JEE Main 27 July 2022 Shift 1 Question Paper

Question 1

Let $R_1$ and $R_2$ be two relations defined on $\mathbb{R}$ by $a\,R_1\,b \Leftrightarrow ab \ge 0$ and $a\,R_2\,b \Leftrightarrow a \ge b$, then

Accepted Answer

(D) neither $R_1$ nor $R_2$ is an equivalence relation

Answer

(A) $R_1$ is an equivalence relation but not $R_2$

Answer

(B) $R_2$ is an equivalence relation but not $R_1$

Answer

(C) both $R_1$ and $R_2$ are equivalence relations

Question 2

Let $f, g : \mathbb{N}-\{1\} 	o \mathbb{N}$ be functions defined by $f(a) = \alpha$, where $\alpha$ is the maximum of the powers of those primes p such that $p^{\alpha}$ divides $a$, and $g(a) = a+1$, for all $a \in \mathbb{N}-\{1\}$. Then, the function $f + g$ is

Accepted Answer

(D) neither one-one nor onto

Answer

(A) one-one but not onto

Answer

(B) onto but not one-one

Answer

(C) both one-one and onto

Question 3

Let the minimum value $v_0$ of $v = |z|^2 + |z-3|^2 + |z-6i|^2$, $z \in \mathbb{C}$ is attained at $z = z_0$. Then $\left| 2z_0^2 - \bar{z}_0^3 + 3 \right|^2 + v_0^2$ is equal to

Accepted Answer

(A) 1000

Answer

(B) 1024

Answer

(C) 1105

Answer

(D) 1196

Question 4

Let $A = \begin{pmatrix} 1 & 2 \ -2 & -5 \end{pmatrix}$. Let $\alpha, \beta \in \mathbb{R}$ be such that $\alpha A^2 + \beta A = 2I$. Then $\alpha + \beta$ is equal to -

Accepted Answer

(D) 10

Answer

(A) -10

Answer

(B) -6

Answer

(C) 6

Question 5

The remainder when $(2021)^{2022} + (2022)^{2021}$ is divided by 7 is

Accepted Answer

(A) 0

Answer

(B) 1

Answer

(C) 2

Answer

(D) 6

Question 6

Suppose $a_1, a_2$, ...., $a_n$,... be an arithmetic progression of natural numbers. If the ratio of the sum of the first five terms of the sum of first nine terms of the progression is 5 : 17 and $110 < a_{15} < 120$, then the sum of the first ten terms of the progression is equal to -

Accepted Answer

(B) 380

Answer

(A) 290

Answer

(C) 460

Answer

(D) 510

Question 7

Let $f : \mathbb{R} 	o \mathbb{R}$ be a function defined as $f(x) = a\sin\left(\frac{\pi[x]}{2}ight) + [2-x]$, $a \in \mathbb{R}$, where [t] is the greatest integer less than or equal to $t$. If $\lim_{x 	o -1} f(x)$ exists, then the value of $\int_{0}^{4} f(x)\,dx$ is equal to :

Accepted Answer

(B) -2

Answer

(A) -1

Answer

(C) 1

Answer

(D) 2

Question 8

$I = \int_{\pi/4}^{\pi/3}\left(\frac{8\sin x - \sin 2x}{x}\right)dx$. Then

Accepted Answer

(C) $\frac{5\pi}{12} < I < \frac{\sqrt{2}}{3}\pi$

Answer

(A) $\frac{\pi}{2} < I < \frac{3\pi}{4}$

Answer

(B) $\frac{\pi}{5} < I < \frac{5\pi}{12}$

Answer

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

Question 9

The area of the smaller region enclosed by the curves $y^2 = 8x + 4$ and $x^2 + y^2 + 4\sqrt{3}x - 4 = 0$ is equal to

Accepted Answer

(C) $\frac{1}{3}\left(4 - 12\sqrt{3} + 8\pi\right)$

Answer

(A) $\frac{1}{3}\left(2 - 12\sqrt{3} + 8\pi\right)$

Answer

(B) $\frac{1}{3}\left(2 - 12\sqrt{3} + 6\pi\right)$

Answer

(D) $\frac{1}{3}\left(4 - 12\sqrt{3} + 6\pi\right)$

Question 10

Let $y = y_1(x)$ and $y = y_2(x)$ be two distinct solutions of the differential equation $\frac{dy}{dx} = x + y$, with $y_1(0) = 0$ and $y_2(0) = 1$ respectively. Then, the number of points of intersection of $y = y_1(x)$ and $y = y_2(x)$ is

Accepted Answer

(A) 0

Answer

(B) 1

Answer

(C) 2

Answer

(D) 3

Question 11

Let P $(a, b)$ be a point on the parabola $y^2 = 8x$ such that the tangent at P passes through the centre of the circle $x^2 + y^2 - 10x - 14y + 65 = 0$. Let A be the product of all possible values of $a$ and $B$ be the product of all possible values of $b$. Then the value of A + B is equal to :

Accepted Answer

(D) 65

Answer

(A) 0

Answer

(B) 25

Answer

(C) 40

Question 12

Let $\vec{a} = \alpha\hat{i} + \hat{j} + \beta\hat{k}$ and $\vec{b} = 3\hat{i} - 5\hat{j} + 4\hat{k}$ be two vectors, such that $\vec{a} 	imes \vec{b} = -\hat{i} + 9\hat{i} + 12k$. Then the projection of $\vec{b} - 2\vec{a}$ on $\vec{b} + \vec{a}$ is equal to

Accepted Answer

(D) $\frac{46}{5}$

Answer

(A) 2

Answer

(B) $\frac{39}{5}$

Answer

(C) 9

Question 13

Let $\vec{a} = 2\hat{i} - \hat{j} + 5\hat{k}$ and $\vec{b} = \alpha\hat{i} + \beta\hat{j} + 2\hat{k}$. If $\left(\left(\vec{a} 	imes \vec{b}ight) 	imes \hat{i}ight).\hat{k} = \frac{23}{2}$, then $\left| \vec{b} 	imes 2\hat{j} ight|$ is equal to

Accepted Answer

(B) 5

Answer

(A) 4

Answer

(C) $\sqrt{21}$

Answer

(D) $\sqrt{17}$

Question 14

Let S be the sample space of all five digit numbers. If $p$ is the probability that a randomly selected number from S, is a multiple of 7 but not divisible by 5, then $9p$ is equal to

Accepted Answer

(C) 1.0285

Answer

(A) 1.0146

Answer

(B) 1.2085

Answer

(D) 1.1521

Question 15

Let a vertical tower AB of height $2h$ stands on a horizontal ground. Let from a point P on the ground a man can see upto height $h$ of the tower with an angle of elevation $2\alpha$. When from $P$, he moves a distance d in the direction of $\overrightarrow{AP}$, he can see the top B of the tower with an angle of elevation $\alpha$. If $d = \sqrt{7}h$, then $	an\alpha$ is equal to

Accepted Answer

(C) $\sqrt{7} - 2$

Answer

(A) $\sqrt{5} - 2$

Answer

(B) $\sqrt{3} - 1$

Answer

(D) $\sqrt{7} - \sqrt{3}$

Question 16

$\left(p\wedge r\right)\Leftrightarrow\left(p\wedge\left(\sim q\right)\right)$ is equivalent to $\left(\sim p\right)$ when r is

Accepted Answer

(C) $q$

Answer

(A) $p$

Answer

(B) $\sim p$

Answer

(D) $\sim q$

Question 17

If the plane P passes through the intersection of two mutually perpendicular planes 2x + ky − 5z = 1 and 3kx − ky + z = 5, k < 3 and intercepts a unit length on positive x-axis, then the intercept made by the plane P on the y-axis is

Accepted Answer

(D) 7

Answer

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

Answer

(B) $\frac{5}{11}$

Answer

(C) 6

Question 18

Let A(1, 1), B(-4, 3) C(-2, -5) be vertices of a triangle ABC, P be a point on side BC, and $\Delta_{1}$ and $\Delta_{2}$ be the areas of triangle APB and ABC. Respectively. If $\Delta_{1}:\Delta_{2}=4:7$, then the area enclosed by the lines AP, AC and the x-axis is

Accepted Answer

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

Answer

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

Answer

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

Answer

(D) 1

Question 19

If the circle $x^{2}+y^{2}-2gx+6y-19c=0$, $g,c\in\mathbb{R}$ passes through the point (6, 1) and its centre lies on the line x − 2cy = 8, then the length of intercept made by the circle on x-axis is

Accepted Answer

(D) $2\sqrt{23}$

Answer

(A) $\sqrt{11}$

Answer

(B) 4

Answer

(C) 3

Question 20

Let a function $f:\mathbb{R}ightarrow\mathbb{R}$ be defined as :
$f\left(xight)=\begin{cases}\int_{0}^{x}\left(5-\left|t-3ight|ight)dt, & x>4\ x^{2}+bx, & x\le 4\end{cases}$
where $b\in\mathbb{R}$. If $f$ is continuous at x = 4, then which of the following statements is NOT true ?

Accepted Answer

(C) $f$ is increasing in $\left(-\infty,\frac{1}{8}\right)\cup\left(8,\infty\right)$

Answer

(A) $f$ is not differentiable at x = 4

Answer

(B) $f\,'\left(3\right)+f\,'\left(5\right)=\frac{35}{4}$

Answer

(D) $f$ has a local minima at $x=\frac{1}{8}$

Question 21

For $k\in\mathbb{R}$, let the solutions of the equation $\cos\left(\sin^{-1}\left(x\cot\left(	an^{-1}\left(\cos\left(\sin^{-1}xight)ight)ight)ight)ight)=k,\;0<\left|xight|<\frac{1}{\sqrt{2}}$ be $\alpha$ and $\beta$, where the inverse trigonometric functions take only principal values. If the solutions of the equation $x^{2}-bx-5=0$ are $\frac{1}{\alpha^{2}}+\frac{1}{\beta^{2}}$ and $\frac{\alpha}{\beta}$, then $\frac{b}{k^{2}}$ is equal to ______.

Accepted Answer

12

Question 22

The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation. Then, the correct standard deviation is __________.

Accepted Answer

2

Question 23

Let the line $\frac{x-3}{7}=\frac{y-2}{-1}=\frac{z-3}{-4}$ intersect the plane containing the lines $\frac{x-4}{1}=\frac{y+1}{-2}=\frac{z}{1}$ and $4ax-y+5z-7a=0=2x-5y-z-3$, $a\in\mathbb{R}$ at the point $P\left(\alpha,\beta,\gamma\right)$. Then the value of $\alpha+\beta+\gamma$ equals ______.

Accepted Answer

12

Question 24

An ellipse $E:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ passes through the vertices of the hyperbola $H:\frac{x^{2}}{49}-\frac{y^{2}}{64}=-1$. Let the major and minor axes of the ellipse E coincide with the transverse and conjugate axes of the hyperbola H. Let the product of the eccentricities of E and H be $\frac{1}{2}$. If $l$ is the length of the latus rectum of the ellipse E, then the value of $113l$ is equal to ______.

Accepted Answer

1552

Question 25

Let y = y(x) be the solution curve of the differential equation
$\sin\left(2x^{2}ight)\log_{e}\left(	an x^{2}ight)dy+\left(4xy-4\sqrt{2}x\sin\left(x^{2}-\frac{\pi}{4}ight)ight)dx=0$, $0<x<\sqrt{\frac{\pi}{2}}$, which passes through the point $\left(\sqrt{\frac{\pi}{6}},1ight)$. Then $\left|y\left(\sqrt{\frac{\pi}{3}}ight)ight|$ is equal to ______.

Accepted Answer

1

Question 26

Let $M$ and $N$ be the number of points on the curve $y^{5}-9xy+2x=0$, where the tangents to the curve are parallel to x-axis and y-axis, respectively. Then the value of M + N equals ________.

Accepted Answer

2

Question 27

Let $f\left(x\right)=2x^{2}-x-1$ and $S=\left\{n\in\mathbb{Z}:\left|f\left(n\right)\right|\le 800\right\}$. Then, the value of $\sum_{n\in S}f\left(n\right)$ is equal to ________.

Accepted Answer

10620

Question 28

Let S be the set containing all $3	imes 3$ matrices with entries from $\{-1,\,0,\,1\}$. The total number of matrices $A\in S$ such that the sum of all the diagonal elements of $A^{T}A$ is 6 is __________.

Accepted Answer

5376

Question 29

If the length of the latus rectum of the ellipse $x^{2}+4y^{2}+2x+8y-\lambda=0$ is 4, and $l$ is the length of its major axis, then $\lambda+l$ is equal to ______.

Accepted Answer

75

Question 30

Let $S=\left\{z\in\mathbb{C}:z^{2}+\bar{z}=0\right\}$. Then $\sum_{z\in S}\left(\mathrm{Re}\left(z\right)+\mathrm{Im}\left(z\right)\right)$ is equal to ______.

Accepted Answer

0

Question 31

A torque meter is calibrated to reference standards of mass, length and time each with 5% accuracy. After calibration, the measured torque with this torque meter will have net accuracy of :

Accepted Answer

(B) 25%

Answer

(A) 15%

Answer

(C) 75%

Answer

(D) 5%

Question 32

A bullet is shot vertically downwards with an initial velocity of 100 m/s from a certain height. Within 10 s, the bullet reaches the ground and instantaneously comes to rest due to the perfectly inelastic collision. The velocity-time curve for total time t = 20 s will be : (Take g = 10 m/s$^{2}$)

Accepted Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Answer

(D) (D)

Question 33

Sand is being dropped from a stationary dropper at a rate of 0.5 kgs$^{-1}$ on a conveyor belt moving with a velocity of 5 ms$^{-1}$. The power needed to keep belt moving with the same velocity will be :

Accepted Answer

(D) 12.5 W

Answer

(A) 1.25 W

Answer

(B) 2.5 W

Answer

(C) 6.25 W

Question 34

A bag is gently dropped on a conveyor belt moving at a speed of 2 m/s. The coefficient of friction between the conveyor belt and bag is 0.4 Initially, the bag slips on the belt before it stops due to friction. The distance travelled by the bag on the belt during slipping motion is : [Take g = 10 m/s$^{-2}$]

Accepted Answer

(B) 0.5 m

Answer

(A) 2 m

Answer

(C) 3.2 m

Answer

(D) 0.8 ms

Question 35

Two cylindrical vessels of equal cross-sectional area 16 cm$^{2}$ contain water upto heights 100 cm and 150 cm respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is [Take density of water = 10$^{3}$ kg/m$^{3}$ and g = 10 ms$^{-2}$]

Accepted Answer

(B) 1 J

Answer

(A) 0.25 J

Answer

(C) 8 J

Answer

(D) 12 J

Question 36

Two satellites A and B having masses in the ratio 4:3 are revolving in circular orbits of radii 3r and 4 r respectively around the earth. The ratio of total mechanical energy of A to B is :

Accepted Answer

(B) 16 : 9

Answer

(A) 9 : 16

Answer

(C) 1 : 1

Answer

(D) 4 : 3

Question 37

If K$_{1}$ and K$_{2}$ are the thermal conductivities L$_{1}$ and L$_{2}$ are the lengths and A$_{1}$ and A$_{2}$ are the cross sectional areas of steel and copper rods respectively such that $\frac{K_{2}}{K_{1}} = 9, \frac{A_{1}}{A_{2}} = 2, \frac{L_{1}}{L_{2}} = 2$ . Then, for the arrangement as shown in the figure. The value of temperature T of the steel – copper junction in the steady state will be :

Accepted Answer

(C) 45 ºC

Answer

(A) 18ºC

Answer

(B) 14 ºC

Answer

(D) 150 ºC

Question 38

Read the following statements :
A. When small temperature difference between a liquid and its surrounding is doubled the rate of loss of heat of the liquid becomes twice.
B. Two bodies P and Q having equal surface areas are maintained at temperature 10ºC and 20 ºC. The thermal radiation emitted in a given time by P and Q are in the ratio 1 : 1.15
C. A carnot Engine working between 100 K and 400 K has an efficiency of 75%
D. When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice.
Choose the correct answer from the options given below :

Accepted Answer

(A) A, B, C only

Answer

(B) A, B only

Answer

(C) A, C only

Answer

(D) B, C, D only

Question 39

Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is 1:4, then
A. The r.m.s. velocity of gas molecules in two vessels will be the same.
B. The ratio of pressure in these vessels will be 1 : 4
C. The ratio of pressure will be 1 : 1
D. The r.m.s. velocity of gas molecules in two vessels will be in the ratio of 1 : 4

Accepted Answer

(C) A and B only

Answer

(A) A and C only

Answer

(B) B and D only

Answer

(D) C and D only

Question 40

Two identical positive charges Q each are fixed at a distance of ‘2a’ apart from each other. Another point charge q$_{0}$ with mass ‘m’ is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge q$_{0}$ executes SHM. The time period of oscillation of charge q$_{0}$ will be :

Accepted Answer

(A) $\sqrt{\dfrac{4\pi^{3}\varepsilon_{0}ma^{3}}{q_{0}Q}}$

Answer

(B) $\sqrt{\dfrac{q_{0}Q}{4\pi^{3}\varepsilon_{0}ma^{3}}}$

Answer

(C) $\sqrt{\dfrac{2\pi^{2}\varepsilon_{0}ma^{3}}{q_{0}Q}}$

Answer

(D) $\sqrt{\dfrac{8\pi^{3}\varepsilon_{0}ma^{3}}{q_{0}Q}}$

Question 41

Two sources of equal emfs are connected in series. This combination is connected to an external resistance R. The internal resistances of the two sources are r$_{1}$ and r$_{2}$ (r$_{1}$ > r$_{2}$). If the potential difference across the source of internal resistance r$_{1}$ is zero then the value of R will be

Accepted Answer

(A) $r_{1} - r_{2}$

Answer

(B) $\dfrac{r_{1}r_{2}}{r_{1}+r_{2}}$

Answer

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

Answer

(D) $r_{2} - r_{1}$

Question 42

Two bar magnets oscillate in a horizontal plane in earth’s magnetic field with time periods of 3 s and 4 s respectively. If their moments of inertia are in the ratio of 3 : 2 then the ratio of their magnetic moments will e :

Accepted Answer

(B) 8 : 3

Answer

(A) 2 : 1

Answer

(C) 1 : 3

Answer

(D) 27 : 16

Question 43

A magnet hung at 45º with magnetic meridian makes an angle of 60º with the horizontal. The actual value of the angle of dip is

Accepted Answer

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

Answer

(B) $	an^{-1}\left(\sqrt{6}ight)$

Answer

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

Answer

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

Question 44

A direct current of 4 A and an alternating current of peak value 4 A flow through resistance of 3 Ω and 2 Ω respectively. The ratio of heat produced in the two resistances in same interval of time will be :

Accepted Answer

(B) 3 : 1

Answer

(A) 3 : 2

Answer

(C) 3 : 4

Answer

(D) 4 : 3

Question 45

A beam of light travelling along X-axis is described by the electric field E$_{y}$ = 900 sin $\omega$(t–x/c). The ratio of electric force to magnetic force on a charge q moving along Y-axis with a speed of 3 × 10$^{7}$ ms$^{-1}$ will be : [Given speed of light = 3 × 10$^{8}$ ms$^{-1}$]

Accepted Answer

(C) 10 : 1

Answer

(A) 1 : 1

Answer

(B) 1 : 10

Answer

(D) 1 : 2

Question 46

An electron (mass m) with an initial velocity $\vec{v} = v_0\hat{i}\,(v_0 > 0)$ is moving in an electric field $\vec{E} = -E_0\hat{i}\,(E_0 > 0)$ where $E_0$ is constant. If at t = 0 de Broglie wavelength is $\lambda_0 = \frac{h}{mv_0}$, then its de Broglie wavelength after time t is given by

Accepted Answer

(D) $\dfrac{\lambda_0}{\left(1 + \frac{eE_0t}{mv_0}\right)}$

Answer

(A) $\lambda_0$

Answer

(B) $\lambda_0\left(1 + \frac{eE_0t}{mv_0}\right)$

Answer

(C) $\lambda_0 t$

Question 47

What is the half-life period of a radioactive material if its activity drops to $1/16^{	ext{th}}$ of its initial value of 30 years ?

Accepted Answer

(C) 7.5 years

Answer

(A) 9.5 years

Answer

(B) 8.5 years

Answer

(D) 10.5 years

Question 48

A logic gate circuit has two inputs A and B and output Y. The voltage waveforms of A, B and Y are shown below
The logic gate circuit is

Accepted Answer

(A) AND gate

Answer

(B) OR gate

Answer

(C) NOR gate

Answer

(D) NAND gate

Question 49

At a particular station, the TV transmission tower has a height of 100 m. To triple its coverage range, height of the tower should be increased to

Accepted Answer

(D) 900 m

Answer

(A) 200 m

Answer

(B) 300 m

Answer

(C) 600 m

Question 50

In meter bridge experiment for measuring unknown resistance 'S', the null point is obtained at a distance 30 cm from the left side as shown at point D. If R is 5.6 $\mathrm{k}\Omega$, then the value of unknown resistance 'S' will be ________ $\Omega$.

Accepted Answer

2400

Question 51

The one division of main scale of vernier callipers reads 1 mm and 10 divisions of Vernier scale is equal to the 9 divisions on main scale. When the two jaws of the instrument touch each other the zero of the Vernier lies to the right of zero of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the zero of the Vernier scale lies in between 4.1 cm and 4.2 cm and $6^{	ext{th}}$ Vernier division coincides with a main scale division. The diameter of the bob will be______ $10^{-2}$ cm

Accepted Answer

412

Question 52

Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the two beams are $\pi/2$ and $\pi/3$ at points A and B respectively. The difference between the resultant intensities at the two points is xI. The value of x will be ______ .

Accepted Answer

2

Question 53

To light, a 50 W, 100 V lamp is connected, in series with a capacitor of capacitance $\frac{50}{\pi\sqrt{x}}\,\mu\mathrm{F}$, with 200 V, 50Hz AC source. The value of x will be ____ .

Accepted Answer

3

Question 54

A 1 m long copper wire carries a current of 1 A. If the cross section of the wire is 2.0 $\mathrm{mm}^{2}$ and the resistivity of copper is $1.7 	imes 10^{-8}\ \Omega\,\mathrm{m}$. the force experienced by moving electron in the wire is ______ $	imes\ 10^{-23}$ N. (charge on electron $= 1.6 	imes 10^{-19}$ C)

Accepted Answer

136

Question 55

A long cylindrical volume contains a uniformly distributed charge of density $\rho$ $\mathrm{Cm}^{-3}$. The electric field inside the cylindrical volume at a distance $x = \frac{2\varepsilon_0}{\rho}$ m from its axis is ______ $\mathrm{Vm}^{-1}$

Accepted Answer

1

Question 56

A mass 0.9 kg, attached to a horizontal spring, executes SHM with an amplitude $A_1$. When this mass passes through its mean position, then a smaller mass of 124 g is placed over it and both masses move together with amplitude $A_2$. If the ratio $\frac{A_1}{A_2}$ is $\frac{\alpha}{\alpha-1}$, then the value of $\alpha$ will be ____ .

Accepted Answer

16

Question 57

A square aluminium (shear modulus is $25 	imes 10^{9}\ \mathrm{Nm}^{-2}$) slab of side 60 cm and thickness 15 cm is subjected to a shearing force (on its narrow face) of $18.0 	imes 10^{4}$ N. The lower edge is riveted to the floor. The displacement of the upper edge is ____ $\mu$ m.

Accepted Answer

48

Question 58

A pulley of radius 1.5 m is rotated about its axis by a force $F = (12t - 3t^{2})$ N applied tangentially (while t is measured in seconds). If moment of inertia of the pulley about its axis of rotation is 4.5 kg $\mathrm{m}^{2}$, the number of rotations made by the pulley before its direction of motion is reversed, will be $\frac{K}{\pi}$. The value of K is ____ .

Accepted Answer

18

Question 59

A ball of mass m is thrown vertically upward. Another ball of mass 2 m is thrown an angle $	heta$ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is $\frac{1}{x}$. The value of x is ______ .

Accepted Answer

1

Question 60

250 g solution of D-glucose in water contains 10.8% of carbon by weight. The molality of the solution is nearest to
(Given: Atomic Weights are H, 1u ; C, 12u ; O, 16u)

Accepted Answer

(B) 2.06

Answer

(A) 1.03

Answer

(C) 3.09

Answer

(D) 5.40

Question 61

Given below are two statements.
Statement I : $O_{2}$ , $Cu^{2+}$ and $Fe^{3+}$ are weakly attracted by magnetic field and are magnetized in the same direction as magnetic field.
Statement II : NaCl and $H_{2}O$ are weakly magnetized in opposite direction to magnetic field.
In the light of the above statements, choose the most appropriate answer form the options given below :

Accepted Answer

(A) Both Statement I and Statement II are correct.

Answer

(B) Both Statement I and Statement II are incorrect.

Answer

(C) Statement I is correct but Statement II is incorrect.

Answer

(D) Statement I is incorrect but Statement II is correct.

Question 62

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Energy of 2s orbital of hydrogen atom is greater than that of 2s orbital of lithium.
Reason R : Energies of the orbitals in the same subshell decrease with increase in the atomic number.
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 the correct explanation of A.

Answer

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

Answer

(C) A is true but R is false.

Answer

(D) A is false but R is true.

Question 63

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Activated charcoal adsorbs $SO_{2}$ more efficiently than $CH_{4}$.
Reason R : Gases with lower critical temperatures are readily adsorbed by activated charcoal.
In the light of the above statements, choose the correct answer from the options given below.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 64

Boiling point of a 2% aqueous solution of a non-volatile solute A is equal to the boiling point of 8% aqueous solution of a non-volatile solute B. The relation between molecular weights of A and B is.

Accepted Answer

(B) $M_{B} = 4M_{A}$

Answer

(A) $M_{A} = 4M_{B}$

Answer

(C) $M_{A} = 8M_{B}$

Answer

(D) $M_{B} = 8M_{A}$

List I (Pollutant)	List II (Disease /sickness)
A.Sulphate (>500 ppm)	I.Methemoglobinemia
B.Nitrate (>50 ppm)	II.Brown mottling of teeth
C.Lead (> 50 ppb)	III.Laxative effect
D.Fluoride (>2 ppm)	IV.Kidney damage

List I (Polymers)	List II (Commenrcial names)
A.Phenol-formaldehyde resin	I.Glyptal
B.Copolymer of 1,3-butadiene and styrene	II.Novolac
C.Polyester of glycol and phthalic acid	III.Buna-S
D.Polyester of glycol and terephthalic acid	IV.Dacron

List I	List II
A.see figure	I.Anti-depressant
B.see figure	II.550 times sweeter than cane sugar
C.see figure	III.Narcotic analgesic
D.see figure	IV.Antiseptic

List I	List II
A.Benzenesulphonyl chloride	I.Test for primary amines
B.Hoffmann bromamide reaction	II.Anti Saytzeff
C.Carbylamine reaction	III.Hinsberg reagent
D.Hoffmann orientation	IV.Known reaction of Isocyanates.

Reaction serial number	Initial pressure of $H_{2}$ / kPa	Initial Pressure of NO/ kPa	Initial rate $\left(\frac{-dp}{dt}\right)/\left(kPa/s\right)$
1	65.6	40.0	0.135
2	65.6	20.1	0.033
3	38.6	65.6	0.214
4	19.2	65.6	0.106

JEE Main 27 July 2022 Shift 1 Question Paper with Answers

Physics — JEE Main 27 July 2022 Shift 1

Chemistry — JEE Main 27 July 2022 Shift 1

Mathematics — JEE Main 27 July 2022 Shift 1

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