JEE Main 2023 · 24 Jan 2023 · Shift 2

Q1.The electric potential at the centre of two concentric half rings of radii $R_1$ and $R_2$, having same linear charge density $\lambda$ is

Q2.Let ${\gamma }_1$ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and ${\gamma }_2$ be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio, …

Q3.An $\alpha$-particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their De-Broglie wavelength:

Q4.If the distance of the earth from Sun is $1.5\times 10^6$ km. Then the distance of an imaginary planet from Sun, if its period of revolution is 2.83 years is:

Q5.The logic gate equivalent to the given circuit diagram is :

Q6.A long solenoid is formed by winding 70 turns cm${}^{-1}$. If 2.0 A current flows, then the magnetic field produced inside the solenoid is ______ (${\mu }_0=4\pi \times 10^{-7}$ TmA${}^{-1}$)

Q7.Given below are two statements:

Statement I: Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface.

Statement II: Acceleration due to earth's gravity is same at a height 'h' and depth 'd' from earth's surface, if h=d.

In the light of above …

Q8.A metallic rod of length 'L' is rotated with an angular speed of '$\omega$' normal to a uniform magnetic field 'B' about an axis passing through one end of rod as shown in figure. The induced emf will be :

Q9.When a beam of white light is allowed to pass through convex lens parallel to principal axis, the different colours of light converge at different point on the principle axis after refraction. This is called :

Q10.The frequency ($v$) of an oscillating liquid drop may depend upon radius (r) of the drop, density ($\rho$) of liquid and the surface tension (s) of the liquid as : $v=r^a{\rho }^b{s}^c$. The values of $a,b$ and $c$ respectively are

Q11.A body of mass 200 g is tied to a spring of spring constant $12.5$ N/m, while the other end of spring is fixed at point O. If the body moves about O in a circular path on a smooth horizontal surface with constant angular speed $5$ rad/s, then the ratio of extension in the spring …

Q12.A cell of emf 90 V is connected across series combination of two resistors each of $100\Omega$ resistance. A voltmeter of resistance $400\Omega$ is used to measure the potential difference across each resistor. The reading of the voltmeter will be :

Q13.The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by
${\mathrm{E}}_{\mathrm{x}}={\mathrm{E}}_0\sin (\mathrm{kz}-\omega \mathrm{t})$
${\mathrm{B}}_{\mathrm{y}}={\mathrm{B}}_0\sin (\mathrm{kz}-\omega \mathrm{t})$
Then th …

Q14.The velocity time graph of a body moving in a straight line is shown in figure.

The ratio of displacement to distance travelled by the body in time 0 to 10 s is

Q15.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: Steel is used in the construction of buildings and bridges.

Reason R: Steel is more elastic and its elastic limit is high.

In the light of above statements, choose …

Q16.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: A pendulum clock when taken to Mount Everest becomes fast.

Reason R: The value of $\mathbf{g}$ (acceleration due to gravity) is less at Mount Everest than its va …

Q17.A photon is emitted in transition from $n=4$ to $n=1$ level in hydrogen atom. The corresponding wavelength for this transition is (given, $\mathrm{h}=4\times 10^{-15}\mathrm{eVs}$) :

Q18.In an Isothermal change, the change in pressure and volume of a gas can be represented for three different temperature; ${\mathrm{T}}_3>{\mathrm{T}}_2>{\mathrm{T}}_1$ as :

Q19.If two vectors $P=\hat{i}+2m\hat{j}+m\hat{k}$ and $\overrightarrow{\mathrm{Q}}=4\hat{\mathrm{i}}-2\hat{\mathrm{j}}+\mathrm{m}\hat{\mathrm{k}}$ are perpendicular to each other. Then, the value of m will be :

Q20.A uniform solid cylinder with radius R and length L has moment of inertia ${\mathrm{I}}_1$, about the axis of cylinder. A concentric solid cylinder of radius ${\mathrm{R}}^{\prime }=\frac{\mathrm{R}}{2}$ and length ${\mathrm{L}}^{\prime }=\frac{\mathrm{L}}{2}$ is carved out of th …

Q21.A mass $m$ attached to free end of a spring executes SHM with a period of 1s. If the mass is increased by 3 kg the period of oscillation increases by one second, the value of mass $m$ is ____ kg.

Q22.The energy released per fission of nucleus of ${}^{240}\mathrm{X}$ is 200 MeV. The energy released if all the atoms in 120 g of pure ${}^{240}\mathrm{X}$ undergo fission is ____ $\times 10^{25}$ MeV.
(Given ${\mathrm{N}}_{\mathrm{A}}=6\times 10^{23}$)

Q23.A parallel plate capacitor with air between the plate has a capacitance of 15 pF. The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant 3.5. Then the capacitance becomes $\frac{\mathrm{X}}{4}$ pF. The value of …

Q24.A body of mass 1 kg begins to move under the action of a time dependent force $\vec{F}=\left(t\hat{i}+3t^2\hat{j}\right)$ N, where $\hat{i}$ and $\hat{j}$ are the unit vectors along $x$ and $y$ axis. The power developed by above force, at the time $t=2$ s, will be ______ W.

Q25.If a copper wire is stretched to increase its length by $20\%$. The percentage increase in resistance of the wire is ______ %.

Q26.A single turn current loop in the shape of a right angle triangle with sides $5$ cm, $12$ cm, $13$ cm is carrying a current of 2 A. The loop is in a uniform magnetic field of magnitude 0.75 T whose direction is parallel to the current in the 13 cm side of the loop. The magnitude …

Q27.Three identical resistors with resistance $R=12\Omega$ and two identical inductors with self inductance $L=5$ mH are connected to an ideal battery with emf of 12 V as shown in figure. The current through the battery long after the switch has been closed will be ______ A.

Q28.A convex lens of refractive index 1.5 and focal length 18 cm in air is immersed in water. The change in focal length of the lens will be ______ cm.
(Given refractive index of water $=\frac{4}{3}$)

Q29.A Spherical ball of radius 1 mm and density $10.5$ g/cc is dropped in glycerine of coefficient of viscosity 9.8 poise and density $1.5$ g/cc. Viscous force on the ball when it attains constant velocity is $3696\times 10^{-x}$ N. The value of $x$ is
(Given, $g=9.8$ m/s${}^2$ and …

Q1.Which one amongst the following are good oxidizing agents?
A. ${\mathrm{Sm}}^{2+}$
B. ${\mathrm{Ce}}^{2+}$
C. ${\mathrm{Ce}}^{4+}$
D. ${\mathrm{Tb}}^{4+}$

Choose the most appropriate answer from the options given below :

Q2.What is the number of unpaired electron(s) in the highest occupied molecular orbital of the following species : ${\mathrm{N}}_2:{\mathrm{N}}_2{}^{+};{\mathrm{O}}_2;{\mathrm{O}}_2{}^{+}$?

Q3.Which of the following cannot be explained by crystal field theory?

Q4.A student has studied the decomposition of a gas ${\mathrm{AB}}_3$ at $25^{\circ }\mathrm{C}$. He obtained the following data.

The order of the reaction is

Q5.The number of s-electrons present in an ion with 55 protons in its unipositive state is

Q6.In which of the following reactions the hydrogen peroxide acts as a reducing agent?

Q7.The metal which is extracted by oxidation and subsequent reduction from its ore is :

Q8.Given below are two statements :

Statement I :

under Clemmensen reduction conditions will give HOOC .

Statement II :

under Wolff-Kishner reduction condition will give

In the light of the above statements, choose the correct answer from the options given below :

Q9.Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Beryllium has less negative value of reduction potential compared to the other alkaline earth metals.
Reason R : Beryllium has large hydration energy due to small s …

Q10.Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Benzene is more stable than hypothetical cyclohexatriene.
Reason R : The delocalized $\pi$ electron cloud is attracted more strongly by nuclei of carbon atoms. In th …

Q11.Choose the correct representation of conductometric titration of benzoic acid vs sodium hydroxide.

Q12.Find out the major products from the following reactions.

Q13.Correct statement is :

Q14.Given below are two statements :
Statement I: Pure Aniline and other arylamines are usually colourless.
Statement II : Arylamines get coloured on storage due to atmospheric reduction.
In the light of the above statements, choose the most appropriate answer from the options given …

Q15.Which will undergo deprotonation most readily in basic medium?

Q16.Choose the correct colour of the product for the following reaction.

Q17.Identify the correct statements about alkali metals.
A. The order of standard reduction potential $\left({\mathrm{M}}^{+}\mid \mathrm{M}\right)$ for alkali metal ions is $\mathrm{Na}>\mathrm{Rb}>\mathrm{Li}$.
B. CsI is highly soluble in water.
C. Lithium carbonate is highly st …

Q18.The hybridization and magnetic behaviour of cobalt ion in ${\left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_6\right]}^{3+}$ complex, respectively is

Q19.${\mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7$ paper acidified with dilute ${\mathrm{H}}_2{\mathrm{SO}}_4$ turns green when exposed to

Q20.The number of statement/s which are the characteristics of physisorption is ______.
A. It is highly specific in nature
B. Enthalpy of adsorption is high
C. It decreases with increase in temperature
D. It results into unimolecular layer
E. No activation energy is needed

Q21.Sum of $\pi$-bonds present in peroxodisulphuric acid and pyrosulphuric acid is

Q22.Maximum number of isomeric monochloro derivatives which can be obtained from 2,2,5,5tetramethylhexane by chlorination is ______

Q23.Total number of tripeptides possible by mixing of valine and proline is ______

Q24.The number of units, which are used to express concentration of solutions from the following is ____.
Mass percent, Mole, Mole fraction, Molarity, ppm, Molality.

Q25.The number of statement's, which are correct with respect to the compression of carbon dioxide from point (a) in the Andrews isotherm from the following is ____.

A. Carbon dioxide remains as a gas upto point (b)
B. Liquid carbon dioxide appears at point (c)
C. Liquid and gaseous …

Q26.The Total pressure observed by mixing two liquid A and B is 350 mm Hg when their mole fractions are 0.7 and 0.3 respectively.
The Total pressure becomes 410 mm Hg if the mole fractions are changed to 0.2 and 0.8 respectively for A and B. The vapour pressure of pure A is ____ mm H …

Q27.One mole of an ideal monoatomic gas is subjected to changes as shown in the graph. The magnitude of the work done (by the system or on the system) is ____ J (nearest integer).

Given: $\log 2=0.3,\ln 10=2.3$

Q28.If the pKa of lactic acid is 5, then the pH of 0.005 M calcium lactate solution at $25^{\circ }\mathrm{C}$ is ____ $\times 10^{-1}$ (Nearest integer)

Lactic acid

Q29.Following figure shows spectrum of an ideal black body at four different temperatures. The number of correct statement/s from the following is ____.

A. ${\mathrm{T}}_4>{\mathrm{T}}_3>{\mathrm{T}}_2>{\mathrm{T}}_1$
B. The black body consists of particles performing simple harmoni …

Q1.The distance of the point $(7,-3,-4)$ from the plane passing through the points $(2,-3,1),(-1,1,-2)$ and $(3,-4,2)$ is :

Q2.${\lim }_{t\to 0}{\left(1^{\frac{1}{{\sin }^{2}t}}+2^{\frac{1}{{\sin }^{2}t}}+\dots .+n^{\frac{1}{{\sin }^{2}t}}\right)}^{{\sin }^{2}t}$ is equal to

Q3.Let $\overrightarrow{\mathrm{u}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}-2\mathrm{k},\overrightarrow{\mathrm{v}}=2\hat{\mathrm{i}}+\hat{\mathrm{j}}-\mathrm{k},\overrightarrow{\mathrm{v}}\cdot \overrightarrow{\mathrm{w}}=2$ and …

Q4.The value ${\sum }_{\mathrm{r}=0}^{22}{}^{22}{\mathrm{C}}_{\mathrm{r}}{}^{23}{\mathrm{C}}_{\mathrm{r}}$ is

Q5.Let a tangent to the curve ${\mathrm{y}}^2=24\mathrm{x}$ meet the curve $\mathrm{xy}=2$ at the points A and B . Then the mid points of such line segments AB lie on a parabola with the

Q6.Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations
$\mathrm{x}+\mathrm{y}+\mathrm{z}=1$
$2\mathrm{x}+\mathrm{Ny}+2\mathrm{z}=2$
$3\mathrm{x}+3\mathrm{y}+\mathrm{Nz}=3$
has unique solution is $\frac{k}{6}$, …

Q7.${\tan }^{-1}\left(\frac{1+\sqrt{3}}{3+\sqrt{3}}\right)+{\sec }^{-1}\left(\sqrt{\frac{8+4\sqrt{3}}{6+3\sqrt{3}}}\right)$ is equal to

Q8.Let PQR be a triangle. The points $\mathrm{A},\mathrm{B}$ and C are on the sides $\mathrm{QR},\mathrm{RP}$ and PQ respectively such that $\frac{\mathrm{QA}}{\mathrm{AR}}=\frac{\mathrm{RB}}{\mathrm{BP}}=\frac{\mathrm{PC}}{\mathrm{CQ}}=\frac{1}{2}$. Then …

Q9.If A and B are two non-zero $\mathrm{n}\times \mathrm{n}$ matrics such that ${\mathrm{A}}^2+\mathrm{B}={\mathrm{A}}^2\mathrm{B}$, then

Q10.Let $\mathrm{y}=\mathrm{y}(\mathrm{x})$ be the solution of the differential equation $x^{3}dy+(xy-1)dx=0,x>0$, $y\left(\frac{1}{2}\right)=3-e$. Then $y(1)$ is equal to

Q11.Let $\alpha$ be a root of the equation
$(\mathrm{a}-\mathrm{c}){\mathrm{x}}^2+(\mathrm{b}-\mathrm{a})\mathrm{x}+(\mathrm{c}-\mathrm{b})=0$ where $\mathrm{a},\mathrm{b},\mathrm{c}$ are distinct real numbers such that the matrix …

Q12.The distance of the point $(-1,9,-16)$ from the plane $2x+3y-z=5$ measured parallel to the line $\frac{x+4}{3}=\frac{2-y}{4}=\frac{z-3}{12}$ is

Q13.For three positive integers $p,q,r,x^{p{q}^2}=y^{qr}=z^{p^{2}r}$ and $\mathrm{r}=\mathrm{pq}+1$ such that $3,3{\log }_{\mathrm{y}}\mathrm{x},3{\log }_{\mathrm{z}}\mathrm{y},7{\log }_{\mathrm{x}}\mathrm{z}$ are in A.P. with common difference $\frac{1}{2}$. Then …

Q14.Let $\mathrm{p},\mathrm{q}\in \mathbb{R}$ and $(1-\sqrt{3}\mathrm{i}{)}^{200}=2^{199}(\mathrm{p}+\mathrm{iq})$, $\mathrm{i}=\sqrt{-1}$. Then $\mathrm{p}+\mathrm{q}+{\mathrm{q}}^2$ and $\mathrm{p}-\mathrm{q}+{\mathrm{q}}^2$ are roots of the equation.

Q15.The relation $\mathrm{R}=\{(\mathrm{a},\mathrm{b}):\gcd (\mathrm{a},\mathrm{b})=1,2\mathrm{a}\ne \mathrm{b},\mathrm{a},\mathrm{b}\in \mathbb{Z}\}$ is:

Q16.The compound statement
$(\sim (\mathrm{P}\wedge \mathrm{Q}))\vee ((\sim \mathrm{P})\wedge \mathrm{Q})\Rightarrow ((\sim \mathrm{P})\wedge (\sim \mathrm{Q}))$ is equivalent to

Q17.Let $\mathrm{f}(\mathrm{x})=\{\begin{array}{cc}{\mathrm{x}}^2\sin \left(\frac{1}{\mathrm{x}}\right)& ,x\ne 0\\ 0& ,x=0\end{array}$; Then at $\mathrm{x}=0$

Q18.The equation $x^2-4x+[x]+3=x[x]$, where $[x]$ denotes the greatest integer function, has:

Q19.Let $\Omega$ be the sample space and $\mathrm{A}\subseteq \Omega$ be an event. Given below are two statements:
(S1): If $\mathrm{P}(\mathrm{A})=0$, then $\mathrm{A}=\varphi$
(S2): If $\mathrm{P}(\mathrm{A})=1$, then $\mathrm{A}=\Omega$
Then

Q20.Suppose ${\sum }_{\mathrm{r}=0}^{2023}{\mathrm{r}}^2{}^{2023}{\mathrm{C}}_{\mathrm{r}}=2023\times \alpha \times 2^{2022}$. Then the value of $\alpha$ is

Q21.The value of $12{\int }_0^3\left|{\mathrm{x}}^2-3\mathrm{x}+2\right|\mathrm{dx}$ is

Q22.The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that the even digits occupy only even places, is

Q23.Let $\lambda \in \mathbb{R}$ and let the equation E be $|\mathrm{x}{|}^2-2|\mathrm{x}|+|\lambda -3|=0$. Then the largest element in the set $\mathrm{S}=\{\mathrm{x}+\lambda :\mathrm{x}$ is an integer solution of E$\}$ is

Q24.A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses. If he can choose at most two language courses, then the number of ways he can choose five courses is

Q25.Let a tangent to the Curve $9x^2+16y^2=144$ intersect the coordinate axes at the points A and B. Then, the minimum length of the line segment AB is

Q26.The value of $\frac{8}{\pi }{\int }_0^{\frac{\pi }{2}}\frac{(\cos x{)}^{2023}}{(\sin x{)}^{2023}+(\cos x{)}^{2023}}dx$ is

Q27.The shortest distance between the lines $\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-6}{2}$ and $\frac{x-6}{3}=\frac{1-y}{2}=\frac{z+8}{0}$ is equal to

Q28.The $4^{\text{th}}$ term of GP is 500 and its common ratio is $\frac{1}{m},m\in N$. Let $S_n$ denote the sum of the first $n$ terms of this GP. If ${\mathrm{S}}_6>{\mathrm{S}}_5+1$ and ${\mathrm{S}}_7<{\mathrm{S}}_6+\frac{1}{2}$, then the number of possible values …