JEE Main 13 April 2023 Shift 1 Question Paper

Question 1

$\displaystyle\int_{0}^{2}\dfrac{6}{e^{3x}+6e^{2x}+11e^{x}+6}\,dx$ is equal to:

Accepted Answer

(B) $\log_e\dfrac{32}{27}$

Answer

(A) $\log_e\dfrac{512}{81}$

Answer

(C) $\log_e\dfrac{256}{81}$

Answer

(D) $\log_e\dfrac{64}{27}$

Question 2

$\displaystyle\max_{0\le x\le\pi/2}\left\{x-2\sin x\cos x+\dfrac13\sin 3x\right\}=$

Accepted Answer

(A) $\dfrac{5\pi+2+3\sqrt3}{6}$

Answer

(B) $\dfrac{5\pi+2-3\sqrt3}{6}$

Answer

(C) $\pi$

Answer

(D) $0$

Question 3

The set of all $a\in\mathbb{R}$ for which the equation $x|x-1|+|x+2|+a=0$ has exactly one real root is:

Accepted Answer

(B) $(-\infty,\infty)$

Answer

(A) $(-6,-3)$

Answer

(C) $(-6,\infty)$

Answer

(D) $(-\infty,-3)$

Question 4

The negation of the statement $((A\wedge(B\vee C))\Rightarrow(A\vee B))\Rightarrow A$ is:

Accepted Answer

(A) equivalent to $\sim A$

Answer

(B) equivalent to $\sim C$

Answer

(C) equivalent to $B\vee\sim C$

Answer

(D) a fallacy

Question 5

The distance of the point $(-1,2,3)$ from the plane $\vec r\cdot(\hat i-2\hat j+3\hat k)=10$ parallel to the line of the shortest distance between the lines $\vec r=(\hat i-\hat j)+\lambda(2\hat i+\hat k)$ and $\vec r=(2\hat i-\hat j)+\mu(\hat i-\hat j+\hat k)$ is:

Accepted Answer

(C) $2\sqrt6$

Answer

(A) $3\sqrt6$

Answer

(B) $3\sqrt5$

Answer

(D) $2\sqrt5$

Question 6

A coin is biased so that a head is $3$ times as likely to occur as a tail. This coin is tossed until a head or three tails occur. If $X$ denotes the number of tosses of the coin, then the mean of $X$ is:

Accepted Answer

(A) $\dfrac{21}{16}$

Answer

(B) $\dfrac{81}{64}$

Answer

(C) $\dfrac{15}{16}$

Answer

(D) $\dfrac{37}{16}$

Question 7

For the system of linear equations $2x+4y+2az=b,\,x+2y+3z=4,\,2x-5y+2z=8$, which of the following is NOT correct?

Accepted Answer

(A) It has infinitely many solutions if $a=3,\,b=6$

Answer

(B) It has unique solution if $a=b=6$

Answer

(C) It has unique solution if $a=b=8$

Answer

(D) It has infinitely many solution if $a=3,\,b=8$

Question 8

For the differentiable function $f:\mathbb{R}\setminus\{0\}	o\mathbb{R}$, if $3f(x)+2f\left(\dfrac{1}{x}ight)=\dfrac{1}{x}-10$, then $\left|f(3)+f\,'\!\left(\dfrac14ight)ight|$ is equal to:

Accepted Answer

(D) $13$

Answer

(A) $7$

Answer

(B) $\dfrac{33}{5}$

Answer

(C) $\dfrac{29}{5}$

Question 9

Let the tangent and normal at the point $(3\sqrt3,1)$ on the ellipse $\dfrac{x^2}{36}+\dfrac{y^2}{4}=1$ meet the $y$-axis at the points $A$ and $B$ respectively. Let the circle $C$ be drawn taking $AB$ as a diameter and the line $x=2\sqrt5$ intersect $C$ at the points $P$ and $Q$. If the tangents at the points $P$ and $Q$ on the circle intersect at the point $(\alpha,0)$ and $(\beta,0)$, then $\alpha^2-\beta^2$ is equal to:

Accepted Answer

(B) $\dfrac{304}{5}$

Answer

(A) $\dfrac{314}{5}$

Answer

(C) $60$

Answer

(D) $61$

Question 10

The area of the region enclosed by the curve $f(x)=\max\{\sin x,\cos x\},\,-\pi\le x\le\pi$ and the $x$-axis is:

Accepted Answer

(D) $4$

Answer

(A) $2(\sqrt2+1)$

Answer

(B) $2\sqrt2(\sqrt2+1)$

Answer

(C) $4(\sqrt2)$

Question 11

The number of symmetric matrices of order $3$, with all the entries from the set $\{0,1,2,3,4,5,6,7,8,9\}$ is:

Accepted Answer

(D) $10^{6}$

Answer

(A) $6^{10}$

Answer

(B) $9^{10}$

Answer

(C) $10^{3}$

Question 12

Among:
(S1): $\displaystyle\lim_{n	o\infty}\dfrac{1}{n^{2}}(2+4+6+\dots+2n)=1$
(S2): $\displaystyle\lim_{n	o\infty}\dfrac{1}{n^{16}}(1^{15}+2^{15}+3^{15}+\dots+n^{15})=\dfrac{1}{16}$

Accepted Answer

(A) Both (S1) and (S2) are false

Answer

(B) Both (S1) and (S2) are true

Answer

(C) Only (S2) is true

Answer

(D) Only (S1) is true

Question 13

Let $PQ$ be a focal chord of the parabola $y^{2}=36x$ of length $100$, making an acute angle with the positive $x$-axis. Let the ordinate of $P$ be positive and $M$ be the point on the line segment $PQ$ such that $PM:MQ=3:1$. Then which of the following points does NOT lie on the line passing through $M$ and perpendicular to the line $PQ$?

Accepted Answer

(A) $(-3,43)$

Answer

(B) $(-6,45)$

Answer

(C) $(3,33)$

Answer

(D) $(6,29)$

Question 14

For $x\in\mathbb{R}$, two real valued functions $f(x)$ and $g(x)$ are such that $g(x)=\sqrt x+1$ and $f(g(x))=x+3-\sqrt x$. Then $f(0)$ is equal to:

Accepted Answer

(C) $5$

Answer

(A) $1$

Answer

(B) $-3$

Answer

(D) $0$

Question 15

Fractional part of the number $\dfrac{4^{2022}}{15}$ is equal to:

Accepted Answer

(B) $\dfrac{1}{15}$

Answer

(A) $\dfrac{4}{15}$

Answer

(C) $\dfrac{14}{15}$

Answer

(D) $\dfrac{8}{15}$

Question 16

Let $\vec a=\hat i+4\hat j+2\hat k,\,\vec b=3\hat i-2\hat j+7\hat k$ and $\vec c=2\hat i-\hat j+4\hat k$. If a vector $\vec d$ satisfies $\vec d	imes\vec b=\vec c	imes\vec b$ and $\vec a\cdot\vec d=24$, then $|\vec d|^{2}$ is equal to:

Accepted Answer

(A) $413$

Answer

(B) $423$

Answer

(C) $323$

Answer

(D) $313$

Question 17

Let $B=\begin{bmatrix} 1 & 3 & \alpha \ 1 & 2 & 3 \ \alpha & \alpha & 4 \end{bmatrix},\,\alpha>2$ be the adjoint of a matrix $A$ and $|A|=2$, then $[\alpha\,-2\alpha\,\alpha]\begin{bmatrix} \alpha \ -2\alpha \ \alpha \end{bmatrix}$ is equal to:

Accepted Answer

(C) $-16$

Answer

(A) $16$

Answer

(B) $32$

Answer

(D) $0$

Question 18

Let $s_{1},s_{2},s_{3},\dots,s_{10}$ respectively be the sum to $12$ terms of $10$ A.P.'s whose first terms are $1,2,3,\dots,10$ and the common differences are $1,3,5,\dots,19$ respectively. Then $\displaystyle\sum_{i=1}^{10}s_{i}$ is equal to:

Accepted Answer

(D) $7260$

Answer

(A) $7380$

Answer

(B) $7220$

Answer

(C) $7360$

Question 19

Let $y=y_{1}(x)$ and $y=y_{2}(x)$ be the solution curves of the differential equation $\dfrac{dy}{dx}=y+7$ with initial conditions $y_{1}(0)=0,\,y_{2}(0)=1$ respectively. Then the curves $y=y_{1}(x)$ and $y=y_{2}(x)$ intersect at:

Accepted Answer

(B) no point

Answer

(A) Two points

Answer

(C) infinite number of points

Answer

(D) one point

Question 20

Let the equation of the plane passing through the line of intersection of the planes $x+2y+az=2$ and $x-y+z=3$ be $5x-11y+bz=6a-1$. For $c\in\mathbb{Z}$, if the distance of this plane from the point $(a,-c,c)$ is $\dfrac{2}{\sqrt a}$, then $\dfrac{a+b}{c}$ is equal to:

Accepted Answer

(C) $-4$

Answer

(A) $-2$

Answer

(B) $2$

Answer

(D) $4$

Question 21

Let $\alpha$ be the constant term in the binomial expansion of $\left(\sqrt x-\dfrac{6}{x^{3/2}}\right)^{n},\,n\le 15$. If the sum of the coefficients of the remaining terms in the expansion is $649$ and the coefficient of $x^{-n}$ is $\lambda\alpha$, then $\lambda$ is equal to _____.

Accepted Answer

36

Question 22

Let $S=\left\{x\in\mathbb{R}:\sin^{-1}\left(\dfrac{x+1}{\sqrt{x^{2}+2x+2}}\right)-\sin^{-1}\left(\dfrac{x}{\sqrt{x^{2}+1}}\right)=\dfrac{\pi}{4}\right\}$. Then $\displaystyle\sum_{x\in S}\left(\sin\!\left((x^{2}+x+5)\dfrac{\pi}{2}\right)-\cos\!\left((x^{2}+x+5)\pi\right)\right)$ is equal to _____.

Accepted Answer

4

Question 23

Let $\omega=z\bar z+k_{1}z+\bar k_{1}\bar z+\lambda(1+i),\,k_{1}\in\mathbb{C}$. $\operatorname{Re}(\omega)=0$ be the circle $C$ of radius $1$ in the first quadrant touching the line $y=1$ and the $y$-axis. If the curve $\operatorname{Im}(\omega)=0$ intersects $C$ at $A$ and $B$, then $30(AB)^{2}$ is equal to _____.

Accepted Answer

24

Question 24

Let for $x\in\mathbb{R},\,S_{0}(x)=x,\,S_{k}(x)=C_{k}+k\displaystyle\int_{0}^{x}S_{k-1}(t)dt$, where $C_{k}=1-\displaystyle\int_{0}^{1}S_{k-1}(x)dx,\,k=1,2,3,\dots$. Then $S_{2}(3)+6C_{3}$ is equal to _____.

Accepted Answer

18

Question 25

The sum to $20$ terms of the series $2\cdot 2^{2}-3^{2}+2\cdot 4^{2}-5^{2}+2\cdot 6^{2}-\dots$ is equal to _____.

Accepted Answer

1310

Question 26

The number of seven digit positive integers formed using the digits $1,\,2,\,3$ and $4$ only and sum of the digits equal to $12$ is _____.

Accepted Answer

413

Question 27

Let $m_{1}$ and $m_{2}$ be the slopes of the tangents drawn from the point $P(4,1)$ to the hyperbola $H:\dfrac{y^{2}}{25}-\dfrac{x^{2}}{16}=1$. If $Q$ is the point from which the tangents drawn to $H$ have slopes $|m_{1}|$ and $|m_{2}|$ and they make positive intercepts $\alpha$ and $\beta$ on the $x$-axis, then $\dfrac{(PQ)^{2}}{\alpha\beta}$ is equal to _____.

Accepted Answer

8

Question 28

Let the image of the point $\left(\dfrac{5}{3},\dfrac{5}{3},\dfrac{8}{3}\right)$ in the plane $x-2y+z-2=0$ be $P$. If the distance of point $Q(6,-2,\alpha),\,\alpha>0$ from $P$ is $13$, then $\alpha$ is equal to _____.

Accepted Answer

15

Question 29

Let $\vec a=3\hat i+\hat j-\hat k$ and $\vec c=2\hat i-3\hat j+3\hat k$. If $\vec b$ is a vector such that $\vec a=\vec b	imes\vec c$ and $|\vec b|=\sqrt{50}$, then $\left|72-|\vec b+\vec c|^{2}ight|$ is equal to _____.

Accepted Answer

66

Question 30

Let the mean of the data: $\begin{array}{|c|c|c|c|c|c|}\hline x & 1 & 3 & 5 & 7 & 9 \\hline 	ext{Frequency }(f) & 4 & 24 & 28 & \alpha & 8 \\hline\end{array}$ be $5$. If $m$ and $\sigma^{2}$ are respectively the mean deviation about the mean and the variance of the data, then $\dfrac{3\alpha}{m+\sigma^{2}}$ is equal to _____.

Accepted Answer

8

Question 31

Which of the following Maxwell's equations is valid for time varying conditions but not valid for static conditions:

Accepted Answer

(C) $\displaystyle\oint\vec E\cdot d\vec l=-\dfrac{\partial\Phi_{B}}{\partial t}$

Answer

(A) $\displaystyle\oint\vec B\cdot d\vec l=\mu_{0}I$

Answer

(B) $\displaystyle\oint\vec E\cdot d\vec l=0$

Answer

(D) $\displaystyle\oint\vec D\cdot d\vec A=Q$

Question 32

Different combinations of $3$ resistors of equal resistance $R$ are shown in the figures. The increasing order for power dissipation is:

Accepted Answer

(D) $P_{A}<P_{C}<P_{D}<P_{B}$

Answer

(A) $P_{A}<P_{B}<P_{C}<P_{D}$

Answer

(B) $P_{C}<P_{D}<P_{A}<P_{B}$

Answer

(C) $P_{B}<P_{D}<P_{C}<P_{A}$

Question 33

A vessel of depth $'d'$ is half filled with oil of refractive index $n_{1}$ and the other half is filled with water of refractive index $n_{2}$. The apparent depth of this vessel when viewed from above will be:

Accepted Answer

(B) $\dfrac{d(n_{1}+n_{2})}{2n_{1}n_{2}}$

Answer

(A) $\dfrac{d\,n_{1}n_{2}}{(n_{1}+n_{2})}$

Answer

(C) $\dfrac{d\,n_{1}n_{2}}{2(n_{1}+n_{2})}$

Answer

(D) $\dfrac{2d(n_{1}+n_{2})}{n_{1}n_{2}}$

Question 34

The source of time varying magnetic field may be:
(A) A permanent magnet
(B) An electric field changing linearly with time
(C) Direct current
(D) A decelerating charge particle
(E) An antenna fed with a digital signal
Choose the correct answer from the options given below:

Accepted Answer

(A) (D) only

Answer

(B) (C) and (E) only

Answer

(C) (A) only

Answer

(D) (B) and (D) only

Question 35

Two trains 'A' and 'B' of length $'l'$ and $'4l'$ are travelling into a tunnel of length $'L'$ in parallel tracks from opposite directions with velocities $108\,km/h$ and $72\,km/h$ respectively. If train 'A' takes $35\,s$ less time than train 'B' to cross the tunnel, then length 'L' of the tunnel is: (Given $L=60\,l$)

Accepted Answer

(C) $1800\,m$

Answer

(A) $1200\,m$

Answer

(B) $2200\,m$

Answer

(D) $900\,m$

Question 36

The ratio of powers of two motors is $\dfrac{3\sqrt x}{\sqrt x+1}$, that are capable of raising $300\,kg$ of water in $5$ minutes and $50\,kg$ of water in $2$ minutes respectively from a well of $100\,m$ deep. The value of $x$ will be:

Accepted Answer

(D) $16$

Answer

(A) $2$

Answer

(B) $4$

Answer

(C) $2.4$

Question 37

A planet having mass $9\,M_{e}$ and radius $4\,R_{e}$, where $M_{e}$ and $R_{e}$ are mass and radius of earth respectively, has escape velocity in $km/s$ given by: (Given escape velocity on earth $V_{e}=11.2	imes10^{3}\,m/s$)

Accepted Answer

(B) $16.8$

Answer

(A) $67.2$

Answer

(C) $33.6$

Answer

(D) $11.2$

Question 38

The difference between threshold wavelengths for two metal surfaces $A$ and $B$ having work function $\varphi_{A}=9\,eV$ and $\varphi_{B}=4.5\,eV$ in nm is: (Given, $hc=1242\,eV\,nm$)

Accepted Answer

(B) $138$

Answer

(A) $264$

Answer

(C) $276$

Answer

(D) $540$

Question 39

A bullet $10\,g$ leaves the barrel of gun with a velocity of $600\,m/s$. If the barrel of gun is $50\,cm$ long and mass of gun is $3\,kg$, then value of impulse supplied to the gun will be:

Accepted Answer

(B) $6\,Ns$

Answer

(A) $12\,Ns$

Answer

(C) $36\,Ns$

Answer

(D) $3\,Ns$

Question 40

Two charges each of magnitude $0.01\,C$ and separated by a distance of $0.4\,m$ constitute an electric dipole. If the dipole is placed in an uniform electric field $\vec E$ of $10\,dyne/C$ making $30^\circ$ angle with $\vec E$, the magnitude of torque acting on the dipole is:

Accepted Answer

(B) $2.0	imes10^{-5}\,Nm$

Answer

(A) $4.0	imes10^{-5}\,Nm$

Answer

(C) $4.0	imes10^{-8}\,Nm$

Answer

(D) $1.5	imes10^{-5}\,Nm$

Question 41

A disc is rolling without slipping on a surface. The radius of the disc is $R$. At $t=0$, the top most point on the disc is $A$ as shown in figure. When the disc completes half of its rotation, the displacement of point $A$ from its initial position is:

Accepted Answer

(A) $R\sqrt{\pi^{2}+4}$

Answer

(B) $R\sqrt{\pi^{2}+1}$

Answer

(C) $2R$

Answer

(D) $2R\sqrt{1+4\pi^{2}}$

Question 42

Match List I with List II.
Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 43

The $rms$ speed of oxygen molecules in a vessel at particular temperature is $\left(1+\dfrac{5}{x}\right)^{1/2}\,v$, where $v$ is the average speed of the molecule. The value of $x$ will be: (Take $\pi=\dfrac{22}{7}$)

Accepted Answer

(A) $28$

Answer

(B) $27$

Answer

(C) $8$

Answer

(D) $4$

Question 44

A body of mass $(5\pm 0.5)\,kg$ is moving with a velocity of $(20\pm 0.4)\,m/s$. Its kinetic energy will be:

Accepted Answer

(A) $(1000\pm 140)\,J$

Answer

(B) $(1000\pm 0.14)\,J$

Answer

(C) $(500\pm 0.14)\,J$

Answer

(D) $(500\pm 140)\,J$

Question 45

Two bodies are having kinetic energies in the ratio $16:9$. If they have same linear momentum, the ratio of their masses respectively is:

Accepted Answer

(D) $9:16$

Answer

(A) $4:3$

Answer

(B) $3:4$

Answer

(C) $16:9$

Question 46

The figure shows a liquid of given density flowing steadily in a horizontal tube of varying cross-section. Cross sectional areas at $A$ is $1.5\,cm^{2}$ and at $B$ is $25\,mm^{2}$. If the speed of the liquid at $B$ is $60\,cm/s$ then $(P_{A}-P_{B})$ is: (Given $P_{A}$ and $P_{B}$ are liquid pressures at $A$ and $B$ points. Density $\rho=1000\,kg\,m^{-3}$)

Accepted Answer

(A) $175\,Pa$

Answer

(B) $27\,Pa$

Answer

(C) $135\,Pa$

Answer

(D) $36\,Pa$

Question 47

Under isothermal condition, the pressure of a gas is given by $P=aV^{-3}$, where $a$ is a constant and $V$ is the volume of the gas. The bulk modulus at constant temperature is equal to:

Accepted Answer

(B) $3P$

Answer

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

Answer

(C) $2P$

Answer

(D) $P$

Question 48

For the following circuit and given inputs $A$ and $B$, choose the correct option for output $'Y'$:

Accepted Answer

(D) (4)

Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Question 49

Which graph represents the difference between total energy and potential energy of a particle executing SHM Vs its distance from mean position:

Accepted Answer

(D) (4)

Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Question 50

$^{238}_{92}U	o ^{234}_{90}\!Th+^{4}_{2}\!D+Q$. In the above nuclear reaction, the approximate amount of energy released will be: [Given, mass of $^{238}_{92}U=238.05079	imes 931.5\,MeV/c^{2}$, mass of $^{234}_{90}Th=234.04363	imes 931.5\,MeV/c^{2}$, mass of $^{4}_{2}D=4.00260	imes 931.5\,MeV/c^{2}$]

Accepted Answer

(D) $4.25\,MeV$

Answer

(A) $3.82\,MeV$

Answer

(B) $5.9\,MeV$

Answer

(C) $2.12\,MeV$

Question 51

The elastic potential energy stored in a steel wire of length $20\,m$ stretched through $2\,cm$ is $80\,J$. The cross sectional area of the wire is _____ $mm^{2}$. (Given, $y=2.0	imes10^{11}\,Nm^{-2}$)

Accepted Answer

40

Question 52

A potential $V_{0}$ is applied across a uniform wire of resistance $R$. The power dissipation is $P_{1}$. The wire is then cut into two equal parts and a potential of $V_{0}$ is applied across the length of each half. The total power dissipation across two wires is $P_{2}$. The ratio $P_{2}:P_{1}$ is $\sqrt x:1$. The value of $x$ is _____.

Accepted Answer

16

Question 53

At a given point of time the value of displacement of a simple harmonic oscillator is given as $y=A\cos(30^\circ)$. If amplitude is $40\,cm$ and kinetic energy at that time is $200\,J$, the value of force constant is $1.0	imes 10^{x}\,Nm^{-1}$. The value of $x$ is _____.

Accepted Answer

4

Question 54

When a resistance of $5\,\Omega$ is shunted with a moving coil galvanometer, it shows a full scale deflection for a current of $250\,mA$, however when $1050\,\Omega$ resistance is connected with it in series, it gives full scale deflection for $25$ volt. The resistance of galvanometer is _____ $\Omega$.

Accepted Answer

50

Question 55

The radius of $2^{nd}$ orbit of $He^{+}$ of Bohr's model is $r_{1}$ and that of fourth orbit of $Be^{+3}$ is represented as $r_{2}$. Now the ratio $\dfrac{r_{2}}{r_{1}}$ is $x:1$. The value of $x$ is _____.

Accepted Answer

2

Question 56

A thin infinite sheet charge and an infinite line charge of respective charge densities $+\sigma$ and $+\lambda$ are placed parallel at $5\,m$ distance from each other. Points 'P' and 'Q' are at $\dfrac{3}{\pi}\,m$ and $\dfrac{4}{\pi}\,m$ perpendicular distance from line charge towards sheet charge, respectively. $'E_{P}'$ and $'E_{Q}'$ are the magnitudes of resultant electric field intensities at point 'P' and 'Q', respectively. If $\dfrac{E_{P}}{E_{Q}}=\dfrac{4}{a}$ for $2|\sigma|=|\lambda|$. Then the value of $a$ is _____.

Accepted Answer

6

Question 57

In the given figure, an inductor and a resistor are connected in series with a battery of emf $E$ volt. $\dfrac{E^{2}}{2b}\,J/s$ represents the maximum rate at which the energy is stored in the magnetic field (inductor). The numerical value of $\dfrac{b}{a}$ will be _____.

Accepted Answer

25

Question 58

A fish rising vertically upward with a uniform velocity of $8\,ms^{-1}$, observes that a bird is diving vertically downward towards the fish with the velocity of $12\,ms^{-1}$. If the refractive index of water is $\dfrac{4}{3}$, then the actual velocity of the diving bird to pick the fish, will be _____ $ms^{-1}$.

Accepted Answer

3

Question 59

A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is $\pi:22$ then, the value of its angular speed will be _____ rad/s.

Accepted Answer

4

Question 60

From the given transfer characteristic of a transistor in CE configuration, the value of power gain of this configuration is $10^{x}$, for $R_{B}=10\,k\Omega$ and $R_{C}=1\,k\Omega$. The value of $x$ is _____.

Accepted Answer

3

Question 61

In the reaction given below, $'A'$ is:

Accepted Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Answer

(D) (4)

Question 62

Given below are two statements:
Statement-I: Permutit process is more efficient compared to the synthetic resin method for the softening of water.
Statement-II: Synthetic resin method results in the formation of soluble sodium salts.
In the light of the above statements, choose the most appropriate answer from the options given below:

Accepted Answer

(D) Both the Statements I and II are incorrect

Answer

(A) Both the Statements I and II are correct

Answer

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

Answer

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

Question 63

The mismatched combinations are:
A. Chlorophyll - Co
B. Water hardness - EDTA
C. Photography - $[Ag(CN)_{2}]^{-}$
D. Wilkinson catalyst - $[(Ph_{3}P)_{3}\,RhCl]$
E. Chelating ligand - D-Penicillamine
Choose the correct answer from the options given below:

Accepted Answer

(A) A and C Only

Answer

(B) A and E Only

Answer

(C) D and E Only

Answer

(D) A, C and E Only

Question 64

In which of the following processes, the bond order increases and paramagnetic character changes to diamagnetic one?

Accepted Answer

(B) $NO	o NO^{+}$

Answer

(A) $O_{2}	o O_{2}^{+}$

Answer

(C) $N_{2}	o N_{2}^{+}$

Answer

(D) $O_{2}	o O_{2}^{-}$

List I (Layer of atmosphere)	List II (Approximate height over earth's surface)
A. $F_{1}$ Layer	I. $10\,km$
B.D Layer	II. $170-190\,km$
C.Troposphere	III. $100\,km$
D.E Layer	IV. $65-75\,km$

JEE Main 13 April 2023 Shift 1 Question Paper with Answers

Physics — JEE Main 13 April 2023 Shift 1

Chemistry — JEE Main 13 April 2023 Shift 1

Mathematics — JEE Main 13 April 2023 Shift 1

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