JEE Main 30 January 2023 Shift 2 Question Paper

Question 1

A vector $\vec{v}$ in the first octant is inclined to the x-axis at $60^{\circ}$, to the y-axis at $45^{\circ}$ and to the z-axis at an acute angle. If a plane passing through the points $(\sqrt{2}, -1, 1)$ and $(a, b, c)$ is normal to $\vec{v}$, then:

Accepted Answer

(B) $a + \sqrt{2}b + c = 1$

Answer

(A) $\sqrt{2}a + b + c = 1$

Answer

(C) $a + b + \sqrt{2}c = 1$

Answer

(D) $\sqrt{2}a - b + c = 1$

Question 2

Let $a, b, c > 1$; $a^3, b^3$ and $c^3$ be in A.P., and $\log_a b, \log_c a$ and $\log_b c$ be in G.P. If the sum of the first 20 terms of an A.P., whose first term is $\dfrac{a + 4b + c}{3}$ and the common difference is $\dfrac{a - 8b + c}{10}$, is $-444$, then $abc$ is equal to:

Accepted Answer

(B) $216$

Answer

(A) $\dfrac{125}{8}$

Answer

(C) $343$

Answer

(D) $\dfrac{343}{8}$

Question 3

Let $a_1=1, a_2, a_3, a_4, \ldots$ be consecutive natural numbers. Then $	an^{-1}\left(\dfrac{1}{1 + a_1 a_2}ight) + 	an^{-1}\left(\dfrac{1}{1 + a_2 a_3}ight) + \cdots + 	an^{-1}\left(\dfrac{1}{1 + a_{2021} a_{2022}}ight)$ is equal to:

Accepted Answer

(C) $	an^{-1}(2022) - \dfrac{\pi}{4}$

Answer

(A) $\cot^{-1}(2022) - \dfrac{\pi}{4}$

Answer

(B) $\dfrac{\pi}{4} - \cot^{-1}(2022)$

Answer

(D) $\dfrac{\pi}{4} - 	an^{-1}(2022)$

Question 4

Let $\lambda \in \mathbb{R}$, $\vec{a}=\lambda \hat{i} + 2\hat{j} - 3\hat{k}$, $\vec{b}=\hat{i} - \lambda\hat{j} + 2\hat{k}$. If $\left((\vec{a} + \vec{b}) 	imes (\vec{a} 	imes \vec{b})ight) 	imes (\vec{a} - \vec{b})=8\hat{i} - 40\hat{j} - 24\hat{k}$, then $\left|\lambda(\vec{a} + \vec{b}) 	imes (\vec{a} - \vec{b})ight|^2$ is equal to:

Accepted Answer

(C) $140$

Answer

(A) $132$

Answer

(B) $136$

Answer

(D) $144$

Question 5

Let $q$ be the maximum integral value of $p$ in $[0, 10]$ for which the roots of the equation $x^2 - px + \dfrac{5}{4}p=0$ are rational. Then the area of the region $\{(x, y): 0 \le y \le (x - q)^2,\ 0 \le x \le q\}$ is:

Accepted Answer

(A) $243$

Answer

(B) $164$

Answer

(C) $\dfrac{125}{3}$

Answer

(D) $25$

Question 6

Let $f, g$ and $h$ be the real valued functions defined on $\mathbb{R}$ as $f(x)=\begin{cases} \dfrac{x}{|x|}, & x 
e 0 \ 1, & x=0 \end{cases}$, $g(x)=\begin{cases} \dfrac{\sin(x + 1)}{(x + 1)}, & x 
e -1 \ 1, & x=-1 \end{cases}$ and $h(x)=2[x] - f(x)$, where $[x]$ is the greatest integer $\le x$. Then the value of $\displaystyle\lim_{x 	o 1} g(h(x - 1))$ is:

Accepted Answer

(D) $1$

Answer

(A) $-1$

Answer

(B) $0$

Answer

(C) $\sin(1)$

Question 7

Let $S$ be the set of all values of $a_1$ for which the mean deviation about the mean of 100 consecutive positive integers $a_1, a_2, a_3, \ldots, a_{100}$ is $25$. Then $S$ is:

Accepted Answer

(A) $\mathbb{N}$

Answer

(B) $\phi$

Answer

(C) $\{99\}$

Answer

(D) $\{9\}$

Question 8

For $\alpha, \beta \in \mathbb{R}$, suppose the system of linear equations $x - y + z=1$, $2x + 2y + \alpha z=8$, $3x - y + 4z=\beta$ has infinitely many solutions. Then $\alpha$ and $\beta$ are the roots of:

Accepted Answer

(C) $x^2 - 18x + 56=0$

Answer

(A) $x^2 + 14x + 24=0$

Answer

(B) $x^2 + 18x + 56=0$

Answer

(D) $x^2 - 10x + 16=0$

Question 9

Let $\vec{a}$ and $\vec{b}$ be two vectors. Let $|\vec{a}|=1$, $|\vec{b}|=4$ and $\vec{a} \cdot \vec{b}=2$. If $\vec{c}=(2\vec{a} 	imes \vec{b}) - 3\vec{b}$, then the value of $\vec{b} \cdot \vec{c}$ is:

Accepted Answer

(C) $-48$

Answer

(A) $-24$

Answer

(B) $-84$

Answer

(D) $-60$

Question 10

If the functions $f(x)=\dfrac{x^3}{3} + 2bx + \dfrac{ax^2}{2}$ and $g(x)=\dfrac{x^3}{3} + ax + bx^2$, $a 
e 2b$, have a common extreme point, then $a + 2b + 7$ is equal to:

Accepted Answer

(D) $6$

Answer

(A) $\dfrac{3}{2}$

Answer

(B) $3$

Answer

(C) $4$

Question 11

If $P$ is a $3 	imes 3$ real matrix such that $P^T=aP + (a - 1)I$, where $a > 1$, then:

Accepted Answer

(B) $|\mathrm{Adj}\,P|=1$

Answer

(A) $|\mathrm{Adj}\,P|=\dfrac{1}{2}$

Answer

(C) $P$ is a singular matrix

Answer

(D) $|\mathrm{Adj}\,P| > 1$

Question 12

The number of ways of selecting two numbers $a$ and $b$, $a \in \{2, 4, 6, \ldots, 100\}$ and $b \in \{1, 3, 5, \ldots, 99\}$, such that $2$ is the remainder when $a + b$ is divided by $23$, is:

Accepted Answer

(B) $108$

Answer

(A) $268$

Answer

(C) $54$

Answer

(D) $186$

Question 13

$\displaystyle\lim_{n 	o \infty} \dfrac{3}{n}\left\{4 + \left(2 + \dfrac{1}{n}ight)^2 + \left(2 + \dfrac{2}{n}ight)^2 + \cdots + \left(3 - \dfrac{1}{n}ight)^2ight\}$ is equal to:

Accepted Answer

(D) $19$

Answer

(A) $12$

Answer

(B) $\dfrac{19}{3}$

Answer

(C) $0$

Question 14

Let $A$ be a point on the x-axis. Common tangents are drawn from $A$ to the curves $x^2 + y^2=8$ and $y^2=16x$. If one of these tangents touches the two curves at $Q$ and $R$, then $(QR)^2$ is equal to:

Accepted Answer

(B) $72$

Answer

(A) $81$

Answer

(C) $76$

Answer

(D) $64$

Question 15

If a plane passes through the points $(-1, k, 0), (2, k, -1), (1, 1, 2)$ and is parallel to the line $\dfrac{x - 1}{1}=\dfrac{2y + 1}{2}=\dfrac{z + 1}{-1}$, then the value of $\dfrac{k^2 + 1}{(k - 1)(k - 2)}$ is:

Accepted Answer

(B) $\dfrac{13}{6}$

Answer

(A) $\dfrac{17}{5}$

Answer

(C) $\dfrac{6}{13}$

Answer

(D) $\dfrac{5}{17}$

Question 16

The range of the function $f(x)=\sqrt{3 - x} + \sqrt{2 + x}$ is:

Accepted Answer

(D) $[\sqrt{5}, \sqrt{10}]$

Answer

(A) $[2\sqrt{2}, \sqrt{11}]$

Answer

(B) $[\sqrt{5}, \sqrt{13}]$

Answer

(C) $[\sqrt{2}, \sqrt{7}]$

Question 17

The solution of the differential equation $\dfrac{dy}{dx}=-\left(\dfrac{x^2 + 3y^2}{3x^2 + y^2}\right)$, $y(1)=0$, is:

Accepted Answer

(B) $\log_e|x + y| + \dfrac{2xy}{(x + y)^2}=0$

Answer

(A) $\log_e|x + y| - \dfrac{xy}{(x + y)^2}=0$

Answer

(C) $\log_e|x + y| - \dfrac{2xy}{(x + y)^2}=0$

Answer

(D) $\log_e|x + y| + \dfrac{xy}{(x + y)^2}=0$

Question 18

The parabolas $ax^2 + 2bx + cy=0$ and $dx^2 + 2ex + fy=0$ intersect on the line $y=1$. If $a, b, c, d, e, f$ are positive real numbers and $a, b, c$ are in G.P., then:

Accepted Answer

(B) $\dfrac{d}{a}, \dfrac{e}{b}, \dfrac{f}{c}$ are in A.P.

Answer

(A) $d, e, f$ are in G.P.

Answer

(C) $d, e, f$ are in A.P.

Answer

(D) $\dfrac{d}{a}, \dfrac{e}{b}, \dfrac{f}{c}$ are in G.P.

Question 19

Consider the following statements: P: I have fever; Q: I will not take medicine; R: I will take rest. The statement "If I have fever, then I will take medicine and I will take rest" is equivalent to:

Accepted Answer

(A) $((\sim P) \vee \sim Q) \wedge ((\sim P) \vee R)$

Answer

(B) $(P \vee Q) \wedge ((\sim P) \vee R)$

Answer

(C) $((\sim P) \vee \sim Q) \wedge ((\sim P) \vee \sim R)$

Answer

(D) $(P \vee \sim Q) \wedge (P \vee \sim R)$

Question 20

$x=(8\sqrt{3} + 13)^{13}$ and $y=(7\sqrt{2} + 9)^{9}$. If $[t]$ denotes the greatest integer $\le t$, then:

Accepted Answer

(B) $[x] + [y]$ is even

Answer

(A) $[x]$ is odd but $[y]$ is even

Answer

(C) $[x]$ and $[y]$ are both odd

Answer

(D) $[x]$ is even but $[y]$ is odd

Question 21

Let a line $L$ pass through the point $P(2, 3, 1)$ and be parallel to the line $x + 3y - 2z - 2=0=x - y + 2z$. If the distance of $L$ from the point $(5, 3, 8)$ is $\alpha$, then $3\alpha^2$ is equal to _______.

Accepted Answer

158

Question 22

A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is $p$. Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colour is $q$. If $p:q=m:n$, where $m$ and $n$ are coprime, then $m + n$ is equal to _______.

Accepted Answer

14

Question 23

Let $P(a_1, b_1)$ and $Q(a_2, b_2)$ be two distinct points on a circle with center $C(\sqrt{2}, \sqrt{3})$. Let $O$ be the origin and $OC$ be perpendicular to both $CP$ and $CQ$. If the area of the triangle $OCP$ is $\dfrac{\sqrt{35}}{2}$, then $a_1^2 + a_2^2 + b_1^2 + b_2^2$ is equal to _______.

Accepted Answer

24

Question 24

Let $A$ be the area of the region $\{(x, y): y \ge x^2,\ y \ge (1 - x)^2,\ y \le 2x(1 - x)\}$. Then $540\,A$ is equal to _______.

Accepted Answer

25

Question 25

The $8^{th}$ common term of the series $S_1=3 + 7 + 11 + 15 + 19 + \cdots$ and $S_2=1 + 6 + 11 + 16 + 21 + \cdots$ is _______.

Accepted Answer

151

Question 26

Let $A=\{1, 2, 3, 5, 8, 9\}$. Then the number of possible functions $f: A 	o A$ such that $f(m \cdot n)=f(m) \cdot f(n)$ for every $m, n \in A$ with $m \cdot n \in A$ is equal to _______.

Accepted Answer

432

Question 27

If $\displaystyle\int \sqrt{\sec 2x - 1}\,dx=\alpha \log_e\left|\cos 2x + \beta + \sqrt{\cos 2x\left(1 + \cos\dfrac{1}{\beta}xight)}ight| + 	ext{constant}$, then $\beta - \alpha$ is equal to _______.

Accepted Answer

1

Question 28

If the value of the real number $a > 0$ for which $x^2 - 5ax + 1=0$ and $x^2 - ax - 5=0$ have a common real root is $\dfrac{3}{\sqrt{2\beta}}$, then $\beta$ is equal to _______.

Accepted Answer

13

Question 29

The $50^{th}$ root of a number $x$ is $12$ and the $50^{th}$ root of another number $y$ is $18$. Then the remainder obtained on dividing $(x + y)$ by $25$ is _______.

Accepted Answer

23

Question 30

The number of seven-digit odd numbers that can be formed using all the seven digits $1, 2, 2, 2, 3, 3, 5$ is _______.

Accepted Answer

240

Question 31

A current carrying rectangular loop PQRS is made of uniform wire with $PR=QS=5$ cm and $PQ=RS=100$ cm. If the current reading changes from $I$ to $2I$, the ratio of the magnetic force per unit length on the wire PQ due to wire RS in the two cases respectively ($f_{PQ}^{I}:f_{PQ}^{2I}$) is:

Accepted Answer

(C) $1:4$

Answer

(A) $1:2$

Answer

(B) $1:3$

Answer

(D) $1:5$

Question 32

The output Y for the inputs A and B of the circuit shown in the figure is given by the truth table (choose the correct truth table from the options shown in the figure):

Accepted Answer

(C) (3)

Answer

(A) (1)

Answer

(B) (2)

Answer

(D) (4)

Question 33

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Efficiency of a reversible heat engine will be highest at $-273\,^{\circ}$C temperature of the cold reservoir.
Reason R: The efficiency of Carnot's engine depends not only on temperature of the cold reservoir but it depends on the temperature of the hot reservoir too and is given as $\eta=\left(1-\dfrac{T_2}{T_1}\right)$.
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 34

A point charge $Q$ is placed at the centre of a conducting spherical shell of inner radius $a$ and outer radius $b$. The electric field due to charge $Q$ in the three regions I ($r<a$), II ($a<r<b$) and III ($r>b$) is given by:

Accepted Answer

(C) $E_I
eq0,\ E_{II}=0,\ E_{III}
eq0$

Answer

(A) $E_I=0,\ E_{II}=0,\ E_{III}=0$

Answer

(B) $E_I=0,\ E_{II}=0,\ E_{III}
eq0$

Answer

(D) $E_I
eq0,\ E_{II}=0,\ E_{III}=0$

Question 35

The equivalent resistance between A and B for the network shown in the figure is:

Accepted Answer

(D) $\dfrac{2}{3}\,\Omega$

Answer

(A) $\dfrac{1}{3}\,\Omega$

Answer

(B) $\dfrac{1}{2}\,\Omega$

Answer

(C) $\dfrac{3}{2}\,\Omega$

Question 36

A vehicle travels 4 km with a speed of 3 km/h and another 4 km with a speed of 5 km/h, then its average speed is:

Accepted Answer

(D) $3.75$ km/h

Answer

(A) $3.50$ km/h

Answer

(B) $4.25$ km/h

Answer

(C) $4.00$ km/h

Question 37

In a series AC circuit with inductive reactance $X_L=200\,\Omega$, capacitive reactance $X_C=100\,\Omega$ and resistance $R=100\,\Omega$ connected to a source of $V_{rms}=200\sqrt{2}$ V, the rms value of current ($I_{rms}$) through the resistor R is:

Accepted Answer

(B) $2$ A

Answer

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

Answer

(C) $20$ A

Answer

(D) $\dfrac{1}{2}$ A

Question 38

A point source of 100 W emits light with 5% efficiency. At a distance of 5 m from the source, the intensity produced by the electric field component is:

Accepted Answer

(D) $\dfrac{1}{40\pi}\ \dfrac{W}{m^2}$

Answer

(A) $\dfrac{1}{2\pi}\ \dfrac{W}{m^2}$

Answer

(B) $\dfrac{1}{20\pi}\ \dfrac{W}{m^2}$

Answer

(C) $\dfrac{1}{10\pi}\ \dfrac{W}{m^2}$

Question 39

A block of $\sqrt{3}$ kg is attached to a string whose other end is attached to the wall. An unknown horizontal force F is applied so that the string makes an angle of $30^{\circ}$ with the wall. The tension T is: (Given $g=10$ ms$^{-2}$)

Accepted Answer

(A) $20$ N

Answer

(B) $10$ N

Answer

(C) $15$ N

Answer

(D) $25$ N

Question 40

Match List-I (communication-system terms) with List-II (their descriptions). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 41

An electron accelerated through a potential difference $V_1$ has a de-Broglie wavelength of $\lambda$. When the potential is changed to $V_2$, its de-Broglie wavelength increases by 50%. The value of $\dfrac{V_1}{V_2}$ is equal to:

Accepted Answer

(D) $\dfrac{9}{4}$

Answer

(A) $3$

Answer

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

Answer

(C) $4$

Question 42

A flask contains hydrogen and oxygen in the ratio of 2:1 by mass at temperature $27\,^{\circ}$C. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is:

Accepted Answer

(B) $1:1$

Answer

(A) $2:1$

Answer

(C) $1:4$

Answer

(D) $4:1$

Question 43

A current of 2 A is flowing in an equilateral triangle of side $4\sqrt{3}$ cm. The magnetic field at the centroid O of the triangle is (neglect the effect of earth's magnetic field):

Accepted Answer

(C) $3\sqrt{3}	imes10^{-5}$ T

Answer

(A) $1.4\sqrt{3}	imes10^{-5}$ T

Answer

(B) $4\sqrt{3}	imes10^{-4}$ T

Answer

(D) $\sqrt{3}	imes10^{-4}$ T

Question 44

An object is allowed to fall from a height $R$ above the earth, where $R$ is the radius of the earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be:

Accepted Answer

(D) $\sqrt{gR}$

Answer

(A) $\sqrt{2gR}$

Answer

(B) $\sqrt{\dfrac{gR}{2}}$

Answer

(C) $2\sqrt{gR}$

Question 45

Match List-I (physical quantities) with List-II (their dimensional formulae). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 46

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The nuclear density of nuclides $^{10}_{5}B$, $^{6}_{3}Li$, $^{56}_{26}Fe$, $^{20}_{10}Ne$ and $^{209}_{83}Bi$ can be arranged as $\rho^{N}_{Bi}>\rho^{N}_{Fe}>\rho^{N}_{Ne}>\rho^{N}_{B}>\rho^{N}_{Li}$.
Reason R: The radius R of a nucleus is related to its mass number A as $R=R_0 A^{1/3}$, where $R_0$ is a constant.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

(A) A is false but R is true

Answer

(B) A is true but R is false

Answer

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

Answer

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

Question 47

A force is applied to a steel wire 'A', rigidly clamped at one end. As a result the elongation in the wire is 0.2 mm. If the same force is applied to another steel wire 'B' of double the length and a diameter 2.4 times that of wire 'A', the elongation in wire 'B' will be (wires having uniform circular cross sections):

Accepted Answer

(D) $6.9	imes10^{-2}$ mm

Answer

(A) $6.06	imes10^{-2}$ mm

Answer

(B) $2.77	imes10^{-2}$ mm

Answer

(C) $3.0	imes10^{-2}$ mm

Question 48

A thin prism $P_1$ with an angle $6^{\circ}$ and made of glass of refractive index 1.54 is combined with another prism $P_2$ made from glass of refractive index 1.72 to produce dispersion without average deviation. The angle of prism $P_2$ is:

Accepted Answer

(C) $4.5^{\circ}$

Answer

(A) $1.3^{\circ}$

Answer

(B) $6^{\circ}$

Answer

(D) $7.8^{\circ}$

Question 49

A machine gun of mass 10 kg fires 20 g bullets at the rate of 180 bullets per minute with a speed of 100 m s$^{-1}$ each. The recoil velocity of the gun is:

Accepted Answer

(B) $0.6$ m/s

Answer

(A) $1.5$ m/s

Answer

(C) $2.5$ m/s

Answer

(D) $0.02$ m/s

Question 50

For a simple harmonic motion in a mass-spring system on a frictionless surface, the angular frequency is $\omega_1$ when the mass of the block is 1 kg and $\omega_2$ when the mass is 2 kg. The ratio $\dfrac{\omega_2}{\omega_1}$ is:

Accepted Answer

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

Answer

(B) $\sqrt{2}$

Answer

(C) $2$

Answer

(D) $\dfrac{1}{2}$

Question 51

A uniform disc of mass 0.5 kg and radius $r$ is projected with velocity 18 m/s at $t=0$ s on a rough horizontal surface. It starts with a purely sliding motion at $t=0$ s and after 2 s it acquires a purely rolling motion. The total kinetic energy of the disc after 2 s will be _______ J. (Given coefficient of friction is 0.3 and $g=10$ m/s$^2$)

Accepted Answer

54

Question 52

For the bridge network shown in the figure, if the potential difference between B and D is zero, the value of $x$ is $\dfrac{1}{n}\,\Omega$. The value of $n$ is _______.

Accepted Answer

2

Question 53

A stone tied to a 180 cm long string at its end is making 28 revolutions in a horizontal circle in every minute. The magnitude of acceleration of the stone is $\dfrac{1936}{x}$ ms$^{-2}$. The value of $x$ is _______. (Take $\pi=\dfrac{22}{7}$)

Accepted Answer

125

Question 54

A radioactive nucleus decays by two different processes. The half life of the first process is 5 minutes and that of the second process is 30 s. The effective half-life of the nucleus is calculated to be $\dfrac{\alpha}{11}$ s. The value of $\alpha$ is _______.

Accepted Answer

300

Question 55

A faulty thermometer reads $5\,^{\circ}$C in melting ice and $95\,^{\circ}$C in steam. The correct temperature on the absolute scale will be _______ K when the faulty thermometer reads $41\,^{\circ}$C.

Accepted Answer

313

Question 56

In an ac generator, a rectangular coil of 100 turns each having area $14	imes10^{-2}$ m$^2$ is rotated at 360 rev/min about an axis perpendicular to a uniform magnetic field of magnitude 3.0 T. The maximum value of the emf produced will be _______ V. (Take $\pi=\dfrac{22}{7}$)

Accepted Answer

1584

Question 57

A body of mass 2 kg is initially at rest. It starts moving unidirectionally under the influence of a source of constant power P. Its displacement in 4 s is $\dfrac{1}{3}\alpha^{2}\sqrt{\dfrac{2P}{m}}$. The value of $\alpha$ will be _______.

Accepted Answer

4

Question 58

A cuboid with one corner at the origin and edges of length 1 m, 2 m and 3 m along the x, y and z axes respectively lies in a region with electric field $\vec{E}=2x^{2}\hat{i}-4y\hat{j}+6\hat{k}$ N/C. The magnitude of charge within the cuboid is $n\varepsilon_0$ C. The value of $n$ is _______.

Accepted Answer

12

Question 59

In a Young's double slit experiment, the intensities at two points, for the path differences $\dfrac{\lambda}{4}$ and $\dfrac{\lambda}{3}$ ($\lambda$ being the wavelength of light used) are $I_1$ and $I_2$ respectively. If $I_0$ denotes the intensity produced by each one of the individual slits, then $\dfrac{I_1+I_2}{I_0}=$ _______.

Accepted Answer

3

Question 60

The velocity of a particle executing SHM varies with displacement ($x$) as $4v^{2}=50-x^{2}$. The time period of oscillation is $\dfrac{x}{7}$ s. The value of $x$ is _______. (Take $\pi=\dfrac{22}{7}$)

Accepted Answer

88

Question 61

The Cl$-$Co$-$Cl bond angle value(s) in a fac-$[Co(NH_3)_3Cl_3]$ complex is/are:

Accepted Answer

(A) $90^{\circ}$

Answer

(B) $90^{\circ}\ \&\ 120^{\circ}$

Answer

(C) $180^{\circ}$

Answer

(D) $90^{\circ}\ \&\ 180^{\circ}$

Question 62

The correct order of pKa values for the following compounds (a, b, c, d shown in the figure) is:

Accepted Answer

(C) $b>d>a>c$

Answer

(A) $c>a>d>b$

Answer

(B) $b>a>d>c$

Answer

(D) $a>b>c>d$

Question 63

Given below are two statements:
Statement I: During electrolytic refining, the pure metal is made to act as anode and its impure metallic form is used as cathode.
Statement II: During the Hall-Heroult electrolysis process, purified $Al_2O_3$ is mixed with $Na_3AlF_6$ to lower the melting point of the mixture.
In the light of the above statements, choose the most appropriate answer from the options given below:

Accepted Answer

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

Answer

(A) Statement I is correct but Statement II is incorrect

Answer

(B) Both Statement I and Statement II are incorrect

Answer

(C) Both Statement I and Statement II are correct

Question 64

Match List-I (Mixture) with List-II (Separation Technique). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

List-I	List-II
A.Attenuation	I.Combination of a receiver and transmitter
B.Transducer	II.Process of retrieval of information from the carrier wave at receiver
C.Demodulation	III.Converts one form of energy into another
D.Repeater	IV.Loss of strength of a signal while propagating through a medium

List-I	List-II
A.Torque	I. $kg\,m^{-1}\,s^{-2}$
B.Energy density	II. $kg\,m\,s^{-1}$
C.Pressure gradient	III. $kg\,m^{-2}\,s^{-2}$
D.Impulse	IV. $kg\,m^{2}\,s^{-2}$

List-I (Mixture)	List-II (Separation Technique)
A. $CHCl_3 + C_6H_5NH_2$	I.Steam distillation
B. $C_6H_{14} + C_5H_{12}$	II.Differential extraction
C. $C_6H_5NH_2 + H_2O$	III.Distillation
D.Organic compound in $H_2O$	IV.Fractional distillation

List-I (Complexes)	List-II (Hybridisation)
A. $[Ni(CO)_4]$	I. $sp^3$
B. $[Cu(NH_3)_4]^{2+}$	II. $dsp^2$
C. $[Fe(NH_3)_6]^{2+}$	III. $sp^3d^2$
D. $[Fe(H_2O)_6]^{2+}$	IV. $d^2sp^3$

JEE Main 30 January 2023 Shift 2 Question Paper with Answers

Physics — JEE Main 30 January 2023 Shift 2

Chemistry — JEE Main 30 January 2023 Shift 2

Mathematics — JEE Main 30 January 2023 Shift 2

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