JEE Main 25 July 2021 Shift 1 Question Paper

Question 1

The area (in sq. units) of the region, given by the set
$\left\{(x, y) \in R 	imes R \mid x \geq 0, 2x^{2} \leq y \leq 4 - 2xight\}$ is :

Accepted Answer

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

Answer

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

Answer

(B) $\frac{8}{3}$

Answer

(D) $\frac{13}{3}$

Question 2

Let 9 distinct balls be distributed among 4 boxes, $B_1, B_2, B_3$ and $B_4$. If the probability that $B_3$ contains exactly 3 balls is $k\left(\frac{3}{4}\right)^{9}$ then k lies in the set :

Accepted Answer

(C) $\left\{x \in R : \left|x - 3\right| < 1\right\}$

Answer

(A) $\left\{x \in R : \left|x - 2\right| \leq 1\right\}$

Answer

(B) $\left\{x \in R : \left|x - 5\right| \leq 1\right\}$

Answer

(D) $\left\{x \in R : \left|x - 1\right| < 1\right\}$

Question 3

The number of real roots of the equation $e^{6x} - e^{4x} - 2e^{3x} - 12e^{2x} + e^{x} + 1 = 0$ is :

Accepted Answer

(C) 2

Answer

(A) 1

Answer

(B) 4

Answer

(D) 6

Question 4

The values of a and b, for which the system of equations
2x + 3y + 6z = 8
x + 2y + az = 5
3x + 5y + 9z = b
Has no solution, are :

Accepted Answer

(C) a = 3, b $
eq$ 13

Answer

(A) $a 
eq 3$, b = 3

Answer

(B) $a 
eq 3$, b $
eq$ 13

Answer

(D) a = 3, b = 13

Question 5

Let f : R → R be defined as
$f(x) = \begin{cases} \dfrac{\lambda\left|x^{2} - 5x + 6ight|}{\mu\left(5x - x^{2} - 6ight)}, & x < 2 \ e^{\frac{	an(x-2)}{x-[x]}}, & x > 2 \ \mu, & x = 2 \end{cases}$
where [x] is the greatest integer less than or equal to x. If f is continuous at x = 2, then $\lambda + \mu$ is equal to :

Accepted Answer

(A) $e(-e + 1)$

Answer

(B) $e(e - 2)$

Answer

(C) $2e - 1$

Answer

(D) 1

Question 6

Let the foot of perpendicular from a point $P(1,2,-1)$ to the straight line $L:\frac{x}{1}=\frac{y}{0}=\frac{z}{-1}$ be N. Let a line be drawn from P parallel to the plane $x+y+2z=0$ which meets L and point Q. If $\alpha$ is the acute angle between the lines PN and PQ, then $\cos\alpha$ is equal to……

Accepted Answer

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

Answer

(A) $\frac{1}{\sqrt{5}}$

Answer

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

Answer

(D) $\frac{1}{2\sqrt{3}}$

Question 7

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

Accepted Answer

(C) ~ p

Answer

(A) q

Answer

(B) p

Answer

(D) ~ q

Question 8

Let an ellipse $E:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1, a^{2}>b^{2}$, passes through $\left(\sqrt{\frac{3}{2}},1\right)$ and has eccentricity $\frac{1}{\sqrt{3}}$. If a circle, centered at focus $F(\alpha,0), \alpha>0$, of E and radius $\frac{2}{\sqrt{3}}$, intersects E at two points P and Q, then $PQ^{2}$ is equal to :

Accepted Answer

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

Answer

(B) 3

Answer

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

Answer

(D) $\frac{8}{3}$

Question 9

A spherical gas balloon of radius 16 meter subtends an angle 60° at the eye of the observer A while the angle of elevation of its center from the eye of A is 75°. Then the height (in meter) of the top most point of the balloon from the level of the observer's eye is :

Accepted Answer

(B) $8\left(\sqrt{6}+\sqrt{2}+2\right)$

Answer

(A) $8\left(2+2\sqrt{3}+\sqrt{2}\right)$

Answer

(C) $8\left(\sqrt{6}-\sqrt{2}+2\right)$

Answer

(D) $8\left(\sqrt{2}+2+\sqrt{3}\right)$

Question 10

Let a parabola P be such that its vertex and focus lie on the positive x-axis at a distance 2 and 4 units from the origin, respectively. If tangents are drawn from O(0, 0) to the parabola P which meet P at S and R, then the area (in sq. units) of ΔSOR is equal to :

Accepted Answer

(C) 16

Answer

(A) 32

Answer

(B) $8\sqrt{2}$

Answer

(D) $16\sqrt{2}$

Question 11

The locus of the centroid of the triangle formed by any point P on this hyperbola $16x^{2}-9y^{2}+32x+36y-164=0$, and its foci is :

Accepted Answer

(B) $16x^{2}-9y^{2}+32x+36y-36=0$

Answer

(A) $16x^{2}-9y^{2}+32x+36y-144=0$

Answer

(C) $9x^{2}-16y^{2}+36x+32y-144=0$

Answer

(D) $9x^{2}-16y^{2}+36x+32y-36=0$

Question 12

Let $S_{n}$ be the sum of the first n terms of an arithmetic progression. If $S_{3n}=3S_{2n}$, then the value of $\frac{S_{4n}}{S_{2n}}$ is ;

Accepted Answer

(B) 6

Answer

(A) 2

Answer

(C) 8

Answer

(D) 4

Question 13

Let $f:[0,\infty) \rightarrow [0,\infty)$ be defined as
$f(x)=\int_{0}^{x}[y]\,dy$
where [x] is the greatest integer less than or equal to x. Which of the following is true?

Accepted Answer

(C) f is continuous at every point in $[0,\infty)$ and differentiable except at the integer points.

Answer

(A) f is differentiable at every point in $[0,\infty)$

Answer

(B) f is continuous everywhere except at the integer points in $[0,\infty)$.

Answer

(D) f is both continuous and differentiable except at the integer points in $[0,\infty)$.

Question 14

Let the vectors
$\left(2+a+b\right)\hat{i}+\left(a+2b+c\right)\hat{j}-\left(b+c\right)\hat{k},$
$\left(1+b\right)\hat{i}+2b\hat{j}-b\hat{k}$ and $\left(2+b\right)\hat{i}+2b\hat{j}+\left(1-b\right)\hat{k}, a,b,c \in R$ be co-planar. Then which of the following is true?

Accepted Answer

(B) $2b=a+c$

Answer

(A) $2a=b+c$

Answer

(C) $a=b+2c$

Answer

(D) $3c=a+b$

Question 15

Let $g:N \rightarrow N$ be defined as
$g(3n+1)=3n+2,$
$g(3n+2)=3n+3,$
$g(3n+3)=3n+1$, for all n ≥ 0
Then which of the following statements is true?

Accepted Answer

(D) There exists on onto function $f:N \rightarrow N$ such that $fog=f$

Answer

(A) There exists a function $f:N \rightarrow N$ such that $gof=f$

Answer

(B) gogog = g

Answer

(C) There exists a one-one function $f:N \rightarrow N$ such that $fog=f$

Question 16

Let $f(x)=3\sin^{4}x+10\sin^{3}x+6\sin^{2}x-3$, $x \in \left[-\frac{\pi}{6},\frac{\pi}{2}\right]$. Then, f is :

Accepted Answer

(C) decreasing in $\left(-\frac{\pi}{6},0\right)$

Answer

(A) decreasing in $\left(0,\frac{\pi}{2}\right)$

Answer

(B) increasing in $\left(-\frac{\pi}{6},\frac{\pi}{2}\right)$

Answer

(D) increasing in $\left(-\frac{\pi}{6},0\right)$

Question 17

The value of the definite integral
$\int_{\pi/24}^{5\pi/24}\frac{dx}{1+\sqrt[3]{	an 2x}}$ is :

Accepted Answer

(B) $\frac{\pi}{12}$

Answer

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

Answer

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

Answer

(D) $\frac{\pi}{18}$

Question 18

The sum of all values of x in $[0,2\pi]$, for which $\sin x+\sin 2x+\sin 3x+\sin 4x=0$, is equal to :

Accepted Answer

(B) $9\pi$

Answer

(A) $11\pi$

Answer

(C) $8\pi$

Answer

(D) $12\pi$

Question 19

If b is very small as compared to the value of a, so that the cube and other higher powers of $\frac{b}{a}$ can be neglected in the identity
$\frac{1}{a-b}+\frac{1}{a-2b}+\frac{1}{a-3b}+....+\frac{1}{a-nb}=\alpha n+\beta n^{2}+\gamma n^{3}$,

Accepted Answer

(C) $\frac{b^{2}}{3a^{3}}$

Answer

(A) $\frac{a+b}{3a^{2}}$

Answer

(B) $\frac{a^{2}+b}{3a^{3}}$

Answer

(D) $\frac{a+b^{2}}{3a^{3}}$

Question 20

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

Accepted Answer

(C) $\left(1-\sqrt{3}\right)-\log_{e}\left(\sqrt{3}-1\right)$

Answer

(A) $\left(1+\sqrt{3}\right)-\log_{e}\left(\sqrt{3}-1\right)$

Answer

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

Answer

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

Question 21

There are 5 students in class 10, 6 students in class 11 and 8 students in class 12. If the number of ways, in which 10 students can be selected from them so as to include at least 2 students from each class and at most 5 students from the total 11 students of class 10 and 11 is $100k$, then $k$ is equal to.......

Accepted Answer

238

Question 22

Let $\vec{p} = 2\hat{i} + 3\hat{j} + \hat{k}$ and $\vec{q} = \hat{i} + 2\hat{j} + \hat{k}$ be two vectors. If a vector : $\vec{r} = \left( \alpha\hat{i} + \beta\hat{j} + \gamma\hat{k} \right)$ is perpendicular to each of the vectors $\left( \vec{p} + \vec{q} \right)$ and $\left( \vec{p} - \vec{q} \right)$, and $\left| \vec{r} \right| = \sqrt{3}$, then $\left| \alpha \right| + \left| \beta \right| + \left| \gamma \right|$ is equal to......

Accepted Answer

3

Question 23

the term independent of 'x' in the expression of $\left( \frac{x+1}{x^{2/3} - x^{1/3} + 1} - \frac{x-1}{x - x^{1/2}} ight)^{10}$, where $x 
eq 0, 1$ is equal to.......

Accepted Answer

210

Question 24

Let $y = y(x)$ be solution of the following differential equation $e^y \frac{dy}{dx} - 2e^y \sin x + \sin x \cos^2 x = 0$, $y\left( \frac{\pi}{2} \right) = 0$. If $y(0) = \log_e \left( \alpha + \beta e^{-2} \right)$, then $4\left( \alpha + \beta \right)$ is equal to.......

Accepted Answer

4

Question 25

Let $M = \left\{ A = \begin{pmatrix} a & b \ c & d \end{pmatrix} : a,b,c,d \in \left\{ \pm 3, \pm 2, \pm 1, 0 ight\} ight\}$. Define $f : M ightarrow Z$, as $f\left( A ight) = \det\left( A ight)$, for all $A \in M$, where $Z$ is set of all integers. Then the number of $A \in M$ such that $f\left( A ight) = 15$ is equal to...........

Accepted Answer

16

Question 26

The ratio of the coefficient of the middle term in the expansion of $\left( 1+x \right)^{20}$ and the sum of the coefficients of two middle terms in expansion of $\left( 1+x \right)^{19}$ is.......

Accepted Answer

1

Question 27

Consider the following frequency distribution : Class : 10-20, 20-30, 30-40, 40-50, 50-60; Frequency : $\alpha$, 110, 54, 30, $\beta$. If the sum of all frequencies is 584 and median is 45, then $\left| \alpha - \beta \right|$ is equal to.......

Accepted Answer

164

Question 28

If $\alpha, \beta$ are roots of the equation $x^2 + 5\left( \sqrt{2} \right)x + 10 = 0$, $\alpha > \beta$ and $P_n = \alpha^n - \beta^n$ for each positive integer n, then the value of $\left( \frac{P_{17}P_{20} + 5\sqrt{2}P_{17}P_{19}}{P_{18}P_{19} + 5\sqrt{2}P_{18}^2} \right)$ is equal to..........

Accepted Answer

1

Question 29

If the value of $\left( 1 + \dfrac{2}{3} + \dfrac{6}{3^{2}} + \dfrac{10}{3^{3}} + .... 	ext{upto } \infty ight)^{\log_{0.25}\left( \dfrac{1}{3} + \dfrac{1}{3^{2}} + .... 	ext{upto } \infty ight)}$ is l, then $l^{2}$ is equal to ........

Accepted Answer

3

Question 30

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Moment of inertia of a circular disc 'M' and radius 'R' about X, Y axes (passing through its plane) and Z-axis which is perpendicular to its plane were found to be $I_x$, $I_y$ & $I_z$ respectively. The respective radii of gyration about all the three axes will be the same.
Reason R : A rigid body making rotational motion has fixed mass and shape.
In the light of the above statements, choose the most appropriate answer from the options given below :

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 B are correct and R is the correct explanation of A .

Answer

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

Question 31

Match List I with List II.

Choose the correct answer from the options given below :

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 32

In the Young's double slit experiment, the distance between the slits varies in time as $d(t) = d_0 + a_0 \sin \omega t$ ; where $d_0$, $\omega$ and $a_0$ are constants. The difference between the largest fringe width and the smallest fringe width obtained over time is given as :

Accepted Answer

(C) $\frac{2\lambda\ Da_0}{\left(d_0^2 - a_0^2\right)}$

Answer

(A) $\frac{\lambda D}{d_0 + a_0}$

Answer

(B) $\frac{\lambda D}{d_0^2}\ a_0$

Answer

(D) $\frac{2\lambda\ D\left(d_0\right)}{\left(d_0^2 - a_0^2\right)}$

Question 33

The minimum and maximum distances of a planet revolving around the Sun are $x_1$ and $x_2$. If the minimum speed of the planet on its trajectory is $v_0$ then its maximum speed will be :

Accepted Answer

(C) $\frac{v_0 x_2}{x_1}$

Answer

(A) $\frac{v_0 x_1^2}{x_2^2}$

Answer

(B) $\frac{v_0 x_2^2}{x_1^2}$

Answer

(D) $\frac{v_0 x_1}{x_2}$

Question 34

Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as :
(where $\lambda$ is the decay constant)

Accepted Answer

(A) $\frac{\ell n \frac{3}{2}}{\lambda}$

Answer

(B) $\frac{\ell n 2}{\lambda}$

Answer

(C) $\frac{2 \ell n 2}{\lambda}$

Answer

(D) $\frac{1}{2}\ \frac{\ell n 2}{\lambda}$

Question 35

A ray of laser of a wavelength 630 nm is incident at an angle of 30° at the diamond- air interface. It is going from diamond to air. The refractive index diamond is 2.42 and that of air is 1. Choose the correct option.

Accepted Answer

(D) refraction is not possible

Answer

(A) angle of refraction is 53.4°

Answer

(B) angle of refraction is 30°

Answer

(C) angle of refraction is 24.41°

Question 36

What should be the order of arrangement of de-Broglie wavelength of electron $\left(\lambda_e\right)$, an $\alpha-$ particle $\left(\lambda_\alpha\right)$ and proton $\left(\lambda_p\right)$ given that all have the same kinetic energy ?

Accepted Answer

(D) $\lambda_e > \lambda_p > \lambda_\alpha$

Answer

(A) $\lambda_e = \lambda_p = \lambda_\alpha$

Answer

(B) $\lambda_e < \lambda_p < \lambda_\alpha$

Answer

(C) $\lambda_e = \lambda_p > \lambda_\alpha$

Question 37

Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at 4$^{th}$ second after its fall to the next droplet is 34.3 m. At what rate the droplets are coming from the tap ? (Take g = 9.8 m/s$^2$)

Accepted Answer

(C) 1 drop / second

Answer

(A) 1 drop / 7 seconds

Answer

(B) 3 drops / 2 seconds

Answer

(D) 2 drops / second

Question 38

Two billiard balls of equal mass 30g strike a rigid wall with same speed of 108 kmph (as shown) but at different angles. If the balls get reflected with the same speed then the ratio of the magnitude of impulses imparted to ball 'a' and ball 'b' by the wall along 'X' direction is :

Accepted Answer

(A) $\sqrt{2}:1$

Answer

(B) $1:\sqrt{2}$

Answer

(C) 1 : 1

Answer

(D) 2 : 1

Question 39

Two different metal bodies A and B of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies is graphically represented as shown in the figure. The ratio of specific heat capacities is :

Accepted Answer

(A) $\frac{3}{8}$

Answer

(B) $\frac{8}{3}$

Answer

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

Answer

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

Question 40

A linearly polarized electromagnetic wave in vacuum is
$E = 3.1 \cos\left[\left(1.8ight)z - \left(5.4 	imes 10^6ight)tight]\hat{i}\ N/C$
Is incident normally on a perfectly reflecting wall at z = a. Choose the correct option

Accepted Answer

(C) The reflected wave will be $3.1 \cos\left[\left(1.8ight)z + \left(5.4 	imes 10^6ight)tight]\hat{i}\ N/C$

Answer

(A) The frequency of electromagnetic wave is $54 	imes 10^4$ Hz.

Answer

(B) The transmitted wave will be $3.1 \cos\left[\left(1.8ight)z - \left(5.4 	imes 10^6ight)tight]\hat{i}\ N/C$

Answer

(D) The wavelength is 5.4 m

Question 41

In the given figure, there is a circuit of potentiometer of length AB = 10m. The resistance per unit length is 0.1Ω per cm. Across AB, a battery of emf E and internal resistance 'r' is connected. The maximum value of emf measured by this potentiometer is :

Accepted Answer

(C) 5 V

Answer

(A) 2.75 V

Answer

(B) 6 V

Answer

(D) 2.25 V

Question 42

A monoatomic ideal gas, initially at temperature $T_1$ is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. If $\ell_1$ and $\ell_2$ are the lengths of the gas column, before and after the expansion respectively, then the value of $\frac{T_1}{T_2}$ will be :

Accepted Answer

(D) $\left(\frac{\ell_2}{\ell_1}\right)^{\frac{2}{3}}$

Answer

(A) $\frac{\ell_2}{\ell_1}$

Answer

(B) $\left(\frac{\ell_1}{\ell_2}\right)^{\frac{2}{3}}$

Answer

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

Question 43

For a gas $C_P - C_V = $ R in a state P and $C_P - C_V = $ 1.10 R in a state Q, $T_P$ and $T_Q$ are the temperatures in two different states P and Q respectively. Then

Accepted Answer

(C) $T_P > T_Q$

Answer

(A) $T_P < T_Q$

Answer

(B) $T_P = 0.9\ T_Q$

Answer

(D) $T_P = T_Q$

Question 44

In Amplitude Modulation, the message signal $V_m\left(tight) = 10\sin\left(2\pi 	imes 10^5 tight)$ volts and carrier signal $V_c\left(tight) = 20\sin\left(2\pi 	imes 10^7 tight)$ volts. The modulated signal now contains the message signal with lower side band and upper side band frequency, therefore the bandwidth of modulated signal is $\alpha$ kHz. The value of $\alpha$ is :

Accepted Answer

(A) 200 kHz

Answer

(B) 100 kHz

Answer

(C) 0

Answer

(D) 50 kHz

Question 45

Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are $Y_1$ and $Y_2$. The combination behaves as a single wire then its Young's modulus is :

Accepted Answer

(D) $Y = \frac{2Y_1 Y_2}{Y_1 + Y_2}$

Answer

(A) $Y = \frac{Y_1 Y_2}{2\left(Y_1 + Y_2\right)}$

Answer

(B) $Y = \frac{2Y_1 Y_2}{3\left(Y_1 + Y_2\right)}$

Answer

(C) $Y = \frac{Y_1 Y_2}{Y_1 + Y_2}$

Question 46

A parallel plate capacitor with plate area 'A' and distance of separation 'd' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as:
$\varepsilon\left(x\right) = \varepsilon_0 + kx$, for $\left(0 < x \leq \frac{d}{2}\right)$
$\varepsilon\left(x\right) = \varepsilon_0 + k\left(d - x\right)$, for $\left(\frac{d}{2} \leq x \leq d\right)$

Accepted Answer

(C) $\frac{kA}{2\ \ell n\left(\frac{2\varepsilon_0 + kd}{2\varepsilon_0}\right)}$

Answer

(A) 0

Answer

(B) $\frac{kA}{2}\ \ell n\left(\frac{2\varepsilon_0}{2\varepsilon_0 - kd}\right)$

Answer

(D) $\left(\varepsilon_0 + \frac{kd}{2}\right)^{2/kA}$

Question 47

The half-life of $^{198}$Au is 3 days. If atomic weight of $^{198}$Au is 198 g /mol then the activity of 2 mg of $^{198}$Au is [ in disintegration / second ] :

Accepted Answer

(C) $16.18 	imes 10^{12}$

Answer

(A) $6.06 	imes 10^{18}$

Answer

(B) $2.67 	imes 10^{12}$

Answer

(D) $32.36 	imes 10^{12}$

Question 48

A particle of mass 4M at rest disintegrates into two particles of mass M and 3M respectively having non zero velocities. The ratio of de-Broglie wavelength of particle of mass M to that of mass 3M will be :

Accepted Answer

(B) 1 : 1

Answer

(A) 3 : 1

Answer

(C) 1 : 3

Answer

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

Question 49

Identify the logic operation carried out.

Accepted Answer

(C) AND

Answer

(A) OR

Answer

(B) NOR

Answer

(D) NAND

Question 50

A particle of mass 'm' is moving in time 't' on a trajectory given by
$\vec{r} = 10\alpha t^2\hat{i} + 5\beta\left(t - 5\right)\hat{j}$
Where α and β are dimensional constants.
The angular momentum of the particle become the same as it was for t = 0 at time
t = ________seconds.

Accepted Answer

10

Question 51

In the reported figure, two bodies A and B of masses 200g and 800g are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be _______ rad /s when k = 20 N / m.

Accepted Answer

10

Question 52

A particle of mass 1 mg and charge q is lying at the mid-point of two stationary particles kept at a distance '2 m' when each is carrying same change 'q'. If the free charged particle is displaced from its equilibrium position through distance 'x' (x << 1m). The particle executes SHM. Its angular frequency of oscillation will be ________ $	imes 10^5$ rad /s if $q^2 = 10C^2$.

Accepted Answer

6000

Question 53

An inductor of 10 mH is connected to a 20 V battery through a resistor of 10kΩ and a switch . After a long time, when maximum current is set up in the circuit, the current is switched off. The current in the circuit after 1 μs is $\frac{x}{100}$ mA. Then x is equal to ________.
(Take $e^{-1}$ = 0.37 )

Accepted Answer

74

Question 54

A pendulum bob has a speed of 3 m / s at its lowest position. The pendulum is 50 cm long. The speed of bob, when the length makes an angle of 60° to the vertical will be
$\left(g = 10m/s^2\right)$ __________ m/s.

Accepted Answer

2

Question 55

A body of mass 2 kg moving with a speed of 4 m /s. makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial speed. The speed of the two body centre of mass is $\frac{x}{10}$ m / s. Then the value of x is ___________.

Accepted Answer

25

Question 56

An electric bulb rated as 200 W at 100 V is used in a circuit having 200 V supply. The resistance 'R' that must be put in series with the bulb so that the bulb delivers the same power is __________ Ω .

Accepted Answer

50

Question 57

Student A and Student B used two screw gauges of equal pitch and 100 equal circular divisions to measure the radius of a given wire. The actual value of the radius of the wire is 0.322 cm. The absolute value of the difference between the final circular scale readings observed by the students A and B is ____________.
[Figure shows position of reference 'O' when jaws of screw gauge are closed ]
Given pitch = 0.1 cm.

Accepted Answer

13

Question 58

The value of aluminium susceptibility is $2.2 	imes 10^{-5}$ . The percentage increase in the magnetic field if space within a current carrying toroid is filled with Aluminium is $\frac{x}{10^4}$. Then the value of x is __________.

Accepted Answer

22

Question 59

A circular conducting coil of radius 1 m being heated by the change of magnetic field $\vec{B}$ passing perpendicular to the plane in which the coil is laid. The resistance of the coil is 2μΩ .The magnetic field is slowly switched off such that its magnitude changes in time as
$B = \frac{4}{\pi} 	imes 10^{-3}\ 	ext{T}\left(1 - \frac{t}{100}ight)$
The energy dissipated by the coil before the magnetic field is switched off completely is
E = _________ mJ

Accepted Answer

80

Question 60

The given reaction can occur in the presence of:
(a) Bromine water (b) $Br_2$ in $CS_2$, 273 K (c) $Br_2$ / $FeBr_3$ (d) $Br_2$ in $CHCl_3$, 273 K
Choose the correct answer from the options given below:

Accepted Answer

(C) (b) and (d) only

Answer

(A) (a) and (c) only

Answer

(B) (b), (c) and (d) only

Answer

(D) (a), (b) and (d) only

Question 61

Consider the given reaction, the product 'X' is:

Accepted Answer

(C) (C)

Answer

(A) (A)

Answer

(B) (B)

Answer

(D) (D)

Question 62

Given below are two statements, one is labelled as Assertion (A) and other is labelled as Reason (R)
Assertion (A): Gabriel phthalimide synthesis cannot be used to prepare aromatic primary amines.
Reason (R): Aryl halides do not undergo nucleophilic substitution reaction.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 63

At 298.2 K the relationship between enthalpy of bond dissociation ( in kJ mol$^{-1}$) for hydrogen ($E_H$) and its isotope, deuterium ($E_D$), is best described by:

Accepted Answer

(D) $E_H \cong E_D - 7.5$

Answer

(A) $E_H = E_D$

Answer

(B) $E_H = \frac{1}{2}E_D$

Answer

(C) $E_H = 2E_D$

Question 64

An organic compound 'A' $C_4H_8$ on treatment with $KMnO_4$ / $H^+$ yields compound 'B' $C_3H_6O$. Compound 'A' also yields compound 'B' on ozonolysis. Compound 'A' is:

Accepted Answer

(A) 2-Methylpropene

Answer

(B) 1-Methylcyclopropane

Answer

(C) Cyclobutane

Answer

(D) But-2-ene

List-I	List-II
a. $\vec{C}-\vec{A}-\vec{B}=0$	i.(drawn vector diagram — see figure)
b. $\vec{A}-\vec{C}-\vec{B}=0$	ii.(drawn vector diagram — see figure)
c. $\vec{B}-\vec{A}-\vec{C}=0$	iii.(drawn vector diagram — see figure)
d. $\vec{A}+\vec{B}=-\vec{C}$	iv.(drawn vector diagram — see figure)

JEE Main 25 July 2021 Shift 1 Question Paper with Answers

Physics — JEE Main 25 July 2021 Shift 1

Chemistry — JEE Main 25 July 2021 Shift 1

Mathematics — JEE Main 25 July 2021 Shift 1

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