JEE Main 2025 (Online) 23rd January Evening Shift

Given below are two statements :
Statement (I) : The boiling points of alcohols and phenols increase with increase in the number of C -atoms.
Statement (II) : The boiling points of alcohols and phenols are higher in comparison to other clas...

A compound ' $\mathrm{X}^{\prime}$ absorbs 2 moles of hydrogen and ' X ' upon oxidation with $\mathrm{KMnO}_4 \mid \mathrm{H}^{+}$ gives

The total number of $\sigma$ bonds present in the compound ' $X^{\prime}$ ' is __________.

Given below are two statements:
Consider the following reaction

Statement (I): In the case of formaldehyde is about 2280, due to small substituents, hydration is faster.
Statement (II) : In the case of trichloro acetaldehyde is about 200...

The $\alpha$-Helix and $\beta$ - Pleated sheet structures of protein are associated with its :

Consider the reaction
\(\mathrm{X}_2 \mathrm{Y}(\mathrm{~g}) \rightleftharpoons \mathrm{X}_2(\mathrm{~g})+\frac{1}{2} \mathrm{Y}_2(\mathrm{~g})\)
The equation representing correct relationship between the degree of dissociation (x) of $\mat...

Which of the following graphs most appropriately represents a zero order reaction?

Consider the following sequence of reactions.

Total number of $\mathrm{sp}^3$ hybridised carbon atoms in the major product C formed is _________.

Identify the coordination complexes in which the central metal ion has $\mathrm{d}^4$ configuration.
(A) $\left[\mathrm{FeO}_4\right]^{2-}$
(B) $\quad\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-}$
(C) $\left[\mathrm{Fe}(\mathrm{CN})_6\right]...

Match List - I with List - II

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:10px 5px;word-break:norma...

Consider the following reactions
$$\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7 \xrightarrow[-\mathrm{H}_2 \mathrm{O}]{\mathrm{KOH}}[\mathrm{~A}] \xrightarrow[-\mathrm{H}_2 \mathrm{O}]{\mathrm{H}_2 \mathrm{SO}_4}[\mathrm{~B}]+\mathrm{K}_2 \mathr...

Standard electrode potentials for a few half cells are mentioned below :
$$\begin{aligned}
& \mathrm{E}_{\mathrm{Cu}^{2+} / \mathrm{Cu}}^{\circ}=0.34 \mathrm{~V}, \mathrm{E}_{\mathrm{Zn}^{2+} / \mathrm{Zn}}^{\circ}=-0.76 \mathrm{~V} \\
& \m...

Identify the products [A] and [B], respectively in the following reaction:

The ascending order of relative rate of solvolysis of following compounds is :

Match List - I with List - II

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:10px 5px;word-break:norma...

pH of water is 7 at $25^{\circ} \mathrm{C}$. If water is heated to $80^{\circ} \mathrm{C}$., it's pH will :

Given below are the atomic numbers of some group 14 elements. The atomic number of the element with lowest melting point is :

Identify A, B and C in the given below reaction sequence

When a non-volatile solute is added to the solvent, the vapour pressure of the solvent decreases by 10 mm of Hg . The mole fraction of the solute in the solution is 0.2 . What would be the mole fraction of the solvent if decrease in vapour ...

Consider a binary solution of two volatile liquid components 1 and $2 . x_1$ and $y_1$ are the mole fractions of component 1 in liquid and vapour phase, respectively. The slope and intercept of the linear plot of $\frac{1}{x_1}$ vs $\frac{1...

0.01 mole of an organic compound $(X)$ containing $10 \%$ hydrogen, on complete combustion produced $0.9 \mathrm{~g} \mathrm{H}_2 \mathrm{O}$. Molar mass of $(\mathrm{X})$ is _________ $\mathrm{g} \mathrm{~mol}^{-1}$.

When 81.0 g of aluminium is allowed to react with 128.0 g of oxygen gas, the mass of aluminium oxide produced in grams is ________ . (Nearest integer)
Given :
Molar mass of Al is $27.0 \mathrm{~g} \mathrm{~mol}^{-1}$
Molar mass of O is $16....

Given below are two statements :
Statement (I) : For a given shell, the total number of allowed orbitals is given by $n^2$.
Statement (II) : For any subshell, the spatial orientation of the orbitals is given by $-l$ to $+l$ values including...

Given below are two statements about X-ray spectra of elements :
Statement (I) : A plot of $\sqrt{v}$ ( $v=$ frequency of X-rays emitted) vs atomic mass is a straight line.
Statement (II) : A plot of $v(\nu=$ frequency of $X$-rays emitted) ...

The effect of temperature on spontaneity of reactions are represented as :

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
over...

The bond dissociation enthalpy of $\mathrm{X}_2 \Delta \mathrm{H}_{\text {bond }}^{\circ}$ calculated from the given data is ___________ $\mathrm{kJ} \mathrm{mol}^{-1}$. (Nearest integer)
$$\begin{aligned}
& \mathrm{M}^{+} \mathrm{X}^{-}(\m...

If the square of the shortest distance between the lines $\frac{x-2}{1}=\frac{y-1}{2}=\frac{z+3}{-3}$ and $\frac{x+1}{2}=\frac{y+3}{4}=\frac{z+5}{-5}$ is $\frac{m}{n}$, where $m$, $n$ are coprime numbers, then $m+n$ is equal to :

The distance of the line $\frac{x-2}{2}=\frac{y-6}{3}=\frac{z-3}{4}$ from the point $(1,4,0)$ along the line $\frac{x}{1}=\frac{y-2}{2}=\frac{z+3}{3}$ is :

A spherical chocolate ball has a layer of ice-cream of uniform thickness around it. When the thickness of the ice-cream layer is 1 cm , the ice-cream melts at the rate of $81 \mathrm{~cm}^3 / \mathrm{min}$ and the thickness of the ice-cream...

If the area of the region $\left\{(x, y):-1 \leq x \leq 1,0 \leq y \leq \mathrm{a}+\mathrm{e}^{|x|}-\mathrm{e}^{-x}, \mathrm{a}>0\right\}$ is $\frac{\mathrm{e}^2+8 \mathrm{e}+1}{\mathrm{e}}$, then the value of $a$ is :

If in the expansion of $(1+x)^{\mathrm{p}}(1-x)^{\mathrm{q}}$, the coefficients of $x$ and $x^2$ are 1 and -2 , respectively, then $\mathrm{p}^2+\mathrm{q}^2$ is equal to :

The number of complex numbers $z$, satisfying $|z|=1$ and $\left|\frac{z}{\bar{z}}+\frac{\bar{z}}{z}\right|=1$, is :

Let $\alpha, \beta$ be the roots of the equation $x^2-\mathrm{ax}-\mathrm{b}=0$ with $\operatorname{Im}(\alpha)<\operatorname{Im}(\beta)$. Let $\mathrm{P}_{\mathrm{n}}=\alpha^{\mathrm{n}}-\beta^{\mathrm{n}}$. If $\mathrm{P}_3=-5 \sqrt{7} i,...

If $\mathrm{I}=\int_0^{\frac{\pi}{2}} \frac{\sin ^{\frac{3}{2}} x}{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x} \mathrm{~d} x$, then $\int_0^{2I} \frac{x \sin x \cos x}{\sin ^4 x+\cos ^4 x} \mathrm{~d} x$ equals :

Let $x=x(y)$ be the solution of the differential equation $y=\left(x-y \frac{\mathrm{~d} x}{\mathrm{~d} y}\right) \sin \left(\frac{x}{y}\right), y>0$ and $x(1)=\frac{\pi}{2}$. Then $\cos (x(2))$ is equal to :

The length of the chord of the ellipse $\frac{x^2}{4}+\frac{y^2}{2}=1$, whose mid-point is $\left(1, \frac{1}{2}\right)$, is :

Let $\int x^3 \sin x \mathrm{~d} x=g(x)+C$, where $C$ is the constant of integration. If $8\left(g\left(\frac{\pi}{2}\right)+g^{\prime}\left(\frac{\pi}{2}\right)\right)=\alpha \pi^3+\beta \pi^2+\gamma, \alpha, \beta, \gamma \in Z$, then $\a...

$\lim \limits_{x \rightarrow \infty} \frac{\left(2 x^2-3 x+5\right)(3 x-1)^{\frac{x}{2}}}{\left(3 x^2+5 x+4\right) \sqrt{(3 x+2)^x}}$ is equal to :

The system of equations
$$\begin{aligned} & x+y+z=6, \\ & x+2 y+5 z=9, \\ & x+5 y+\lambda z=\mu, \end{aligned}$$
has no solution if

Let $A=\left[a_{i j}\right]$ be a $3 \times 3$ matrix such that $A\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 1\end{array}\right], A\left[\begin{array}{l}4 \\ 1 \\ 3\end{array}\right]=\left[\begin{arr...

Let the shortest distance from $(a, 0), a>0$, to the parabola $y^2=4 x$ be 4 . Then the equation of the circle passing through the point $(a, 0)$ and the focus of the parabola, and having its centre on the axis of the parabola is :

The focus of the parabola $y^2=4 x+16$ is the centre of the circle $C$ of radius 5 . If the values of $\lambda$, for which C passes through the point of intersection of the lines $3 x-y=0$ and $x+\lambda y=4$, are $\lambda_1$ and $\lambda_2...

The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together, is ________.

A board has 16 squares as shown in the figure :

Out of these 16 squares, two squares are chosen at random. The probability that they have no side in common is :

The roots of the quadratic equation $3 x^2-p x+q=0$ are $10^{\text {th }}$ and $11^{\text {th }}$ terms of an arithmetic progression with common difference $\frac{3}{2}$. If the sum of the first 11 terms of this arithmetic progression is 88...

Let $\mathrm{X}=\mathbf{R} \times \mathbf{R}$. Define a relation R on X as :
\(\left(a_1, b_1\right) R\left(a_2, b_2\right) \Leftrightarrow b_1=b_2\)
Statement I: $\quad \mathrm{R}$ is an equivalence relation.
Statement II : For some $(\mat...

Let $\mathrm{A}=\{(x, y) \in \mathbf{R} \times \mathbf{R}:|x+y| \geqslant 3\}$ and $\mathrm{B}=\{(x, y) \in \mathbf{R} \times \mathbf{R}:|x|+|y| \leq 3\}$.
If $\mathrm{C}=\{(x, y) \in \mathrm{A} \cap \mathrm{B}: x=0$ or $y=0\}$, then $\sum_...

The variance of the numbers $8,21,34,47, \ldots, 320$ is _______.

A rod of length eight units moves such that its ends $A$ and $B$ always lie on the lines $x-y+2=0$ and $y+2=0$, respectively. If the locus of the point $P$, that divides the rod $A B$ internally in the ratio $2: 1$ is $9\left(x^2+\alpha y^2...

Let the range of the function $f(x)=6+16 \cos x \cdot \cos \left(\frac{\pi}{3}-x\right) \cdot \cos \left(\frac{\pi}{3}+x\right) \cdot \sin 3 x \cdot \cos 6 x, x \in \mathbf{R}$ be $[\alpha, \beta]$. Then the distance of the point $(\alpha, ...

Let the point A divide the line segment joining the points $\mathrm{P}(-1,-1,2)$ and $\mathrm{Q}(5,5,10)$ internally in the ratio $r: 1(r>0)$. If O is the origin and $(\overrightarrow{\mathrm{OQ}} \cdot \overrightarrow{\mathrm{OA}})-\frac{1...