JEE Main 16 March 2021 Shift 2 Question Paper

Question 1

The maximum value of $f(x)=\begin{vmatrix} \sin^{2}x & 1+\cos^{2}x & \cos 2x \ 1+\sin^{2}x & \cos^{2}x & \cos 2x \ \sin^{2}x & \cos^{2}x & \sin 2x \end{vmatrix}$, $x \in R$ is:

Accepted Answer

(C) $\sqrt{5}$

Answer

(A) $\sqrt{7}$

Answer

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

Answer

(D) $5$

Question 2

Let A denote the event that a 6-digit integer formed by 0, 1, 2, 3, 4, 5, 6 without repetitions, be divisible by 3. Then probability of event A is equal to :

Accepted Answer

(B) $\frac{4}{9}$

Answer

(A) $\frac{9}{56}$

Answer

(C) $\frac{3}{7}$

Answer

(D) $\frac{11}{27}$

Question 3

Let $\alpha \in R$ be such that the function $f(x)=\begin{cases} \dfrac{\cos^{-1}(1-\{x\}^{2})\sin^{-1}(1-\{x\})}{\{x\}-\{x\}^{3}}, & x 
eq 0 \ \alpha, & x=0 \end{cases}$ is continuous at $x = 0$, where $\{x\} = x - [x]$, $[x]$ is the greatest integer less than or equal to x. Then :

Accepted Answer

(C) no such $\alpha$ exists

Answer

(A) $\alpha = \frac{\pi}{\sqrt{2}}$

Answer

(B) $\alpha = 0$

Answer

(D) $\alpha = \frac{\pi}{4}$

Question 4

If (x, y, z) be an arbitrary point lying on a plane P which passes through the point (42, 0, 0), (0, 42, 0) and (0, 0, 42), then the value of expression $3+\frac{x-11}{(y-19)^{2}(z-12)^{2}}+\frac{y-19}{(x-11)^{2}(z-12)^{2}}+\frac{z-12}{(x-11)^{2}(y-19)^{2}}-\frac{x+y+z}{14(x-11)(y-19)(z-12)}$

Accepted Answer

(B) $3$

Answer

(A) $0$

Answer

(C) $39$

Answer

(D) $-45$

Question 5

Consider the integral $I=\int\limits_{0}^{10}\frac{[x]\,e^{[x]}}{e^{x-1}}dx,$ where [x] denotes the greatest integer less than or equal to x. Then the value of I is equal to:

Accepted Answer

(C) $45(e-1)$

Answer

(A) $9(e-1)$

Answer

(B) $45(e+1)$

Answer

(D) $9(e+1)$

Question 6

Let C be the locus of the mirror image of a point on the parabola $y^{2}=4x$ with respect to the line $y = x$. Then the equation of tangent to C at P(2,1) is :

Accepted Answer

(A) $x-y=1$

Answer

(B) $2x+y=5$

Answer

(C) $x+3y=5$

Answer

(D) $x+2y=4$

Question 7

If $y = y(x)$ is the solution of the differential equation $\frac{dy}{dx}+(	an x)\,y=\sin x,\ 0 \le x \le \frac{\pi}{3}$, with $y(0) = 0$, then $y\left(\frac{\pi}{4}ight)$ equal to :

Accepted Answer

(B) $\left(\frac{1}{2\sqrt{2}}\right)\log_{e}2$

Answer

(A) $\frac{1}{4}\log_{e}2$

Answer

(C) $\log_{e}2$

Answer

(D) $\frac{1}{2}\log_{e}2$

Question 8

Let $A = \{2, 3, 4, 5, ...., 30\}$ and '$\simeq$' be an equivalence relation on $A 	imes A$, defined by $(a, b) \simeq (c, d)$, if and only if $ad = bc$. Then the number of ordered pairs which satisfy this equivalence relation with ordered pair (4, 3) is equal to :

Accepted Answer

(D) $7$

Answer

(A) $5$

Answer

(B) $6$

Answer

(C) $8$

Question 9

Let the lengths of intercepts on x-axis and y-axis made by the circle $x^{2}+y^{2}+ax+2ay+c=0$, $(a < 0)$ be $2\sqrt{2}$ and $2\sqrt{5}$, respectively. Then the shortest distance from origin to a tangent to this circle which is perpendicular to the line $x + 2y = 0$, is euqal to :

Accepted Answer

(C) $\sqrt{6}$

Answer

(A) $\sqrt{11}$

Answer

(B) $\sqrt{7}$

Answer

(D) $\sqrt{10}$

Question 10

The least value of $|z|$ where z is complex number which satisfies the inequality $\exp\left(\frac{\left(|z|+3\right)\left(|z|-1\right)}{\left||z|+1\right|}\log_{e}2\right) \ge \log_{\sqrt{2}}\left|5\sqrt{7}+9i\right|,$ $i=\sqrt{-1}$, is equal to :

Accepted Answer

(A) $3$

Answer

(B) $\sqrt{5}$

Answer

(C) $2$

Answer

(D) $8$

Question 11

Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA respectively. Let $\alpha$ be the number of triangles having these points from different sides as vertices and $\beta$ be the number of quadrilaterals having these points from different sides as vertices. Then $(\beta-\alpha)$ is equal to :

Accepted Answer

(D) $717$

Answer

(A) $795$

Answer

(B) $1173$

Answer

(C) $1890$

Question 12

If the point of intersections of the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{b^{2}}=1$ and the circle $x^{2}+y^{2}=4b$, $b > 4$ lie on the curve $y^{2}=3x^{2}$, then b is equal to:

Accepted Answer

(A) $12$

Answer

(B) $5$

Answer

(C) $6$

Answer

(D) $10$

Question 13

Given that the inverse trigonometric functions take principal values only. Then, the number of real values of x which satisfy $\sin^{-1}\left(\frac{3x}{5}\right)+\sin^{-1}\left(\frac{4x}{5}\right)=\sin^{-1}x$ is equal to:

Accepted Answer

(C) $3$

Answer

(A) $2$

Answer

(B) $1$

Answer

(D) $0$

Question 14

Let A(-1, 1), B(3, 4) and C(2, 0) be given three points. A line $y = mx$, $m > 0$, intersects lines AC and BC at point P and Q respectively. Let $A_{1}$ and $A_{2}$ be the areas of $\Delta ABC$ and $\Delta PQC$ respectively, such that $A_{1}=3A_{2}$, then the value of m is equal to :

Accepted Answer

(B) $1$

Answer

(A) $\frac{4}{15}$

Answer

(C) $2$

Answer

(D) $3$

Question 15

Let f be a real valued function, defined on $R - \{-1, 1\}$ and given by $f(x) = 3\log_{e}\left|\frac{x-1}{x+1}\right|-\frac{2}{x-1}.$ Then in which of the following intervals, function f(x) is increasing?

Accepted Answer

(A) $(-\infty,-1)\cup\left(\left[\frac{1}{2},\infty\right)-\{1\}\right)$

Answer

(B) $(-\infty, \infty)-\{-1, 1\}$

Answer

(C) $\left(-1,\frac{1}{2}\right]$

Answer

(D) $\left(-\infty,\frac{1}{2}\right]-\{-1\}$

Question 16

Let $f : S \rightarrow S$ where $S = (0, \infty)$ be a twice differentiable function such that $f(x + 1) = x f(x)$. If $g : S \rightarrow R$ be defined as $g(x)=\log_{e}f(x)$, then the value of $\left|g''(5)-g''(1)\right|$ is equal to :

Accepted Answer

(A) $\frac{205}{144}$

Answer

(B) $\frac{197}{144}$

Answer

(C) $\frac{187}{144}$

Answer

(D) $1$

Question 17

Let $P(x)=x^{2}+bx+c$ be a quadratic polynomial with real coefficients such that $\int\limits_{0}^{1}P(x)dx=1$ and P(x) leaves remainder 5 when it is divided by $(x - 2)$. Then the value of $9(b + c)$ is equal to:

Accepted Answer

(C) $7$

Answer

(A) $9$

Answer

(B) $15$

Answer

(D) $11$

Question 18

If the foot of the perpendicular from point (4, 3, 8) on the line $L_{1}:\frac{x-a}{l}=\frac{y-2}{3}=\frac{z-b}{4}$, $l 
eq 0$ is (3, 5, 7), then the shortest distance between the line $L_{1}$ and line $L_{2}:\frac{x-2}{3}=\frac{y-4}{4}=\frac{z-5}{5}$ is equal to :

Accepted Answer

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

Answer

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

Answer

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

Answer

(D) $\frac{1}{\sqrt{3}}$

Question 19

Let $C_{1}$ be the curve obtained by the solution of differential equation $2xy\frac{dy}{dx}=y^{2}-x^{2}$, $x > 0$. Let the curve $C_{2}$ be the solution of $\frac{2xy}{x^{2}-y^{2}}=\frac{dy}{dx}$. If both the curves pass through (1,1), then the area enclosed by the curves $C_{1}$ and $C_{2}$ is equal to :

Accepted Answer

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

Answer

(A) $\pi-1$

Answer

(C) $\pi+1$

Answer

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

Question 20

Let $\vec{a}=\hat{i}+2\hat{j}-3\hat{k}$ and $\vec{b}=2\hat{i}-3\hat{j}+5\hat{k}$. If $\vec{r}	imes\vec{a}=\vec{b}	imes\vec{r}$, $\vec{r}.\left(\alpha\hat{i}+2\hat{j}+\hat{k}ight)=3$ and $\vec{r}.\left(2\hat{i}+5\hat{j}-\alpha\hat{k}ight)=-1$, $\alpha \in R$, then the value of $\alpha+\left|\vec{r}ight|^{2}$ is equal to :

Accepted Answer

(B) $15$

Answer

(A) $9$

Answer

(C) $13$

Answer

(D) $11$

Question 21

If the distance of the point (1, -2, 3) from the plane $x + 2y - 3z + 10 = 0$ measured parallel to the line, $\frac{x-1}{3}=\frac{2-y}{m}=\frac{z+3}{1}$ is $\sqrt{\frac{7}{2}}$, then the value of $|m|$ is equal to _______.

Accepted Answer

2

Question 22

Consider the statistics of two sets of observations as follows :
Size   Mean   Variance
Observation I    10    2    2
Observation II    n    3    1
If the variance of the combined set of these two observations is $\frac{17}{9}$, then the value of n is equal to _________.

Accepted Answer

5

Question 23

Let $A=\begin{bmatrix} a_{1} \ a_{2} \end{bmatrix}$ and $B=\begin{bmatrix} b_{1} \ b_{2} \end{bmatrix}$ be two $2 	imes 1$ matrices with real entries such that $A = XB$, where $X=\frac{1}{\sqrt{3}}\begin{bmatrix} 1 & -1 \ 1 & k \end{bmatrix}$, and $k \in R$. If $a_{1}^{2}+a_{2}^{2}=\frac{2}{3}\left(b_{1}^{2}+b_{2}^{2}ight)$ and $(k^{2}+1)b_{2}^{2} 
eq -2b_{1}b_{2}$, then the value of k is ________.

Accepted Answer

1

Question 24

For real numbers $\alpha$, $\beta$, $\gamma$ and $\delta$, if $\int\frac{(x^{2}-1)+	an^{-1}\left(\frac{x^{2}+1}{x}ight)}{(x^{4}+3x^{2}+1)	an^{-1}\left(\frac{x^{2}+1}{x}ight)}dx$ $=\alpha\log_{e}\left(	an^{-1}\left(\frac{x^{2}+1}{x}ight)ight)+\beta	an^{-1}\left(\frac{\gamma(x^{2}-1)}{x}ight)+\delta	an^{-1}\left(\frac{x^{2}+1}{x}ight)+C$ where C is an arbitrary constant, then the value of $10(\alpha+\beta\gamma+\delta)$ is equal to __________.

Accepted Answer

6

Question 25

Let $f : R ightarrow R$ and $g : R ightarrow R$ be defined as $f(x)=\begin{cases} x+a, & x<0 \ |x-1|, & x \ge 0 \end{cases}$ and $g(x)=\begin{cases} x+1, & x<0 \ (x-1)^{2}+b, & x \ge 0 \end{cases}$ where a, b are non-negative real numbers. If $(gof)(x)$ is continuous for all $x \in R$, then $a + b$ is equal to ___________.

Accepted Answer

1

Question 26

Let $\frac{1}{16}$, a and b be in G.P. and $\frac{1}{a},\frac{1}{b},6$ be in A.P., where a, b > 0. Then $72(a + b)$ is equal to _________.

Accepted Answer

14

Question 27

In $\Delta ABC$, the lengths of sides AC and AB are 12 cm and 5 cm, respectively. If the area of $\Delta ABC$ is 30 cm$^{2}$ and R and r are respectively the radii of circumcircle and incircle of $\Delta ABC$, then the value of $2R + r$ (in cm) is equal to _______.

Accepted Answer

15

Question 28

Let n be a positive integer. Let $A=\sum\limits_{k=0}^{n}(-1)^{k}\ {}^{n}C_{k}\left[\left(\frac{1}{2}\right)^{k}+\left(\frac{3}{4}\right)^{k}+\left(\frac{7}{8}\right)^{k}+\left(\frac{15}{16}\right)^{k}+\left(\frac{31}{32}\right)^{k}\right]$ If $63A = 1-\frac{1}{2^{30}}$, then n is equal to _______.

Accepted Answer

6

Question 29

Let $\vec{c}$ be a vector perpendicular to the vectors $\vec{a}=\hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=\hat{i}+2\hat{j}+\hat{k}$. If $\vec{c}.\left(\hat{i}+\hat{j}+3\hat{k}ight)=8$ then the value of $\vec{c}.\left(\vec{a}	imes\vec{b}ight)$ is equal to _________.

Accepted Answer

28

Question 30

Let $S_{n}(x)=\log_{a^{1/2}}x+\log_{a^{1/3}}x+\log_{a^{1/6}}x$ $+\log_{a^{1/11}}x+\log_{a^{1/18}}x+\log_{a^{1/27}}x+.....$ up to n-terms, where a > 1. If $S_{24}(x) = 1093$ and $S_{12}(2x) = 265$, then value of a is equal to _______.

Accepted Answer

16

Question 31

The following logic gate is equivalent to :

Accepted Answer

(A) NOR Gate

Answer

(B) OR Gate

Answer

(C) AND Gate

Answer

(D) NAND Gate

Question 32

A large block of wood of mass M = 5.99 kg is hanging from two long massless cords. A bullet of mass m = 10g is fired into the block and gets embedded in it. The (block + bullet) then swing upwards, their centre of mass rising a vertical distance h = 9.8 cm before the (block + bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before collision is : (Take g = 9.8 ms$^{-2}$)

Accepted Answer

(C) 831.4 m/s

Answer

(A) 841.4 m/s

Answer

(B) 811.4 m/s

Answer

(D) 821.4 m/s

Question 33

A charge Q is moving $\overrightarrow{dI}$ distance in the magnetic field $\vec{B}$. Find the value of work done by $\vec{B}$.

Accepted Answer

(C) Zero

Answer

(A) 1

Answer

(B) Infinite

Answer

(D) −1

Question 34

What will be the nature of flow of water from a circular tap, when its flow rate increased from 0.18 L/min to 0.48 L/min ? The radius of the tap and viscosity of water are 0.5 cm and 10$^{-3}$ Pa s, respectively.
(Density of water : 10$^{3}$ kg/m$^{3}$)

Accepted Answer

(D) Steady flow to unsteady flow

Answer

(A) Unsteady to steady flow

Answer

(B) Remains steady flow

Answer

(C) Remains turbulent flow

Question 35

Find out the surface charge density at the intersection of point x = 3 m plane and x-axis, in the region of uniform line charge of 8 nC/ m lying along the z-axis in free space.

Accepted Answer

(A) 0.424 nC m$^{-2}$

Answer

(B) 47.88 C/m

Answer

(C) 0.07 nC m$^{-2}$

Answer

(D) 4.0 nC m$^{-2}$

Question 36

The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of 100 V. What should nearly be the ratio of their wavelengths ? (m$_{P}$ = 1.00727 u, m$_{e}$ = 0.00055u)

Accepted Answer

(D) 43 : 1

Answer

(A) 1860 : 1

Answer

(B) (1860)$^{2}$ : 1

Answer

(C) 41.4 : 1

Question 37

For the given circuit, comment on the type of transformer used :

Accepted Answer

(C) Step-up transformer

Answer

(A) Auxilliary transformer

Answer

(B) Auto transformer

Answer

(D) Step down transformer

Question 38

The half-life of Au$^{198}$ is 2.7 days. The activity of 1.50 mg of Au$^{198}$ if its atomic weight is 198 g mol$^{-1}$ is, (N$_{A}$ = 6 × 10$^{23}$/mol)

Accepted Answer

(B) 357 Ci

Answer

(A) 240 Ci

Answer

(C) 535 Ci

Answer

(D) 252 Ci

Question 39

Calculate the value of mean free path (λ) for oxygen molecules at temperature 27°C and pressure 1.01 × 10$^{5}$ Pa. Assume the molecular diameter 0.3 nm and the gas is ideal.
(k = 1.38 × 10$^{-23}$ JK$^{-1}$)

Accepted Answer

(D) 102 nm

Answer

(A) 58 nm

Answer

(B) 32 nm

Answer

(C) 86 nm

Question 40

The refractive index of a converging lens is 1.4. What will be the focal length of this lens if it is placed in a medium of same refractive index ? (Assume the radii of curvature of the faces of lens are R$_{1}$ and R$_{2}$ respectively)

Accepted Answer

(B) Infinite

Answer

(A) 1

Answer

(C) $\frac{R_{1}R_{2}}{R_{1}-R_{2}}$

Answer

(D) Zero

Question 41

In order to determine the Young's Modulus of a wire of radius 0.2 cm (measured using a scale of least count = 0.001 cm) and length 1m (measured using a scale of least count = 1 mm), a weight of mass 1kg (measured using a scale of least count = 1g) was hanged to get the elongation of 0.5 cm (measured using a scale of least count 0.001 cm). What will be the fractional error in the value of Young's Modulus determined by this experiment ?

Accepted Answer

(D) 1.4%

Answer

(A) 0.14%

Answer

(B) 0.9%

Answer

(C) 9%

Question 42

A bimetallic strip consists of metals A and B. It is mounted rigidly as shown. The metal A has higher coefficient of expansion compared to that of metal B. When the bimetallic strip is placed in a cold both, it will :

Accepted Answer

(D) Bend towards the left

Answer

(A) Bend towards the right

Answer

(B) Not bend but shrink

Answer

(C) Neither bend nor shrink

Question 43

A resistor develops 500 J of thermal energy in 20s when a current of 1.5 A is passed through it. If the current is increased from 1.5 A to 3A, what will be the energy developed in 20 s.

Accepted Answer

(D) 2000 J

Answer

(A) 1500 J

Answer

(B) 1000 J

Answer

(C) 500 J

Question 44

Statement I : A cyclist is moving on an unbanked road with a speed of 7 kmh$^{-1}$ and takes a sharp circular turn along a path of radius of 2m without reducing the speed. The static friction coefficient is 0.2. The cyclist will not slip and pass the curve (g = 9.8 m/s$^{2}$)
Statement II : If the road is banked at an angle of 45°, cyclist can cross the curve of 2m radius with the speed of 18.5 kmh$^{-1}$ without slipping.
In the light of the above statements, choose the correct answer from the options given below.

Accepted Answer

(D) Both statement I and statement II are true

Answer

(A) Statement I is incorrect and statement II is correct

Answer

(B) Statement I is correct and statement II is incorrect

Answer

(C) Both statement I and statement II are false

Question 45

Two identical antennas mounted on identical towers are separated from each other by a distance of 45 km. What should nearly be the minimum height of receiving antenna to receive the signals in line of sight ? (Assume radius of earth is 6400 km)

Accepted Answer

(B) 39.55 m

Answer

(A) 19.77 m

Answer

(C) 79.1 m

Answer

(D) 158.2 m

Question 46

The magnetic field in a region is given by $\vec{B} = B_{0}\left(\frac{x}{a}\right)\hat{k}$. A square loop of side d is placed with its edges along the x and y axes. The loop is moved with a constant velocity $\vec{v} = v_{0}\hat{i}$. The emf induced in the loop is :

Accepted Answer

(C) $\frac{B_{0}v_{0}d^{2}}{a}$

Answer

(A) $\frac{B_{0}v_{0}^{2}d}{2a}$

Answer

(B) $\frac{B_{0}v_{0}d}{2a}$

Answer

(D) $\frac{B_{0}v_{0}d^{2}}{2a}$

Question 47

Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass = 500g, Decay constant = 20 g/s then how much time is required for the amplitude of the system to drop to half of its initial value ? (ln 2 = 0.693)

Accepted Answer

(A) 34.65 s

Answer

(B) 17.32 s

Answer

(C) 0.034 s

Answer

(D) 15.01 s

Question 48

Calculate the time interval between 33% decay and 67% decay if half-life of a substance is 20 minutes.

Accepted Answer

(B) 20 minutes

Answer

(A) 60 minutes

Answer

(C) 40 minutes

Answer

(D) 13 minutes

Question 49

Red light differs from blue light as they have :

Accepted Answer

(A) Different frequencies and different wavelengths

Answer

(B) Different frequencies and same wavelengths

Answer

(C) Same frequencies and same wavelengths

Answer

(D) Same frequencies and different wavelengths

Question 50

The energy dissipated by a resistor is 10 mJ in 1s when an electric current of 2 mA flows through it. The resistance is _______ Ω. (Round off to the Nearest Integer)

Accepted Answer

2500

Question 51

In a parallel plate capacitor set up, the plate area of capacitor is 2 m$^{2}$ and the plates are separated by 1m. If the space between the plates are filled with a dielectric material of thickness 0.5 m and area 2m$^{2}$ (see fig.) the capacitance of the set-up will be _______ ε$_{0}$.
(Dielectric constant of the material = 3.2)
(Round off to the Nearest Integer)

Accepted Answer

3

Question 52

A force $\vec{F} = 4\hat{i} + 3\hat{j} + 4\hat{k}$ is applied on an intersection point of x = 2 plane and x-axis. The magnitude of torque of this force about a point (2, 3, 4) is ________. (Round off to the Nearest Integer)

Accepted Answer

20

Question 53

If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs to be supplied will be $\frac{x}{5}\frac{GM^{2}}{R}$ where x is ____ (Round off to the Nearest Integer)
(M is the mass of earth, R is the radius of earth, G is the gravitational constant)

Accepted Answer

3

Question 54

A deviation of 2° is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of crown and flint glass are 0.02 and 0.03 respectively and refractive index for yellow light for these glasses are 1.5 and 1.6 respectively. The refracting angles for crown glass prism will be ________° (in degree)
(Round off to the Nearest Integer)

Accepted Answer

12

Question 55

A body of mass 2kg moves under a force of $(2\hat{i} + 3\hat{j} + 5\hat{k})$ N. It starts from rest and was at the origin initially. After 4s, its new coordinates are (8, b, 20). The value of b is __________.
(Round off to the Nearest Integer)

Accepted Answer

12

Question 56

A swimmer can swim with velocity of 12 km/h in still water. Water flowing in a river has velocity 6 km/h. The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is _________°. (Round off to the Nearest Integer) (find the angle in degree)

Accepted Answer

120

Question 57

A closed organ pipe of length L and an open organ pipe contain gases of densities ρ$_{1}$ and ρ$_{2}$ respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open pipe is $\frac{x}{3}L\sqrt{\frac{\rho_{1}}{\rho_{2}}}$ where x is ________. (Round off to the Nearest Integer)

Accepted Answer

4

Question 58

A solid disc of radius 'a' and mass 'm' rolls down without slipping on an inclined plane making an angle θ with the horizontal. The acceleration of the disc will be $\frac{2}{b}g\sin	heta$ where b is ______. (Round off to the Nearest Integer)
(g = acceleration due to gravity)
(θ = angle as shown in figure)

Accepted Answer

3

Question 59

For an ideal heat engine, the temperature of the source is 127°C. In order to have 60% efficiency the temperature of the sink should be _______°C. (Round off to the Nearest Integer)

Accepted Answer

-113

Question 60

The green house gas/es is (are) :
(A) Carbon dioxide
(B) Oxygen
(C) Water vapour
(D) Methane
Choose the most appropriate answer from the options given below :

Accepted Answer

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

Answer

(A) (A) and (C) only

Answer

(B) (A) only

Answer

(D) (A) and (B) only

Question 61

In the above reaction, the reagent "A" is :

Accepted Answer

(C) Alkaline KMnO$_{4}$, H$^{+}$

Answer

(A) NaBH$_{4}$, H$_{3}$O$^{+}$

Answer

(B) LiAlH$_{4}$

Answer

(D) HCl, Zn-Hg

Question 62

Which of the following reduction reaction CANNOT be carried out with coke ?

Accepted Answer

(A) Al$_{2}$O$_{3}$ → Al

Answer

(B) ZnO → Zn

Answer

(C) Fe$_{2}$O$_{3}$ → Fe

Answer

(D) Cu$_{2}$O → Cu

Question 63

Identify the elements X and Y using the ionisation energy values given below :
Ionization energy (kJ/mol)
1$^{st}$        2$^{nd}$
X        495        4563
Y        731        1450

Accepted Answer

(A) X = Na ; Y = Mg

Answer

(B) X = Mg ; Y = F

Answer

(C) X = Mg ; Y = Na

Answer

(D) X = F ; Y = Mg

Question 64

Identify the reagent(s) 'A' and condition(s) for the reaction :

Accepted Answer

(C) A = Cl$_{2}$; UV light

Answer

(A) A = HCl; Anhydrous AlCl$_{3}$

Answer

(B) A = HCl, ZnCl$_{2}$

Answer

(D) A = Cl$_{2}$; dark, Anhydrous AlCl$_{3}$

List-I (Test/Reagents/Observation(s))	List-II (Species detected)
a.Lassaigne's Test	i.Carbon
b.Cu(II) oxide	ii.Sulphur
c.Silver nitrate	iii.N, S, P, and halogen
d.The sodium fusion extract gives black precipitate with acetic acid and lead acetate	iv.Halogen Specifically

JEE Main 16 March 2021 Shift 2 Question Paper with Answers

Physics — JEE Main 16 March 2021 Shift 2

Chemistry — JEE Main 16 March 2021 Shift 2

Mathematics — JEE Main 16 March 2021 Shift 2

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