JEE Main 2023 · 25 Jan 2023 · Shift 2

Q1.Match List I with List II

List I:
A. Young's Modulus (Y)
B. Co-efficient of Viscosity ($\eta$)
C. Planck's Constant (h)
D. Work Function $(\varphi )$

List II:
I. $[\mathrm{M}{\mathrm{L}}^{-1}{\mathrm{T}}^{-1}]$
II. $[\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-1}]$
III. …

Q2.According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is :-

Q3.The light rays from an object have been reflected towards an observer from a standard flat mirror, the image observed by the observer are :-
A. Real
B. Erect
C. Smaller in size then object
D. Laterally inverted

Choose the most appropriate answer from the options given below :

Q4.For a moving coil galvanometer, the deflection in the coil is 0.05 rad when a current of 10 mA is passed through it. If the torsional constant of suspension wire is $4.0\times 10^{-5}\mathrm{Nm}{\mathrm{rad}}^{-1}$, the magnetic field is 0.01 T and the number of turns in the c …

Q5.The graph between two temperature scales P and Q is shown in the figure. Between upper fixed point and lower fixed point there are 150 equal divisions of scale P and 100 divisions on scale Q . The relationship for conversion between the two scales is given by :

Q6.Match List I with List II :

List I:
A. Gauss's Law in Electrostatics
B. Faraday's Law
C. Gauss's Law in Magnetism
D. Ampere-Maxwell Law

List II:
I. $\oint \vec{E}.d\vec{l}=-\frac{d{\varphi }_B}{dt}$
II. …

Q7.Statement I: When a Si sample is doped with Boron, it becomes P type and when doped by Arsenic it becomes N-type semi conductor such that P-type has excess holes and N-type has excess electrons.

Statement II : When such P-type and N-type semi-conductors, are fused to make a junc …

Q8.Consider a block kept on an inclined plane (inclined at $45^{\circ }$ ) as shown in the figure. If the force required to just push it up the incline is 2 times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined pla …

Q9.A point charge of $10\mu \mathrm{C}$ is placed at the origin. At what location on the X -axis should a point charge of $40\mu \mathrm{C}$ be placed so that the net electric field is zero at $\mathrm{x}=2\mathrm{cm}$ on the X -axis?

Q10.The energy levels of an atom is shown is figure. Which one of these transitions will result in the emission of a photon of wavelength 124.1 nm ? Given ( $\mathrm{h}=6.62\times 10^{-34}\mathrm{Js}$ )

Q11.A particle executes simple harmonic motion between $\mathrm{x}=-\mathrm{A}$ and $\mathrm{x}=+\mathrm{A}$. If time taken by particle to go from $x=0$ to $\frac{\mathrm{A}}{2}$ is 2 s ; then time taken by particle in going from $x=\frac{A}{2}$ to $A$ is :

Q12.Match List I with List II :

List I:
A. Isothermal Process
B. Adiabatic Process
C. Isochoric Process
D. Isobaric Process

List II:
I. Work done by the gas decreases internal energy
II. No change in internal energy
III. The heat absorbed goes partly to increase internal energy and …

Q13.A body of mass is taken from earth surface to the height $h$ equal to twice the radius of earth $(R_e)$, the increase in potential energy will be : ( $g=$ acceleration due to gravity on the surface of Earth)

Q14.A wire of length 1 m moving with velocity $8\mathrm{m}/\mathrm{s}$ at right angles to a magnetic field of 2 T . The magnitude of induced emf, between the ends of wire will be :

Q15.The distance travelled by a particle is related to time t as $\mathrm{x}=4{\mathrm{t}}^2$. The velocity of the particle at $\mathrm{t}=$ 5 s is .

Q16.Two objects are projected with same velocity 'u' however at different angles $\alpha$ and $\beta$ with the horizontal. If $\alpha +\beta =90^{\circ }$, the ratio of horizontal range of the first object to the $2^{\text{nd}}$ object will be :

Q17.The resistance of a wire is $5\Omega$. It's new resistance in ohm if stretched to 5 times of it's original length will be :

Q18.Given below are two statements :

Statement I : Stopping potential in photoelectric effect does not depend on the power of the light source.

Statement II : For a given metal, the maximum kinetic energy of the photoelectron depends on the wavelength of the incident light.

In the …

Q19.Every planet revolves around the sun in an elliptical orbit :

A. The force acting on a planet is inversely proportional to square of distance from sun.

B. Force acting on planet is inversely proportional to product of the masses of the planet and the sun

C. The centripetal for …

Q20.A capacitor has capacitance $5\mu \mathrm{F}$ when it's parallel plates are separated by air medium of thickness d . A slab of material of dielectric constant 1.5 having area equal to that of plates but thickness $\frac{d}{2}$ is inserted between the plates. Capacitance of the …

Q21.A train blowing a whistle of frequency 320 Hz approaches an observer standing on the platform at a speed of $66\mathrm{m}/\mathrm{s}$. The frequency observed by the observer will be (given speed of sound $=330{\mathrm{ms}}^{-1}$) $\_\_\_\_$ Hz.

Q22.An object is placed on the principal axis of convex lens of focal length 10 cm as shown. A plane mirror is placed on the other side of lens at a distance of 20 cm . The image produced by the plane mirror is 5 cm inside the mirror. The distance of the object from the lens is …

Q23.Two long parallel wires carrying currents 8 A and 15 A in opposite directions are placed at a distance of 7 cm from each other. A point P is at equidistant from both the wires such that the lines joining the point P to the wires are perpendicular to each other. The magnitude of m …

Q24.A spherical drop of liquid splits into 1000 identical spherical drops. If $u_i$ is the surface energy of the original drop and $u_f$ is the total surface energy of the resulting drops, the (ignoring evaporation). $\frac{u_f}{u_i}=\left(\frac{10}{x}\right)$. Then value of …

Q25.A body of mass 1 kg collides head on elastically with a stationary body of mass 3 kg. After collision, the smaller body reverses its direction of motion and moves with a speed of $2m/s$. The initial speed of the smaller body before collision is ____ ${\mathrm{ms}}^{-1}$.

Q26.A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3:2$. The ratio of their nuclear sizes will be ${\left(\frac{x}{3}\right)}^{\frac{1}{3}}$. The value of 'x' is:

Q27.Two cells are connected between points A and B as shown. Cell 1 has emf of 12 V and internal resistance of $3\Omega$. Cell 2 has emf of 6 V and internal resistance of $6\Omega$. An external resistor R of $4\Omega$ is connected across A and B. The current flowing through R will be …

Q28.A series LCR circuit is connected to an AC source of $220\mathrm{V}$, $50\mathrm{Hz}$. The circuit contains a resistance $R=80\Omega$, an inductor of inductive reactance $X_L=70\Omega$, and a capacitor of capacitive reactance $X_C=130\Omega$. The power factor of circuit is …

Q29.If a solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius. Then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be $\frac{x}{7}$. The value of $x$ is ____.

Q1.Match List I with List II

Choose t …

Q2.Given below are two statements :-

Statement I :- In froth floatation method a rotating paddle agitates the mixture to drive air out of it.

Statement II :- Iron pyrites are generally avoided for extraction of iron due to environmental reasons.

In the light of the above statemen …

Q3.Which of the following represents the correct order of metallic character of the given elements?

Q4.Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R

Assertion A :- The alkali metals and their salts impart characteristic colour to reducing flame.

Reason R :- Alkali metals can be detected using flame tests.

In the light of th …

Q5.What is the mass ratio of ethylene glycol (C₂H₆O₂, molar mass = 62 g/mol) required for making 500 g of 0.25 molal aqueous solution and 250 mL of 0.25 molar aqueous solution ?

Q6.Statement I :- Dipole moment is a vector quantity and by convention it is depicted by a small arrow with tail on the negative centre and head pointing towards the positive centre.

Statement II :- The crossed arrow of the dipole moment symbolizes the direction of the shift of cha …

Q7.Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R

Assertion A :- Butylated hydroxyl anisole when added to butter increases its shelf life.

Reason R :- Butylated hydroxyl anisole is more reactive towards oxygen than food.

In th …

Q8.A. Ammonium salts produce haze in atmosphere.
B. Ozone gets produced when atmospheric oxygen reacts with chlorine radicals.
C. Polychlorinated biphenyls act as cleansing solvents.
D. 'Blue baby' syndrome occurs due to the presence of excess of sulphate ions in water.

Choose the …

Q9.Match List I with List II

Choose the correct answer from the options giv …

Q10.Which one among the following metals is the weakest reducing agent ?

Q11.Match List I with List II.
| C. | Ethanamide and Hydroxyethanimine | III. | Functi …

Q12.Match List I with List II

Choose the correct answer fro …

Q13.Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R

Assertion A :- Carbon forms two important oxides -CO and ${\mathrm{CO}}_2$. CO is neutral whereas ${\mathrm{CO}}_2$ is acidic in nature.

Reason R:- ${\mathrm{CO}}_2$ can combine …

Q14.Potassium dichromate acts as a strong oxidizing agent in acidic solution. During this process, the oxidation state changes from

Q15.When the hydrogen ion concentration [${\mathrm{H}}^{+}$] changes by a factor of 1000, the value of pH of the solution
______ .

Q16.'A' in the given reaction is

Q17.The isomeric deuterated bromide with molecular formula ${\mathrm{C}}_4{\mathrm{H}}_8\mathrm{DBr}$ having two chiral carbon atoms is

Q18.A chloride salt solution acidified with dil. ${\mathrm{HNO}}_3$ gives a curdy white precipitate, [A], on addition of ${\mathrm{AgNO}}_3$. [A] on treatment with ${\mathrm{NH}}_4\mathrm{OH}$ gives a clear solution, B .

Q19.The number of given orbitals which have electron density along the axis is ____

${\mathrm{p}}_{\mathrm{x}}$, ${\mathrm{p}}_{\mathrm{y}}$, ${\mathrm{p}}_{\mathrm{z}}$, ${\mathrm{d}}_{\mathrm{xy}}$, ${\mathrm{d}}_{\mathrm{yz}}$, ${\mathrm{d}}_{\mathrm{xz}}$, ${\mathrm{d}}_{{\mathrm{z}}^2}$, …

Q20.Number of compounds giving (i) red colouration with ceric ammonium nitrate and also (ii) positive iodoform test from the following is ____

Q21.The number of pairs of the solution having the same value of the osmotic pressure from the following is ____.
(Assume 100% ionization)

A. $0.500\mathrm{M}$ ${\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH}(\mathrm{aq})$ and $0.25\mathrm{M}$ $\mathrm{KBr}(\mathrm{aq})$
B. …

Q22.28.0 L of ${\mathrm{CO}}_2$ is produced on complete combustion of 16.8 L gaseous mixture of ethene and methane at $25^{\circ }\mathrm{C}$ and 1 atm. Heat evolved during the combustion process is ____ kJ.

Given: …

Q23.Total number of moles of AgCl precipitated on addition of excess of ${\mathrm{AgNO}}_3$ to one mole each of the following complexes $\left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_4{\mathrm{Cl}}_2\right]\mathrm{Cl}$, …

Q24.Number of hydrogen atoms per molecule of a hydrocarbon A having 85.8% carbon is ____
(Given : Molar mass of A $=84\mathrm{g}{\mathrm{mol}}^{-1}$ )

Q25.$\mathrm{Pt}(\mathrm{s}){\mathrm{H}}_2(\mathrm{g})(1\mathrm{bar})\left|{\mathrm{H}}^{+}(\mathrm{aq})(1\mathrm{M})\right|\left|{\mathrm{M}}^{3+}(\mathrm{aq}),{\mathrm{M}}^{+}(\mathrm{aq})\right|\mathrm{Pt}(\mathrm{s})$

The ${\mathrm{E}}_{\text{cell }}$ for the given cell …

Q26.Based on the given figure, the number of correct statement/s is/are ____

A. Surface tension is the outcome of equal attractive and repulsion forces acting on the liquid molecule in bulk.
B. Surface tension is due to uneven forces acting on the molecules present on the surfac …

Q27.A first order reaction has the rate constant, $\mathrm{k}=4.6$
$\times 10^{-3}{\mathrm{s}}^{-1}$. The number of correct statement/s from the following is/are ____.

Given : $\log 3=0.48$
A. Reaction completes in 1000 s.
B. The reaction has a half-life of 500 s.
C. The t …

Q28.The number of incorrect statement/s from the following is/are ____
A. Water vapours are adsorbed by anhydrous calcium chloride.
B. There is a decrease in surface energy during adsorption.
C. As the adsorption proceeds, $\Delta \mathrm{H}$ becomes more and more negative.
D. …

Q1.Let the function $f(x)=2x^3+(2p-7)x^2+3(2p-9)x-6$ have a maxima for some value of $\mathrm{x}<0$ and a minima for some value of $\mathrm{x}>0$. Then, the set of all values of $p$ is

Q2.Let $z$ be a complex number such that $\left|\frac{\mathrm{z}-2\mathrm{i}}{\mathrm{z}+\mathrm{i}}\right|=2,\mathrm{z}\ne -\mathrm{i}$. Then z lies on the circle of radius 2 and centre

Q3.If the function
$f(x)=\{\begin{array}{cl}(1+|\cos x|)\frac{\lambda }{|\cos x|},& 0<x<\frac{\pi }{2}\\ \mu ,& x=\frac{\pi }{2}\text{ is continuous at }\\ e^{\frac{\cot 6x}{\cot 4x}}& ,\frac{\pi }{2}<x<\pi \end{array}$
$\mathrm{x}=\frac{\pi }{2}$, th …

Q4.Let $\mathrm{f}(\mathrm{x})=2{\mathrm{x}}^{\mathrm{n}}+\lambda ,\lambda \in \mathbb{R},\mathrm{n}\in \mathbb{N}$, and $\mathrm{f}(4)=133$, $f(5)=255$. Then the sum of all the positive integer divisors of ( $\mathrm{f}(3)-\mathrm{f}(2)$ ) is

Q5.If the four points, whose position vectors are $3\hat{i}-4\hat{j}+2\hat{k},\hat{i}+2\hat{j}-\hat{k},-2\hat{i}-\hat{j}+3\hat{k}$ and $5\hat{i}-2\alpha \hat{j}+4\hat{k}$ are coplanar, then $\alpha$ is equal to

Q6.Let $\mathrm{A}=\left[\begin{array}{cc}\frac{1}{\sqrt{10}}& \frac{3}{\sqrt{10}}\\ \frac{-3}{\sqrt{10}}& \frac{1}{\sqrt{10}}\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{cc}1& -\mathrm{i}\\ 0& 1\end{array}\right]$, where $\mathrm{i}=\sqrt{-1}$. If …

Q7.Let $\Delta ,\nabla \in \{\wedge ,\vee \}$ be such that $(\mathrm{p}\to \mathrm{q})\Delta (\mathrm{p}\nabla \mathrm{q})$ is a tautology. Then

Q8.The number of numbers, strictly between 5000 and 10000 can be formed using the digits $1,3,5,7,9$ without repetition, is

Q9.The number of functions $f:\{1,2,3,4\}\to \{a\in \mathbb{Z}:|a|\le 8\}$ satisfying $f(n)+\frac{1}{n}f(n+1)=1,\forall n\in \{1,2,3\}$ is

Q10.The equations of two sides of a variable triangle are $\mathrm{x}=0$ and $\mathrm{y}=3$, and its third side is a tangent to the parabola ${\mathrm{y}}^2=6\mathrm{x}$. The locus of its circumcentre is :

Q11.Let $\mathrm{f}:\mathbb{R}\to \mathbb{R}$ be a function defined by $\mathrm{f}(\mathrm{x})={\log }_{\sqrt{m}}\{\sqrt{2}(\sin x-\cos x)+m-2\}$, for some $m$, such that the range of f is $[0,2]$. Then the value of m is

Q12.Let $\mathrm{A},\mathrm{B},\mathrm{C}$ be $3\times 3$ matrices such that A is symmetric and B and C are skew-symmetric.

Consider the statements
(S1) ${\mathrm{A}}^{13}{\mathrm{B}}^{26}-{\mathrm{B}}^{26}{\mathrm{A}}^{13}$ is symmetric
(S2) …

Q13.Let $y=y(t)$ be a solution of the differential equation
$\frac{dy}{dt}+\alpha y=\gamma e^{-\beta t}$
Where, $\alpha >0,\beta >0$ and $\gamma >0$. Then ${\mathrm{Lim}}_{\mathrm{t}\to \infty }\mathrm{y}(\mathrm{t})$

Q14.${\sum }_{\mathrm{k}=0}^6{}^{51-\mathrm{k}}{\mathrm{C}}_3$ is equal to

Q15.The shortest distance between the lines $x+1=2y=-12z$ and $x=y+2=6z-6$ is

Q16.Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that $\mathrm{N}-2,\sqrt{3\mathrm{N}},\mathrm{N}+2$ are in geometric progression be $\frac{\mathrm{k}}{48}$. Then the value of k is

Q17.The integral $16{\int }_1^2\frac{\mathrm{dx}}{{\mathrm{x}}^3{\left({\mathrm{x}}^2+2\right)}^2}$ is equal to

Q18.Let T and C respectively be the transverse and conjugate axes of the hyperbola $16x^2-y^2+64x+4y+44=0$. Then the area of the region above the parabola $x^2=y+4$, below the transverse axis T and on the right of the conjugate axis C is:

Q19.Let $\vec{a}=-\hat{i}-\hat{j}+\hat{k},\vec{a}\cdot \vec{b}=1$ and $\vec{a}\times \vec{b}=\hat{i}-\hat{j}$. Then $\overrightarrow{\mathrm{a}}-6\overrightarrow{\mathrm{b}}$ is equal to

Q20.The foot of perpendicular of the point $(2,0,5)$ on the line $\frac{x+1}{2}=\frac{y-1}{5}=\frac{z+1}{-1}$ is $(\alpha ,\beta ,\gamma )$. Then.
Which of the following is NOT correct?

Q21.For the two positive numbers $\mathrm{a},\mathrm{b}$, if $\mathrm{a},\mathrm{b}$ and $\frac{1}{18}$ are in a geometric progression, while $\frac{1}{\mathrm{a}},10$ and $\frac{1}{\mathrm{b}}$ are in an arithmetic progression, then, $16\mathrm{a}+12\mathrm{b}$ is …

Q22.Points $P(-3,2),Q(9,10)$ and $R(\alpha ,4)$ lie on a circle $C$ with PR as its diameter. The tangents to C at the points Q and R intersect at the point S . If S lies on the line $2\mathrm{x}-\mathrm{ky}=1$, then k is equal to ____ .

Q23.Let $\mathrm{a}\in \mathrm{R}$ and let $\alpha ,\beta$ be the roots of the equation ${\mathrm{x}}^2+60^{\frac{1}{4}}\mathrm{x}+\mathrm{a}=0$. If ${\alpha }^4+{\beta }^4=-30$, then the product of all possible values of a is ______.

Q24.Suppose Anil's mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white apples and 8 oranges. If in the selected 5 fruits, at least 2 orange, at least one red apple and at least one white apple must be given, then the number of ways, Anil's mother can of …

Q25.If m and n respectively are the numbers of positive and negative value of $\theta$ in the interval $[-\pi ,\pi ]$ that satisfy the equation $\cos 2\theta \cos \frac{\theta }{2}=\cos 3\theta \cos \frac{9\theta }{2}$, then mn is equal to ______.

Q26.If ${\int }_{\frac{1}{3}}^3|{\log }_{e}x|dx=\frac{m}{n}{\log }_e\left(\frac{n^2}{e}\right)$, where $m$ and $n$ are coprime natural numbers, then ${\mathrm{m}}^2+{\mathrm{n}}^2-5$ is equal to ______.

Q27.The remainder when $(2023{)}^{2023}$ is divided by 35 is ______.

Q28.If the shortest distance between the line joining the points $(1,2,3)$ and $(2,3,4)$, and the line $\frac{\mathrm{x}-1}{2}=\frac{\mathrm{y}+1}{-1}=\frac{\mathrm{z}-2}{0}$ is $\alpha$, then $28{\alpha }^2$ is equal to ______.

Q29.25% of the population are smokers. A smoker has 27 times more chances to develop lung cancer then a non-smoker. A person is diagnosed with lung cancer and the probability that this person is a smoker is $\frac{k}{10}$. Then the value of k is ______.