JEE Main 29 July 2022 Shift 2 Question Paper

Question 1

If $z 
eq 0$ be a complex number such that $\left| z - \frac{1}{z} ight| = 2$, then the maximum value of $|z|$ is:

Accepted Answer

(D) $\sqrt{2} + 1$

Answer

(A) $\sqrt{2}$

Answer

(B) $1$

Answer

(C) $\sqrt{2} - 1$

Question 2

Which of the following matrices can NOT be obtained from the matrix $\begin{bmatrix} -1 & 2 \ 1 & -1 \end{bmatrix}$ by a single elementary row operation?

Accepted Answer

(C) $\begin{bmatrix} -1 & 2 \ -2 & 7 \end{bmatrix}$

Answer

(A) $\begin{bmatrix} 0 & 1 \ 1 & -1 \end{bmatrix}$

Answer

(B) $\begin{bmatrix} 1 & -1 \ -1 & 2 \end{bmatrix}$

Answer

(D) $\begin{bmatrix} -1 & 2 \ -1 & 3 \end{bmatrix}$

Question 3

If the system of equations
$x + y + z = 6$
$2x + 5y + \alpha z = \beta$
$x + 2y + 3z = 14$
has infinitely many solutions, then $\alpha + \beta$ is equal to :

Accepted Answer

(C) $44$

Answer

(A) $8$

Answer

(B) $36$

Answer

(D) $48$

Question 4

Let the function
$f(x) = \begin{cases} \dfrac{\log_e (1 + 5x) - \log_e (1 + \alpha x)}{x} & ; 	ext{if } x 
eq 0 \ 10 & ; 	ext{if } x = 0 \end{cases}$
be continuous at $x = 0$. The $\alpha$ is equal to :

Accepted Answer

(D) $-5$

Answer

(A) $10$

Answer

(B) $-10$

Answer

(C) $5$

Question 5

If $[t]$ denotes the greatest integer $\leq t$, then the value of $\int_{0}^{1} \left[ 2x - |3x^2 - 5x + 2| + 1 \right] dx$ is:

Accepted Answer

(A) $\frac{\sqrt{37} + \sqrt{13} - 4}{6}$

Answer

(B) $\frac{\sqrt{37} - \sqrt{13} - 4}{6}$

Answer

(C) $\frac{-\sqrt{37} - \sqrt{13} + 4}{6}$

Answer

(D) $\frac{-\sqrt{37} + \sqrt{13} + 4}{6}$

Question 6

Let $\{a_n\}_{n=0}^{\infty}$ be a sequence such that $a_0 = a_1 = 0$ and $a_{n+2} = 3a_{n+1} - 2a_n + 1$, $\forall\ n \geq 0$.
Then $a_{25}\, a_{23} - 2\, a_{25}\, a_{22} - 2\, a_{23}\, a_{24} + 4\, a_{22}\, a_{24}$ is equal to:

Accepted Answer

(B) $528$

Answer

(A) $483$

Answer

(C) $575$

Answer

(D) $624$

Question 7

$\sum_{r=1}^{20} \left( r^2 + 1 \right)\left( r! \right)$ is equal to:

Accepted Answer

(B) $22! - 2\,(21!)$

Answer

(A) $22! - 21!$

Answer

(C) $21! - 2\,(20!)$

Answer

(D) $21! - 20!$

Question 8

For $I(x) = \int \frac{\sec^2 x - 2022}{\sin^{2022} x} dx$, if $I\left( \frac{\pi}{4} \right) = 2^{1011}$, then

Accepted Answer

(A) $3^{1010} I\left( \frac{\pi}{3} \right) - I\left( \frac{\pi}{6} \right) = 0$

Answer

(B) $3^{1010} I\left( \frac{\pi}{6} \right) - I\left( \frac{\pi}{3} \right) = 0$

Answer

(C) $3^{1011} I\left( \frac{\pi}{3} \right) - I\left( \frac{\pi}{6} \right) = 0$

Answer

(D) $3^{1011} I\left( \frac{\pi}{6} \right) - I\left( \frac{\pi}{3} \right) = 0$

Question 9

If the solution curve of the differential equation $\frac{dy}{dx} = \frac{x + y - 2}{x - y}$ passes through the point $(2, 1)$ and $(k + 1, 2)$, $k > 0$, then

Accepted Answer

(A) $2	an^{-1}\left( \frac{1}{k} ight) = \log_e \left( k^2 + 1 ight)$

Answer

(B) $	an^{-1}\left( \frac{1}{k} ight) = \log_e \left( k^2 + 1 ight)$

Answer

(C) $2	an^{-1}\left( \frac{1}{k + 1} ight) = \log_e \left( k^2 + 2k + 2 ight)$

Answer

(D) $2	an^{-1}\left( \frac{1}{k} ight) = \log_e \left( \frac{k^2 + 1}{k^2} ight)$

Question 10

Let $y = y(x)$ be the solution curve of the differential equation $\frac{dy}{dx} + \left( \frac{2x^2 + 11x + 13}{x^3 + 6x^2 + 11x + 6} \right) y = \frac{(x + 3)}{x + 1}$, $x > -1$, which passes through the point $(0, 1)$. Then $y(1)$ is equal to:

Accepted Answer

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

Answer

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

Answer

(C) $\frac{5}{2}$

Answer

(D) $\frac{7}{2}$

Question 11

Let $m_1$, $m_2$ be the slopes of two adjacent sides of a square of side $a$ such that $a^2 + 11a + 3\left( m_2^2 + m_2^2 \right) = 220$. If one vertex of the square is $(10(\cos\alpha - \sin\alpha),\ 10(\sin\alpha + \cos\alpha))$, where $\alpha \in \left( 0, \frac{\pi}{2} \right)$ and the equation of one diagonal is $(\cos\alpha - \sin\alpha)x + (\sin\alpha + \cos\alpha)y = 10$, then $72(\sin^4\alpha + \cos^4\alpha) + a^2 - 3a + 13$ is equal to:

Accepted Answer

(B) $128$

Answer

(A) $119$

Answer

(C) $145$

Answer

(D) $155$

Question 12

The number of elements in the set $S = \left\{ x \in \mathbb{R} : 2\cos\left( \frac{x^2 + x}{6} \right) = 4^x + 4^{-x} \right\}$ is:

Accepted Answer

(A) $1$

Answer

(B) $3$

Answer

(C) $0$

Answer

(D) infinite

Question 13

Let $A(\alpha, -2)$, $B(\alpha, 6)$ and $C\left( \frac{\alpha}{4}, -2 ight)$ be vertices of a $	riangle ABC$. If $\left( 5, \frac{\alpha}{4} ight)$ is the circumcentre of $	riangle ABC$, then which of the following is NOT correct about $	riangle ABC$:

Accepted Answer

(B) perimeter is 25

Answer

(A) ares is 24

Answer

(C) circumradius is 5

Answer

(D) inradius is 2

Question 14

Let Q be the foot of perpendicular drawn from the point $P(1, 2, 3)$ to the plane $x + 2y + z = 14$. If R is a point on the plane such that $\angle PRQ = 60^\circ$, then the area of $	riangle PQR$ is equal to:

Accepted Answer

(B) $\sqrt{3}$

Answer

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

Answer

(C) $2\sqrt{3}$

Answer

(D) $3$

Question 15

If $(2, 3, 9)$, $(5, 2, 1)$, $(1, \lambda, 8)$ and $(\lambda, 2, 3)$ are coplanar, then the product of all possible values of $\lambda$ is:

Accepted Answer

(D) $\frac{95}{8}$

Answer

(A) $\frac{21}{2}$

Answer

(B) $\frac{59}{8}$

Answer

(C) $\frac{57}{8}$

Question 16

Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is draw from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is:

Accepted Answer

(B) $\frac{5}{18}$

Answer

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

Answer

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

Answer

(D) $\frac{3}{10}$

Question 17

Let $S = \{ z = x + iy : |z - 1 + i| \ge |z|, |z| < 2, |z + i| = |z - 1| \}$. Then the set of all values of x, for which $w = 2x + iy \in S$ for some $y \in \mathbb{R}$, is

Accepted Answer

(B) $\left(-\frac{1}{\sqrt{2}}, \frac{1}{4}\right]$

Answer

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

Answer

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

Answer

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

Question 18

Let $\vec{a}, \vec{b}, \vec{c}$ be three coplanar concurrent vectors such that angles between any two of them is same. If the product of their magnitudes is 14 and $\left(\vec{a} 	imes \vec{b}ight) \cdot \left(\vec{b} 	imes \vec{c}ight) + \left(\vec{b} 	imes \vec{c}ight) \cdot \left(\vec{c} 	imes \vec{a}ight) + \left(\vec{c} 	imes \vec{a}ight) \cdot \left(\vec{a} 	imes \vec{b}ight) = 168$ then $|\vec{a}| + |\vec{b}| + |\vec{c}|$ is equal to:

Accepted Answer

(C) 16

Answer

(A) 10

Answer

(B) 14

Answer

(D) 18

Question 19

The domain of the function $f(x) = \sin^{-1}\left(\frac{x^2 - 3x + 2}{x^2 + 2x + 7}\right)$ is :

Accepted Answer

(C) $[-1, \infty)$

Answer

(A) $[1, \infty)$

Answer

(B) $(-1, 2]$

Answer

(D) $(-\infty, 2]$

Question 20

The statement $\left(p \Rightarrow q\right) \vee \left(p \Rightarrow r\right)$ is NOT equivalent to:

Accepted Answer

(B) $(\sim q) \Rightarrow \left((\sim r) \vee p\right)$

Answer

(A) $\left(p \wedge (\sim r)\right) \Rightarrow q$

Answer

(C) $p \Rightarrow (q \vee r)$

Answer

(D) $\left(p \wedge (\sim q)\right) \Rightarrow r$

Question 21

The sum and product of the mean and variance of a binomial distribution are 82.5 and 1350 respectively. They the number of trials in the binomial distribution is:

Accepted Answer

96

Question 22

Let $\alpha, \beta$ $(\alpha > \beta)$ be the roots of the quadratic equation $x^2 - x - 4 = 0$. If $P_n = \alpha^n - \beta^n$, $n \in \mathbb{N}$, then $\frac{P_{15}P_{16} - P_{14}P_{16} - P_{15}^2 + P_{14}P_{15}}{P_{13}P_{14}}$ is equal to ______.

Accepted Answer

16

Question 23

Let $x = \begin{bmatrix} 1 \ 1 \ 1 \end{bmatrix}$ and $A = \begin{bmatrix} -1 & 2 & 3 \ 0 & 1 & 6 \ 0 & 0 & -1 \end{bmatrix}$. For $k \in \mathbb{N}$, if $X' A^k X = 33$, then k is equal to:

Accepted Answer

10

Question 24

The number of natural numbers lying between 1012 and 23421 that can be formed using the digits 2, 3, 4, 5, 6 (repetition of digits is not allowed) and divisible by 55 is____,

Accepted Answer

6

Question 25

If $\sum_{k=1}^{10} K^2 \left({}^{10}C_K\right)^2 = 22000L$, then L is equal to ___.

Accepted Answer

221

Question 26

If [t] denotes the greatest integer $\le t$, then number of points, at which the function $f(x) = 4|2x + 3| + 9\left[x + \frac{1}{2}\right] - 12[x + 20]$ is not differentiable in the open interval $(-20, 20)$, is___.

Accepted Answer

79

Question 27

If the tangent to the curve $y = x^3 - x^2 + x$ at the point $(a, b)$ is also tangent to the curve $y = 5x^2 + 2x - 25$ at the point $(2, -1)$, then $|2a + 9b|$ is equal to ______.

Accepted Answer

195

Question 28

Let AB be a chord of length 12 of the circle $(x - 2)^2 + (y + 1)^2 = \frac{169}{4}$. If tangents drawn to the circle at points A and B intersect at the point P, then five times the distance of point P from chord AB is equal to ___.

Accepted Answer

72

Question 29

Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{a} + \vec{b}|^2 = |\vec{a}|^2 + 2|\vec{b}|^2$, $\vec{a} \cdot \vec{b} = 3$ and $|\vec{a} 	imes \vec{b}|^2 = 75$. Then $|\vec{a}|^2$ is equal to____.

Accepted Answer

14

Question 30

Let $S = \left\{ (x, y) \in \mathbb{N} 	imes \mathbb{N} : 9(x - 3)^2 + 16(y - 4)^2 \le 144 ight\}$ and $T = \left\{ (x, y) \in \mathbb{R} 	imes \mathbb{R} : (x - 7)^2 + (y - 4)^2 \le 36 ight\}$. The $n(S \cap T)$ is equal to______.

Accepted Answer

27

Question 31

Two identical metallic spheres A and B when placed at certain distance in air repel each other with a force of F. Another identical uncharged sphere C is first placed in contact with A and then in contact with B and finally placed at midpoint between spheres A and B. The force experienced by sphere C will be :

Accepted Answer

(B) 3F/4

Answer

(A) 3F/2

Answer

(C) F

Answer

(D) 2F

Question 32

Match List I with List II.
List I
A. Torque
B. Stress
C. Latent Heat
D. Power
List II
I. Nms$^{-1}$
II. J kg$^{-1}$
III. Nm
IV. Nm$^{-2}$
Choose the correct answer from the options given below:

Accepted Answer

(B) A-III, B-IV, C-II, D-I

Answer

(A) A-III, B-II, C-I, D-IV

Answer

(C) A-IV, B-I, C-III, D-II

Answer

(D) A-II, B-III, C-I, D-IV

Question 33

Two identical thin metal plates has charge $q_1$ and $q_2$ respectively such that $q_1 > q_2$. The plates were brought close to each other to form a parallel plate capacitor of capacitance C. The potential difference between them is :

Accepted Answer

(C) $\frac{(q_1 - q_2)}{2C}$

Answer

(A) $\frac{(q_1 + q_2)}{C}$

Answer

(B) $\frac{(q_1 - q_2)}{C}$

Answer

(D) $\frac{2(q_1 - q_2)}{C}$

Question 34

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Alloys such as constantan and manganin are used in making standard resistance coils.
Reason R: Constantan and manganin have very small value of temperature coefficient of resistance.
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 35

A 1 m long wire is broken into two unequal parts X and Y The X part of the wire is streched into another wire W. Length of W is twice the length of X and the resistance of W is twice that of Y. Find the ratio of length of X and Y.

Accepted Answer

(B) 1 : 2

Answer

(A) 1 : 4

Answer

(C) 4 :1

Answer

(D) 2 : 1

Question 36

A wire X of length 50 cm carrying a current of 2 A is placed parallel to a long wire Y of length 5 m. The wire Y carries a current of 3 A. The distance between two wires is 5 cm and currents flow in the same direction. The force acting on the wire Y is :

Accepted Answer

(A) $1.2 	imes 10^{-5}$ N directed towards wire X.

Answer

(B) $1.2 	imes 10^{-4}$ N directed away from wire X.

Answer

(C) $1.2 	imes 10^{-4}$ N directed towards wire X.

Answer

(D) $2.4 	imes 10^{-5}$ N directed towards wire X.

Question 37

A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws n balls per second, the maximum height the balls can reach is

Accepted Answer

(D) $g/2n^{2}$

Answer

(A) g/2n

Answer

(B) g/n

Answer

(C) 2gn

Question 38

A circuit element X when connected to an a.c. supply of peak voltage 100 V gives a peak current of 5 A which is in phase with the voltage. A second element Y when connected to the same a.c. supply also gives the same value of peak current which lags behind the voltage by $\frac{\pi}{2}$. If X and Y are connected in series to the same supply, what will be the rms value of the current in ampere ?

Accepted Answer

(D) $\frac{5}{2}$

Answer

(A) $\frac{10}{\sqrt{2}}$

Answer

(B) $\frac{5}{\sqrt{2}}$

Answer

(C) $5\sqrt{2}$

Question 39

An unpolarised light beam of intensity $2I_0$ is passed through a polaroid P and then through another polaroid Q which is oriented in such a way that its passing axis makes an angle of 30° relative to that of P. The intensity of the emergent light is

Accepted Answer

(C) $\frac{3I_0}{4}$

Answer

(A) $\frac{I_0}{4}$

Answer

(B) $\frac{I_0}{2}$

Answer

(D) $\frac{3I_0}{2}$

Question 40

An α particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particals will be :

Accepted Answer

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

Answer

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

Answer

(C) $4\sqrt{2} : 1$

Answer

(D) 8 : 1

Question 41

Read the following statements:
(A) Volume of the nucleus is directly proportional to the mass number.
(B) Volume of the nucleus is independent of mass number.
(C) Density of the nucleus is directly proportional to the mass number.
(D) Density of the nucleus is directly proportional to the cube root of the mass number.
(E) Density of the nucleus is independent of the mass number.
Choose the correct option from the following options.

Accepted Answer

(B) (A) and (E) only.

Answer

(A) (A) and (D) only.

Answer

(C) (B) and (E) only.

Answer

(D) (A) and (C) only

Question 42

An object of mass 1 kg is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be
[If, g=10ms$^{-2}$ and radius of earth = 6400 km]

Accepted Answer

(A) 48 MJ

Answer

(B) 24 MJ

Answer

(C) 36 MJ

Answer

(D) 12 MJ

Question 43

A ball is released from a height h. If $t_1$ and $t_2$ be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between $t_1$ and $t_2$.

Accepted Answer

(D) $t_2 = \left(\sqrt{2} - 1\right)t_1$

Answer

(A) $t_1 = \left(\sqrt{2}\right)t_2$

Answer

(B) $t_1 = \left(\sqrt{2} - 1\right)t_2$

Answer

(C) $t_2 = \left(\sqrt{2} + 1\right)t_1$

Question 44

Two bodies of masses $m_1 = 5$ kg and $m_2 = 3$ kg are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass $m_1$ will be :[Take $g = 10$ ms$^{-2}$]

Accepted Answer

(B) 40 N

Answer

(A) 30 N

Answer

(C) 50 N

Answer

(D) 60 N

Question 45

If momentum of a body is increased by 20%, then its kinetic energy increases by :

Accepted Answer

(C) 44%

Answer

(A) 36%

Answer

(B) 40%

Answer

(D) 48%

Question 46

The torque of a force $5\hat{i} + 3\hat{j} - 7\hat{k}$ about the origin is τ. If the force acts on a particle whose position vector is $2\hat{i} + 2\hat{j} + \hat{k}$, then the value of τ will be :

Accepted Answer

(C) $-17\hat{i} + 19\hat{j} - 4\hat{k}$

Answer

(A) $11\hat{i} + 19\hat{j} - 4\hat{k}$

Answer

(B) $-11\hat{i} + 9\hat{j} - 16\hat{k}$

Answer

(D) $17\hat{i} + 9\hat{j} + 16\hat{k}$

Question 47

A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the figure. Its volume is then reduced to the original volume from E to F by an isobaric process. The total work done by the gas from D to E to F will be

Accepted Answer

(B) 450 J

Answer

(A) −450 J

Answer

(C) 900 J

Answer

(D) 1350 J

Question 48

The vertical component of the earth's magnetic field is $6 	imes 10^{-5}$ T at any place where the angle of dip is 37º. The earth's resultant magnetic field at that place will be (Given tan 37º $= \frac{3}{4}$)

Accepted Answer

(D) $1 	imes 10^{-4}$ T

Answer

(A) $8 	imes 10^{-5}$ T

Answer

(B) $6 	imes 10^{-5}$ T

Answer

(C) $5 	imes 10^{-4}$ T

Question 49

The root mean square speed of smoke particles of mass $5 	imes 10^{-17}$ kg in their Brownian motion in air at NTP is approximately. [Given k $= 1.38 	imes 10^{-23}$ JK$^{-1}$]

Accepted Answer

(C) 15 mm s$^{-1}$

Answer

(A) 60 mm s$^{-1}$

Answer

(B) 12 mm s$^{-1}$

Answer

(D) 36 mm s$^{-1}$

Question 50

Light enters from air into a given medium at an angle of 45° with interface of the air-medium surface. After refraction, the light ray is deviated through an angle of 15° from its original direction. The refractive index of the medium is :

Accepted Answer

(C) 1.414

Answer

(A) 1.732

Answer

(B) 1.333

Answer

(D) 2.732

Question 51

A tube of length 50 cm is filled completely with an incompressible liquid of mass 250 g and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity $x\sqrt{F}$ rad s$^{-1}$. If F be the force exerted by the liquid at the other end then the value of x will be ______.

Accepted Answer

4

Question 52

Nearly 10% of the power of a 110 W light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of 1 m from the bulb to a distance of 5 m is $a 	imes 10^{-2}$ W/m$^2$. The value of 'a' will be

Accepted Answer

84

Question 53

A metal wire of length 0.5 m and cross-sectional area $10^{-4}$ m$^2$ has breaking stress $5 	imes 10^{8}$ Nm$^{-2}$. A block of 10 kg is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be____ ms$^{-1}$.

Accepted Answer

50

Question 54

The velocity of a small ball of mass 0.3g and density 8g/cc when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 1.3 g/cc, then the value of viscous force acting on the ball will be $x 	imes 10^{-4}$ N, the value of x is____. [use g $= 10$m/s$^2$]

Accepted Answer

25

Question 55

A modulating signal $2\sin(6.28 	imes 10^{6})t$ is added to the carrier signal $4\sin(12.56 	imes 10^{9})t$ for amplitude modulation. The combined signal is passed through a non-linear square law device. The output is then passed through a band pass filter. The bandwidth of the output signal of band pass filter will be___MHz.

Accepted Answer

2

Question 56

The speed of a transverse wave passing through a string of length 50 cm and mass 10 g is 60 ms$^{-1}$. The area of cross-section of the wire is 2.0 mm$^2$ and its Young's modulus is $1.2 	imes 10^{11}$ Nm$^{-2}$. The extension of the wire over its natural length due to its tension will be $x 	imes 10^{-5}$ m. The value of x is_______.

Accepted Answer

15

Question 57

The metallic bob of simple pendulum has the relative density 5. The time period of this pendulum is 10 s. If the metallic bob is immersed in water, then the new time period becomes $5\sqrt{x}$ s. The value of x will be ________.

Accepted Answer

5

Question 58

A 8 V Zener diode along with a series resistance R is connected across a 20 V supply (as shown in the figure). If the maximum Zener current is 25 mA, then the minimum value of R will be ______Ω.

Accepted Answer

480

Question 59

Two radioactive materials A and B have decay constants 25λ and 16λ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be "e" after a time $\frac{1}{a\lambda}$. The value of a is________.

Accepted Answer

9

Question 60

A capacitor of capacitance 500 μF is charged completely using a dc supply of 100 V. It is now connected to an inductor of inductance 50 mH to form an LC circuit. The maximum current in LC circuit will be _______ A.

Accepted Answer

10

Question 61

Consider the reaction
4HNO$_{3}$(l) + 3KCl(s) → Cl$_{2}$(g) + NOCl(g) + 2H$_{2}$O(g) + 3KNO$_{3}$(s)
The amount of HNO$_{3}$ required to produce 110.0 g of KNO$_{3}$ is :
(Given : Atomic masses of H, O, N and K are 1, 16, 14 and 39, respectively.)

Accepted Answer

(C) 91.5 g

Answer

(A) 32.2 g

Answer

(B) 69.4 g

Answer

(D) 162.5 g

Question 62

Given below are the quantum numbers for 4 electrons.
A. n = 3, $l$ = 2, m$_{l}$ = 1, m$_{s}$ = +1/2
B. n = 4, $l$ = 1, m$_{l}$ = 0, m$_{s}$ = +1/2
C. n = 4, $l$ = 2, m$_{l}$ = −2, m$_{s}$ = −1/2
D. n = 3, $l$ = 1, m$_{l}$ = −1, m$_{s}$ = +1/2
The correct order of increasing energy is :

Accepted Answer

(B) D < A < B < C

Answer

(A) D < B < A < C

Answer

(C) B < D < A < C

Answer

(D) B < D < C < A

Question 63

C(s) + O$_{2}$(g) → CO$_{2}$(g) + 400 kJ
C(s) + $\frac{1}{2}$O$_{2}$(g) → CO(g) + 100 kJ
When coal of purity 60% is allowed to burn in presence of insufficient oxygen, 60% of carbon is converted into 'CO' and the remaining is converted into 'CO$_{2}$'.
The heat generated when 0.6 kg of coal is burnt is ______.

Accepted Answer

(D) 6600 kJ

Answer

(A) 1600 kJ

Answer

(B) 3200 kJ

Answer

(C) 4400 kJ

Question 64

200 mL of 0.01 M HCl is mixed with 400 mL of 0.01M H$_{2}$SO$_{4}$. The pH of the mixture is ____.

Accepted Answer

(B) 1.78

Answer

(A) 1.14

Answer

(C) 2.34

Answer

(D) 3.02

JEE Main 29 July 2022 Shift 2 Question Paper with Answers

Physics — JEE Main 29 July 2022 Shift 2

Chemistry — JEE Main 29 July 2022 Shift 2

Mathematics — JEE Main 29 July 2022 Shift 2

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