JEE Main 2023 (Online) 31st January Evening Shift

Paper was held on
Tue, Jan 31, 2023 9:30 AM

## Chemistry

When a hydrocarbon A undergoes complete combustion it requires 11 equivalents of oxygen and produces 4 equivalents of wa

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The normal rain water is slightly acidic and its $\mathrm{pH}$ value is $5.6$ because of which one of the following ?

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The element playing significant role in neuromuscular function and interneuronal transmission is :

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Cyclohexylamine when treated with nitrous acid yields $(\mathrm{P})$. On treating $(\mathrm{P})$ with $\mathrm{PCC}$ res

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Given below are two statements :
Statement I : $ \mathrm{H}_{2} \mathrm{O}_{2}$ is used in the synthesis of Cephalospori

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Compound $\mathrm{A}, \mathrm{C}_{5} \mathrm{H}_{10} \mathrm{O}_{5}$, given a tetraacetate with $\mathrm{Ac}_{2} \mathrm

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An organic compound $[\mathrm{A}]\left(\mathrm{C}_{4} \mathrm{H}_{11} \mathrm{~N}\right)$, shows optical activity and gi

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Which of the following elements have half-filled f-orbitals in their ground state?
(Given : atomic number $\mathrm{Sm}=

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Match List I with List II
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Which of the following compounds are not used as disinfectants ?
A. Chloroxylenol
B. Bithional
C. Veronal
D. Prontosil
E

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The Lewis acid character of boron tri halides follows the order :

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Evaluate the following statements for their correctness.
A. The elevation in boiling point temperature of water will be

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Which one of the following statements is incorrect?

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Arrange the following orbitals in decreasing order of energy.
A. $\mathrm{n}=3, \mathrm{l}=0, \mathrm{~m}=0$
B. $\mathrm

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In Dumas method for the estimation of $\mathrm{N}_{2}$, the sample is heated with copper oxide and the gas evolved is pa

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

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A hydrocarbon ' $\mathrm{X}$ ' with formula $\mathrm{C}_{6} \mathrm{H}_{8}$ uses two moles of $\mathrm{H}_{2}$ on cataly

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Given below are two statements :
Statement I: Upon heating a borax bead dipped in cupric sulphate in a luminous flame, t

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In the following halogenated organic compounds, the one with the maximum number of chlorine atoms in its structure is :

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The incorrect statement for the use of indicators in acid-base titration is :

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Assume carbon burns according to the following equation :
$2 \mathrm{C}_{(\mathrm{s})}+\mathrm{O}_{2(\mathrm{~g})} \rig

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The number of molecules which gives the haloform test among the following molecules is ________.

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Amongst the following, the number of species having the linear shape is _________.
$\mathrm{XeF}_{2}, \mathrm{I}_{3}^{+

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The number of alkali metal(s), from $\mathrm{Li}, \mathrm{K}, \mathrm{Cs}$, Rb having ionization enthalpy greater than $

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Enthalpies of formation of $\mathrm{CCl}_{4}(\mathrm{~g}), \mathrm{H}_{2} \mathrm{O}(\mathrm{g}), \mathrm{CO}_{2}(\mathr

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At $298 \mathrm{~K}$, the solubility of silver chloride in water is $1.434 \times 10^{-3} \mathrm{~g} \mathrm{~L}^{-1}$.

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The resistivity of a $0.8 \mathrm{M}$ solution of an electrolyte is $5 \times 10^{-3} \Omega~ \mathrm{cm}$. Its molar c

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A sample of a metal oxide has formula $\mathrm{M}_{0.83} \mathrm{O}_{1.00}$. The metal $\mathrm{M}$ can exist in two oxi

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If the CFSE of $\left[\mathrm{Ti}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}$ is $-96.0 \mathrm{~kJ} / \mathr

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The rate constant for a first order reaction is $20 \mathrm{~min}^{-1}$. The time required for the initial concentration

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## Mathematics

Let : $\vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}, \vec{b}=\hat{i}-\hat{j}+2 \hat{k}$ and $\vec{c}=5 \hat{i}-3 \hat{j}+3 \hat{k

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Let $f: \mathbb{R}-\{2,6\} \rightarrow \mathbb{R}$ be real valued function defined as $f(x)=\frac{x^2+2 x+1}{x^2-8 x+12}

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Let the plane $\mathrm{P}: 8 x+\alpha_{1} y+\alpha_{2} z+12=0$ be parallel to the line $\mathrm{L}: \frac{x+2}{2}=\frac{

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The equation $\mathrm{e}^{4 x}+8 \mathrm{e}^{3 x}+13 \mathrm{e}^{2 x}-8 \mathrm{e}^{x}+1=0, x \in \mathbb{R}$ has :

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Let (a, b) $\subset(0,2 \pi)$ be the largest interval for which $\sin ^{-1}(\sin \theta)-\cos ^{-1}(\sin \theta)>0, \the

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Let $\alpha>0$. If $\int\limits_0^\alpha \frac{x}{\sqrt{x+\alpha}-\sqrt{x}} \mathrm{~d} x=\frac{16+20 \sqrt{2}}{15}$, th

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Let the mean and standard deviation of marks of class A of 100 students be respectively 40 and $\alpha(>$
0 ), and the

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Let $a_1, a_2, a_3, \ldots$ be an A.P. If $a_7=3$, the product $a_1 a_4$ is minimum and the sum of its first $n$ terms i

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The number of values of $\mathrm{r} \in\{\mathrm{p}, \mathrm{q}, \sim \mathrm{p}, \sim \mathrm{q}\}$ for which $((\mathr

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The complex number $z=\frac{i-1}{\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}}$ is equal to :

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Among the relations
$\mathrm{S}=\left\{(\mathrm{a}, \mathrm{b}): \mathrm{a}, \mathrm{b} \in \mathbb{R}-\{0\}, 2+\frac{\

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The foot of perpendicular from the origin $\mathrm{O}$ to a plane $\mathrm{P}$ which meets the co-ordinate axes at the p

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Let $P$ be the plane, passing through the point $(1,-1,-5)$ and perpendicular to the line joining the points $(4,1,-3)$

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The absolute minimum value, of the function
$f(x)=\left|x^{2}-x+1\right|+\left[x^{2}-x+1\right]$,
where $[t]$ denotes t

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If $\phi(x)=\frac{1}{\sqrt{x}} \int\limits_{\frac{\pi}{4}}^x\left(4 \sqrt{2} \sin t-3 \phi^{\prime}(t)\right) d t, x>0$,

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If a point $\mathrm{P}(\alpha, \beta, \gamma)$ satisfying
$$\left( {\matrix{
\alpha & \beta & \gamma \cr
} } \

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Let $\mathrm{H}$ be the hyperbola, whose foci are $(1 \pm \sqrt{2}, 0)$ and eccentricity is $\sqrt{2}$. Then the length

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$$
\lim\limits_{x \rightarrow \infty} \frac{(\sqrt{3 x+1}+\sqrt{3 x-1})^6+(\sqrt{3 x+1}-\sqrt{3 x-1})^6}{\left(x+\sqrt{x

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Let $y=y(x)$ be the solution of the differential equation
$\left(3 y^{2}-5 x^{2}\right) y \mathrm{~d} x+2 x\left(x^{2}-

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The set of all values of $a^{2}$ for which the line $x+y=0$ bisects two distinct chords drawn from a point $\mathrm{P}\l

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Let A be a $n \times n$ matrix such that $|\mathrm{A}|=2$. If the determinant of the matrix
$\operatorname{Adj}\left(2

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Let $\mathrm{S}$ be the set of all $\mathrm{a} \in \mathrm{N}$ such that the area of the triangle formed by the tangent

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Let the area of the region
$\left\{(x, y):|2 x-1| \leq y \leq\left|x^{2}-x\right|, 0 \leq x \leq 1\right\}$ be $\mathrm{

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The coefficient of $x^{-6}$, in the
expansion of $\left(\frac{4 x}{5}+\frac{5}{2 x^{2}}\right)^{9}$, is

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Let $\mathrm{A}=\left[\mathrm{a}_{i j}\right], \mathrm{a}_{i j} \in \mathbb{Z} \cap[0,4], 1 \leq i, j \leq 2$.
The numbe

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If ${ }^{2 n+1} \mathrm{P}_{n-1}:{ }^{2 n-1} \mathrm{P}_{n}=11: 21$,
then $n^{2}+n+15$ is equal to :

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Let $\vec{a}, \vec{b}, \vec{c}$ be three vectors such that
$|\vec{a}|=\sqrt{31}, 4|\vec{b}|=|\vec{c}|=2$ and $2(\vec{a}

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Let A be the event that the absolute difference between two randomly choosen real numbers in the sample space $[0,60]$ i

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If the constant term in the binomial expansion of $\left(\frac{x^{\frac{5}{2}}}{2}-\frac{4}{x^{l}}\right)^{9}$ is $-84$

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The sum $1^{2}-2 \cdot 3^{2}+3 \cdot 5^{2}-4 \cdot 7^{2}+5 \cdot 9^{2}-\ldots+15 \cdot 29^{2}$ is _________.

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## Physics

For a solid rod, the Young's modulus of elasticity is $3.2 \times 10^{11} \mathrm{Nm}^{-2}$ and density is $8 \times 10^

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Heat energy of $735 \mathrm{~J}$ is given to a diatomic gas allowing the gas to expand at constant pressure.
Each gas m

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The radius of electron's second stationary orbit in Bohr's atom is R. The radius of 3rd orbit will be

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If the two metals $\mathrm{A}$ and $\mathrm{B}$ are exposed to radiation of wavelength $350 \mathrm{~nm}$. The work func

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The number of turns of the coil of a moving coil galvanometer is increased in order to increase current sensitivity by $

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Match List I with List II
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The $\mathrm{H}$ amount of thermal energy is developed by a resistor in $10 \mathrm{~s}$ when a current of $4 \mathrm{~A

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A body weight $\mathrm{W}$, is projected vertically upwards from earth's surface to reach a height above the earth which

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Considering a group of positive charges, which of the following statements is correct ?

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Given below are two statements :
Statement I : For transmitting a signal, size of antenna ( $l$ ) should be comparable t

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A body of mass $10 \mathrm{~kg}$ is moving with an initial speed of $20 \mathrm{~m} / \mathrm{s}$. The body stops after

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A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the ratio of final

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A long conducting wire having a current I flowing through it, is bent into a circular coil of $\mathrm{N}$ turns. Then i

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A microscope is focused on an object at the bottom of a bucket. If liquid with refractive index $\frac{5}{3}$
is poured

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Match List I with List II
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Under the same load, wire A having length $5.0 \mathrm{~m}$ and cross section $2.5 \times 10^{-5} \mathrm{~m}^{2}$ stret

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An alternating voltage source $\mathrm{V}=260 \sin (628 \mathrm{t}$ ) is connected across a pure inductor of $5 \mathrm{

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Given below are two statements :
Statement I: In a typical transistor, all three regions emitter, base and collector hav

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A stone of mass $1 \mathrm{~kg}$ is tied to end of a massless string of length $1 \mathrm{~m}$. If the breaking tension

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A body is moving with constant speed, in a circle of radius $10 \mathrm{~m}$. The body completes one revolution in $4 \m

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A water heater of power $2000 \mathrm{~W}$ is used to heat water. The specific heat capacity of water is $4200 \mathrm{~

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A series $\mathrm{LCR}$ circuit consists of $\mathrm{R}=80 \Omega, \mathrm{X}_{\mathrm{L}}=100 \Omega$, and $\mathrm{X}_

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Two light waves of wavelengths 800 and $600 \mathrm{~nm}$ are used in Young's double slit experiment to obtain interfere

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Two bodies are projected from ground with same speeds $40 \mathrm{~ms}^{-1}$ at two different angles with respect to hor

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The displacement equations of two interfering waves are given by
$y_{1}=10 \sin \left(\omega t+\frac{\pi}{3}\right) \ma

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For the given circuit, in the steady state, $\left|\mathrm{V}_{\mathrm{B}}-\mathrm{V}_{\mathrm{D}}\right|=$
________ V.

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Two discs of same mass and different radii are made of different materials such that their
thicknesses are $1 \mathrm{~

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A ball is dropped from a height of $20 \mathrm{~m}$. If the coefficient of restitution for the collision between ball an

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If the binding energy of ground state electron in a hydrogen atom is $13.6\, \mathrm{eV}$, then, the energy required to

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Two parallel plate capacitors $C_{1}$ and $C_{2}$ each having capacitance of $10 \mu \mathrm{F}$ are individually charge

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