $\frac{4}{T}$

Answer

(A) $\frac{1}{T}$

Answer

(B) $\frac{2}{T}$

Answer

(D) $\frac{3}{T}$

Question 41

In a photoelectric experiment, increasing the intensity of incident light :

Accepted Answer

(D) increases the number of photons incident and the K.E. of the ejected electrons remains unchanged

Answer

(A) increases the number of photons incident and also increases the K.E. of the ejected electrons

Answer

(B) increases the frequency of photons incident and increases the K.E. of the ejected electrons.

Answer

(C) increases the frequency of photons incident and the K.E. of the ejected electrons remains unchanged

Question 42

Two ions of masses 4 amu and 16 amu have charges +2e and +3e respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then :

Accepted Answer

(B) lighter ion will be deflected more than heavier ion

Answer

(A) lighter ion will be deflected less than heavier ion

Answer

(C) both ions will be deflected equally

Answer

(D) no ion will be deflected.

Question 43

Find the distance of the image from object O, formed by the combination of lenses in the figure :

Accepted Answer

(A) 75 cm

Answer

(B) 10 cm

Answer

(C) 20 cm

Answer

(D) infinity

Question 44

In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius $2.0 	imes 10^{-5}$ m and density $1.2 	imes 10^{3}$ kgm$^{-3}$ ? Take viscosity of liquid = $1.8 	imes 10^{-5}$ Nsm$^{-2}$. (Neglect buoyancy due to air).

Accepted Answer

(B) $3.9 	imes 10^{-10}$ N

Answer

(A) $3.8 	imes 10^{-11}$ N

Answer

(C) $1.8 	imes 10^{-10}$ N

Answer

(D) $5.8 	imes 10^{-10}$ N

Question 45

Electric field in a plane electromagnetic wave is given by $E = 50 \sin(500x - 10 	imes 10^{10}t)$ V/m The velocity of electromagnetic wave in this medium is : (Given C = speed of light in vacuum)

Accepted Answer

(C) $\frac{2}{3}C$

Answer

(A) $\frac{3}{2}C$

Answer

(B) $C$

Answer

(D) $\frac{C}{2}$

Question 46

Five identical cells each of internal resistance 1$\Omega$ and emf 5V are connected in series and in parallel with an external resistance 'R'. For what value of 'R', current in series and parallel combination will remain the same ?

Accepted Answer

(A) 1 $\Omega$

Answer

(B) 25 $\Omega$

Answer

(C) 5 $\Omega$

Answer

(D) 10 $\Omega$

Question 47

The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure. The potential energy U(x) versus time (t) plot of the particle is correctly shown in figure :

Accepted Answer

(D) (4)

Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Question 48

A body of mass (2M) splits into four masses $\{m, M - m, m, M - m\}$, which are rearranged to form a square as shown in the figure. The ratio of $\frac{M}{m}$ for which, the gravitational potential energy of the system becomes maximum is x : 1. The value of x is ....... .

Accepted Answer

2

Question 49

The alternating current is given by
$$i = \left\{\sqrt{42}\sin\left(\frac{2\pi}{T}t\right) + 10\right\}A$$
The r.m.s. value of this current is ........ A.

Accepted Answer

11

Question 50

A uniform conducting wire of length is 24a, and resistance R is wound up as a current carrying coil in the shape of an equilateral triangle of side 'a' and then in the form of a square of side 'a'. The coil is connected to a voltage source $V_0$. The ratio of magnetic moment of the coils in case of equilateral triangle to that for square is $1 : \sqrt{y}$ where y is ....... .

Accepted Answer

3

Question 51

A circuit is arranged as shown in figure. The output voltage $V_0$ is equal to ....... V.

Accepted Answer

5

Question 52

First, a set of n equal resistors of 10 $\Omega$ each are connected in series to a battery of emf 20V and internal resistance 10 $\Omega$. A current I is observed to flow. Then, the n resistors are connected in parallel to the same battery. It is observed that the current is increased 20 times, then the value of n is ......... .

Accepted Answer

20

Question 53

Two cars X and Y are approaching each other with velocities 36 km/h and 72 km/h respectively. The frequency of a whistle sound as emitted by a passenger in car X, heard by the passenger in car Y is 1320 Hz. If the velocity of sound in air is 340 m/s, the actual frequency of the whistle sound produced is ........ Hz.

Accepted Answer

1210

Question 54

If the velocity of a body related to displacement x is given by $\upsilon = \sqrt{5000 + 24x}$ m/s, then the acceleration of the body is ....... $m/s^2$.

Accepted Answer

12

Question 55

A rod CD of thermal resistance 10.0 $KW^{-1}$ is joined at the middle of an identical rod AB as shown in figure, The end A, B and D are maintained at 200$^\circ$C, 100$^\circ$C and 125$^\circ$C respectively. The heat current in CD is P watt. The value of P is ....... .

Accepted Answer

2

Question 56

Two persons A and B perform same amount of work in moving a body through a certain distance d with application of forces acting at angle 45$^\circ$ and 60$^\circ$ with the direction of displacement respectively. The ratio of force applied by person A to the force applied by person B is $\frac{1}{\sqrt{x}}$. The value of x is ....... .

Accepted Answer

2

Question 57

A transmitting antenna has a height of 320 m and that of receiving antenna is 2000 m. The maximum distance between them for satisfactory communication in line of sight mode is 'd'. The value of 'd' is ........ km.

Accepted Answer

224

Question 58

In the following sequence of reactions, the final product D is :

Accepted Answer

(D) $\mathrm{CH_3-CH_2-CH_2-CH_2-CH_2-}\overset{\mathrm{O}}{\overset{\|}{\mathrm{C}}}\mathrm{-CH_3}$

Answer

(A) $\mathrm{H_3C-CH_2-CH_2-CH_2-CH_2-}\overset{\mathrm{O}}{\overset{\|}{\mathrm{C}}}\mathrm{-H}$

Answer

(B) $\mathrm{CH_3-CH=CH-CH_2-CH_2-CH_2-COOH}$

Answer

(C) $\mathrm{H_3C-CH=CH-CH(OH)-CH_2-CH_2-CH_3}$

Question 59

The structure of the starting compound $\mathbf{P}$ used in the reaction given below is :

Accepted Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Answer

(D) (4)

Question 60

Match List-I with List-II :
List-I (Species)
List-II (Number of lone pairs of electrons on the central atom)
(a) $\mathrm{XeF_2}$
(b) $\mathrm{XeO_2F_2}$
(c) $\mathrm{XeO_3F_2}$
(d) $\mathrm{XeF_4}$
(i) 0
(ii) 1
(iii) 2
(iv) 3
Choose the most appropriate answer from the options given below :

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 61

In which one of the following molecules strongest back donation of an electron pair from halide to boron is expected?

Accepted Answer

(B) $\mathrm{BF_3}$

Answer

(A) $\mathrm{BCl_3}$

Answer

(C) $\mathrm{BBr_3}$

Answer

(D) $\mathrm{BI_3}$

Question 62

Deuterium resembles hydrogen in properties but :

Accepted Answer

(A) reacts slower than hydrogen

Answer

(B) reacts vigorously than hydrogen

Answer

(C) reacts just as hydrogen

Answer

(D) emits $\beta^+$ particles

Question 63

Which refining process is generally used in the purification of low melting metals ?

Accepted Answer

(B) Liquation

Answer

(A) Chromatographic method

Answer

(C) Electrolysis

Answer

(D) Zone refining

Question 64

Match items of List-I with those of List-II :
List-I (Property)
List-II (Example)
(a) Diamagnetism
(b) Ferrimagnetism
(c) Paramagnetism
(d) Antiferromagnetism
(i) MnO
(ii) $\mathrm{O_2}$
(iii) NaCl
(iv) $\mathrm{Fe_3O_4}$
Choose the most appropriate answer from the options given below :

Accepted Answer

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

Answer

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

Answer

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

Answer

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

JEE Main 27 August 2021 Shift 1 Question Paper with Answers

Physics — JEE Main 27 August 2021 Shift 1

Chemistry — JEE Main 27 August 2021 Shift 1

Mathematics — JEE Main 27 August 2021 Shift 1

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