JEE Main 27 July 2021 Shift 2 Question Paper

Question 1

Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three vectors such that $\vec{a} = \vec{b} 	imes \left( \vec{b} 	imes \vec{c} ight)$. If magnitudes of the vectors $\vec{a}, \vec{b}$ and $\vec{c}$ are √2, 1 and 2 respectively and the angle between $\vec{b}$ and $\vec{c}$ is $	heta\left( 0 < 	heta < \frac{\pi}{2} ight)$, then the value of 1 + tan θ is equal to :

Accepted Answer

(C) 2

Answer

(A) √3 + 1

Answer

(B) $\frac{\sqrt{3} + 1}{\sqrt{3}}$

Answer

(D) 1

Question 2

Let N be the set of natural numbers and a relation R on N be defined by R = $\left\{ (x, y) \in \mathbb{N} 	imes \mathbb{N} : x^3 - 3x^2 y - xy^2 + 3y^3 = 0 ight\}$. Then the relation R is :

Accepted Answer

(A) reflexive but neither symmetric nor transitive

Answer

(B) an equivalence relation

Answer

(C) symmetric but neither reflexive nor transitive

Answer

(D) reflexive and symmetric, but not transitive

Question 3

Let y = y(x) be the solution of the differential equation $\left( x - x^3 \right) dy = \left( y + yx^2 - 3x^4 \right) dx$, x > 2. If y(3) = 3 then y(4) is equal to

Accepted Answer

(A) 12

Answer

(B) 4

Answer

(C) 8

Answer

(D) 16

Question 4

Let f : [0, ∞) → [0, 3] be a function defined by f(x) = $\begin{cases} \max\left\{ \sin t : 0 \le t \le x ight\}, & 0 \le x \le \pi \ 2 + \cos x, & x > \pi \end{cases}$ Then which of the following is true?

Accepted Answer

(A) f is differentiable everywhere in $\left( 0, \infty \right)$

Answer

(B) f is not continuous exactly at two points in $\left( 0, \infty \right)$

Answer

(C) f is continuous everywhere but not differentiable exactly at two points in $\left( 0, \infty \right)$

Answer

(D) f is continuous everywhere but not differentiable exactly at one point in $\left( 0, \infty \right)$

Question 5

If $	an\left( \frac{\pi}{9} ight)$, x, $	an\left( \frac{7\pi}{18} ight)$ are in arithmetic progression and $	an\left( \frac{\pi}{9} ight)$, y, $	an\left( \frac{5\pi}{18} ight)$ are also in arithmetic progression, then $\left| x - 2y ight|$ is equal to :

Accepted Answer

(B) 0

Answer

(A) 1

Answer

(C) 4

Answer

(D) 3

Question 6

The area of the region bounded by y − x = 2 and x$^2$ = y is equal to :

Accepted Answer

(B) $\frac{9}{2}$

Answer

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

Answer

(C) $\frac{16}{3}$

Answer

(D) $\frac{4}{3}$

Question 7

Let f : ℝ → ℝ be defined as f(x + y) + f(x − y) = 2f(x) f(y), $f\left( \frac{1}{2} \right)$ = −1. Then, the value of $\sum_{k=1}^{20} \frac{1}{\sin\left( k \right) \sin\left( k + f\left( k \right) \right)}$ is equal to :

Accepted Answer

(D) $\cosec^2\left( 1 \right) \cosec\left( 21 \right) \sin\left( 20 \right)$

Answer

(A) $\cosec^2\left( 21 \right) \cos\left( 20 \right) \cos\left( 2 \right)$

Answer

(B) $\sec^2\left( 1 \right) \sec\left( 21 \right) \cos\left( 20 \right)$

Answer

(C) $\sec^2\left( 21 \right) \sin\left( 20 \right) \sin\left( 2 \right)$

Question 8

Let the mean and variance of the frequency distribution
x: x$_1$ = 2, x$_2$ = 6, x$_3$ = 8, x$_4$ = 9
f: 4, 4, α, β
be 6 and 6.8 respectively. If x$_3$ is changed from 8 to 7, then the mean for the new data will be :

Accepted Answer

(C) $\frac{17}{3}$

Answer

(A) 4

Answer

(B) 5

Answer

(D) $\frac{16}{3}$

Question 9

The point P(a, b) undergoes the following three transformations successively :
(a) reflection about the line y = x
(b) translation through 2 units along the positive direction of x-axis.
(c) rotation through angle $\frac{\pi}{4}$ about the origin in the anti-clockwise direction.
If the co-ordinates of the final position of the point P are $\left( -\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}} \right)$, then the value of 2a + b is equal to :

Accepted Answer

(D) 9

Answer

(A) 5

Answer

(B) 7

Answer

(C) 13

Question 10

Consider a circle C which touches the y-axis at (0, 6) and cuts off an intercept 6√5 on the x-axis. Then the radius of the circle C is equal to :

Accepted Answer

(A) 9

Answer

(B) √82

Answer

(C) 8

Answer

(D) √53

Question 11

Let A and B be two 3 x 3 real matrices such that $(A^2 - B^2)$ is invertible matrix. If $A^5 = B^5$ and $A^3B^2 = A^2B^3$, then the value of the determinant of the matrix $A^3 + B^3$ is equal to :

Accepted Answer

(C) 0

Answer

(A) 2

Answer

(B) 1

Answer

(D) 4

Question 12

Let $\alpha = \max_{x \in R} \left\{ 8^{2\sin 3x} . 4^{4\cos 3x} \right\}$ and $\beta = \min_{x \in R} \left\{ 8^{2\sin 3x} . 4^{4\cos 3x} \right\}$. If $8x^2 + bx + c = 0$ is a quadratic equation whose roots are $\alpha^{1/5}$ and $\beta^{1/5}$, then the value of c − b is equal to :

Accepted Answer

(A) 42

Answer

(B) 43

Answer

(C) 47

Answer

(D) 50

Question 13

Let c be the set of all complex numbers. Let
S$_1$ = $\left\{ z \in C : |z - 2| \le 1 \right\}$ and
S$_2$ = $\left\{ z \in C : z(1+i) + \bar{z}(1-i) \ge 4 \right\}$.
Then, the maximum value of $\left| z - \frac{5}{2} \right|^2$ for $z \in S_1 \cap S_2$ is equal to :

Accepted Answer

(A) $\frac{5 + 2\sqrt{2}}{4}$

Answer

(B) $\frac{5 + 2\sqrt{2}}{2}$

Answer

(C) $\frac{3 + 2\sqrt{2}}{4}$

Answer

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

Question 14

A possible value of 'x', for which the ninth term in the expansion of $\left\{ 3^{\log_3 \sqrt{25^{x-1} + 7}} + 3^{\left( -\frac{1}{8} \right) \log_3 \left( 5^{x-1} + 1 \right)} \right\}^{10}$ in the increasing powers of $3^{\left( -\frac{1}{8} \right) \log_3 \left( 5^{x-1} + 1 \right)}$ is equal to 180, is :

Accepted Answer

(A) 1

Answer

(B) 2

Answer

(C) 0

Answer

(D) −1

Question 15

The value of $\lim_{x 	o 0} \left( \frac{x}{\sqrt[8]{1 - \sin x} - \sqrt[8]{1 + \sin x}} ight)$ is equal to :

Accepted Answer

(C) −4

Answer

(A) 4

Answer

(B) 0

Answer

(D) −1

Question 16

For real numbers α and β ≠ 0, if the point of intersection of the straight lines $\frac{x - \alpha}{1} = \frac{y - 1}{2} = \frac{z - 1}{3}$ and $\frac{x - 4}{\beta} = \frac{y - 6}{3} = \frac{z - 7}{3}$, lies on the plane x + 2y − z = 8, then α − β is equal to :

Accepted Answer

(C) 7

Answer

(A) 3

Answer

(B) 9

Answer

(D) 5

Question 17

Two sides of a parallelogram are along the lines 4x + 5y = 0 and 7x + 2y = 0. If the equation of one of the diagonals of the parallelogram is 11x + 7y = 9, then other diagonal passes through the point :

Accepted Answer

(B) $(2,2)$

Answer

(A) $(2,1)$

Answer

(C) $(1,3)$

Answer

(D) $(1,2)$

Question 18

Which of the following is the negation of the statement "for all M > 0, there exists x ∈ S such that x ≥ M"?

Accepted Answer

(D) there exists M > 0, such that x < M for all x ∈ S

Answer

(A) there exists M > 0, there exists x ∈ S such that x < M

Answer

(B) there exists M > 0, such that x ≥ M for all x ∈ S

Answer

(C) there exists M > 0, there exists x ∈ S such that x ≥ M

Question 19

A student appeared in an examination consisting of 8 true − false type questions. The student guesses the answers with equal probability. The smallest value of n, so that the probability of guessing at least 'n' correct answers is less than $\frac{1}{2}$, is :

Accepted Answer

(A) 5

Answer

(B) 6

Answer

(C) 3

Answer

(D) 4

Question 20

Let f : (a,b) → R be twice differentiable such that $f(x) = \int_a^x g(t) dt$ for a differentiable function g(x). If f(x) = 0 has exactly five distinct roots in (a, b), then $g(x)g'(x) = 0$ has at least :

Accepted Answer

(A) seven roots in (a, b)

Answer

(B) twelve roots in (a, b)

Answer

(C) five roots in (a, b)

Answer

(D) three roots in (a, b)

Question 21

The number of real roots of the equation $e^{4x}$ − $e^{3x}$ − $4e^{2x}$ − $e^{x}$ + 1 = 0 is equal to…………

Accepted Answer

2

Question 22

If the real part of the complex number z = $\frac{3+2i\cos	heta}{1-3i\cos	heta}$ , θ ∈ $\left(0,\frac{\pi}{2}ight)$ is zero, then the value of $\sin^{2}3	heta$ + $\cos^{2}	heta$ is equal to………

Accepted Answer

1

Question 23

Let n be a non-negative integer. Then the number of divisors of the form "4n + 1" of the number $(10)^{10}$ . $(11)^{10}$ . $(13)^{13}$ is equal to……….

Accepted Answer

924

Question 24

The distance of the point P(3,4,4) from the point of intersection of the line joining the points Q(3,−4,−5) and R(2, −3, 1) and the plane 2x + y + z = 7 , is equal to………….

Accepted Answer

7

Question 25

Let A = {n ∈ N|n$^2$ ≤ n + 10,000}, B = {3k + 1|k ∈ N} and C = {2k|k ∈ N} , then the sum of all the elements of the set A ∩ (B − C) is equal to……

Accepted Answer

832

Question 26

If $\int_{0}^{\pi}\left(\sin^{3}x\right)e^{-\sin^{2}x}dx$ = α − $\frac{\beta}{e}\int_{0}^{1}\sqrt{t}\ e^{t}dt$, then α + β is equal to……….

Accepted Answer

5

Question 27

Let E be an ellipse whose axes are parallel to the co-ordinates axes, having its center at (3,−4), one focus at (4,−4) and one vertex at (5,−4) . If mx − y = 4, m > 0 is a tangent to the ellipse E, then the value of 5m$^2$ is equal to……………

Accepted Answer

3

Question 28

Let y = y$\left(x\right)$ be the solution of the differential equation dy = $e^{\alpha x+y}$dx; α ∈ N . If y$\left(\log_{e}2\right)$ = $\log_{e}2$ and y(0) = $\log_{e}\left(\frac{1}{2}\right)$, then the value of α is equal to………….

Accepted Answer

2

Question 29

Let $\vec{a}$ = î − αĵ + βk̂, $\vec{b}$ = 3î + βĵ − αk̂ and $\vec{c}$ = −αî − 2ĵ + k̂, where α and β are integers. If $\vec{a}\cdot\vec{b}$ = −1 and $\vec{b}\cdot\vec{c}$ = 10, then $\left(\vec{a}	imes\vec{b}ight)\cdot\vec{c}$ is equal to…….

Accepted Answer

9

Question 30

The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an  orbital radius of 9.0 × 10$^3$ km. Find the mass of Mars.
{Given $\frac{4\pi^2}{G}$ = 6 × 10$^{11}$ N$^{-2}$ kg$^2$}

Accepted Answer

(B) 6.00 × 10$^{23}$ kg

Answer

(A) 3.25 × 10$^{21}$ kg

Answer

(C) 5.96 × 10$^{19}$ kg

Answer

(D) 7.02 × 10$^{25}$ kg

Question 31

A raindrop with radius R = 0.2 mm falls from a cloud at a height h = 2000 m  above the ground. Assume that the drop is spherical through its fall and the force of buoyancy may be neglected, then the terminal speed attained by the raindrop is :
[Density of water  f$_w$ = 1000 kg m$^{-3}$
and Density of air  f$_a$ = 1.2 kg m$^{-3}$,
g = 10 m / s$^2$
Coefficient of viscosity of air  = 1.8 × 10$^{-5}$ Nsm$^{-2}$]

Accepted Answer

(A) 4.94 ms$^{-1}$

Answer

(B) 14.4 ms$^{-1}$

Answer

(C) 43.56 ms$^{-1}$

Answer

(D) 250.6 ms$^{-1}$

Question 32

Figure A and B show long straight wires of circular cross − section (a and b with a < b), carrying current I which is uniformly distributed across the cross − section. The magnitude of magnetic field B varies with radius r and can be represented as :

Accepted Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Answer

(D) (D)

Question 33

The resistance of a conductor at 15°C is 16 Ω and at 100°C is 20 Ω . What will be the temperature coefficient of resistance of the conductor ?

Accepted Answer

(A) 0.003°C$^{-1}$

Answer

(B) 0.042°C$^{-1}$

Answer

(C) 0.033°C$^{-1}$

Answer

(D) 0.010°C $^{-1}$

Question 34

Two identical particles of mass 1 kg each go round a circle of radius R, under the action  of  their mutual gravitational attraction. The angular speed of each particle is :

Accepted Answer

(A) $\frac{1}{2}\sqrt{\frac{G}{R^3}}$

Answer

(B) $\sqrt{\frac{G}{2R^3}}$

Answer

(C) $\frac{1}{2R}\sqrt{\frac{1}{G}}$

Answer

(D) $\sqrt{\frac{2G}{R^3}}$

Question 35

Consider the following statements :
(A) Atoms of each element emit characteristics spectrum.
(B) According to Bohr's Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit.
(C) The density of nuclear matter depends on the size of the nucleus.
(D) A free neutron is stable but a free proton decay is possible.
(E) Radioactivity is an indication of the instability of nuclei.
Choose the correct answer from the options given below :

Accepted Answer

(D) A, B and E only

Answer

(A) B and D only

Answer

(B) A, C and E only

Answer

(C) A, B, C, D and E

Question 36

Match List I with List II.
List I
(a) Capacitance, C
(b) Permittivity of free space, $\varepsilon_0$
(c) Permeability of free space, $\mu_0$
(d) Electric field, E
List II
(i) M$^1$L$^1$T$^{-3}$ A$^{-1}$
(ii) M$^{-1}$L$^{-3}$ T$^4$ A$^2$
(iii) M$^{-1}$L$^{-2}$ T$^4$ A$^2$
(iv) M$^1$L$^1$T$^{-2}$A$^{-2}$
Choose the correct answer from the options given below :

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 37

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from 27°C to 37°C. If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes, which of the following of the following is true ?
[R = 8.314 J mol$^{-1}$ K$^{-1}$]

Accepted Answer

(B) Work done on the gas in close to 582 J

Answer

(A) Work done by the gas is close to 582 J

Answer

(C) Work done on the gas is close to 332 J

Answer

(D) Work done by the gas is close to 332 J

Question 38

Two Carnot engines A and operate in series such that engine A absorbs heat at T$_1$ and rejects heat to a sink at temperature T. Engine B absorbs half of the heat rejected by Engine A and rejects heat to the sink at T$_3$ . When work done in both the cases is equal, the value of T is :

Accepted Answer

(C) $\frac{2}{3}T_1+\frac{1}{3}T_3$

Answer

(A) $\frac{3}{2}T_1+\frac{1}{3}T_3$

Answer

(B) $\frac{2}{3}T_1+\frac{3}{2}T_3$

Answer

(D) $\frac{1}{3}T_1+\frac{2}{3}T_3$

Question 39

An electron and proton are separated by a large distance. The electron starts approaching the proton with energy 3 eV. The proton captures the electron and forms a hydrogen atom in second excited state. The resulting photon is incident on a photosensitive metal of threshold wavelength 4000 Å. What is the maximum kinetic energy of the emitted photoelectron ?

Accepted Answer

(A) 1.41 eV

Answer

(B) 7.61 eV .

Answer

(C) 3.3 eV

Answer

(D) No photoelectron would be emitted

Question 40

An object of mass 0.5 kg executing simple harmonic motion. Its amplitude is 5 cm and time period (T) is 0.2 s. What will be the potential energy of the object at an instant t = $\frac{T}{4}$ s starting from mean position. Assume that the initial phase of the oscillation is zero.

Accepted Answer

(B) 0.62 J

Answer

(A) 6.2 × 10$^{-3}$ J

Answer

(C) 6.2 × 10$^{3}$ J

Answer

(D) 1.2 × 10$^{3}$ J

Question 41

A 100 Ω resistance, a 0.1 μF capacitor and an inductor are connected in series across a 250 V supply at variable frequency. Calculate the value if inductance of inductor at which resonance will occur. Given that the resonant frequency is 60 Hz.

Accepted Answer

(B) 70.3 H

Answer

(A) 7.03 × 10$^{-5}$ H

Answer

(C) 70.3 mH

Answer

(D) 0.70 H

Question 42

An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by :

Accepted Answer

(A) $\left(\frac{8P}{9m}\right)^{\frac{1}{2}}t^{\frac{3}{2}}$

Answer

(B) $\left(\frac{9P}{8m}\right)^{\frac{1}{2}}t^{\frac{3}{2}}$

Answer

(C) $\left(\frac{9m}{8P}\right)^{\frac{1}{2}}t^{\frac{3}{2}}$

Answer

(D) $\left(\frac{8P}{9m}\right)^{\frac{1}{2}}t^{\frac{2}{3}}$

Question 43

Find the truth table for the function Y of A and B represented in the following figure.

Accepted Answer

(B) (B)

Answer

(A) (A)

Answer

(C) (C)

Answer

(D) (D)

Question 44

A simple pendulum of mass 'm', length '$\ell$' and charge '+q' suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be :

Accepted Answer

(D) $	an^{-1}\left[\frac{q}{mg} 	imes \frac{C_2(V_1 + V_2)}{(C_1 + C_2)(d - t)}ight]$

Answer

(A) $	an^{-1}\left[\frac{q}{mg} 	imes \frac{C_2(V_2 - V_1)}{(C_1 + C_2)(d - t)}ight]$

Answer

(B) $	an^{-1}\left[\frac{q}{mg} 	imes \frac{C_1(V_1 + V_2)}{(C_1 + C_2)(d - 1)}ight]$

Answer

(C) $	an^{-1}\left[\frac{q}{mg} 	imes \frac{C_1(V_2 - V_1)}{(C_1 + C_2)(d - t)}ight]$

Question 45

Given below is the plot of a potential energy function U(x) for a system, in which a particle is in one dimensional motion, while a conservation force F(x) acts on it. Suppose that $E_{mech}$ = 8J, the incorrect statement for this system is : [ where K.E. = kinetic energy]

Accepted Answer

(C) at x < x$_1$, K.E. is smallest and the particle is moving at the slowest speed.

Answer

(A) at x = x$_3$, K.E. = 4J.

Answer

(B) at x > x$_4$, K.E. is constant throughout the region .

Answer

(D) at x = x$_2$, K.E. is greatest and the particle is moving at the fastest speed.

Question 46

The expected graphical representation of the variation of angle of deviation 'δ' with angle of incidence 'i' in a prism is :

Accepted Answer

(B) (B)

Answer

(A) (A)

Answer

(C) (C)

Answer

(D) (D)

Question 47

A physical 'y' is represented by the formula y = m$^2$ r$^{-4}$ g$^x$ $\ell^{-\frac{3}{2}}$ if the percentage errors found in y, m, r, $\ell$ and g are 18, 1, 0.5, 4 and p respectively, then find the value of x and p.

Accepted Answer

(B) $\frac{16}{3}$ and ± $\frac{3}{2}$

Answer

(A) 5 and ± 2

Answer

(C) 8 and ± 2

Answer

(D) 4 and ± 3

Question 48

A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation $F = F_0\left[1 - \left(\frac{t - T}{T}\right)^2\right]$ Where F$_0$ and T are constants. The force acts only for the time interval 2T. The velocity υ of the particle after time 2T is :

Accepted Answer

(C) 4F$_0$ T / 3M

Answer

(A) F$_0$T / 3M

Answer

(B) 2F$_0$ T / M

Answer

(D) F$_0$T / 2M

Question 49

A swimmer wants to cross a river from point A to point B. Line AB makes an angle of 30° with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle θ with the line AB should be ________°, so that the swimmer reaches point B.

Accepted Answer

30

Question 50

For the circuit shown, the value of current at time t = 3.2 s will be ________ A. [Voltage distribution V(t) is shown by Fig.(1) and the circuit is shown in Fig.(2)]

Accepted Answer

1

Question 51

The difference in the number of waves when yellow light propagates through air and vacuum columns of the same thickness is one. The thickness of the air column is ________ mm. [Refractive index of air = 1.0003 , wavelength of yellow light in vacuum = 6000 Å ]

Accepted Answer

2

Question 52

In the given figure the magnetic flux through the loop increases according to the relation φ$_\beta$(t)10t$^2$ + 20t, where φ$_\beta$ is in milliwebers and t is in seconds. The magnitude of current throughR = 2Ω resistor at t = 5s is ________ mA.

Accepted Answer

60

Question 53

The water is filled upto height of 12 m in a tank having vertical sidewalls. A hole is made in one of the walls at a depth 'h' below the water level. The value of 'h' for which the emerging stream of water strikes the ground at the maximum range is __________ m.

Accepted Answer

6

Question 54

The K$_\alpha$ - X ray of molybdenum has wavelength 0.071 nm. If the energy of a molybdenum atom with a K electron knocked out is 27.5 ke V, the energy of this atom when an L electron is knocked out will be ________ ke V. (Round off to the nearest integer) [ h = 4.14×10$^{-15}$ eVs,c = 3×10$^8$ ms$^{-1}$ ]

Accepted Answer

10

Question 55

The maximum amplitude wave is found to be 12 V while the minimum amplitude is found to be 3 V. The modulation index is 0.6x where x is __________.

Accepted Answer

1

Question 56

A small block slides down from the top of hemisphere of radius R = 3m as shown in the figure. The height ' h' at which the block will lose contact with the surface of the sphere is __________ m. (Assume there is no friction between the block and the hemisphere)

Accepted Answer

2

Question 57

In the given figure, two wheels P and Q are connected by a belt B. The radius of P is three times as that of Q. In case of same rotational kinetic energy, the ratio of rotational inertias $\left(\frac{I_1}{I_2}\right)$ will be x : 1. The value of x will be __________.

Accepted Answer

9

Question 58

A particle executes simple harmonic motion represented by displacement function as x(t) = A sin(ωt + φ) If the position and velocity of the particle at t = 0s are 2cm and 2ω cm s$^{-1}$ respectively, then its amplitude is x√2 cm where the value of x is __________.

Accepted Answer

2

Question 59

Select the correct statements.
(A) Crystalline solids have long range order.
(B) Crystalline solids are isotropic.
(C) Amorphous solids are sometimes called pseudo solids
(D) Amorphous solids soften over a range of temperatures.
(E) Amorphous solids have a definite heat of fusion
Choose the most appropriate answer from the options given below:

Accepted Answer

(C) (A), (C), (D) only

Answer

(A) (B), (D) only

Answer

(B) (A), (B), (E) only

Answer

(D) (C), (D) only

Question 60

If the Thompson model of the atom was correct, then the result of Rutherford's gold foil experiment would have been:

Accepted Answer

(D) α − particles pass through the gold foil deflected by small angles and with reduced speed.

Answer

(A) All α − particles get bounced back by 180°.

Answer

(B) α − particles are deflected over a wide range of angles.

Answer

(C) All of α − particles pass through the gold foil without decrease in speed.

Question 61

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: SO$_2$(g) is adsorbed to a larger extent than H$_2$(g) on activated charcoal.
Reason R: SO$_2$(g) has a higher critical temperature than H$_2$(g)
In the light of the above statements, choose the most appropriate answer from the option given below.

Accepted Answer

(D) Both A and R are correct and R is the correct explanation of A.

Answer

(A) Both A and R are correct but R is not the correct explanation of A.

Answer

(B) A is not correct but R is correct.

Answer

(C) A is correct but R is not correct.

Question 62

Compound A gives D-Galactose and D-Glucose on hydrolysis. The compound A is:

Accepted Answer

(D) Lactose

Answer

(A) Amylose

Answer

(B) Sucrose

Answer

(C) Maltose

Question 63

Given below are two statements:
Statement I : Hyper conjugation is permanent effect.
Statement II : Hyper conjugation in ethyl cation (CH$_3$−C$^+$H$_2$) involves the overlapping of Csp$^2$−H$_{1s}$ bond with empty 2p orbital of other carbon.
Choose the correct option:

Accepted Answer

(B) Statement I is correct but Statement II is false.

Answer

(A) Statement I is incorrect but Statement II is true.

Answer

(C) Both Statement I and Statement II are false.

Answer

(D) Both Statement I and Statement II are true.

Question 64

What is A in the following reaction?

Accepted Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Answer

(D) (D)

JEE Main 27 July 2021 Shift 2 Question Paper with Answers

Physics — JEE Main 27 July 2021 Shift 2

Chemistry — JEE Main 27 July 2021 Shift 2

Mathematics — JEE Main 27 July 2021 Shift 2

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