JEE Main 17 March 2021 Shift 2 Question Paper

Question 1

Let $f : R \rightarrow R$ be defined as $f(x) = e^{-x}\sin x$. If $F : [0, 1] \rightarrow R$ is a differentiable function such that $F(x) = \int_{0}^{x} f(t)\,dt$, then the value of $\int_{0}^{1}\left(F'(x) + f(x)\right)e^{x}dx$ lies in the interval

Accepted Answer

(B) $\left[\frac{330}{360}, \frac{331}{360}\right]$

Answer

(A) $\left[\frac{327}{360}, \frac{329}{360}\right]$

Answer

(C) $\left[\frac{331}{360}, \frac{334}{360}\right]$

Answer

(D) $\left[\frac{335}{360}, \frac{336}{360}\right]$

Question 2

If the integral $\int_{0}^{10}\frac{[\sin 2\pi x]}{e^{x-[x]}}dx = \alpha e^{-1} + \beta e^{-\frac{1}{2}} + \gamma$, where $\alpha, \beta, \gamma$ are integers and $[x]$ denotes the greatest integer less than or equal to $x$, then the value of $\alpha + \beta + \gamma$ is equal to :

Accepted Answer

(A) $0$

Answer

(B) $20$

Answer

(C) $25$

Answer

(D) $10$

Question 3

Let $y = y(x)$ be the solution of the differential equation
$\cos x\,(3\sin x + \cos x + 3)dy = (1 + y\sin x\,(3\sin x + \cos x + 3))dx$,
$0 \le x \le \frac{\pi}{2}$, $y(0) = 0$. Then, $y\left(\frac{\pi}{3}\right)$ is equal to:

Accepted Answer

(B) $2\log_{e}\left(\frac{2\sqrt{3}+10}{11}\right)$

Answer

(A) $2\log_{e}\left(\frac{2\sqrt{3}+9}{6}\right)$

Answer

(C) $2\log_{e}\left(\frac{\sqrt{3}+7}{2}\right)$

Answer

(D) $2\log_{e}\left(\frac{3\sqrt{3}-8}{4}\right)$

Question 4

The value of $\sum_{r=0}^{6}\left({}^{6}C_{r}\cdot{}^{6}C_{6-r}\right)$ is equal to :

Accepted Answer

(D) $924$

Answer

(A) $1124$

Answer

(B) $1324$

Answer

(C) $1024$

Question 5

The value of $\lim_{n\rightarrow\infty}\frac{[r]+[2r]+.....+[nr]}{n^{2}}$, where $r$ is non-zero real number and $[r]$ denotes the greatest integer less than or equal to $r$, is equal to :

Accepted Answer

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

Answer

(B) $r$

Answer

(C) $2r$

Answer

(D) $0$

Question 6

The number of solutions of the equation $\sin^{-1}\left[x^{2}+\frac{1}{3}\right]+\cos^{-1}\left[x^{2}-\frac{2}{3}\right] = x^{2}$, for $x \in [-1, 1]$, and $[x]$ denotes the greatest integer less than or equal to $x$, is :

Accepted Answer

(B) $0$

Answer

(A) $2$

Answer

(C) $4$

Answer

(D) Infinite

Question 7

Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be $\frac{1}{2}$ and probability of occurrence of 0 at the odd place be $\frac{1}{3}$. Then the probability that '10' is followed by '01' is equal to :

Accepted Answer

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

Answer

(A) $\frac{1}{18}$

Answer

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

Answer

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

Question 8

The number of solutions of the equation $x + 2	an x = \frac{\pi}{2}$ in the interval $[0, 2\pi]$ is :

Accepted Answer

(A) $3$

Answer

(B) $4$

Answer

(C) $2$

Answer

(D) $5$

Question 9

Let $S_{1}$, $S_{2}$ and $S_{3}$ be three sets defined as
$S_{1} = \left\{z \in \mathbb{C} : |z-1| \le \sqrt{2}\right\}$
$S_{2} = \left\{z \in \mathbb{C} : \mathrm{Re}\left((1-i)z\right) \ge 1\right\}$
$S_{3} = \left\{z \in \mathbb{C} : \mathrm{Im}(z) \le 1\right\}$
Then the set $S_{1} \cap S_{2} \cap S_{3}$

Accepted Answer

(C) has infinitely many elements

Answer

(A) is a singleton

Answer

(B) has exactly two elements

Answer

(D) has exactly three elements

Question 10

If the curve $y = y(x)$ is the solution of the differential equation
$2(x^{2} + x^{5/4})dy - y(x + x^{1/4})dx = 2x^{9/4}dx$ , $x > 0$
which passes through the point $\left(1, 1-\frac{4}{3}\log_{e}2\right)$, then the value of $y(16)$ is equal to :

Accepted Answer

(C) $4\left(\frac{31}{3}-\frac{8}{3}\log_{e}3\right)$

Answer

(A) $4\left(\frac{31}{3}+\frac{8}{3}\log_{e}3\right)$

Answer

(B) $\left(\frac{31}{3}+\frac{8}{3}\log_{e}3\right)$

Answer

(D) $\left(\frac{31}{3}-\frac{8}{3}\log_{e}3\right)$

Question 11

If the sides AB, BC and CA of a triangle ABC have 3, 5 and 6 interior points respectively, then the total number of triangles that can be constructed using these points as vertices, is equal to :

Accepted Answer

(C) $333$

Answer

(A) $364$

Answer

(B) $240$

Answer

(D) $360$

Question 12

If $x, y, z$ are in arithmetic progression with common difference $d$, $x 
eq 3d$, and the determinant of the matrix $\begin{bmatrix} 3 & 4\sqrt{2} & x \ 4 & 5\sqrt{2} & y \ 5 & k & z \end{bmatrix}$ is zero, then the value of $k^{2}$ is

Accepted Answer

(A) $72$

Answer

(B) $12$

Answer

(C) $36$

Answer

(D) $6$

Question 13

Let O be the origin. Let $\overrightarrow{OP} = x\hat{i}+y\hat{j}-\hat{k}$ and $\overrightarrow{OQ} = -\hat{i}+2\hat{j}+3x\hat{k}$, $x, y \in R$, $x > 0$, be such that $\left|\overrightarrow{PQ}\right| = \sqrt{20}$ and the vector $\overrightarrow{OP}$ is perpendicular to $\overrightarrow{OQ}$. If $\overrightarrow{OR} = 3\hat{i}+z\hat{j}-7\hat{k}$, $z \in R$, is coplanar with $\overrightarrow{OP}$ and $\overrightarrow{OQ}$, then the value of $x^{2}+y^{2}+z^{2}$ is equal to

Accepted Answer

(B) $9$

Answer

(A) $7$

Answer

(C) $2$

Answer

(D) $1$

Question 14

Two tangents are drawn from a point P to the circle $x^{2}+y^{2}-2x-4y+4=0$, such that the angle between these tangents is $	an^{-1}\left(\frac{12}{5}ight)$, where $	an^{-1}\left(\frac{12}{5}ight) \in (0, \pi)$. If the centre of the circle is denoted by C and these tangents touch the circle at points A and B, then the ratio of the areas of $\Delta PAB$ and $\Delta CAB$ is :

Accepted Answer

(B) $9 : 4$

Answer

(A) $11 : 4$

Answer

(C) $3 : 1$

Answer

(D) $2 : 1$

Question 15

Consider the function $f : R ightarrow R$ defined by $f(x) = \begin{cases} \left(2-\sin\left(\frac{1}{x}ight)ight)|x|, & x 
eq 0 \ 0, & x = 0 \end{cases}$. Then $f$ is :

Accepted Answer

(B) not monotonic on $(-\infty, 0)$ and $(0, \infty)$

Answer

(A) monotonic on $(-\infty, 0) \cup (0, \infty)$

Answer

(C) monotonic on $(0, \infty)$ only

Answer

(D) monotonic on $(-\infty, 0)$ only

Question 16

Let L be a tangent line to the parabola $y^{2} = 4x - 20$ at $(6, 2)$. If L is also a tangent to the ellipse $\frac{x^{2}}{2}+\frac{y^{2}}{b} = 1$, then the value of $b$ is equal to :

Accepted Answer

(B) $14$

Answer

(A) $11$

Answer

(C) $16$

Answer

(D) $20$

Question 17

The value of the limit $\lim_{	hetaightarrow 0}\frac{	an\left(\pi\cos^{2}	hetaight)}{\sin\left(2\pi\sin^{2}	hetaight)}$ is equal to :

Accepted Answer

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

Answer

(B) $-\frac{1}{4}$

Answer

(C) $0$

Answer

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

Question 18

Let the tangent to the circle $x^{2}+y^{2}=25$ at the point $R(3, 4)$ meet x-axis and y-axis at point P and Q, respectively. If $r$ is the radius of the circle passing through the origin O and having centre at the incentre of the triangle OPQ, then $r^{2}$ is equal to

Accepted Answer

(C) $\frac{625}{72}$

Answer

(A) $\frac{529}{64}$

Answer

(B) $\frac{125}{72}$

Answer

(D) $\frac{585}{66}$

Question 19

If the Boolean expression $(p \wedge q) \circledast (p \otimes q)$ is a tautology, then $\circledast$ and $\otimes$ are respectively given by

Accepted Answer

(A) $\rightarrow, \rightarrow$

Answer

(B) $\wedge, \vee$

Answer

(C) $\vee, \rightarrow$

Answer

(D) $\wedge, \rightarrow$

Question 20

If the equation of plane passing through the mirror image of a point $(2, 3, 1)$ with respect to line $\frac{x+1}{2}=\frac{y-3}{1}=\frac{z+2}{-1}$ and containing the line $\frac{x-2}{3}=\frac{1-y}{2}=\frac{z+1}{1}$ is $\alpha x + \beta y + \gamma z = 24$, then $\alpha + \beta + \gamma$ is equal to :

Accepted Answer

(B) $19$

Answer

(A) $20$

Answer

(C) $18$

Answer

(D) $21$

Question 21

If $1$, $\log_{10}(4^{x}-2)$ and $\log_{10}\left(4^{x}+\frac{18}{5}ight)$ are in arithmetic progression for a real number $x$, then the value of the determinant $\begin{vmatrix} 2\left(x-\frac{1}{2}ight) & x-1 & x^{2} \ 1 & 0 & x \ x & 1 & 0 \end{vmatrix}$ is equal to :

Accepted Answer

2

Question 22

Let $f : [-1, 1] \rightarrow R$ be defined as $f(x) = ax^{2}+bx+c$ for all $x \in [-1, 1]$, where $a, b, c \in R$ such that $f(-1) = 2$, $f'(-1) = 1$ and for $x \in (-1, 1)$ the maximum value of $f''(x)$ is $\frac{1}{2}$. If $f(x) \le \alpha$, $x \in [-1, 1]$, then the least value of $\alpha$ is equal to ______.

Accepted Answer

5

Question 23

Let $f : [-3, 1] ightarrow R$ be given as $f(x) = \begin{cases} \min\left\{(x+6), x^{2}ight\}, & -3 \le x \le 0 \ \max\left\{\sqrt{x}, x^{2}ight\}, & 0 \le x \le 1. \end{cases}$ If the area bounded by $y = f(x)$ and x-axis is A, then the value of $6A$ is equal to ______.

Accepted Answer

41

Question 24

Let $	an\alpha$, $	an\beta$ and $	an\gamma$; $\alpha, \beta, \gamma 
eq \frac{(2n-1)\pi}{2}$, $n \in N$ be the slopes of three line segments OA, OB and OC, respectively, where O is origin. If circumcentre of $\Delta ABC$ coincides with origin and its orthocentre lies on y-axis, then the value of $\left(\frac{\cos 3\alpha + \cos 3\beta + \cos 3\gamma}{\cos\alpha\cos\beta\cos\gamma}ight)^{2}$ is equal to :

Accepted Answer

144

Question 25

Consider a set of $3n$ numbers having variance 4. In this set, the mean of first $2n$ numbers is 6 and the mean of the remaining $n$ numbers is 3. A new set is constructed by adding 1 into each of first $2n$ numbers, and subtracting 1 from each of the remaining $n$ numbers. If the variance of the new set is $k$, then $9k$ is equal to ______.

Accepted Answer

68

Question 26

Let the coefficients of third, fourth and fifth terms in the expansion of $\left(x+\frac{a}{x^{2}}ight)^{n}$, $x 
eq 0$, be in the ratio $12 : 8 : 3$. Then the term independent of $x$ in the expansion, is equal to ________.

Accepted Answer

4

Question 27

Let $A = \begin{bmatrix} a & b \ c & d \end{bmatrix}$ and $B = \begin{bmatrix} \alpha \ \beta \end{bmatrix} 
eq \begin{bmatrix} 0 \ 0 \end{bmatrix}$ such that $AB = B$ and $a + d = 2021$, then the value of $ad - bc$ is equal to ________.

Accepted Answer

2020

Question 28

Let $\vec{x}$ be a vector in the plane containing vectors $\vec{a} = 2\hat{i}-\hat{j}+\hat{k}$ and $\vec{b} = \hat{i}+2\hat{j}-\hat{k}$. If the vector $\vec{x}$ is perpendicular to $\left(3\hat{i}+2\hat{j}-\hat{k}\right)$ and its projection on $\vec{a}$ is $\frac{17\sqrt{6}}{2}$, then the value of $\left|\vec{x}\right|^{2}$ is equal to ________.

Accepted Answer

486

Question 29

Let $I_{n} = \int_{1}^{e} x^{19}\left(\log|x|\right)^{n}dx$, where $n \in N$. If $(20)I_{10} = \alpha I_{9} + \beta I_{8}$, for natural numbers $\alpha$ and $\beta$, then $\alpha - \beta$ equal to _______.

Accepted Answer

1

Question 30

Let P be an arbitrary point having sum of the squares of the distance from the planes $x+y+z=0$, $lx-nz=0$ and $x-2y+z=0$, equal to 9. If the locus of the point P is $x^{2}+y^{2}+z^{2}=9$, then the value of $l-n$ is equal to _______.

Accepted Answer

0

Question 31

A rubber ball is released from a height of 5 m above the floor. It bounces back repeatedly, always rising to $\frac{81}{100}$ of the height through which it falls. Find the average speed of the ball. (Take g = 10 ms$^{-2}$)

Accepted Answer

(D) 2.50 ms$^{-1}$

Answer

(A) 3.0 ms$^{-1}$

Answer

(B) 3.50 ms$^{-1}$

Answer

(C) 2.0 ms$^{-1}$

Question 32

If one mole of the polyatomic gas is having two vibrational modes and β is the ratio of molar specific heats for polyatomic gas $\left(\beta = \frac{C_{P}}{C_{V}}\right)$ then the value of β is :

Accepted Answer

(B) 1.2

Answer

(A) 1.02

Answer

(C) 1.25

Answer

(D) 1.35

Question 33

Which one of the following will be the output of the given circuit ?

Accepted Answer

(D) XOR Gate

Answer

(A) NOR Gate

Answer

(B) NAND Gate

Answer

(C) AND Gate

Question 34

An object is located at 2 km beneath the surface of the water. If the fractional compression $\frac{\Delta V}{V}$ is 1.36% , the ratio of hydraulic stress to the corresponding hydraulic strain will be ___________.
[Given : density of water is 1000 kg m$^{-3}$ and g = 9.8 ms$^{-2}$.]

Accepted Answer

(D) 1.44 × 10$^{9}$ Nm$^{-2}$

Answer

(A) 1.96 × 10$^{7}$ Nm$^{-2}$

Answer

(B) 1.44 × 10$^{7}$ Nm$^{-2}$

Answer

(C) 2.26 × 10$^{9}$ Nm$^{-2}$

Question 35

A geostationary satellite is orbiting around an arbitary planet 'P' at a height of 11R above the surface of 'P' , R being the radius of 'P'. The time period of another satellite in hours at a height of 2R from the surface of 'P' is__________.'P' has the time period of 24 hours.

Accepted Answer

(C) 3

Answer

(A) $6\sqrt{2}$

Answer

(B) $\frac{6}{\sqrt{2}}$

Answer

(D) 5

Question 36

A sound wave of frequency 245 Hz travels with the speed of 300 ms$^{-1}$ along the positive x-axis. Each point of the wave moves to and fro through a total distance of 6 cm. What will be the mathematical expression of this travelling wave ?

Accepted Answer

(D) Y(x,t) = 0.03 [sin 5.1 x − (1.5 × 10$^{3}$)t]

Answer

(A) Y(x,t) = 0.03 [sin 5.1 x − (0.2 × 10$^{3}$)t]

Answer

(B) Y(x,t) = 0.06 [sin 5.1 x − (1.5 × 10$^{3}$)t]

Answer

(C) Y(x,t) = 0.06 [sin 0.8 x − (0.5 × 10$^{3}$)t]

Question 37

Which one is the correct option for the two different thermodynamic processes ?

Accepted Answer

(B) (c) and (d)

Answer

(A) (c) and (a)

Answer

(C) (a) only

Answer

(D) (b) and (c)

Question 38

The velocity of a particle is v = v$_{0}$ + gt + Ft$^{2}$. Its position is x = 0 at t = 0 ; then its displacement after time (t = 1) is :

Accepted Answer

(B) v$_{0}$ + $\frac{g}{2}$ + $\frac{F}{3}$

Answer

(A) v$_{0}$ + g + F

Answer

(C) v$_{0}$ + $\frac{g}{2}$ + F

Answer

(D) v$_{0}$ + 2g + 3F

Question 39

A carrier signal C(t) = 25 sin (2.512 × 10$^{10}$ t) is amplitude modulated by a message signal m(t) = 5 sin (1.57 × 10$^{8}$ t) and transmitted through an antenna.What will be the bandwidth of the modulated signal ?

Accepted Answer

(D) 50 MHz

Answer

(A) 8 GHz

Answer

(B) 2.01 GHz

Answer

Question 40

Two cells of emf 2E and E with internal resistance r$_{1}$ and r$_{2}$ respectively are connected in series to an external resistor R (see figure). The value of R, at which the potential difference across the terminals of the first cell becomes zero is

Accepted Answer

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

Answer

(A) r$_{1}$ + r$_{2}$

Answer

(C) $\frac{r_{1}}{2} + r_{2}$

Answer

(D) r$_{1}$ − r$_{2}$

Question 41

A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point P which lies on the centre of the semicircle ?

Accepted Answer

(B) $\frac{\mu_{0}I}{4\pi r}\left(2 + \pi\right)$

Answer

(A) $\frac{\mu_{0}I}{4\pi r}\left(2 - \pi\right)$

Answer

(C) $\frac{\mu_{0}I}{2\pi r}\left(2 + \pi\right)$

Answer

(D) $\frac{\mu_{0}I}{2\pi r}\left(2 - \pi\right)$

Question 42

The four arms of a Wheatstone bridge have resistances as shown in the figure. A galvanometer of 15 Ω resistance is connected across BD. Calculate the current through the galvanometer when a potential difference of 10V is maintained across AC.

Accepted Answer

(C) 4.87 mA

Answer

(A) 2.44 μA

Answer

(B) 2.44 mA

Answer

(D) 4.87 μA

Question 43

Two particles A and B of equal masses are suspended from two massless springs of spring constants K$_{1}$ and K$_{2}$ respectively.If the maximum velocities during oscillations are equal, the ratio of the amplitude of A and B is

Accepted Answer

(D) $\sqrt{\frac{K_{2}}{K_{1}}}$

Answer

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

Answer

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

Answer

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

Question 44

Match List-I with List-II
Choose the most appropriate answer from the options given below :

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 45

The atomic hydrogen emits a line spectrum consisting of various series.Which series of hydrogen atomic spectra is lying in the visible region ?

Accepted Answer

(D) Balmer series

Answer

(A) Brackett series

Answer

(B) Paschen series

Answer

(C) Lyman series

Question 46

Two identical photocathodes receive the light of frequencies f$_{1}$ and f$_{2}$ respectively. If the velocities of the photo-electrons coming out are v$_{1}$ and v$_{2}$ respectively, then

Accepted Answer

(A) $v_{1}^{2} - v_{2}^{2} = \frac{2h}{m}\left[f_{1} - f_{2}\right]$

Answer

(B) $v_{1}^{2} + v_{2}^{2} = \frac{2h}{m}\left[f_{1} + f_{2}\right]$

Answer

(C) $v_{1} + v_{2} = \left[\frac{2h}{m}\left(f_{1} + f_{2}\right)\right]^{\frac{1}{2}}$

Answer

(D) $v_{1} - v_{2} = \left[\frac{2h}{m}\left(f_{1} - f_{2}\right)\right]^{1/2}$

Question 47

What happens to the inductive reactance and the current in a purely inductive circuit if the frequency is halved ?

Accepted Answer

(B) Inductive reactance will be halved and current will be doubled.

Answer

(A) Both, inductive reactance and current will be halved.

Answer

(C) Inductive reactance will be doubled and current will be halved.

Answer

(D) Both, inducting reactance and current will be doubled.

Question 48

A sphere of mass 2kg and radius 0.5 m is rolling with an initial speed of 1 ms$^{-1}$ goes up an inclined plane which makes an angle of 30° with the horizontal plane, without slipping. How low will the sphere take to return to the starting point A ?

Accepted Answer

(C) 0.57 s

Answer

(A) 0.60 s

Answer

(B) 0.52 s

Answer

(D) 0.80 s

Question 49

The electric field intensity produced by the radiation coming from a 100 W bulb at a distance of 3m is E. The electric field intensity produced by the radiation coming from 60 W at the same distance is $\sqrt{\frac{x}{5}}$E. Where the value of x =_________.

Accepted Answer

3

Question 50

A body of mass 1 kg rests on a horizontal floor with which it has a coefficient of static friction $\frac{1}{\sqrt{3}}$ . It is desired to make the body move by applying the minimum possible force F N. The value of F will be ___________. (Round off to the Nearest Integer)
[Take g = 10 ms$^{-2}$]

Accepted Answer

5

Question 51

A boy of mass 4 kg is standing on a piece of wood having mass 5kg . If the coefficient of friction between the wood and the floor is 0.5, the maximum force that the boy can exert on the rope so that the piece of wood does not move from its place is _________N.(Round off to the Nearest Integer)
[Take g = 10 ms$^{-2}$]

Accepted Answer

30

Question 52

Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes 0.01 cm$^{3}$ of oleic acid per cm$^{3}$ of the solution. Then you make a thin film of this solution (monomolecular thickness) of area 4 cm$^{2}$ by considering 100 spherical drops of radius $\left(\frac{3}{40\pi}ight)^{\frac{1}{3}} 	imes 10^{-3}$ cm. Then the thickness of oleic acid layer will be x × 10$^{-14}$ m.
Where x is___________.

Accepted Answer

25

Question 53

A particle of mass m moves in a circular orbit in a central potential field U(r) = U$_{0}$r$^{4}$ . If Bohr's quantization conditions are applied, radii of possible orbitals r$_{n}$ vary with n$^{1/\alpha}$ , where α is___________.

Accepted Answer

3

Question 54

The electric field in a region is given by $\vec{E} = \frac{2}{5}E_{0}\hat{i} + \frac{3}{5}E_{0}\hat{j}$ with E$_{0}$ = 4.0 × 10$^{3}$ $\frac{N}{C}$ .The flux of this field through a rectangular surface area 0.4 m$^{2}$ parallel to the Y − Z plane is _________Nm$^{2}$C$^{-1}$.

Accepted Answer

640

Question 55

The disc of mass M with uniform surface mass density σ is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position $\frac{x}{3}\frac{a}{\pi}$ , $\frac{x}{3}\frac{a}{\pi}$ where x is ________.
(Round off to the Nearest Integer)
[a is an area as shown in the figure]

Accepted Answer

4

Question 56

The image of an object placed in air formed by a convex refracting surface is at a distance of 10 m behind the surface. The image is real and is at $\frac{2^{rd}}{3}$ of the distance of the object from the surface .The wavelength of light inside the surface is $\frac{2}{3}$ times the wavelength in air. The radius of the curved surface is $\frac{x}{13}$ m. the value of 'x' is__________.

Accepted Answer

30

Question 57

A 2 μF capacitor C$_{1}$ is first charged to a potential difference of 10 V using a battery.Then the battery is removed and the capacitor is connected to an uncharged capacitor C$_{2}$ of 8μF. The charge in C$_{2}$ on equilibrium condition is_______μC. (Round off to the Nearest Integer)

Accepted Answer

16

Question 58

Seawater at a frequency f = 9 × 10$^{2}$ Hz, has permittivity ε = 80ε$_{0}$ and resistivity ρ = 0.25 Ωm. Imagine a parallel plate capacitor is immersed in seawater and is driven by an alternating voltage source V(t)=V$_{0}$ sin (2πft). Then the conduction current density becomes 10$^{x}$ times the displacement current density after time t = $\frac{1}{800}$ s. The value of x is ________
(Given : $\frac{1}{4\pi\varepsilon_{0}} = 9 	imes 10^{9}\,\mathrm{Nm}^{2}\mathrm{C}^{-2}$)

Accepted Answer

6

Question 59

Fructose is an example of :-

Accepted Answer

(B) Ketohexose

Answer

(A) Pyranose

Answer

(C) Aldohexose

Answer

(D) Heptose

Question 60

The set of elements that differ in mutual relationship from those of the other sets is :

Accepted Answer

(D) Li – Na

Answer

(A) Li – Mg

Answer

(B) B – Si

Answer

(C) Be – Al

Question 61

The functional groups that are responsible for the ion-exchange property of cation and anion exchange resins, respectively, are :

Accepted Answer

(A) –SO$_{3}$H and –NH$_{2}$

Answer

(B) –SO$_{3}$H and –COOH

Answer

(C) –NH$_{2}$ and –COOH

Answer

(D) –NH$_{2}$ and –SO$_{3}$H

Question 62

Match List-I and List-II :
Choose the correct answer from the options given below :

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 63

The correct pair(s) of the ambident nucleophiles is (are) :
(A) AgCN/KCN
(B) RCOOAg/RCOOK
(C) AgNO$_{2}$/KNO$_{2}$
(D) AgI/KI

Accepted Answer

(C) (A) and (C) only

Answer

(A) (B) and (C) only

Answer

(B) (A) only

Answer

(D) (B) only

Question 64

The set that represents the pair of neutral oxides of nitrogen is :

Accepted Answer

(A) NO and N$_{2}$O

Answer

(B) N$_{2}$O and N$_{2}$O$_{3}$

Answer

(C) N$_{2}$O and NO$_{2}$

Answer

(D) NO and NO$_{2}$

List-I	List-II
a.Phase difference between current and voltage in a purely resistive AC circuit	i. $\frac{\pi}{2}$ ; current leads voltage
b.Phase difference between current and voltage in a pure inductive AC circuit	ii.zero
c.Phase difference between current and voltage in a pure capacitive AC circuit	iii. $\frac{\pi}{2}$ ; current lags voltage
d.Phase difference between current and voltage in an LCR series circuit	iv. $\tan^{-1}\left(\frac{X_{C} - X_{L}}{R}\right)$

List-I	List-II
a.Haematite	i.Al $_{2}$ O $_{3}$ .xH $_{2}$ O
b.Bauxite	ii.Fe $_{2}$ O $_{3}$
c.Magnetite	iii.CuCO $_{3}$ .Cu(OH) $_{2}$
d.Malachite	iv.Fe $_{3}$ O $_{4}$

List-I	List-II
a.[Co(NH $_{3}$ ) $_{6}$ ] [Cr(CN) $_{6}$ ]	i.Linkage isomerism
b.[Co(NH $_{3}$ ) $_{3}$ (NO $_{2}$ ) $_{3}$ ]	ii.Solvate isomerism
c.[Cr(H $_{2}$ O) $_{6}$ ]Cl $_{3}$	iii.Co-ordination isomerism
d. $cis$ -[CrCl $_{2}$ (ox) $_{2}$ ] $^{3-}$	iv.Optical isomerism

List-I (Chemical Compound)	List-II (Used as)
a.Sucralose	i.Synthetic detergent
b.Glyceryl ester of stearic acid	ii.Artificial sweetener
c.Sodium benzoate	iii.Antiseptic
d.Bithionol	iv.Food preservative

JEE Main 17 March 2021 Shift 2 Question Paper with Answers

Physics — JEE Main 17 March 2021 Shift 2

Chemistry — JEE Main 17 March 2021 Shift 2

Mathematics — JEE Main 17 March 2021 Shift 2

Chapters tested in this paper

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