JEE Main 2023 (Online) 31st January Evening Shift

Compound $\mathrm{A}, \mathrm{C}_{5} \mathrm{H}_{10} \mathrm{O}_{5}$, given a tetraacetate with $\mathrm{Ac}_{2} \mathrm{O}$ and oxidation of $\mathrm{A}$ with $\mathrm{Br}_{2}-\mathrm{H}_{2} \mathrm{O}$ gives an acid, $\mathrm{C}_{5} \math...

Cyclohexylamine when treated with nitrous acid yields $(\mathrm{P})$. On treating $(\mathrm{P})$ with $\mathrm{PCC}$ results in (Q). When $(\mathrm{Q})$ is heated with dil. $\mathrm{NaOH}$ we get $(\mathrm{R})$ The final product (R) is :

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

Amongst the following, the number of species having the linear shape is _________.

$\mathrm{XeF}_{2}, \mathrm{I}_{3}^{+}, \mathrm{C}_{3} \mathrm{O}_{2}, \mathrm{I}_{3}^{-}, \mathrm{CO}_{2}, \mathrm{SO}_{2}, \mathrm{BeCl}_{2}$ and $\mathrm{...

The rate constant for a first order reaction is $20 \mathrm{~min}^{-1}$. The time required for the initial concentration of the reactant to reduce to its $\frac{1}{32}$ level is _______ $\times 10^{-2} \mathrm{~min}$. (Nearest integer)
(Giv...

Which of the following compounds are not used as disinfectants ?
A. Chloroxylenol
B. Bithional
C. Veronal
D. Prontosil
E. Terpineol

Choose the correct answer from the options given below :

An organic compound $[\mathrm{A}]\left(\mathrm{C}_{4} \mathrm{H}_{11} \mathrm{~N}\right)$, shows optical activity and gives $\mathrm{N}_{2}$ gas on treatment with $\mathrm{HNO}_{2}$. The compound $[\mathrm{A}]$ reacts with $\mathrm{PhSO}_{2...

If the CFSE of $\left[\mathrm{Ti}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}$ is $-96.0 \mathrm{~kJ} / \mathrm{mol}$, this complex will absorb maximum at wavelength ___________ $\mathrm{nm}$. (nearest integer)

Assume Planck's co...

The resistivity of a $0.8 \mathrm{M}$ solution of an electrolyte is $5 \times 10^{-3} \Omega~ \mathrm{cm}$. Its molar conductivity is _________ $\times 10^{4}~ \Omega^{-1} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}$. (Nearest integer)

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

A hydrocarbon ' $\mathrm{X}$ ' with formula $\mathrm{C}_{6} \mathrm{H}_{8}$ uses two moles of $\mathrm{H}_{2}$ on catalytic hydrogenation of its one mole. On ozonolysis, ' $\mathrm{X}$ ' yields two moles of methane dicarbaldehyde. The hydro...

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

Given below are two statements :
Statement I : $ \mathrm{H}_{2} \mathrm{O}_{2}$ is used in the synthesis of Cephalosporin
Statement II : $ \mathrm{H}_{2} \mathrm{O}_{2}$ is used for the restoration of aerobic conditions to sewage wastes.
In...

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

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

(Given mass of $\mathrm{Ag}$ is $107.9...

Which one of the following statements is incorrect?

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

Given below are two statements :
Statement I: Upon heating a borax bead dipped in cupric sulphate in a luminous flame, the colour of the bead becomes green
Statement II: The green colour observed is due to the formation of copper(I) metabor...

Which of the following elements have half-filled f-orbitals in their ground state?

(Given : atomic number $\mathrm{Sm}=62 ; \mathrm{Eu}=63 ; \mathrm{Tb}=65 ; \mathrm{Gd}=64, \mathrm{Pm}=61$ )
A. $\mathrm{Sm}$
B. Eu
C. $\mathrm{Tb}$
D. Gd
E...

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

Assertion (A): The first ionization enthalpy of $3 \mathrm{~d}$ series elements is more than that of group 2 metals

Reason (R): In 3...

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

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

The number of alkali metal(s), from $\mathrm{Li}, \mathrm{K}, \mathrm{Cs}$, Rb having ionization enthalpy greater than $400 \mathrm{~kJ}$ $\mathrm{mol}^{-1}$ and forming stable super oxide is _____________.

Evaluate the following statements for their correctness.

A. The elevation in boiling point temperature of water will be same for $0.1 \mathrm{M} \, \mathrm{NaCl}$ and $0.1 \mathrm{M}$ urea.

B. Azeotropic mixtures boil without change in th...

When a hydrocarbon A undergoes complete combustion it requires 11 equivalents of oxygen and produces 4 equivalents of water. What is the molecular formula of $A$ ?

Assume carbon burns according to the following equation :

$2 \mathrm{C}_{(\mathrm{s})}+\mathrm{O}_{2(\mathrm{~g})} \rightarrow 2 \mathrm{CO}(\mathrm{g})$

when $12 \mathrm{~g}$ carbon is burnt in $48 \mathrm{~g}$ of oxygen, the volume of c...

A sample of a metal oxide has formula $\mathrm{M}_{0.83} \mathrm{O}_{1.00}$. The metal $\mathrm{M}$ can exist in two oxidation states $+2$ and $+3$. In the sample of $\mathrm{M}_{0.83} \mathrm{O}_{1.00}$, the percentage of metal ions existi...

Arrange the following orbitals in decreasing order of energy.
A. $\mathrm{n}=3, \mathrm{l}=0, \mathrm{~m}=0$
B. $\mathrm{n}=4, \mathrm{l}=0, \mathrm{~m}=0$
C. $\mathrm{n}=3, \mathrm{l}=1, \mathrm{~m}=0$
D. $\mathrm{n}=3, \mathrm{l}=2, \math...

Match List I with List II

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...

Enthalpies of formation of $\mathrm{CCl}_{4}(\mathrm{~g}), \mathrm{H}_{2} \mathrm{O}(\mathrm{g}), \mathrm{CO}_{2}(\mathrm{~g})$ and $\mathrm{HCl}(\mathrm{g})$ are $-105,-242,-394$ and $-92 ~\mathrm{kJ}$ $\mathrm{mol}^{-1}$ respectively. The...

Let the plane $\mathrm{P}: 8 x+\alpha_{1} y+\alpha_{2} z+12=0$ be parallel to the line $\mathrm{L}: \frac{x+2}{2}=\frac{y-3}{3}=\frac{z+4}{5}$. If the

intercept of $\mathrm{P}$ on the $y$-axis is 1 , then the distance between $\mathrm{P}$ ...

The foot of perpendicular from the origin $\mathrm{O}$ to a plane $\mathrm{P}$ which meets the co-ordinate axes at the points $\mathrm{A}, \mathrm{B}, \mathrm{C}$ is $(2, \mathrm{a}, 4), \mathrm{a} \in \mathrm{N}$. If the volume of the tetr...

Let $P$ be the plane, passing through the point $(1,-1,-5)$ and perpendicular to the line joining the points $(4,1,-3)$ and $(2,4,3)$. Then the distance of $P$ from the point $(3,-2,2)$ is :

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

} } \right)\left( {\matrix{
2 & {10} & 8 \cr
9 & 3 & 8 \cr
8 & 4 & 8 \cr

} } \right) = \left( {\matrix{
0...

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 $\mathrm{A}$.
Then $(6 \mathrm{~A}+11)^{2}$ is equal to

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

If the constant term in the binomial expansion of $\left(\frac{x^{\frac{5}{2}}}{2}-\frac{4}{x^{l}}\right)^{9}$ is $-84$ and the coefficient of $x^{-3 l}$ is

$2^{\alpha} \beta$, where $\beta<0$ is an odd number, then $|\alpha l-\beta|$ is e...

The set of all values of $a^{2}$ for which the line $x+y=0$ bisects two distinct chords drawn from a point $\mathrm{P}\left(\frac{1+a}{2}, \frac{1-a}{2}\right)$ on the circle $2 x^{2}+2 y^{2}-(1+a) x-(1-a) y=0$, is equal to :

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

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

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

Let $y=y(x)$ be the solution of the differential equation
$\left(3 y^{2}-5 x^{2}\right) y \mathrm{~d} x+2 x\left(x^{2}-y^{2}\right) \mathrm{d} y=0$
such that $y(1)=1$. Then $\left|(y(2))^{3}-12 y(2)\right|$ is equal to :

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

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

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

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

holds. If $\alpha x^{2}+\beta x+\sin ^{-1}\left(x^{2}-6 x+10\right)+\cos ^{-1}\left(x^{2}-6 x+10\righ...

\(\lim\limits_{x \rightarrow \infty} \frac{(\sqrt{3 x+1}+\sqrt{3 x-1})^6+(\sqrt{3 x+1}-\sqrt{3 x-1})^6}{\left(x+\sqrt{x^2-1}\right)^6+\left(x-\sqrt{x^2-1}\right)^6} x^3\)

The number of values of $\mathrm{r} \in\{\mathrm{p}, \mathrm{q}, \sim \mathrm{p}, \sim \mathrm{q}\}$ for which $((\mathrm{p} \wedge \mathrm{q}) \Rightarrow(\mathrm{r} \vee \mathrm{q})) \wedge((\mathrm{p} \wedge \mathrm{r}) \Rightarrow \math...

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

$\operatorname{Adj}\left(2 \cdot \operatorname{Adj}\left(2 \mathrm{~A}^{-1}\right)\right) \cdot$ is $2^{84}$, then $\mathrm{n}$ is equal to :

Let $\mathrm{S}$ be the set of all $\mathrm{a} \in \mathrm{N}$ such that the area of the triangle formed by the tangent at the point $\mathrm{P}(\mathrm{b}$, c), b, c $\in \mathbb{N}$, on the parabola $y^{2}=2 \mathrm{a} x$ and the lines $x...