JEE Main 26 August 2021 Shift 2 Question Paper

Question 1

Let [t] denote the greatest integer less than or equal to t. Let $f(x) = x - [x]$, $g(x) = 1 - x + [x]$, and $h(x) = \min\{f(x), g(x)\}$, $x \in [-2, 2]$. Then h is :

Accepted Answer

(A) continuous in $[-2, 2]$ but not differentiable at more than four points in $(-2, 2)$

Answer

(B) not continuous at exactly three points in $[-2, 2]$

Answer

(C) continuous in $[-2, 2]$ but not differentiable at exactly three points in $(-2, 2)$

Answer

(D) not continuous at exactly four points in $[-2, 2]$

Question 2

Let $A = \begin{pmatrix} 1 & 0 & 0 \ 0 & 1 & 1 \ 1 & 0 & 0 \end{pmatrix}$. Then $A^{2025} - A^{2020}$ is equal to :

Accepted Answer

(A) $A^{6} - A$

Answer

(B) $A^{5}$

Answer

(C) $A^{5} - A$

Answer

(D) $A^{6}$

Question 3

The local maximum value of the function $f(x) = \left(\frac{2}{x}\right)^{x^{2}}$, $x > 0$, is

Accepted Answer

(C) $\left(e\right)^{\frac{2}{e}}$

Answer

(A) $\left(2\sqrt{e}\right)^{\frac{1}{e}}$

Answer

(B) $\left(\frac{4}{\sqrt{e}}\right)^{\frac{e}{4}}$

Answer

(D) $1$

Question 4

If the value of the integral $\int_{0}^{5} \frac{x + [x]}{e^{x - [x]}} dx = \alpha e^{-1} + \beta$, where $\alpha, \beta \in \mathbf{R}$, $5\alpha + 6\beta = 0$, and $[x]$ denotes the greatest integer less than or equal to x; then the value of $(\alpha + \beta)^{2}$ is equal to :

Accepted Answer

(B) $25$

Answer

(A) $100$

Answer

(C) $16$

Answer

(D) $36$

Question 5

The point $P\left(-2\sqrt{6}, \sqrt{3}\right)$ lies on the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ having eccentricity $\frac{\sqrt{5}}{2}$. If the tangent and normal at P to the hyperbola intersect its conjugate axis at the point Q and R respectively, then QR is equal to :

Accepted Answer

(C) $6\sqrt{3}$

Answer

(A) $4\sqrt{3}$

Answer

(B) $6$

Answer

(D) $3\sqrt{6}$

Question 6

Let $y(x)$ be the solution of the differential equation $2x^{2}dy + (e^{y} - 2x)dx = 0$, $x > 0$. If $y(e) = 1$, then $y(1)$ is equal to :

Accepted Answer

(C) $\log_{e} 2$

Answer

(A) $0$

Answer

(B) $2$

Answer

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

Question 7

Consider the two statements :
$(S1) : (p \rightarrow q) \vee (\sim q \rightarrow p)$ is a tautology.
$(S2) : (p \wedge \sim q) \wedge (\sim p \vee q)$ is a fallacy.
Then :

Accepted Answer

(C) both (S1) and (S2) are true.

Answer

(A) only (S1) is true.

Answer

(B) both (S1) and (S2) are false.

Answer

(D) only (S2) is true.

Question 8

The domain of the function $\mathrm{cosec}^{-1}\left(\frac{1 + x}{x}\right)$ is :

Accepted Answer

(D) $\left[-\frac{1}{2}, \infty\right) - \{0\}$

Answer

(A) $\left(-1, -\frac{1}{2}\right] \cup (0, \infty)$

Answer

(B) $\left[-\frac{1}{2}, 0\right) \cup [1, \infty)$

Answer

(C) $\left(-\frac{1}{2}, \infty\right) - \{0\}$

Question 9

A fair die is tossed until six is obtained on it. Let X be the number of required tosses, then the conditional probability $P\left(X \geq 5 \mid X > 2\right)$ is :

Accepted Answer

(D) $\frac{25}{36}$

Answer

(A) $\frac{125}{216}$

Answer

(B) $\frac{11}{36}$

Answer

(C) $\frac{5}{6}$

Question 10

If $\sum_{r=1}^{50} 	an^{-1} \frac{1}{2r^{2}} = p$, then the value of $	an p$ is :

Accepted Answer

(B) $\frac{50}{51}$

Answer

(A) $\frac{101}{102}$

Answer

(C) $100$

Answer

(D) $\frac{51}{50}$

Question 11

Two fair dice are thrown. The numbers on them are taken as $\lambda$ and $\mu$, and a system of linear equations
$x + y + z = 5$
$x + 2y + 3z = \mu$
$x + 3y + \lambda z = 1$
is constructed. If p is the probability that the system has a unique solution and q is the probability that the system has no solution, then :

Accepted Answer

(B) $p = \frac{5}{6}$ and $q = \frac{5}{36}$

Answer

(A) $p = \frac{1}{6}$ and $q = \frac{1}{36}$

Answer

(C) $p = \frac{5}{6}$ and $q = \frac{1}{36}$

Answer

(D) $p = \frac{1}{6}$ and $q = \frac{5}{36}$

Question 12

The locus of the mid points of the chords of the hyperbola $x^{2} - y^{2} = 4$, which touch the parabola $y^{2} = 8x$, is :

Accepted Answer

(C) $y^{2}(x - 2) = x^{3}$

Answer

(A) $y^{3}(x - 2) = x^{2}$

Answer

(B) $x^{3}(x - 2) = y^{2}$

Answer

(D) $x^{2}(x - 2) = y^{3}$

Question 13

The value of $2\sin\left(\frac{\pi}{8}\right)\sin\left(\frac{2\pi}{8}\right)\sin\left(\frac{3\pi}{8}\right)\sin\left(\frac{5\pi}{8}\right)\sin\left(\frac{6\pi}{8}\right)\sin\left(\frac{7\pi}{8}\right)$ is :

Accepted Answer

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

Answer

(A) $\frac{1}{4\sqrt{2}}$

Answer

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

Answer

(D) $\frac{1}{8\sqrt{2}}$

Question 14

If $\left(\sqrt{3} + i\right)^{100} = 2^{99}\left(p + iq\right)$, then p and q are roots of the equation :

Accepted Answer

(A) $x^{2} - \left(\sqrt{3} - 1\right)x - \sqrt{3} = 0$

Answer

(B) $x^{2} + \left(\sqrt{3} + 1\right)x + \sqrt{3} = 0$

Answer

(C) $x^{2} + \left(\sqrt{3} - 1\right)x - \sqrt{3} = 0$

Answer

(D) $x^{2} - \left(\sqrt{3} + 1\right)x + \sqrt{3} = 0$

Question 15

A hall has a square floor of dimension 10m $	imes$ 10m (see the figure) and vertical walls. If the angle GPH between the diagonals AG and BH is $\cos^{-1}\frac{1}{5}$, then the height of the hall (in meters) is :

Accepted Answer

(D) $5\sqrt{2}$

Answer

(A) $5$

Answer

(B) $2\sqrt{10}$

Answer

(C) $5\sqrt{3}$

Question 16

Let P be the plane passing through the point (1,2,3) and the line of intersection of the planes $\vec{r} \cdot \left(\hat{i} + \hat{j} + 4\hat{k}\right) = 16$ and $\vec{r} \cdot \left(-\hat{i} + \hat{j} + \hat{k}\right) = 6$. Then which of the following points does **NOT** lie on P ?

Accepted Answer

(C) $(4, 2, 2)$

Answer

(A) $(3, 3, 2)$

Answer

(B) $(6, -6, 2)$

Answer

(D) $(-8, 8, 6)$

Question 17

A 10 inches long pencil AB with mid point C and a small eraser P are placed on the horizontal top of a table such that $PC = \sqrt{5}$ inches and $\angle PCB = 	an^{-1}(2)$. The acute angle through which the pencil must be rotated about C so that the perpendicular distance between eraser and pencil becomes exactly 1 inch is :

Accepted Answer

(A) $	an^{-1}\left(\frac{3}{4}ight)$

Answer

(B) $	an^{-1}(1)$

Answer

(C) $	an^{-1}\left(\frac{4}{3}ight)$

Answer

(D) $	an^{-1}\left(\frac{1}{2}ight)$

Question 18

The value of $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \left(\frac{1 + \sin^{2} x}{1 + \pi^{\sin x}}\right) dx$ is

Accepted Answer

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

Answer

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

Answer

(B) $\frac{5\pi}{4}$

Answer

(D) $\frac{3\pi}{2}$

Question 19

A circle C touches the line $x = 2y$ at the point $(2,1)$ and intersects the circle $C_{1} : x^{2} + y^{2} + 2y - 5 = 0$ at two points P and Q such that PQ is a diameter of $C_{1}$. Then the diameter of C is :

Accepted Answer

(A) $7\sqrt{5}$

Answer

(B) $15$

Answer

(C) $\sqrt{285}$

Answer

(D) $4\sqrt{15}$

Question 20

$\lim_{x 	o 2}\left(\sum_{n=1}^{9} \frac{x}{n(n + 1)x^{2} + 2(2n + 1)x + 4}ight)$ is equal to :

Accepted Answer

(A) $\frac{9}{44}$

Answer

(B) $\frac{5}{24}$

Answer

(C) $\frac{1}{5}$

Answer

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

Question 21

The sum of all 3-digit numbers less than or equal to 500, that are formed without using the digit "1" and they all are multiple of 11, is ________.

Accepted Answer

7744

Question 22

Let a and b respectively be the points of local maximum and local minimum of the function $f(x) = 2x^{3} - 3x^{2} - 12x$. If A is the total area of the region bounded by $y = f(x)$, the x-axis and the lines $x = a$ and $x = b$, then 4A is equal to ________.

Accepted Answer

114

Question 23

If the projection of the vector $\hat{i} + 2\hat{j} + \hat{k}$ on the sum of the two vectors $2\hat{i} + 4\hat{j} - 5\hat{k}$ and $-\lambda\hat{i} + 2\hat{j} + 3\hat{k}$ is 1, then $\lambda$ is equal to ________.

Accepted Answer

5

Question 24

Let $a_{1}, a_{2}, ....., a_{10}$ be an AP with common difference $-3$ and $b_{1}, b_{2}, ....., b_{10}$ be a GP with common ratio 2. Let $c_{k} = a_{k} + b_{k}$, $k = 1, 2, ..., 10$. If $c_{2} = 12$ and $c_{3} = 13$, then $\sum_{k=1}^{10} c_{k}$ is equal to ________.

Accepted Answer

2021

Question 25

Let Q be the foot of the perpendicular from the point $P(7, -2, 13)$ on the plane containing the lines $\frac{x+1}{6} = \frac{y-1}{7} = \frac{z-3}{8}$ and $\frac{x-1}{3} = \frac{y-2}{5} = \frac{z-3}{7}$. Then $(PQ)^{2}$, is equal to ________.

Accepted Answer

96

Question 26

Let $\begin{pmatrix} n \ k \end{pmatrix}$ denotes $^{n}C_{k}$ and $\begin{bmatrix} n \ k \end{bmatrix} = \begin{cases} \begin{pmatrix} n \ k \end{pmatrix}, & 	ext{if } 0 \le k \le n \ 0, & 	ext{otherwise} \end{cases}$

If $A_{k} = \sum_{i=0}^{9} \begin{pmatrix} 9 \ i \end{pmatrix} \begin{bmatrix} 12 \ 12-k+i \end{bmatrix} + \sum_{i=0}^{8} \begin{pmatrix} 8 \ i \end{pmatrix} \begin{bmatrix} 13 \ 13-k+i \end{bmatrix}$ and $A_{4} - A_{3} = 190\,p$, then p is equal to :

Accepted Answer

49

Question 27

Let $\lambda 
e 0$ be in $\mathbf{R}$. If $\alpha$ and $\beta$ are the roots of the equation $x^{2} - x + 2\lambda = 0$, and $\alpha$ and $\gamma$ are the roots of equation $3x^{2} - 10x + 27\lambda = 0$, then $\frac{\beta\gamma}{\lambda}$ is equal to ________.

Accepted Answer

18

Question 28

Let the mean and variance of four numbers 3, 7, x and $y (x > y)$ be 5 and 10 respectively. Then the mean of four numbers $3 + 2x$, $7 + 2y$, $x + y$ and $x - y$ is ________.

Accepted Answer

12

Question 29

Let A be a $3 	imes 3$ real matrix.
If $\det(2\mathrm{Adj}(2\ \mathrm{Adj}(\mathrm{Adj}(2A)))) = 2^{41}$, then the value of $\det(A^{2})$ equal ________.

Accepted Answer

4

Question 30

The least positive integer n such that $\frac{(2i)^{n}}{(1-i)^{n-2}}, i = \sqrt{-1}$ is a positive integer, is ________.

Accepted Answer

6

Question 31

The temperature of equal masses of three different liquids x,y and z are 10°C, 20°C and 30°C respectively. The temperature of mixture when x is mixed with y is 16°C and that when y is mixed with z is 26°C. The temperature of mixture when x and z are mixed will be :

Accepted Answer

(C) 23.84°C

Answer

(A) 28.32° C

Answer

(B) 25.62° C

Answer

(D) 20.28°C

Question 32

The de-Broglie wavelength of a particle having kinetic energy E is $\lambda$. How much extra energy must be given to this particle so that the de-Broglie wavelength reduces to 75% of the initial value ?

Accepted Answer

(B) $\frac{7}{9}\mathrm{E}$

Answer

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

Answer

(C) E

Answer

(D) $\frac{16}{9}\mathrm{E}$

Question 33

A particle of mass m is suspended from a ceiling through a string of length L. The particle moves in a horizontal circle of radius r such that $r = \frac{L}{\sqrt{2}}$ .The speed of particle will be :

Accepted Answer

(A) $\sqrt{rg}$

Answer

(B) $\sqrt{2rg}$

Answer

(C) $2\sqrt{rg}$

Answer

(D) $\sqrt{\frac{rg}{2}}$

Question 34

A cylindrical container of volume $4.0 	imes 10^{-3}$ m$^{3}$ contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is 400 K. The pressure of the mixture of gases is :
[Take gas constant as 8.3 J mol$^{-1}$ K$^{-1}$]

Accepted Answer

(C) $24.9 	imes 10^{5}$ Pa

Answer

(A) $249 	imes 10^{1}$ Pa

Answer

(B) $24.9 	imes 10^{3}$ Pa

Answer

(D) 24.9 Pa

Question 35

The angle between vector $\left(\vec{A}\right)$ and $\left(\vec{A} - \vec{B}\right)$ is :

Accepted Answer

(C) $	an^{-1}\left(\frac{\sqrt{3}B}{2A - B}ight)$

Answer

(A) $	an^{-1}\left(\frac{-\frac{B}{2}}{A - B\frac{\sqrt{3}}{2}}ight)$

Answer

(B) $	an^{-1}\left(\frac{A}{0.7\,B}ight)$

Answer

(D) $	an^{-1}\left(\frac{B\cos	heta}{A - B\sin	heta}ight)$

Question 36

A light beam is described by $E = 800\ \sin\omega\left(t - \frac{x}{c}ight)$ .An electron is allowed to move normal to the propagation of light beam with a speed of $3 	imes 10^{7}$ ms$^{-1}$. What is the maximum magnetic force exerted on the electron ?

Accepted Answer

(D) $12.8 	imes 10^{-18}$ N

Answer

(A) $1.28 	imes 10^{-18}$ N

Answer

(B) $1.28 	imes 10^{-21}$ N

Answer

(C) $12.8 	imes 10^{-17}$ N

Question 37

The two thin coaxial rings, each of radius 'a' and having charges +Q and –Q respectively are separated by a distance of 's'. The potential difference between the centres of the two rings is :

Accepted Answer

(D) $\frac{Q}{2\pi\varepsilon_{0}}\left[\frac{1}{a} - \frac{1}{\sqrt{s^{2} + a^{2}}}\right]$

Answer

(A) $\frac{Q}{2\pi\varepsilon_{0}}\left[\frac{1}{a} + \frac{1}{\sqrt{s^{2} + a^{2}}}\right]$

Answer

(B) $\frac{Q}{4\pi\varepsilon_{0}}\left[\frac{1}{a} + \frac{1}{\sqrt{s^{2} + a^{2}}}\right]$

Answer

(C) $\frac{Q}{4\pi\varepsilon_{0}}\left[\frac{1}{a} - \frac{1}{\sqrt{s^{2} + a^{2}}}\right]$

Question 38

If you are provided a set of resistances 2Ω, 4Ω, 6Ω and 8Ω. Connect these resistances so as to obtain an equivalent resistance of $\frac{46}{3}\Omega$.

Accepted Answer

(D) 2Ω and 4Ω are in parallel with 6Ω and 8Ω in series

Answer

(A) 4Ω and 6Ω are in parallel with 2Ω and 8 Ω in series

Answer

(B) 6Ω and 8Ω are in parallel with 2Ω and 4Ω in series

Answer

(C) 2Ω and 6Ω are in parallel with 4Ω and 8 Ω in series

Question 39

The solid cylinder of length 80 cm and mass M has a radius of 20 cm. Calculate the density of the material used if the moment  of inertia of the cylinder about an axis CD parallel to AB as shown in figure is 2.7 kg m$^{2}$.

Accepted Answer

(D) $1.49 	imes 10^{2}$ kg / m$^{3}$

Answer

(A) 14.9 kg / m$^{3}$

Answer

(B) $7.5 	imes 10^{1}$ kg / m$^{3}$

Answer

(C) $7.5 	imes 10^{2}$ kg/m$^{3}$

Question 40

A parallel - plate capacitor with plate area A has separation d between the plates. Two dielectric slabs of dielectric constant $K_{1}$ and $K_{2}$ of same area A/2 and thickness d/2 are inserted in the space between the plates. The capacitance of the capacitor will be given by :

Accepted Answer

(A) $\frac{\varepsilon_{0}A}{d}\left(\frac{1}{2} + \frac{K_{1}K_{2}}{K_{1} + K_{2}}\right)$

Answer

(B) $\frac{\varepsilon_{0}A}{d}\left(\frac{1}{2} + \frac{K_{1}K_{2}}{2\left(K_{1} + K_{2}\right)}\right)$

Answer

(C) $\frac{\varepsilon_{0}A}{d}\left(\frac{1}{2} + \frac{K_{1} + K_{2}}{K_{1}K_{2}}\right)$

Answer

(D) $\frac{\varepsilon_{0}A}{d}\left(\frac{1}{2} + \frac{2\left(K_{1} + K_{2}\right)}{K_{1}K_{2}}\right)$

Question 41

A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a :

Accepted Answer

(C) straight line vertically down the plane

Answer

(A) hyperbola

Answer

(B) parabola in the direction of motion of plane

Answer

(D) parabola in a direction opposite to the motion of plane

Question 42

At time t = 0, a material is composed of two radioactive atoms A and B, where $N_{A}(0) = 2N_{B}(0)$. The decay constant of both kind of radioactive atoms is $\lambda$. However, A disintegrates to B and B disintegrates to C. Which of the following figures represents the evolution of $N_{B}(t)$ / $N_{B}(0)$ with respect to time t ?
$\left[\begin{array}{l} N_{A}\left(0ight) = 	ext{No. of A atoms at } t = 0 \\ N_{B}\left(0ight) = 	ext{No. of B atoms at } t = 0 \end{array}ight]$

Accepted Answer

(C) (3)

Answer

(A) (1)

Answer

(B) (2)

Answer

(D) (4)

Question 43

A transmitting antenna at top of a tower has a height of 50 m and the height of receiving antenna is 80 m. What is range of communication for Line of Sight (LoS) mode ?
[use radius of earth = 6400 km]

Accepted Answer

(D) 57.28 km

Answer

(A) 45.5 km

Answer

(B) 80.2 km

Answer

(C) 144.1 km

Question 44

A refrigerator consumes an average 35 W power to operate between temperature –10°C to 25°C. If there is no loss of energy then how much average heat per second does it transfer ?

Accepted Answer

(A) 263 J/s

Answer

(B) 298 J/s

Answer

(C) 350 J/s

Answer

(D) 35 J/s

Question 45

An electric bulb of 500 watt at 100 volt is used in a circuit having a 200 V supply. Calculate the resistance R to be connected in series with the bulb so that the power delivered by the bulb is 500 W.

Accepted Answer

(A) 20 Ω

Answer

(B) 30 Ω

Answer

(C) 5 Ω

Answer

(D) 10 Ω

Question 46

Four NOR gates are connected as shown in figure.
The truth table for the given figure is :

Accepted Answer

(D) A B | Y
0 0 | 1
0 1 | 0
1 0 | 0
1 1 | 1

Answer

(A) A B | Y
0 0 | 1
0 1 | 0
1 0 | 1
1 1 | 0

Answer

(B) A B | Y
0 0 | 0
0 1 | 1
1 0 | 1
1 1 | 0

Answer

(C) A B | Y
0 0 | 0
0 1 | 1
1 0 | 0
1 1 | 1

Question 47

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 48

If the length of the pendulum in pendulum clock increases by 0.1%, then the error in time per day is:

Accepted Answer

(C) 43.2 s

Answer

(A) 86.4 s

Answer

(B) 4.32 s

Answer

(D) 8.64 s

Question 49

Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $\frac{24}{\pi} 	imes 10^{2}$ Nm$^{-2}$. What is the minimum radius of the wire?
(Take g = 10 ms$^{-2}$)

Accepted Answer

(C) 12.5 cm

Answer

(A) 125 cm

Answer

(B) 1250 cm

Answer

(D) 1.25 cm

Question 50

Two waves are simultaneously passing through a string and their equations are :
$y_1 = A_1 \sin k(x-vt)$, $y_2 = A_2 \sin k(x-vt + x_0)$. Given amplitudes $A_1 = 12$ mm and $A_2 = 5$ mm, $x_0 = 3.5$ cm and wave number $k = 6.28$ cm$^{-1}$. The amplitude of resulting wave will be .......... mm.

Accepted Answer

7

Question 51

A source of light is placed in front of a screen. Intensity of light on the screen is I. Two Polaroids $P_1$ and $P_2$ are so placed in between the source of light and screen that the intensity of light on screen is I/2. $P_2$ should be rotated by an angle of ........... (degrees) so that the intensity of light on the screen becomes $\frac{3I}{8}$.

Accepted Answer

30

Question 52

If the maximum value of accelerating potential provided by a ratio frequency oscillator is 12 kV. The number of revolution made by a proton in a cyclotron to achieve one sixth of the speed of light is ............
$[m_p = 1.67 	imes 10^{-27}$ kg, $e = 1.6 	imes 10^{-19}$ C,
Speed of light $= 3 	imes 10^8$ m/s$]$

Accepted Answer

543

Question 53

The acceleration due to gravity is found upto an accuracy of 4% on a planet. The energy supplied to a simple pendulum to known mass 'm' to undertake oscillations of time period T is being estimated. If time period is measured to an accuracy of 3%, the accuracy to which E is known as ..........%

Accepted Answer

14

Question 54

A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad s$^{-1}$ in a uniform horizontal magnetic field of $3.0 	imes 10^{-2}$ T. The maximum emf induced the coil will be .......... $	imes 10^{-2}$ volt (rounded off to the nearest integer)

Accepted Answer

60

Question 55

Two simple harmonic motions are represented by the equations
$x_1 = 5 \sin\left(2\pi t + \frac{\pi}{4}\right)$ and $x_2 = 5\sqrt{2}\,(\sin 2\pi t + \cos 2\pi t)$.
The amplitude of second motion is ............. times the amplitude in first motion.

Accepted Answer

2

Question 56

A coil in the shape of an equilateral triangle of side 10 cm lies in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field 20 mT. The torque acting on the coil when a current of 0.2 A is passed through it and its plane becomes parallel to the magnetic field will be $\sqrt{x} 	imes 10^{-5}$ Nm. The value of x is...........

Accepted Answer

3

Question 57

For the given circuit, the power across zener diode is ............ mW.

Accepted Answer

120

Question 58

An object is placed at a distance of 12 cm from a convex lens. A convex mirror of focal length 15 cm is placed on other side of lens at 8 cm as shown in the figure. Image of object coincides with the object.
When the convex mirror is removed, a real and inverted image is formed at a position. The distance of the image from the object will be ........(cm)

Accepted Answer

50

Question 59

The coefficient of static friction between two blocks is 0.5 and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is .......N.
(take $g = 10$ ms$^{-2}$)

Accepted Answer

15

Question 60

Which one of the following phenols does not give colour when condensed with phthalic anhydride in presence of conc. $\mathrm{H_2SO_4}$ ?

Accepted Answer

(B) (2)

Answer

(A) (1)

Answer

(C) (3)

Answer

(D) (4)

Question 61

Given below are two statements : one is labelled as **Assertion (A)** and the other is labelled as **Reason (R)**.
Assertion (A) : Photochemical smog causes cracking of rubber.
Reason (R) : Presence of ozone, nitric oxide, acrolein, formaldehyde and peroxyacetyl  nitrate in photochemical smog makes it oxidizing.
Choose the most appropriate answer from the options given below :

Accepted Answer

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

Answer

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

Answer

(B) (A) is false but (R) is true.

Answer

(C) (A) is true but (R) is false

Question 62

The interaction energy of London forces between two particles is proportional to $\mathrm{r^x}$, where r is the distance between the particles. The value of x is :

Accepted Answer

(C) $-6$

Answer

(A) 3

Answer

(B) $-3$

Answer

(D) 6

Question 63

The number of non-ionisable hydrogen atoms present in the final product obtained from the hydrolysis of $\mathrm{PCl_5}$ is :

Accepted Answer

(A) 0

Answer

(B) 2

Answer

(C) 1

Answer

(D) 3

Question 64

The bond order and magnetic behaviour of $\mathrm{O_2^-}$ ion are, respectively :

Accepted Answer

(A) 1.5 and paramagnetic

Answer

(B) 1.5 and diamagnetic

Answer

(C) 2 and diamagnetic

Answer

(D) 1 and paramagnetic

List-I	List-II
a.Magnetic Induction	i. $ML^{2}T^{-2}A^{-1}$
b.Magnetic Flux	ii. $M^{0}L^{-1}A$
c.Magnetic Permeability	iii. $MT^{-2}A^{-1}$
d.Magnetization	iv. $MLT^{-2}A^{-2}$

List-I (Chemical Reaction)	List-II (Reagent used)
a. $\mathrm{CH_3COOCH_2CH_3} \rightarrow \mathrm{CH_3CH_2OH}$	i. $\mathrm{CH_3MgBr}$ / $\mathrm{H_3O^+}$ (1.equivalent)
b. $\mathrm{CH_3COOCH_3} \rightarrow \mathrm{CH_3CHO}$	ii. $\mathrm{H_2SO_4}$ / $\mathrm{H_2O}$
c. $\mathrm{CH_3C \equiv N} \rightarrow \mathrm{CH_3CHO}$	iii.DIBAL-H/ $\mathrm{H_2O}$
d. $\mathrm{CH_3C \equiv N} \rightarrow$	iv. $\mathrm{SnCl_2}$ , $\mathrm{HCl/H_2O}$

JEE Main 26 August 2021 Shift 2 Question Paper with Answers

Physics — JEE Main 26 August 2021 Shift 2

Chemistry — JEE Main 26 August 2021 Shift 2

Mathematics — JEE Main 26 August 2021 Shift 2

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