JEE Main 20 July 2021 Shift 1 Question Paper

Question 1

Let 'a' be a real number such that the function $f(x) = ax^2 + 6x - 15$, x ∈ R is increasing in $\left(-\infty, \frac{3}{4}\right)$ and decreasing in $\left(\frac{3}{4}, \infty\right)$. Then the function $g(x) = ax^2 - 6x + 15$, x ∈ R has a :

Accepted Answer

(D) local maximum at $x = -\frac{3}{4}$

Answer

(A) local minimum at $x = \frac{3}{4}$

Answer

(B) local maximum at $x = \frac{3}{4}$

Answer

(C) local minimum at $x = -\frac{3}{4}$

Question 2

Let $A = \left[a_{ij}ight]$ be a 3 x 3 matrix, where $a_{ij} = \begin{cases} 1 , & 	ext{if } i = j \ -x , & 	ext{if } |i - j| = 1 \ 2x+1 , & 	ext{otherwise} \end{cases}$ Let a function $f : R ightarrow R$ be defined as $f(x) = \det(A)$. Then the sum of maximum and minimum values of f on R is equal to :

Accepted Answer

(A) $-\frac{88}{27}$

Answer

(B) $\frac{20}{27}$

Answer

(C) $\frac{88}{27}$

Answer

(D) $-\frac{20}{27}$

Question 3

If z and ω are two complex numbers such that $|z\omega| = 1$ and $\arg(z) - \arg(w) = \frac{3\pi}{2}$, then $\arg\left(\frac{1 - 2\bar{z}\omega}{1 + 3\bar{z}\omega}\right)$ is : (Here arg(z) denotes the principal argument of complex number z)

Accepted Answer

(B) $-\frac{3\pi}{4}$

Answer

(A) $\frac{\pi}{4}$

Answer

(C) $-\frac{\pi}{4}$

Answer

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

Question 4

If in a triangle ABC, AB = 5 units, $\angle B = \cos^{-1}\left(\frac{3}{5}\right)$ and radius of circumcircle of ΔABC is 5 units, then the area (in sq. units) of ΔABC is :

Accepted Answer

(A) $6 + 8\sqrt{3}$

Answer

(B) $8 + 2\sqrt{2}$

Answer

(C) $10 + 6\sqrt{2}$

Answer

(D) $4 + 2\sqrt{3}$

Question 5

Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word is :

Accepted Answer

(B) $\frac{1}{11}$

Answer

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

Answer

(C) $\frac{2}{11}$

Answer

(D) $\frac{1}{66}$

Question 6

The coefficient of $x^{256}$ in the expansion of $(1-x)^{101}\left(x^2+x+1\right)^{100}$ is :

Accepted Answer

(D) ${}^{100}C_{15}$

Answer

(A) $-{}^{100}C_{15}$

Answer

(B) ${}^{100}C_{16}$

Answer

(C) $-{}^{100}C_{16}$

Question 7

The probability of selecting integers $a \in [-5, 30]$ such that $x^2+2(a+4)x-5a+64 > 0$, for all $x \in R$ is :

Accepted Answer

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

Answer

(B) $\frac{1}{6}$

Answer

(C) $\frac{7}{36}$

Answer

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

Question 8

The Boolean expression $(p \wedge \sim q) \Rightarrow (q \vee \sim p)$ is equivalent to :

Accepted Answer

(C) $p \Rightarrow q$

Answer

(A) $q \Rightarrow p$

Answer

(B) $\sim q \Rightarrow p$

Answer

(D) $p \Rightarrow \sim q$

Question 9

Let a be a positive real numbers such that
$\int_{0}^{a} e^{x-[x]}dx = 10e - 9$
where [x] is the greatest integer less than or equal to x. Then a is equal to :

Accepted Answer

(A) $10+\log_e 2$

Answer

(B) $10-\log_e(1+e)$

Answer

(C) $10+\log_e(1+e)$

Answer

(D) $10+\log_e 3$

Question 10

Let $A = \begin{bmatrix} 2 & 3 \ a & 0 \end{bmatrix}$, $a \in R$ be written as P + Q where P is a symmetric matrix and Q is skew symmetric matrix. If $\det(Q) = 9$, then the modulus of the sum of all possible values of determinant of P is equal to :

Accepted Answer

(B) 36

Answer

(A) 18

Answer

(C) 24

Answer

(D) 45

Question 11

If $\alpha$ and $\beta$ are the distinct roots of the equation $x^2+\left(3\right)^{\frac{1}{4}}x+3^{\frac{1}{2}} = 0$, then the value of $\alpha^{96}\left(\alpha^{12}-1\right)+\beta^{96}\left(\beta^{12}-1\right)$ is equal to :

Accepted Answer

(C) $52 	imes 3^{24}$

Answer

(A) $56 	imes 3^{25}$

Answer

(B) $28 	imes 3^{25}$

Answer

(D) $56 	imes 3^{24}$

Question 12

The number of real roots of the equation
$	an^{-1}\sqrt{x(x+1)}+\sin^{-1}\sqrt{x^2+x+1} = \frac{\pi}{4}$ is :

Accepted Answer

(C) 0

Answer

(A) 4

Answer

(B) 1

Answer

(D) 2

Question 13

The value of the integral $\int_{-1}^{1} \log_e\left(\sqrt{1-x}+\sqrt{1+x}\right)dx$ is equal to :

Accepted Answer

(B) $\log_e 2+\frac{\pi}{2}-1$

Answer

(A) $2\log_e 2+\frac{\pi}{4}-1$

Answer

(C) $\frac{1}{2}\log_e 2+\frac{\pi}{4}-\frac{3}{2}$

Answer

(D) $2\log_e 2+\frac{\pi}{2}-\frac{1}{2}$

Question 14

The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2, 4, 5 and 7, then the remaining two observations are :

Accepted Answer

(A) 10, 11

Answer

(B) 3, 18

Answer

(C) 1, 20

Answer

(D) 8, 13

Question 15

Let the tangent to the parabola S : $y^2 = 2x$ at the point P(2, 2) meet the x-axis at Q and normal at it meet the parabola S at the point R. Then the area (in sq. units) of the triangle PQR is equal to :

Accepted Answer

(D) $\frac{25}{2}$

Answer

(A) $\frac{35}{2}$

Answer

(B) $\frac{15}{2}$

Answer

(C) 25

Question 16

Let a function f : R → R be defined as
$f(x) = \begin{cases} \sin x - e^x & 	ext{if } x \leq 0 \ a + [-x] & 	ext{if } 0 < x < 1 \ 2x - b & 	ext{if } x \geq 1 \end{cases}$
where [x] is the greatest integer less than or equal to x. If f is continuous on R, then $\left(a+bight)$ is equal to :

Accepted Answer

(C) 3

Answer

(A) 2

Answer

(B) 5

Answer

(D) 4

Question 17

Let $\vec{a} = 2\hat{i}+\hat{j}-2\hat{k}$ and $\vec{b} = \hat{i}+\hat{j}$. If $\vec{c}$ is a vector such that $\vec{a}.\vec{c} = |\vec{c}|$, $\left|\vec{c}-\vec{a}ight| = 2\sqrt{2}$ and the angle between $\left(\vec{a} 	imes \vec{b}ight)$ and $\vec{c}$ is $\frac{\pi}{6}$, then the value of $\left|\left(\vec{a} 	imes \vec{b}ight) 	imes \vec{c}ight|$ is :

Accepted Answer

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

Answer

(A) 3

Answer

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

Answer

(D) 4

Question 18

Let $y = y(x)$ be the solution of the differential equation
$e^x\sqrt{1-y^2}\,dx+\left(\frac{y}{x}\right)dy = 0$, $y\left(1\right) = -1$
Then the value of $\left(y(3)\right)^2$ is equal to :

Accepted Answer

(D) $1-4e^6$

Answer

(A) $1+4e^6$

Answer

(B) $1-4e^3$

Answer

(C) $1+4e^3$

Question 19

Let [x] denote the greatest integer $\leq x$, where $x \in R$. If the domain of the real valued function $f(x) = \sqrt{\frac{\big|[x]\big|-2}{\big|[x]\big|-3}}$ is $(-\infty, a) \cup [b, c) \cup [4, \infty)$, $a < b < c$, then the value of $a+b+c$ is:

Accepted Answer

(C) -2

Answer

(A) -3

Answer

(B) 8

Answer

(D) 1

Question 20

Let $y = y(x)$ be the solution of the differential equation
$x	an\left(\frac{y}{x}ight)dy = \left(y	an\left(\frac{y}{x}ight)-xight)dx$, $-1 \leq x \leq 1$, $y\left(\frac{1}{2}ight) = \frac{\pi}{6}$
Then the area of the region bounded by the curves $x = 0$, $x = \frac{1}{\sqrt{2}}$ and $y = y(x)$ in the upper half plane is :

Accepted Answer

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

Answer

(A) $\frac{1}{6}(\pi-1)$

Answer

(C) $\frac{1}{4}(\pi-2)$

Answer

(D) $\frac{1}{12}(\pi-3)$

Question 21

Let $A = \begin{pmatrix} 1 & -1 & 0 \ 0 & 1 & -1 \ 0 & 0 & 1 \end{pmatrix}$ and $B = 7A^{20} - 20A^{7} + 2I$ , where $I$ is an identity matrix of order 3 x 3.

If $B = \left[ b_{ij} ight]$, then $b_{13}$ is equal to..........

Accepted Answer

910

Question 22

Let $y = mx + c$, $m > 0$ be the focal chord of $y^2 = -64x$, which is tangent to $\left(x + 10\right)^2 + y^2 = 4$.
Then, the value of $4\sqrt{2}\left(m + c\right)$ is equal to .......

Accepted Answer

34

Question 23

Let a, b, c, d be in arithmetic progression with common difference $\lambda$.
If $\begin{vmatrix} x + a - c & x + b & x + a \ x - 1 & x + c & x + b \ x - b + d & x + d & x + c \end{vmatrix} = 2$, then the value of $\lambda^2$ is equal to.........

Accepted Answer

1

Question 24

Let $\vec{a}, \vec{b}, \vec{c}$ be three mutually perpendicular vectors of the same magnitude and equally inclined at an angle $	heta$, with the vector $\vec{a} + \vec{b} + \vec{c}$. Then $36\cos^2 2	heta$ is equal to.......

Accepted Answer

4

Question 25

There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is ..........

Accepted Answer

777

Question 26

The number of rational terms in the binomial expansion of $\left(4^{\frac{1}{4}} + 5^{\frac{1}{6}}\right)^{120}$ is.....

Accepted Answer

21

Question 27

Let P be a plane passing through the points $\left(1, 0, 1\right)\left(1, -2, 1\right)$ and $\left(0, 1, -2\right)$. Let a vector $\vec{a} = \alpha\hat{i} + \beta\hat{j} + \gamma\hat{k}$ be such that $\vec{a}$ is parallel to the plane P, perpendicular to $\left(\hat{i} + 2\hat{j} + 3\hat{k}\right)$ and $\vec{a}.\left(\hat{i} + \hat{j} + 2\hat{k}\right) = 2$, then $\left(\alpha - \beta + \gamma\right)^2$ equals........

Accepted Answer

81

Question 28

If the value of $\lim_{x 	o 0} \left(2 - \cos x \sqrt{\cos 2x}ight)^{\left(\frac{x + 2}{x^2}ight)}$ is equal to $e^a$, then a is equal to.......

Accepted Answer

3

Question 29

If the shortest distance between the lines $\vec{r}_1 = \alpha\hat{i} + 2\hat{j} + 2\hat{k} + \lambda\left(\hat{i} - 2\hat{j} + 2\hat{k}\right), \lambda \in R$, $\alpha > 0$ and $\vec{r}_2 = -4\hat{i} - \hat{k} + \mu\left(3\hat{i} - 2\hat{j} - 2\hat{k}\right), \mu \in R$ is 9, then $\alpha$ is equal to........

Accepted Answer

6

Question 30

The amount of heat needed to raise the temperature of 4 moles of a rigid diatomic gas from 0°C to 50°C when no work is done is ________. (R is the universal gas constant)

Accepted Answer

(D) 500 R

Answer

(A) 175 R

Answer

(B) 750 R

Answer

(C) 250 R

Question 31

A deuteron and an alpha particle having equal kinetic energy enter perpendicularly into a magnetic field. Let $r_d$ and $r_d$ be their respective radii of circular path. The value of $\frac{r_d}{r_\alpha}$ is equal to :

Accepted Answer

(A) $\sqrt{2}$

Answer

(B) 2

Answer

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

Answer

(D) 1

Question 32

If $\vec{A}$ and $\vec{B}$ are two vectors satisfying the relation $\vec{A}\cdot\vec{B} = \left|\vec{A}	imes\vec{B}ight|$. Then the value of $\left|\vec{A}-\vec{B}ight|$ will be :

Accepted Answer

(A) $\sqrt{A^2+B^2-\sqrt{2}AB}$

Answer

(B) $\sqrt{A^2+B^2}$

Answer

(C) $\sqrt{A^2+B^2+2AB}$

Answer

(D) $\sqrt{A^2+B^2+\sqrt{2}AB}$

Question 33

Consider a mixture of gas molecule of types A, B and C having masses $m_A < m_B < m_C$. The ratio of their root mean square speeds at normal temperature and pressure is :

Accepted Answer

(C) $\frac{1}{\upsilon_A} < \frac{1}{\upsilon_B} < \frac{1}{\upsilon_C}$

Answer

(A) $\frac{1}{\upsilon_A} > \frac{1}{\upsilon_B} > \frac{1}{\upsilon_C}$

Answer

(B) $\upsilon_A = \upsilon_B = \upsilon_C = 0$

Answer

(D) $\upsilon_A = \upsilon_B 
eq \upsilon_C$

Question 34

A nucleus of mass M emits γ − ray photon of frequency 'ν'. The loss of internal energy by the nucleus is : [Take 'c' as the speed of electromagnetic wave ]

Accepted Answer

(A) $h
u\left[1+\frac{h
u}{2Mc^2}ight]$

Answer

(B) 0

Answer

(C) $h
u\left[1-\frac{h
u}{2Mc^2}ight]$

Answer

(D) $h
u$

Question 35

A radioactive material decays by simultaneous emissions of two particles with half lives of 1400 years and 700 years respectively. What will be the time after which one third of the material remains? (Take ln 3 = 1.1)

Accepted Answer

(D) 740 years

Answer

(A) 340 years

Answer

(B) 1110 years

Answer

(C) 700 years

Question 36

The value of current in the 6Ω resistance is :

Accepted Answer

(B) 10 A

Answer

(A) 6 A

Answer

(C) 4 A

Answer

(D) 8 A

Question 37

The radiation corresponding to $3 ightarrow 2$ transition of a hydrogen atom falls on a gold surface to generate photoelectrons. These electrons are passed through a magnetic field of $5 	imes 10^{-4}$ T. Assume that the radius of the largest circular circular path followed by these electrons is 7mm, the work function of the metal is : (Mass of electron = $9.1 	imes 10^{-31}$ kg )

Accepted Answer

(A) 0.82 eV

Answer

(B) 1.88 eV

Answer

(C) 1.36 eV

Answer

(D) 0.16 eV

Question 38

For the circuit shown below, calculate the value of $I_2$ :

Accepted Answer

(C) 25 mA

Answer

(A) 0.15 A

Answer

(B) 0.1 A

Answer

(D) 0.05 A

Question 39

The arm PQ of a rectangular conductor is moving from x = 0 to x = 2b outwards and then inwards from x = 2b to x = 0 as shown in the figure. A uniform magnetic field perpendicular to the plane is acting from x = 0 to x = b. Identify the graph the variation of different quantities with distance.

Accepted Answer

(A) A − Flux, B − EMF, C − Power dissipated

Answer

(B) A − EMF, B − Power dissipated, C − Flux

Answer

(C) A − Power dissipated, B − Flux, C − EMF

Answer

(D) A − Flux, B − Power dissipated, C − EMF

Question 40

Region I and II are separated by a spherical surface of radius 25 cm. An object is kept in region I at a distance of 40 cm from the surface. The distance of the image from the surface is :

Accepted Answer

(C) 37.58 cm

Answer

(A) 9.52 cm

Answer

(B) 18.23 cm

Answer

(D) 55.44 cm

Question 41

The normal reaction 'N' for a vehicle of 800 kg mass, negotiating a turn on a 30° banked road at maximum possible speed without skidding is ________ $	imes 10^{3}$ kg m / s$^2$. [ Given cos30° = 0.87, $\mu_5$ = 0.2 ]

Accepted Answer

(B) 10.2

Answer

(A) 6.96

Answer

(C) 12.4

Answer

(D) 7.2

Question 42

The entropy of any system is given by $S = \alpha^2\beta\ \ell n\left[\frac{\mu kR}{J\beta^2}+3\right]$ Where $\alpha$ and $\beta$ are the constants. μ, J, k and R no. of moles, mechanical equivalent of heat, Boltzmann constant and gas constant respectively . [ Take $S = \frac{dQ}{T}$ ] Choose the incorrect option from the following :

Accepted Answer

(B) α and k have the same dimensions.

Answer

(A) S, β, k and μR have the same dimensions.

Answer

(C) S and α have different dimensions.

Answer

(D) α and J have the same dimensions.

Question 43

A current of 5 A is passing through a non-linear magnesium wire of cross − section $0.04\,m^2$. At every point the direction of current density is at an angle of 60° with unit vector of area of cross -section. The magnitude of electric field at every point of the conductor is : (Resistivity of magnesium ρ = $44 	imes 10^{-8}$ Ωm )

Accepted Answer

(C) $11 	imes 10^{-5}$ V / m

Answer

(A) $11 	imes 10^{-7}$ V / m

Answer

(B) $11 	imes 10^{-2}$ V / m

Answer

(D) $11 	imes 10^{-3}$ V / m

Question 44

The value of tension in a long thin metal wire has been changed from $T_1$ to $T_2$. The lengths of the metal wire at two different values of tension $T_1$ and $T_2$ are $\ell_1$ and $\ell_2$ respectively. The actual length of the metal wire is :

Accepted Answer

(A) $\frac{T_1\ell_2 - T_2\ell_1}{T_1 - T_2}$

Answer

(B) $\sqrt{T_1 T_2 \ell_1 \ell_2}$

Answer

(C) $\frac{\ell_1 + \ell_2}{2}$

Answer

(D) $\frac{T_1\ell_1 - T_2\ell_2}{T_1 - T_2}$

Question 45

AC voltage $V(t) = 20\sin\omega t$ of frequency 50Hz is applied to a parallel plate capacitor. The separation between the plates is 2mm and the area is $1\,m^2$. The amplitude of the oscillating displacement current for the applied Ac voltage is ________. [ Take $\varepsilon_0 = 8.85 	imes 10^{-12}$ F / m ]

Accepted Answer

(D) 27.79 μA

Answer

(A) 83.37 μA

Answer

(B) 55.58 μA

Answer

(C) 21.14 μA

Question 46

A butterfly is flying with a velocity $4\sqrt{2}$ m/s in North − East direction. Wind is slowly blowing at 1m/s from North to South. The resultant displacement of the butterfly in 3 seconds is :

Accepted Answer

(A) 15m

Answer

(B) 20m

Answer

(C) 3 m

Answer

(D) $12\sqrt{2}$ m

Question 47

A certain charge Q is divided into parts q and (Q − q). How should the charges Q and q be divided so that q and (Q − q) placed at a certain distance apart experience maximum electrostatic repulsion ?

Accepted Answer

(C) $Q = 2q$

Answer

(A) $Q = \frac{q}{2}$

Answer

(B) $Q = 4q$

Answer

(D) $Q = 3q$

Question 48

A steel block of 10 kg rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with an acceleration 0.2 m/s$^2$. The normal reaction R' by the floor if mass of the iron cylinders are equal and of 20kg each, is ________ N. [ Take g = 10m / s$^2$ and $\mu_s$ = 0.2 ]

Accepted Answer

(D) 686

Answer

(A) 714

Answer

(B) 684

Answer

(C) 716

Question 49

A person whose mass is 100 kg travels from Earth to Mars in a spaceship. Neglect all other object in sky and take acceleration due to gravity on the surface of the Earth and mars as 10m / s$^2$ and 4m / s$^2$ respectively. Identify from the below figures, the curve that fits best for the weight of the passenger as a function of time.

Accepted Answer

(A) (c)

Answer

(B) (a)

Answer

(C) (b)

Answer

(D) (d)

Question 50

The amplitude of wave disturbance propagating in the positive x-direction is given by $y = \frac{1}{1+(x)^2}$ at time $t = 0$ and $y = \frac{1}{1+(x-2)^2}$ at $t = 1$ s , where x and y are in metres. The shape of wave does not change during the propagation. The velocity of the wave will be ________ m /s.

Accepted Answer

2

Question 51

In the reported figure, heat energy absorbed by a system in going through a cyclic process is ________ $\pi$ J.

Accepted Answer

100

Question 52

In a spring gun having spring constant 100 N / m a small ball 'B' of mass 100 g is put in its barrel (as shown in figure) by compressing the spring through 0.05 m. There should be a box placed at a distance 'd' on the ground so that the ball falls in it. If the ball leaves the gun horizontally at a height of 2 m above the ground . The value of d is ____________ m.

Accepted Answer

1

Question 53

The frequency of a car horn encountered a change from 400 Hz to 500 Hz, when the car approaches a vertical wall. If the speed of sound is 330 m /s. Then the speed of car is __________ km /h.

Accepted Answer

132

Question 54

A body having specific charge 8 μC / g is resting on a frictionless plane at a distance 10 cm from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of 100 V / m is applied horizontally towards the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be ____________ s.

Accepted Answer

1

Question 55

A rod of mass M and length L is lying on a horizontal frictionless surface. A particle of mass 'm' travelling along the surface hits at one end of the rod with a velocity 'u' in a direction perpendicular to the rod. The collision is completely elastic. After collision, particle comes to rest. The ratio of masses $\left( \frac{m}{M} \right)$ is $\frac{1}{x}$. The value of 'x' will be ________.

Accepted Answer

4

Question 56

An object viewed from a near point distance of 25 cm, using a microscopic lens with magnification '6', gives an unresolved image, A resolved image is observed at infinite distance with a total magnification double the earlier using an eyepiece along with the given lens and a tube of length 0.6 m, if the focal length of the eyepiece is equal to _________ cm.

Accepted Answer

25

Question 57

In an LCR series circuit, an inductor 30 mH and a resistor 1 Ω are connected to an Ac source of angular frequency 300 rad /s. The value of capacitance for which, the current leads the voltage by 45° is $\frac{1}{x} 	imes 10^{-3}$ F. Then the value of x is ____________.

Accepted Answer

3

Question 58

A carrier wave $V_C(t) = 160 \sin(2\pi 	imes 10^6 t)$ volts is made to very between $V_{max} = 200$ V and $V_{min} = 120$ V by a message signal $V_m(t) = A_m \sin(2\pi 	imes 10^3 t)$ volts. The peak voltage $A_m$ of the modulating single is _________ V.

Accepted Answer

40

Question 59

Chemical nature of the nitrogen oxide compound obtained from a reaction of concentrated nitric acid and $P_4O_{10}$ (in 4:1 ratio) is:

Accepted Answer

(D) acidic

Answer

(A) basic

Answer

(B) neutral

Answer

(C) amphoteric

Question 60

Compound A is converted to B on reaction with $CHCl_3$ and KOH. The compound B is toxic and can be decomposed by C. A, B and C respectively are:

Accepted Answer

(B) Primary amine, isonitrile compound , conc. HCl

Answer

(A) Primary amine, nitrile compound, conc. HCl

Answer

(C) Secondary amine, isonitrile compound, conc NaOH

Answer

(D) Secondary amine, nitrile compound, conc. NaOH

Question 61

Given below are two statements : One is labelled as **Assertion A** and the other is labelled as **Reason R**.
**Assertion A:** The dihedral angles in $H_2O_2$ in gaseous phase is 90.2° and in solid phase is 111.5°.
**Reason R:** The change in dihedral angle in solid and gaseous phase is due to the difference in the intermolecular forces.
Choose the most appropriate answer from the options given below for **A** and **R**.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 62

Among the given species the Resonance stabilized carbocations are:

Accepted Answer

(D) (A) and (B) only

Answer

(A) (A), (B) and (C) only

Answer

(B) (C) and (D) only

Answer

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

Question 63

A s-block element (M) reacts with oxygen to form an oxide of the formula $MO_2$. The oxide is pale yellow in colour and paramagnetic. The element (M) is:

Accepted Answer

(B) K

Answer

(A) Na

Answer

(C) Mg

Answer

(D) Ca

Question 64

Green chemistry in day- to day life is in the use of:

Accepted Answer

(C) Liquified $CO_{2}$ for dry cleaning of clothes

Answer

(A) Chlorine for bleaching of paper

Answer

(B) Large amount of water alone for washing clothes

Answer

(D) Tetrachloroethene for laundry

JEE Main 20 July 2021 Shift 1 Question Paper with Answers

Physics — JEE Main 20 July 2021 Shift 1

Chemistry — JEE Main 20 July 2021 Shift 1

Mathematics — JEE Main 20 July 2021 Shift 1

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