JEE Main 25 January 2023 Shift 1 Question Paper

Question 1

The points of intersection of the line $ax+by=0$, $(a
e b)$ and the circle $x^2+y^2-2x=0$ are $A(\alpha,0)$ and $B(1,\beta)$. The image of the circle with $AB$ as a diameter in the line $x+y+2=0$ is:

Accepted Answer

(D) $x^2+y^2+5x+5y+12=0$

Answer

(A) $x^2+y^2+3x+3y+4=0$

Answer

(B) $x^2+y^2+3x+5y+8=0$

Answer

(C) $x^2+y^2-5x-5y+12=0$

Question 2

The distance of the point $(6,-2\sqrt{2})$ from the common tangent $y=mx+c$, $m>0$, of the curves $x=2y^2$ and $x=1+y^2$ is:

Accepted Answer

(D) $5$

Answer

(A) $\dfrac{14}{3}$

Answer

(B) $5\sqrt{3}$

Answer

(C) $\dfrac{1}{3}$

Question 3

Let $\vec{a},\vec{b}$ and $\vec{c}$ be three non zero vectors such that $\vec{b}\cdot\vec{c}=0$ and $\vec{a}	imes(\vec{b}	imes\vec{c})=\dfrac{\vec{b}-\vec{c}}{2}$. If $\vec{d}$ be a vector such that $\vec{b}\cdot\vec{d}=\vec{a}\cdot\vec{b}$, then $(\vec{a}	imes\vec{b})\cdot(\vec{c}	imes\vec{d})$ is equal to:

Accepted Answer

(B) $\dfrac{1}{4}$

Answer

(A) $-\dfrac{1}{4}$

Answer

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

Answer

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

Question 4

The vector $\vec{a}=-\hat{i}+2\hat{j}+\hat{k}$ is rotated through a right angle, passing through the $y$-axis in its way and the resulting vector is $\vec{b}$. Then the projection of $3\vec{a}+\sqrt{2}\,\vec{b}$ on $\vec{c}=5\hat{i}+4\hat{j}+3\hat{k}$ is:

Accepted Answer

(C) $3\sqrt{2}$

Answer

(A) $2\sqrt{3}$

Answer

(B) $1$

Answer

(D) $\sqrt{6}$

Question 5

Let $z_1=2+3i$ and $z_2=3+4i$. The set $S=\{z\in\mathbb{C}:|z-z_1|^2-|z-z_2|^2=|z_1-z_2|^2\}$ represents a:

Accepted Answer

(D) straight line with the sum of its intercepts on the coordinate axes equals $14$

Answer

(A) hyperbola with the length of the transverse axis $7$

Answer

(B) hyperbola with eccentricity $2$

Answer

(C) straight line with the sum of its intercepts on the coordinate axes equals $-18$

Question 6

The mean and variance of the marks obtained by the students in a test are $10$ and $4$ respectively. Later, the marks of one of the students is increased from $8$ to $12$. If the new mean of the marks is $10.2$, then their new variance is equal to:

Accepted Answer

(A) $3.96$

Answer

(B) $4.08$

Answer

(C) $4.04$

Answer

(D) $3.92$

Question 7

Let $S_1$ and $S_2$ be respectively the sets of all $a\in\mathbb{R}-\{0\}$ for which the system of linear equations $ax+2ay-3az=1$; $(2a+1)x+(2a+3)y+(a+1)z=2$; $(3a+5)x+(a+5)y+(a+2)z=3$ has unique solution and infinitely many solutions. Then:

Accepted Answer

(D) $S_1=\mathbb{R}-\{0\}$ and $S_2=\Phi$

Answer

(A) $S_1$ is an infinite set and $n(S_2)=2$

Answer

(B) $S_2$ is an infinite set and $n(S_1)=2$

Answer

(C) $S_1=\Phi$ and $S_2=\mathbb{R}-\{0\}$

Question 8

The value of $\displaystyle\lim_{n	o\infty}\dfrac{1+2-3+4+5-6+\cdots+(3n-2)+(3n-1)-3n}{\sqrt{2n^4+4n+3}-\sqrt{n^4+5n+4}}$ is:

Accepted Answer

(A) $\dfrac{3}{2}(\sqrt{2}+1)$

Answer

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

Answer

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

Answer

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

Question 9

The statement $(p\wedge(\sim q))\Rightarrow(p\Rightarrow(\sim q))$ is:

Accepted Answer

(A) a tautology

Answer

(B) a contradiction

Answer

(C) equivalent to $p\vee q$

Answer

(D) equivalent to $(\sim p)\vee(\sim q)$

Question 10

Consider the lines $L_1$ and $L_2$ given by $L_1:\dfrac{x-1}{2}=\dfrac{y-3}{1}=\dfrac{z-2}{2}$, $L_2:\dfrac{x-2}{1}=\dfrac{y-2}{2}=\dfrac{z-3}{3}$. A line $L_3$ having direction ratios $1,-1,-2$, intersects $L_1$ and $L_2$ at the points $P$ and $Q$ respectively. Then the length of line segment $PQ$ is:

Accepted Answer

(D) $2\sqrt{6}$

Answer

(A) $3\sqrt{2}$

Answer

(B) $4\sqrt{3}$

Answer

(C) $4$

Question 11

Let $f(x)=\displaystyle\int\dfrac{2x}{(x^2+1)(x^2+3)}\,dx$. If $f(3)=\dfrac{1}{2}(\log_e 5-\log_e 6)$, then $f(4)$ is equal to:

Accepted Answer

(D) $\dfrac{1}{2}(\log_e 17-\log_e 19)$

Answer

(A) $\log_e 19-\log_e 20$

Answer

(B) $\dfrac{1}{2}(\log_e 17-\log_e 18)$

Answer

(C) $\dfrac{1}{2}(\log_e 19-\log_e 17)$

Question 12

The minimum value of the function $f(x)=\displaystyle\int_0^2 e^{|x-t|}\,dt$ is:

Accepted Answer

(B) $2(e-1)$

Answer

(A) $e(e-1)$

Answer

(C) $2$

Answer

(D) $2e-1$

Question 13

Let $M$ be the maximum value of the product of two positive integers when their sum is $66$. Let the sample space $S=\Big\{x\in\mathbb{Z}:x(66-x)\ge\dfrac{5}{9}M\Big\}$ and the event $A=\{x\in S:x	ext{ is a multiple of }3\}$. Then $P(A)$ is equal to:

Accepted Answer

(D) $\dfrac{1}{3}$

Answer

(A) $\dfrac{15}{22}$

Answer

(B) $\dfrac{1}{5}$

Answer

(C) $\dfrac{15}{44}$

Question 14

Let $x=2$ be a local minima of the function $f(x)=2x^4-18x^2+8x+12$, $x\in(-4,4)$. If $M$ is the local maximum value of the function $f$ in $(-4,4)$, then $M=$

Accepted Answer

(C) $12\sqrt{6}-\dfrac{31}{2}$

Answer

(A) $18\sqrt{6}-\dfrac{31}{2}$

Answer

(B) $18\sqrt{6}+\dfrac{33}{2}$

Answer

(D) $12\sqrt{6}-\dfrac{33}{2}$

Question 15

Let $f:(0,1)	o\mathbb{R}$ be a function defined by $f(x)=\dfrac{1}{1-e^{-x}}$, and $g(x)=(f(-x)-f(x))$. Consider two statements: (I) $g$ is an increasing function in $(0,1)$; (II) $g$ is one-one in $(0,1)$. Then:

Accepted Answer

(A) Both (I) and (II) are true

Answer

(B) Neither (I) nor (II) is true

Answer

(C) Only (I) is true

Answer

(D) Only (II) is true

Question 16

Let $y=(1+x)(1+x^2)(1+x^4)(1+x^8)(1+x^{16})$. Then $y'-y''$ at $x=-1$ is equal to:

Accepted Answer

(D) $496$

Answer

(A) $976$

Answer

(B) $944$

Answer

(C) $464$

Question 17

The distance of the point $P(4,6,-2)$ from the line passing through the point $(-3,2,3)$ and parallel to a line with direction ratios $3,3,-1$ is equal to:

Accepted Answer

(A) $\sqrt{14}$

Answer

(B) $3$

Answer

(C) $\sqrt{6}$

Answer

(D) $2\sqrt{3}$

Question 18

Let $x,y,z>1$ and $A=\begin{bmatrix}1 & \log_x y & \log_x z\ \log_y x & 2 & \log_y z\ \log_z x & \log_z y & 3\end{bmatrix}$. Then $|\mathrm{adj}(\mathrm{adj}\,A^2)|$ is equal to:

Accepted Answer

(A) $2^8$

Answer

(B) $4^9$

Answer

(C) $6^4$

Answer

(D) $2^4$

Question 19

If $a_r$ is the coefficient of $x^{10-r}$ in the Binomial expansion of $(1+x)^{10}$, then $\displaystyle\sum_{r=1}^{10}r^3\left(\dfrac{a_r}{a_{r-1}}\right)^2$ is equal to:

Accepted Answer

(D) $1210$

Answer

(A) $5445$

Answer

(B) $3025$

Answer

(C) $4895$

Question 20

Let $y=y(x)$ be the solution curve of the differential equation $\dfrac{dy}{dx}=\dfrac{y}{x}\big(1+xy^2(1+\log_e x)\big)$, $x>0$, $y(1)=3$. Then $\dfrac{y^2(x)}{9}$ is equal to:

Accepted Answer

(D) $\dfrac{x^2}{5-2x^3(2+\log_e x^3)}$

Answer

(A) $\dfrac{x^2}{2x^3(2+\log_e x^3)-3}$

Answer

(B) $\dfrac{x^2}{3x^3(1+\log_e x^2)-2}$

Answer

(C) $\dfrac{x^2}{7-3x^3(2+\log_e x^2)}$

Question 21

The constant term in the expansion of $\left(2x+\dfrac{1}{x^7}+3x^2\right)^5$ is _______.

Accepted Answer

1080

Question 22

For some $a,b,c\in\mathbb{N}$, let $f(x)=ax-3$ and $g(x)=x^b+c$, $x\in\mathbb{R}$. If $(f\circ g)^{-1}(x)=\left(\dfrac{x-7}{2}\right)^{1/3}$, then $(f\circ g)(ac)+(g\circ f)(b)$ is equal to _______.

Accepted Answer

2039

Question 23

Let $S=\{1,2,3,5,7,10,11\}$. The number of non-empty subsets of $S$ that have the sum of all elements a multiple of $3$, is _______.

Accepted Answer

43

Question 24

Let the equation of the plane passing through the line $x-2y-z-5=0=x+y+3z-5$ and parallel to the line $x+y+2z-7=0=2x+3y+z-2$ be $ax+by+cz=65$. Then the distance of the point $(a,b,c)$ from the plane $2x+2y-z+16=0$ is _______.

Accepted Answer

9

Question 25

If the sum of all the solutions of $	an^{-1}\left(\dfrac{2x}{1-x^2}ight)+\cot^{-1}\left(\dfrac{1-x^2}{2x}ight)=\dfrac{\pi}{3}$, $-1<x<1$, $x
e 0$, is $\alpha-\dfrac{4}{\sqrt{3}}$, then $\alpha$ is equal to _______.

Accepted Answer

2

Question 26

The vertices of a hyperbola $H$ are $(\pm 6,0)$ and its eccentricity is $\dfrac{\sqrt{5}}{2}$. Let $N$ be the normal to $H$ at a point in the first quadrant and parallel to the line $\sqrt{2}x+y=2\sqrt{2}$. If $d$ is the length of the line segment of $N$ between $H$ and the $y$-axis, then $d^2$ is equal to _______.

Accepted Answer

216

Question 27

Let $x$ and $y$ be distinct integers where $1\le x\le 25$ and $1\le y\le 25$. Then, the number of ways of choosing $x$ and $y$, such that $x+y$ is divisible by $5$, is _______.

Accepted Answer

120

Question 28

Let $S=\Big\{\alpha:\log_2(9^{2\alpha-4}+13)-\log_2\big(	frac{5}{2}\cdot 3^{2\alpha-4}+1\big)=2\Big\}$. Then the maximum value of $\beta$ for which the equation $x^2-2\left(\displaystyle\sum_{\alpha\in S}\alphaight)^2 x+\sum_{\alpha\in S}(\alpha+1)^2\,\beta=0$ has real roots, is _______.

Accepted Answer

25

Question 29

If the area enclosed by the parabolas $P_1:2y=5x^2$ and $P_2:x^2-y+6=0$ is equal to the area enclosed by $P_1$ and $y=\alpha x$, $\alpha>0$, then $\alpha^3$ is equal to _______.

Accepted Answer

600

Question 30

Let $A_1,A_2,A_3$ be three A.P. with the same common difference $d$ and having their first terms as $A,A+1,A+2$, respectively. Let $a,b,c$ be the $7^{th},9^{th},17^{th}$ terms of $A_1,A_2,A_3$, respectively, such that $\begin{vmatrix}a & 7 & 1\ 2b & 17 & 1\ c & 17 & 1\end{vmatrix}+70=0$. If $a=29$, then the sum of the first $20$ terms of an AP whose first term is $c-a-b$ and common difference is $\dfrac{d}{12}$, is equal to _______.

Accepted Answer

495

Question 31

Match List-I (physical quantity) with List-II (SI base-unit dimensional form). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 32

The ratio of the density of oxygen nucleus ($^{16}_{8}O$) and helium nucleus ($^{4}_{2}He$) is:

Accepted Answer

(C) $1:1$

Answer

(A) $4:1$

Answer

(B) $2:1$

Answer

(D) $8:1$

Question 33

The root mean square velocity of molecules of a gas is:

Accepted Answer

(D) Proportional to square root of temperature $(\sqrt{T})$

Answer

(A) Inversely proportional to square root of temperature $\left(\dfrac{1}{\sqrt{T}}\right)$

Answer

(B) Proportional to square of temperature $(T^2)$

Answer

(C) Proportional to temperature $(T)$

Question 34

Match List-I (current configurations shown in the figure) with List-II (magnitude of magnetic field at the point O). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 35

A message signal of frequency 5 kHz is used to modulate a carrier signal of frequency 2 MHz. The bandwidth for amplitude modulation is:

Accepted Answer

(C) $10$ kHz

Answer

(A) $20$ kHz

Answer

(B) $5$ kHz

Answer

(D) $2.5$ kHz

Question 36

An object of mass 8 kg hanging from one end of a uniform rod CD of mass 2 kg and length 1 m, pivoted at its end C on a vertical wall, is supported by a cable AB as shown in the figure such that the system is in equilibrium. The tension in the cable is: (Take $g=10$ m/s$^2$)

Accepted Answer

(C) $300$ N

Answer

(A) $90$ N

Answer

(B) $30$ N

Answer

(D) $240$ N

Question 37

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Photodiodes are used in forward bias usually for measuring the light intensity.
Reason R: For a p-n junction diode, at applied voltage V the current in the forward bias is more than the current in the reverse bias for $|V_z|\ge\pm V\ge|V_b|$ where $V_b$ is the threshold voltage and $V_z$ is the breakdown voltage.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

(D) A is false but R is true

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

Question 38

In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes $x$ times its initial resonant frequency $\omega_0$. The value of $x$ is:

Accepted Answer

(D) $\dfrac{1}{4}$

Answer

(A) $4$

Answer

(B) $\dfrac{1}{16}$

Answer

(C) $16$

Question 39

A uniform metallic wire carries a current 2 A, when 3.4 V battery is connected across it. The mass of the uniform metallic wire is $8.92	imes10^{-3}$ kg, density is $8.92	imes10^{3}$ kg/m$^3$ and resistivity is $1.7	imes10^{-8}\ \Omega$-m. The length of the wire is:

Accepted Answer

(A) $l=10$ m

Answer

(B) $l=100$ m

Answer

(C) $l=5$ m

Answer

(D) $l=6.8$ m

Question 40

A car travels a distance of '$x$' with speed $v_1$ and then same distance '$x$' with speed $v_2$ in the same direction. The average speed of the car is:

Accepted Answer

(A) $\dfrac{2v_1 v_2}{v_1+v_2}$

Answer

(B) $\dfrac{2x}{v_1+v_2}$

Answer

(C) $\dfrac{v_1 v_2}{2(v_1+v_2)}$

Answer

(D) $\dfrac{v_1+v_2}{2}$

Question 41

A car is moving with a constant speed of 20 m/s in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be: (Take $g=10$ m/s$^2$)

Accepted Answer

(C) $\dfrac{\pi}{4}$

Answer

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

Answer

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

Answer

(D) $\dfrac{\pi}{6}$

Question 42

A bowl filled with very hot soup cools from $98\,^{\circ}$C to $86\,^{\circ}$C in 2 minutes when the room temperature is $22\,^{\circ}$C. How long will it take to cool from $75\,^{\circ}$C to $69\,^{\circ}$C?

Accepted Answer

(B) $1.4$ minutes

Answer

(A) $1$ minute

Answer

(C) $0.5$ minute

Answer

(D) $2$ minutes

Question 43

A solenoid of 1200 turns is wound uniformly in a single layer on a glass tube 2 m long and 0.2 m in diameter. The magnetic intensity at the center of the solenoid when a current of 2 A flows through it is:

Accepted Answer

(B) $1.2	imes10^{3}\ A\,m^{-1}$

Answer

(A) $2.4	imes10^{3}\ A\,m^{-1}$

Answer

(C) $2.4	imes10^{-3}\ A\,m^{-1}$

Answer

(D) $1\ A\,m^{-1}$

Question 44

In Young's double slit experiment, the position of the $5^{th}$ bright fringe from the central maximum is 5 cm. The distance between slits and screen is 1 m and wavelength of used monochromatic light is 600 nm. The separation between the slits is:

Accepted Answer

(D) $60\,\mu m$

Answer

(A) $48\,\mu m$

Answer

(B) $36\,\mu m$

Answer

(C) $12\,\mu m$

Question 45

An electromagnetic wave is transporting energy in the negative $z$ direction. At a certain point and certain time the direction of electric field of the wave is along positive $y$ direction. What will be the direction of magnetic field of the wave at the point and instant?

Accepted Answer

(C) Positive direction of $x$

Answer

(A) Negative direction of $y$

Answer

(B) Positive direction of $z$

Answer

(D) Negative direction of $x$

Question 46

A parallel plate capacitor has plate area 40 cm$^2$ and plates separation 2 mm. The space between the plates is filled with a dielectric medium of thickness 1 mm and dielectric constant 5. The capacitance of the system is:

Accepted Answer

(B) $\dfrac{10}{3}\varepsilon_0$ F

Answer

(A) $24\varepsilon_0$ F

Answer

(C) $\dfrac{3}{10}\varepsilon_0$ F

Answer

(D) $10\varepsilon_0$ F

Question 47

Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is 100 g. The time period of the motion of the particle will be (approximately): (Take $g=10$ m s$^{-2}$, radius of earth = 6400 km)

Accepted Answer

(D) $1$ hour $24$ minutes

Answer

(A) $12$ hours

Answer

(B) $1$ hour $40$ minutes

Answer

(C) $24$ hours

Question 48

Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV, has a de-Broglie wavelength of $\lambda_0$. If the voltage is increased to 40 kV, then the de-Broglie wavelength associated with the electron beam would be:

Accepted Answer

(C) $\dfrac{\lambda_0}{\sqrt{2}}$

Answer

(A) $3\lambda_0$

Answer

(B) $\dfrac{\lambda_0}{2}$

Answer

(D) $9\lambda_0$

Question 49

A Carnot engine with efficiency 50% takes heat from a source at 600 K. In order to increase the efficiency to 70%, keeping the temperature of sink same, the new temperature of the source will be:

Accepted Answer

(C) $1000$ K

Answer

(A) $1300$ K

Answer

(B) $900$ K

Answer

(D) $360$ K

Question 50

T is the time period of a simple pendulum on the earth's surface. Its time period becomes $xT$ when taken to a height R (equal to earth's radius) above the earth's surface. Then, the value of $x$ will be:

Accepted Answer

(B) $2$

Answer

(A) $4$

Answer

(C) $\dfrac{1}{4}$

Answer

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

Question 51

A uniform electric field of 10 N/C is created between two parallel charged plates. An electron enters the field symmetrically between the plates with a kinetic energy 0.5 eV. The length of each plate is 10 cm. The angle ($	heta$) of deviation of the path of the electron as it comes out of the field is _______ (in degree).

Accepted Answer

45

Question 52

The wavelength of the radiation emitted is $\lambda_0$ when an electron jumps from the second excited state to the first excited state of a hydrogen atom. If the electron jumps from the third excited state to the second excited state of the hydrogen atom, the wavelength of the radiation emitted will be $\dfrac{20}{x}\lambda_0$. The value of $x$ is _______.

Accepted Answer

7

Question 53

In an experiment to determine the Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of $45^{\circ}$ with the load axis. The length of the wire is 62.8 cm and its diameter is 4 mm. The Young's modulus is found to be $x	imes10^{4}\ Nm^{-2}$. The value of $x$ is _______.

Accepted Answer

5

Question 54

$I_{CM}$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of the disc. $I_{AB}$ is its moment of inertia about an axis AB perpendicular to the plane and parallel to axis CM at a distance $\dfrac{2}{3}R$ from the center, where R is the radius of the disc. The ratio of $I_{AB}$ and $I_{CM}$ is $x:9$. The value of $x$ is _______.

Accepted Answer

17

Question 55

An object of mass '$m$' initially at rest on a smooth horizontal plane starts moving under the action of force $F=2$ N. In the process of its linear motion, the angle $	heta$ between the direction of force and horizontal varies as $	heta=kx$, where $k$ is constant and $x$ is the distance covered by the object from the initial position. The expression of kinetic energy of the object will be $E=\dfrac{n}{k}\sin	heta$. The value of $n$ is _______.

Accepted Answer

2

Question 56

An LCR series circuit of capacitance 62.5 nF and resistance of $50\,\Omega$, is connected to an A.C. source of frequency 2.0 kHz. For maximum value of amplitude of current in the circuit, the value of inductance is _______ mH. (Take $\pi^2=10$)

Accepted Answer

100

Question 57

The distance between two consecutive points with phase difference of $60^{\circ}$ in a wave of frequency 500 Hz is 6.0 m. The velocity with which the wave is travelling is _______ km/s.

Accepted Answer

18

Question 58

In the given circuit (shown in the figure), the equivalent resistance between the terminals A and B is _______ $\Omega$.

Accepted Answer

10

Question 59

If $\vec{P}=3\hat{i}+\sqrt{3}\hat{j}+2\hat{k}$ and $\vec{Q}=4\hat{i}+\sqrt{3}\hat{j}+2.5\hat{k}$, then the unit vector in the direction of $\vec{P}	imes\vec{Q}$ is $\dfrac{1}{x}(\sqrt{3}\hat{i}+\hat{j}-2\sqrt{3}\hat{k})$. The value of $x$ is _______.

Accepted Answer

4

Question 60

A ray of light is incident from air on a glass plate having thickness $\sqrt{3}$ cm and refractive index $\sqrt{2}$. The angle of incidence of the ray is equal to the critical angle for the glass-air interface. The lateral displacement of the ray when it passes through the plate is _______ $	imes10^{-2}$ cm. (Given $\sin 15^{\circ}=0.26$)

Accepted Answer

52

Question 61

In the cumene to phenol preparation in presence of air, the intermediate is (structures shown in the figure):

Accepted Answer

(C) (3)

Answer

(A) (1)

Answer

(B) (2)

Answer

(D) (4)

Question 62

The compound which will have the lowest rate towards nucleophilic aromatic substitution on treatment with $OH^-$ is (structures shown in the figure):

Accepted Answer

(C) (3)

Answer

(A) (1)

Answer

(B) (2)

Answer

(D) (4)

Question 63

Match List-I (Elements) with List-II (Colour imparted to the flame). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 64

Which of the following conformations (shown as Newman projections in the figure) will be the most stable?

Accepted Answer

(B) (2)

Answer

(A) (1)

Answer

(C) (3)

Answer

(D) (4)

List-I	List-II
A.Surface tension	I. $kg\,m^{-1}\,s^{-1}$
B.Pressure	II. $kg\,m\,s^{-1}$
C.Viscosity	III. $kg\,m^{-1}\,s^{-2}$
D.Impulse	IV. $kg\,s^{-2}$

List-I (Current configuration)	List-II (Magnitude of magnetic field at point O)
A.see figure	I. $B_0=\dfrac{\mu_0 I}{4\pi r}[\pi+2]$
B.see figure	II. $B_0=\dfrac{\mu_0}{4}\dfrac{I}{r}$
C.see figure	III. $B_0=\dfrac{\mu_0 I}{2\pi r}[\pi-1]$
D.see figure	IV. $B_0=\dfrac{\mu_0 I}{4\pi r}[\pi+1]$

List-I (Elements)	List-II (Colour imparted to the flame)
A.K	I.Brick Red
B.Ca	II.Violet
C.Sr	III.Apple Green
D.Ba	IV.Crimson Red

List-I (Cations)	List-II (Group reagents)
A. $Pb^{2+}, Cu^{2+}$	i. $H_2S$ gas in presence of dilute HCl
B. $Al^{3+}, Fe^{3+}$	ii. $(NH_4)_2CO_3$ in presence of $NH_4OH$
C. $Co^{2+}, Ni^{2+}$	iii. $NH_4OH$ in presence of $NH_4Cl$
D. $Ba^{2+}, Ca^{2+}$	iv. $H_2S$ in presence of $NH_4OH$

Row-I (Haworth structures)	Row-II (Names)
A.see figure	i. $\alpha$ -D-(−)-Fructofuranose
B.see figure	ii. $\beta$ -D-(−)-Fructofuranose
C.see figure	iii. $\alpha$ -D-(−)-Glucopyranose
D.see figure	iv. $\beta$ -D-(−)-Glucopyranose

JEE Main 25 January 2023 Shift 1 Question Paper with Answers

Physics — JEE Main 25 January 2023 Shift 1

Chemistry — JEE Main 25 January 2023 Shift 1

Mathematics — JEE Main 25 January 2023 Shift 1

Chapters tested in this paper

Attempt this paper under exam timing.