JEE Main 2023 January 24, Shift 2 Question Paper with Solutions

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 :

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 to its natural length will be:

The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by
$E_x=E_o\sin (kz-\omega t)$
$B_y=B_o\sin (kz-\omega t)$
Then the correct relation between $E_o$ and $B_o$ is given by

In an isothermal change, the change in pressure and volume of a gas can be represented for three different temperature; $T_3>T_2>T_1$ as :

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 statements, choose the most appropriate answer from the options given below.

Choose the correct answer from the options given below:

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

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 :

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, $\frac{{\gamma }_1}{{\gamma }_2}$ is :

A long solenoid is formed by winding 70 turns c$m^{-1}$. If 2.0 A current flows, then the magnetic field produced inside the solenoid is $\left({\mu }_0=4\pi \times 10^{-7}{\text{T m A}}^{-1}\right)$

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 the most appropriate answer from the options given below.

If the distance of the earth from Sun is $1.5\times 10^8$ km. Then the distance of an imaginary planet from Sun, if its period of revolution is 2.83 years is:

The frequency $(\nu )$ 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 : $\nu =r^a{\rho }^b{s}^c$. The values of a, b and c respectively are

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 :

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

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?

The logic gate equivalent to the given circuit diagram is :

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 $g$ (acceleration due to gravity) is less at Mount Everest than its value on the surface of the earth.
In the light of the above statements, choose the most appropriate answer from the options given below.

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

A spherical ball of radius $1\text{mm}$ and density $10.5\text{g/cc}$ is dropped in glycerine of coefficient of viscosity $9.8\text{poise}$ and density $1.5\text{g/cc}$. Viscous force on the ball when it attains constant velocity is $3696\times 10^{-x}\text{N}$. The value of x is (Given, $g=9.8{\text{m/s}}^2$ and $\pi =\frac{22}{7}$)

A parallel plate capacitor with air between the plate has a capacitance of $15\text{pF}$. 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 $\frac{x}{4}\text{pF}$. The value of x is _______.

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

A single turn current loop in the shape of a right angle triangle with sides $5\text{cm}$, $12\text{cm}$, $13\text{cm}$ is carrying a current of $2\text{A}$. The loop is in a uniform magnetic field of magnitude $0.75\text{T}$ whose direction is parallel to the current in the $13\text{cm}$ side of the loop. The magnitude of the magnetic force on the $5\text{cm}$ side will be $\frac{x}{130}\text{N}$. The value of x is _______.

A uniform solid cylinder with radius R and length L has moment of inertia $I_1$, about the axis of the cylinder. A concentric solid cylinder of radius $R^{\prime }=\frac{R}{2}$ and length $L^{\prime }=\frac{L}{2}$ is carved out of the original cylinder. If $I_2$ is the moment of inertia of the carved out portion of the cylinder then $\frac{I_1}{I_2}=$ _______. (Both $I_1$ and $I_2$ are about the axis of the cylinder)

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

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

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

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

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

In which of the following reactions the hydrogen peroxide acts as a reducing agent?
$\text{(A) HOCl}+{\text{H}}_2{\text{O}}_2\to {\text{H}}_3{\text{O}}^{+}+{\text{Cl}}^{-}+{\text{O}}_2$
$\text{(B) PbS}+4{\text{H}}_2{\text{O}}_2\to {\text{PbSO}}_4+4{\text{H}}_2\text{O}$
${\text{(C) 2Fe}}^{2+}+{\text{H}}_2{\text{O}}_2\to 2{\text{Fe}}^{3+}+2{\text{OH}}^{-}$
${\text{(D) Mn}}^{2+}+{\text{H}}_2{\text{O}}_2\to {\text{Mn}}^{4+}+2{\text{OH}}^{-}$

Choose the correct colour of the product for the following reaction.
[Reaction of a diazonium salt with 1-Naphthyl amine bearing an -SO3H group to give a coupled azo dye]

Which one amongst the following are good oxidizing agents?
${\text{A. Sm}}^{2+}$
${\text{B. Ce}}^{2+}$
${\text{C. Ce}}^{4+}$
${\text{D. Tb}}^{4+}$
Choose the most appropriate answer from the options given below.

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 below:

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

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

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 size of B$e^{2+}$ but relatively large value of atomization enthalpy.
In the light of the above statements, choose the correct answer from the options given below.

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

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

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

Which will undergo deprotonation most readily in basic medium?
[Three 1,3-dicarbonyl type compounds are shown: a, b (an ester MeO...OMe diketone/diester), and c (a beta-keto ester with -OMe)]

Identify the correct statements about alkali metals.
A. The order of standard reduction potential (M${}^{+}$) for alkali metal ions is Na > Rb > Li.
B. CsI is highly soluble in water.
C. Lithium carbonate is highly stable to heat.
D. Potassium dissolved in concentrated liquid ammonia is blue in colour and paramagnetic.
E. All the alkali metal hydrides are ionic solids.
Choose the correct answer from the options given below.

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

Correct statement is:

Choose the correct answer from the options given below:

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

Given below are two statements:

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

A student has studied the decomposition of a gas ${\text{AB}}_3$ at $25{}^{\circ }\text{C}$. He obtained the following data.
p (mm Hg) | 50 | 100 | 200 | 400
relative $t_{1/2}$ (s) | 4 | 2 | 1 | 0.5
The order of the reaction is

Maximum number of isomeric monochloro derivatives which can be obtained from 2,2,5,5-tetramethylhexane by chlorination is________.

Total number of tripeptides possible by mixing of valine and proline is________.

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

The total pressure observed by mixing two liquids 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 Hg. (Nearest integer). Consider the liquids and solutions behave ideally.

If the pKa of lactic acid is 5, then the pH of 0.005 M calcium lactate solution at $25^{\circ }$ C is ________ $\times 10^{-1}$ (Nearest integer)
Lactic acid [drawn structure: ${\text{CH}}_3\text{-CH(OH)-COOH}$]

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 increases in temperature
D. It results into unimolecular layer
E. No activation energy is needed

Following figure shows spectrum of an ideal black body at four different temperatures. The number of correct statement/s from the following is ________
A. $T_4>T_3>T_2>T_1$
B. The black body consists of particles performing simple harmonic motion.
C. The peak of the spectrum shifts to shorter wavelength as temperature increases.
D. $\frac{T_1}{{\nu }_1}=\frac{T_2}{{\nu }_2}=\frac{T_3}{{\nu }_3}=$ constant
E. The given spectrum could be explained using quantisation of energy.

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 carbon dioxide coexist between points (b) and (c)
D. As the volume decreases from (b) to (c), the amount of liquid decreases

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

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

The set of all values of a for which $\underset{x\to a}{\lim }\left([x-5]-[2x+2]\right)=0$, where $[\alpha ]$ denotes the greatest integer less than or equal to $\alpha$ is equal to

Let p and q be two statements. Then $\sim (p\wedge (p\Rightarrow \sim q))$ is equivalent to

The locus of the mid points of the chords of the circle $C_1:(x-4{)}^2+(y-5{)}^2=4$ which subtend an angle ${\theta }_i$ at the centre of the circle $C_1$, is a circle of radius $r_i$. If ${\theta }_1=\frac{\pi }{3}$, ${\theta }_3=\frac{2\pi }{3}$ and $r_1^2=r_2^2+r_3^2$, then ${\theta }_2$ is equal to