JEE Main 2023 (25 Jan Shift 2) As Per Reduced Syllabus

Question Paper

Physics Single Correct (Maximum Marks: 80)

Question No. 1

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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

$3mg{R}_e$
$\frac{1}{3}mg{R}_e$
$\frac{2}{3}mg{R}_e$
$\frac{1}{2}mg{R}_e$

Question No. 2

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

The resistance of a wire is $5 \mathrm{\Omega }$. Its new resistance in ohm, if stretched to $5$ times of its original length will be :

$625$
$125$
$5$
$25$

Question No. 3

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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 force acting on the planet is directed away from the sun.

D. The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit.

Choose the correct answer from the options given below :

A and D only
C and D only
B and C only
A and C only

Question No. 4

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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 $124.1 \mathrm{nm}$?

Given ($h = 6.62 \times {10}^{–34} \mathrm{J} \mathrm{s}$)

 

B
A
C
D

Question No. 5

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Match List I and List II

A	Gauss’s Law in Electrostatics	I	$\oint \overrightarrow{E}·\overrightarrow{\mathrm{d}l}=-\frac{\mathrm{d}{\varphi }_B}{dt}$
B	Faraday's Law	II	$\oint \overrightarrow{B}·\mathrm{d}\overrightarrow{A}=0$
C	Gauss’s Law in Magnetism	III	$\oint \overrightarrow{B}·\mathrm{d}\overrightarrow{l}={\mu }_0{i}_c+{\mu }_0{\in }_0\frac{\mathrm{d}{\varphi }_E}{\mathrm{d}t}$
D	Ampere-Maxwell Law	IV	$\oint \overrightarrow{E}·\mathrm{d}\overrightarrow{s}=\frac{q}{{\in }_0}$

Choose the correct answer from the options given below :

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

Question No. 6

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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 $x=2 \mathrm{cm}$ on the $X$-axis ?

$x=6 \mathrm{cm}$
$x=4 \mathrm{cm}$
$x=8 \mathrm{cm}$
$x=–4 \mathrm{cm}$

Question No. 7

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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

$4 : 1$
$2 : 1$
$1 : 2$
$1 : 1$

Question No. 8

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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 than object

D. Laterally inverted

Choose the most appropriate answer from the options given below:

B and D only
B and C only
A and D only
A, C and D only

Question No. 9

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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

$3 \mathrm{s}$
$2 \mathrm{s}$
$1.5 \mathrm{s}$
$4 \mathrm{s}$

Question No. 10

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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 :-

$\frac{9}{2}R$
$\frac{5}{2}R$
$\frac{3}{2}R$
$\frac{7}{2}R$

Question No. 11

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Length of a string tied to two rigid supports is $40 \mathrm{~cm}$. Maximum length (wave length in $\mathrm{cm}$ ) of a stationary wave produced on it is

20
80
40
120

Question No. 12

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Match List I with List II :

	List I		List II
A	Isothermal Process	I	Work done by the gas decreases internal energy
B	Adiabatic Process	II	No change in internal energy
C	Isochoric Process	III	The heat absorbed goes partly to increase internal energy and partly to do work
D	Isobaric Process	IV	No work is done on or by the gas

Choose the correct answer from the options given below :

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

Question No. 13

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

For a moving coil galvanometer, the deflection in the coil is $0.05 \mathrm{rad}$ when a current of $10 \mathrm{mA}$ is passed through it. If the torsional constant of suspension wire is $4.0 \times {10}^{–5} \mathrm{N} \mathrm{m} {\mathrm{rad}}^{-1}$, the magnetic field is $0.01 \mathrm{T}$ and the number of turns in the coil is $200$, the area of each turn (in ${\mathrm{cm}}^2$ ) is :

$2.0$
$1.0$
$1.5$
$0.5$

Question No. 14

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Consider a block kept on an inclined plane (inclined at $45°$) 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 plane $(\mu )$ is equal to :

.

$0.33$
$0.60$
$0.25$
$0.50$

Question No. 15

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Match List I with List II

	List		List II
A	Young's Modulus $\left(Y\right)$	I	$[{\mathrm{ML}}^{–1} \mathrm{T}{ }^{–1}]$
B	Co-efficient of Viscosity $\left(\eta \right)$	II	$[{\mathrm{ML}}^2 \mathrm{T}{ }^{–1}]$
C	Planck's Constant $\left(h\right)$	III	$[{\mathrm{ML}}^{–1} \mathrm{T}{ }^{–2}]$
D	Work Function $\left(\varphi \right)$	IV	$[{\mathrm{ML}}^2 {\mathrm{T}}^{–2}]$

Choose the correct answer from the options given below:

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

Question No. 16

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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

Statement I is incorrect but statement II is correct
Both Statement I and Statement II are incorrect
Statement I is correct but statement II is incorrect
Both statement I and statement II are correct

Question No. 17

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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

$40 \mathrm{m} {\mathrm{s}}^{–1}$
$25 \mathrm{m} {\mathrm{s}}^{–1}$
$20 \mathrm{m} {\mathrm{s}}^{–1}$
$8 \mathrm{m} {\mathrm{s}}^{–1}$

Question No. 18

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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

$20 \mathrm{V}$
$8 \mathrm{V}$
$12 \mathrm{V}$
$16 \mathrm{V}$

Question No. 19

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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 :

.

$\frac{t_Q}{150}=\frac{{\displaystyle t_P-180}}{100}$
$\frac{t_Q}{100}=\frac{{\displaystyle t_P-30}}{150}$
$\frac{t_P}{180}=\frac{{\displaystyle t_Q-40}}{100}$
$\frac{t_Q}{100}=\frac{{\displaystyle t_P-180}}{150}$

Question No. 20

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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 junction, a current will automatically flow which can be detected with an externally connected ammeter.

In the light of above statements, choose the most appropriate answer from the options given below.

Both Statement I and statement II are incorrect
Statement I is incorrect but statement II is correct
Both Statement I and statement II are correct
Statement I is correct but statement II is incorrect

Physics Numerical (Maximum Marks: 20)

Question No. 1

Numerical Type
The answer has to be filled into the input box provided below.

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:

Question No. 2

Numerical Type
The answer has to be filled into the input box provided below.

If a solid sphere of mass $5 \mathrm{kg}$ and a disc of mass $4 \mathrm{kg}$ 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 ______.

Question No. 3

Numerical Type
The answer has to be filled into the input box provided below.

A capacitor has capacitance $5 \mu \mathrm{F}$ when its 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 capacitor in the presence of slab will be ______ $\mu \mathrm{F}$.

Question No. 4

Numerical Type
The answer has to be filled into the input box provided below.

5 beats/ second are heard when a turning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either $0.95 \mathrm{~m}$ or $1 \mathrm{~m}$. The frequency of the fork will be: (mark answer in Hz)

Question No. 5

Numerical Type
The answer has to be filled into the input box provided below.

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

Question No. 6

Numerical Type
The answer has to be filled into the input box provided below.

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), $\frac{{\mathit{u}}_{\mathit{f}}}{{\mathit{u}}_{\mathit{i}}}=\left(\frac{10}{x}\right)$. Then value of $x$ is ______:

Question No. 7

Numerical Type
The answer has to be filled into the input box provided below.

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

 

Question No. 8

Numerical Type
The answer has to be filled into the input box provided below.

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

 

Question No. 9

Numerical Type
The answer has to be filled into the input box provided below.

A series LCR circuit is connected to an AC source of $220 \mathrm{V}$, $50 \mathrm{Hz}$. The circuit contains a resistance $R=80 \mathrm{\Omega }$, an inductor of inductive reactance $X_L=70 \mathrm{\Omega }$, and a capacitor of capacitive reactance $X_C=130 \mathrm{\Omega }$. The power factor of circuit is $\frac{x}{10}$. The value of $x$ is:

Question No. 10

Numerical Type
The answer has to be filled into the input box provided below.

Two long parallel wires carrying currents $8 \mathrm{A}$ and $15 \mathrm{A}$ in opposite directions are placed at a distance of $7 \mathrm{cm}$ 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 magnetic field at $P$ is ______ $\times {10}^{-6} \mathrm{T}$. (Given: $\sqrt{2}=1.4$)

Chemistry Single Correct (Maximum Marks: 80)

Question No. 1

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Magnetic moment of $\mathrm{Gd}^{3+}$ ion $(\mathrm{Z}=64)$ is

3.62 BM
$9.72 \mathrm{BM}$
7.9 BM
$10.60 \mathrm{BM}$

Question No. 2

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Match List I with List II.

Choose the correct answer from the options given below :-

	List I Isomeric pairs		List II Type of isomers
A	Propanamine and N- Methylethanamine	I	Metamers
B	Hexan-2-one Hexan-3-one	II	Positional isomers
C	Ethanamide and Hydroxyethanimine	III	Functional isomers
D	o-nitrophenol and pnitrophenol	IV	Tautomers

 

$\mathrm{A}-\mathrm{III}, \mathrm{B}-\mathrm{IV}, \mathrm{C}-\mathrm{I}, \mathrm{D}-\mathrm{II}$
$\mathrm{A}-\mathrm{IV}, \mathrm{B}-\mathrm{III}, \mathrm{C}-\mathrm{I}, \mathrm{D}-\mathrm{II}$
$\mathrm{A}-\mathrm{II}, \mathrm{B}-\mathrm{III}, \mathrm{C}-\mathrm{I}, \mathrm{D}-\mathrm{IV}$
$\mathrm{A}-\mathrm{III}, \mathrm{B}-\mathrm{I}, \mathrm{C}-\mathrm{IV}, \mathrm{D}-\mathrm{II}$

Question No. 3

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

The order of increasing sizes of atomic radii among the elements O, $\mathrm{S}$, Se and As is :

As $< \mathrm{S} < \mathrm{O} < \mathrm{Se}$
$\mathrm{Se} < \mathrm{S} < \mathrm{As} < \mathrm{O}$
O $<$ S $<$ As $< \mathrm{Se}$
$\mathrm{O} < \mathrm{S} < \mathrm{Se} < \mathrm{As}$

Question No. 4

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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 $\mathrm{CO}$ and ${\mathrm{CO}}_2$. $\mathrm{CO}$ is neutral whereas ${\mathrm{CO}}_2$ is acidic in nature.

Reason R :  ${\mathrm{CO}}_2$ can combine with water in a limited way to form carbonic acid, while $\mathrm{CO}$ is sparingly soluble in water.

In the light of the above statements, choose the most appropriate answer from the options given below :-

Both A and R are correct but R is NOT the correct explanation of A.
Both A and R are correct and R is the correct explanation of A.
A is not correct but R   is correct. 
A  is correct but R  is not correct. 

Question No. 5

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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

increases by $1000$ units
decreases by $3$ units
decreases by $2$ units
increases by $2$ units

Question No. 6

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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

2-Bromo-1-deuterobutane
2-Bromo-2-deuterobutane
2-Bromo-3-deuterobutane
2-Bromo-1-deutero-2-methylpropane

Question No. 7

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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

$\mathrm{K}$
$\mathrm{Rb}$
$\mathrm{Na}$
$\mathrm{Li}$

Question No. 8

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

What is the mass ratio of ethylene glycol (${\mathrm{C}}_2{\mathrm{H}}_6{\mathrm{O}}_2$, molar mass $=62 \mathrm{g}/\mathrm{mol}$) required for making $500 \mathrm{g}$ of $0.25$ molal aqueous solution and $250 \mathrm{mL}$ of $0.25$ molar aqueous solution?

$1:1$
$3:1$
$2:1$
$1:2$

Question No. 9

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

The electronic configuration with the highest ionization enthalpy is:

$\left[\text{A}\text{r}\right]3{\text{d}}^{10}4{\text{s}}^{2}4{\text{p}}^3$
$\left[\text{N}\text{e}\right]3{\text{s}}^{2}3{\text{p}}^1$
$\left[\text{N}\text{e}\right]3{\text{s}}^{2}3{\text{p}}^3$
$\left[\text{N}\text{e}\right]3{\text{s}}^{2}3{\text{p}}^2$

Question No. 10

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Find out the major product from the following reaction.

 



 



 

Question No. 11

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Match List I with List II

List I (Amines)		List II $\left(\mathrm{pKb}\right)$
A.	Aniline	I.	$3.25$
B.	Ethanamine	II.	$3.00$
C.	N-Ethylethanamine	III.	$9.38$
D.	N, N-Diethylethanamine	IV.	$3.29$

Choose the correct answer from the options given below:-

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

Question No. 12

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

' A ' in the given reaction is

 

 

 



 



 



 

Question No. 13

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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 the light of the above statements, choose the most appropriate answer from the options given below:-

Both A and R are correct and R is the correct explanation of A.
A is correct but R is not correct.
A is not correct but R is correct.
Both A and R are correct but R is NOT the correct explanation of A.

Question No. 14

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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

$\mathrm{H}\left[{\mathrm{AgCl}}_3\right]\&\left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_2\right]\mathrm{Cl}$
$\mathrm{H}\left[{\mathrm{AgCl}}_3\right] \& \left({\mathrm{NH}}_4\right)\left[\mathrm{Ag}(\mathrm{OH}{)}_2\right]$
$\mathrm{AgCl} \& \left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_2\right]\mathrm{Cl}$
$\mathrm{AgCl} \& \left({\mathrm{NH}}_4\right)\left[\mathrm{Ag}(\mathrm{OH}{)}_2\right]$

Question No. 15

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

The rate of a reaction doubles when its temperature changes from $300\mathrm{K} \mathrm{to} 310\mathrm{K}$. Activation energy of such a reaction will be:
​
$\left(\text{R}={\text{8.314 JK}}^{-1}{mol}^{-1} \mathrm{and} log\; 2=\text{0.301}\right)$

$58.5 \mathrm{kJ} {\mathrm{mol}}^{ -1}$
$60.5 \mathrm{kJ} {\mathrm{mol}}^{ -1}$
$53.6 \mathrm{kJ} \mathrm{mol}{ }^{-1}$
$48.6 \mathrm{kJ} {\mathrm{mol}}^{ -1}$

Question No. 16

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Which of the following statements is wrong?

Ethyl chloride on reduction with $\mathrm{Zn}-\mathrm{Cu}$ couple and alcohol gives ethane.
The reaction of methyl magnesium bromide with acetone gives butanol-2.
Alkyl halides follow the following reactivity sequence on reaction with alkenes.
$\mathrm{R}-\mathrm{I}>\mathrm{R}-\mathrm{Br}>\mathrm{R}-\mathrm{Cl}>\mathrm{R}-\mathrm{I}$
$\mathrm{C}_2 \mathrm{H}_4 \mathrm{Cl}_2$ may exist in two isomeric forms

Question No. 17

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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 charges in the molecules.

In the light of the above statements, choose the most appropriate answer from the options given below:-

Both Statement I and Statement II are correct.
Statement I is incorrect but Statement II is correct.
Both Statement I and Statement II are incorrect.
Statement I is correct but Statement II is incorrect.

Question No. 18

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Match List I with List II

	List I Coordination entity		List II Wavelength of light absorbed in nm
A	${\left[\mathrm{CoCl}{\left({\mathrm{NH}}_3\right)}_5\right]}^{2+}$	I.	$310$
B	${\left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_6\right]}^{3+}$	II.	$475$
C	${\left[\mathrm{Co}(\mathrm{CN}{)}_6\right]}^{3-}$	III.	$535$
D	${\left[\mathrm{Cu}{\left({\mathrm{H}}_2\mathrm{O}\right)}_4\right]}^{2+}$	IV.	$600$

Choose the correct answer from the options given below :-

$\mathrm{A}-\mathrm{IV}, \mathrm{B}-\mathrm{I}, \mathrm{C}-\mathrm{III}, \mathrm{D}-\mathrm{II}$
$\mathrm{A}-\mathrm{III}, \mathrm{B}-\mathrm{II}, \mathrm{C}-\mathrm{I}, \mathrm{D}-\mathrm{IV}$
$\mathrm{A}-\mathrm{III}, \mathrm{B}-\mathrm{I}, \mathrm{C}-\mathrm{II}, \mathrm{D}-\mathrm{IV}$
$\mathrm{A}- \mathrm{II}, \mathrm{B}-\mathrm{III}, \mathrm{C}-\mathrm{IV}, \mathrm{D}-\mathrm{I}$

Question No. 19

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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

$\mathrm{Si}<\mathrm{Be}<\mathrm{Mg}<\mathrm{K}$
$\mathrm{Be}<\mathrm{Si}<\mathrm{Mg}<\mathrm{K}$
$\mathrm{K}<\mathrm{Mg}<\mathrm{Be}<\mathrm{Si}$
$\mathrm{Be}<\mathrm{Si}<\mathrm{K}<\mathrm{Mg}$

Question No. 20

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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

$+3$ to $+1$
$+6$ to $+3$
$+2$ to $+1$
$+6$ to $+2$

Chemistry Numerical (Maximum Marks: 20)

Question No. 1

Numerical Type
The answer has to be filled into the input box provided below.

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

The ${\mathrm{E}}_{\text{cell }}$ for the given cell is $0.1115 \mathrm{V}$ at $298 \mathrm{K}$

When $\frac{\left[{\mathrm{M}}^{+}\left(\mathrm{aq}\right)\right]}{\left[{\mathrm{M}}^{3+}\left(\mathrm{aq}\right)\right]}={10}^{\mathrm{a}}$

The value of a is ___________

Given : ${\mathrm{E}}^{\theta }=_{{\mathrm{M}}^{3+}/{\mathrm{M}}^{+}}0.2 \mathrm{V}$

$\frac{2.303\mathrm{RT}}{\mathrm{F}}=0.059 \mathrm{V}$

 

Question No. 2

Numerical Type
The answer has to be filled into the input box provided below.

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

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

Question No. 3

Numerical Type
The answer has to be filled into the input box provided below.

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

Given$:{\mathrm{\Delta H}}_{\mathrm{C}}\left({\mathrm{CH}}_4\right)=-900 \mathrm{kJ} {\mathrm{mol}}^{-1}$

${\mathrm{\Delta H}}_{\mathrm{C}}\left({\mathrm{C}}_2{\mathrm{H}}_4\right)=-1400 \mathrm{kJ} {\mathrm{mol}}^{-1}$.

Question No. 4

Numerical Type
The answer has to be filled into the input box provided below.

${\text{pK}}_{\text{a}}$ of a weak acid $\left(\text{HA}\right)$ and ${\text{pK}}_{\text{b}}$ of a weak base $\left(\text{BOH}\right)$ are $3.2$ and $3.4$ respectively. The $\text{pH}$ of their salt $\left(\text{AB}\right)$ solution at ${\text{25}}^{\text{o}}\text{C}$ is (round off answer to nearest integer)

Question No. 5

Numerical Type
The answer has to be filled into the input box provided below.

The volume of 0.1 M strong dibasic acid sufficient to neutralize 1g of a base that furnishes 0.04 mole of $\mathrm{O}{\mathrm{H}}^{-}$ in aqueous solution is : (mark answer in mL)

Question No. 6

Numerical Type
The answer has to be filled into the input box provided below.

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

A. $0.500 \mathrm{M} {\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH}\left(\mathrm{aq}\right)$ and $0.25 \mathrm{M} \mathrm{KBr}\left(\mathrm{aq}\right)$
B. $0.100 {\mathrm{M}}_{} {\mathrm{K}}_4\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right]\left(\mathrm{aq}\right)$ and $0.100 \mathrm{M}$ ${\mathrm{FeSO}}_4{\left({\mathrm{NH}}_4\right)}_2{\mathrm{SO}}_4\left(\mathrm{aq}\right)$

C. $0.05 \mathrm{M} {\mathrm{K}}_4\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right]$ (aq) and $0.25 \mathrm{M} \mathrm{NaCl}$ $\left(\mathrm{aq}\right)$
D. $0.15 \mathrm{M} \mathrm{NaCl}\left(\mathrm{aq}\right)$ and $0.1 \mathrm{M} {\mathrm{BaCl}}_2\left(\mathrm{aq}\right)$
E. $0.02 \mathrm{M} \mathrm{KCl}.{\mathrm{MgCl}}_2.6{\mathrm{H}}_2\mathrm{O}\left(\mathrm{aq}\right)$ and $0.05 \mathrm{M}$ $\mathrm{KCl}\left(\mathrm{aq}\right)$

Question No. 7

Numerical Type
The answer has to be filled into the input box provided below.

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

 

Question No. 8

Numerical Type
The answer has to be filled into the input box provided below.

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

Question No. 9

Numerical Type
The answer has to be filled into the input box provided below.

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 $1000 \mathrm{s}$.
B. The reaction has a half-life of $500 \mathrm{s}$.
C. The time required for $10\%$ completion is 25 times the time required for 90% completion.
D. The degree of dissociation is equal to $\left(1-{\mathrm{e}}^{-\mathrm{kt}}\right)$.
E. The rate and the rate constant have the same unit.

Question No. 10

Numerical Type
The answer has to be filled into the input box provided below.

Total number of moles of AgCl precipitated on addition of excess of ${\mathrm{AgNO}}_3$ to one mole each of the following complexes $\left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_4{\mathrm{Cl}}_2\right]\mathrm{Cl}$, $\left[\mathrm{Ni}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]{\mathrm{Cl}}_2,\left[\mathrm{Pt}{\left({\mathrm{NH}}_3\right)}_2{\mathrm{Cl}}_2\right]$ and $\left[\mathrm{Pd}{\left({\mathrm{NH}}_3\right)}_4\right]{\mathrm{Cl}}_2$ is

Mathematics Single Correct (Maximum Marks: 80)

Question No. 1

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Let $y=y\left(t\right)$ 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 ${Lim}_{t\to \infty } y\left(t\right)$

is $0$
does not exist
is $1$
is $-1$

Question No. 2

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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

$6$
$12$
$120$
$72$

Question No. 3

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Let $\overline{x}$, $M$ and ${\sigma }^2$ be respectively the mean, mode and variance of $n$ observations $x_1, x_2,...., x_n$ and $d_i=-x_i-a, i=1, 2,...., n,$ where $a$ is any number.

Statement I: Variance of $d_1, d_2,..., d_n$ is ${\sigma }^2$.

Statement II: Mean and mode of $d_1, d_2,...., d_n$ are $-\overline{x}-a$ and $-M-a$, respectively.

Statement I and Statement II are both true 
Statement I and Statement II are both false 
Statement I is true and Statement II is false
Statement I is false and Statement II is true

Question No. 4

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Let $O$ be the vertex and $Q$ be any point on the parabola, $x^2=8y$. If the point $P$ divides the line segment $OQ$ internally in the ratio $1:3$, then the locus of $P$ is

$x^2=2y$
$x^2=y$
$y^2=x$
$y^2=2x$

Question No. 5

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Let $\mathrm{N}$ 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 $\frac{k}{48}$. Then the value of $k$ is

$2$
$4$
$16$
$8$

Question No. 6

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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

Consider the statements

$\left(S1\right) A^{13} B^{26}-B^{26} A^{13}$ is symmetric

$\left(\mathrm{S}2\right) A^{26}{C}^{13}-C^{13} A^{26}$ is symmetric

Then,

Only $S2$ is true
Only $\mathrm{S}1$ is true
Both $S1$ and $S2$ are false
Both $S1$ and $S2$ are true

Question No. 7

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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

$5$
$3$
$2$
$4$

Question No. 8

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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

$2$
$3$
$\frac{5}{2}$
$\frac{3}{2}$

Question No. 9

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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

$4\sqrt{6}+\frac{44}{3}$
$4\sqrt{6}+\frac{28}{3}$
$4\sqrt{6}-\frac{44}{3}$
$4\sqrt{6}-\frac{28}{3}$

Question No. 10

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

If $\vec{a}$ and $\vec{b}$ are non-collinear vectors, then the value of $\alpha$ for which the vectors $\vec{u}=(\alpha-2) \vec{a}+\vec{b}$ and $\vec{v}=(2+3 \alpha) \vec{a}-3 \vec{b}$ are collinear is :

$\frac{3}{2}$
$\frac{2}{3}$
$-\frac{3}{2}$
$-\frac{2}{3}$

Question No. 11

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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

$\frac{\alpha \beta }{\gamma }=\frac{4}{15}$
$\frac{\alpha }{\beta }=-8$
$\frac{\beta }{\gamma }=-5$
$\frac{\gamma }{\alpha }=\frac{5}{8}$

Question No. 12

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

If the function $f(x)=\left\{\begin{array}{cc} (1+|\cos x|)^{\frac{\lambda}{|\cos x |}} & 0 < x < \frac{\pi}{2} \\ \mu, & x=\frac{\pi}{2} \\ e^{\frac{\cot 6 x}{\cot 4 x}}, & \frac{\pi}{2} < x < \pi \end{array}\right.$ is continuous at $x=\frac{\pi}{2}$, then $9 \lambda+6 \log _c \mu+\mu^6-e^{6 \lambda}$ is equal to

$11$
$8$
$2e^4+8$
$10$

Question No. 13

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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

$\left(\frac{9}{2},\infty \right)$
$\left(0,\frac{9}{2}\right)$
$\left(-\infty ,\frac{9}{2}\right)$
$\left(-\frac{9}{2},\frac{9}{2}\right)$

Question No. 14

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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

$3$
$4$
$1$
$2$

Question No. 15

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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

$3\left(\hat{i}-\hat{j}-\hat{k}\right)$
$3\left(\hat{i}+\hat{j}+\hat{k}\right)$
$3\left(\hat{i}-\hat{j}+\hat{k}\right)$
$3\left(\hat{i}+\hat{j}-\hat{k}\right)$

Question No. 16

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

The middle term in the expansion of $\left(1-\frac{1}{x}\right)^n\left(1-x\right)^n$ in powers of $x$ is

$-{ }^{2 n} \mathrm{C}_{n-1}$
$-{ }^{2 n} \mathrm{C}_n$
${ }^{2 n} \mathrm{C}_{n-1}$
${ }^{2 n} \mathrm{C}_n$

Question No. 17

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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

$\frac{11}{6}+{\log }_{e}4$
$\frac{11}{12}+{\log }_{\mathrm{e}}4$
$\frac{11}{12}-{\log }_{e}4$
$\frac{11}{6}-{\log }_{e}4$

Question No. 18

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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 $\mathrm{M}={\mathrm{A}}^{\mathrm{T}}\mathrm{BA}$, then the inverse of the matrix ${\mathrm{AM}}^{2023} {\mathrm{A}}^{\mathrm{T}}$ is

$\left[\begin{array}{cc}1& -2023i\\ 0& 1\end{array}\right]$
$\left[\begin{array}{cc}1& 0\\ -2023i& 1\end{array}\right]$
$\left[\begin{array}{cc}1& 0\\ 2023i& 1\end{array}\right]$
$\left[\begin{array}{cc}1& 2023i\\ 0& 1\end{array}\right]$

Question No. 19

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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

$(2,0)$
$(0,2)$
$(0,0)$
$(0,-2)$

Question No. 20

Only One Option Correct Type
Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

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

$61$
$60$
$58$
$59$

Mathematics Numerical (Maximum Marks: 20)

Question No. 1

Numerical Type
The answer has to be filled into the input box provided below.

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

Question No. 2

Numerical Type
The answer has to be filled into the input box provided below.

The number of common tangents to the circles $x^2+y^2-4x-6y-12=0$ and $x^2+y^2+6x+18y+26=0$, is

Question No. 3

Numerical Type
The answer has to be filled into the input box provided below.

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

Question No. 4

Numerical Type
The answer has to be filled into the input box provided below.

$25\%$ 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 _____ .

Question No. 5

Numerical Type
The answer has to be filled into the input box provided below.

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 offer $5$ fruits to Anil is _____ .

Question No. 6

Numerical Type
The answer has to be filled into the input box provided below.

If $m$ and $M$ are the minimum and the maximum values of $4+\frac{1}{2}{\sin }^{2}2x-2{\cos }^{4}x, x \in R,$ then $M-m$ is equal to: K, find 4K.

Question No. 7

Numerical Type
The answer has to be filled into the input box provided below.

A triangle is formed by $X$-axis, $Y$-axis and the line $3x+4y=60$. Then the number of points $P\left(a,b\right)$ which lie strictly inside the triangle, where $a$ is an integer and $b$ is a multiple of $a$, is _____ .

Question No. 8

Numerical Type
The answer has to be filled into the input box provided below.

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

Question No. 9

Numerical Type
The answer has to be filled into the input box provided below.

The remainder when ${\left(2023\right)}^{2023}$ is divided by $35$ is

Question No. 10

Numerical Type
The answer has to be filled into the input box provided below.

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