JEE Main 2025 (Online) 29th January Evening Shift

Which one of the following, with HBr will give a phenol?

In the Claisen-Schmidt reaction to prepare, dibenzalacetone from 5.3 g of benzaldehyde, a total of 3.51 g of product was obtained. The percentage yield in this reaction was _______ %.

Given below are two statements :
Statement (I): On nitration of m-xylene with $\mathrm{HNO}_3, \mathrm{H}_2 \mathrm{SO}_4$ followed by oxidation, 4-nitrobenzene-1,3-dicarboxylic acid is obtained as the major product.
Statement (II) : $-\mat...

Identify the essential amino acids from below:(A) Valine(B) Proline(C) Lysine(D) Threonine(E) TyrosineChoose the correct answer from the options given below:

Total number of non-bonded electrons present in NO2$-$ ion based on Lewis theory is ______.

Consider the equilibrium
\(\mathrm{CO}(\mathrm{g})+3 \mathrm{H}_2(\mathrm{~g}) \rightleftharpoons \mathrm{CH}_4(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{~g})\)
If the pressure applied over the system increases by two fold at constant ...

Drug $X$ becomes ineffective after $50 \%$ decomposition. The original concentration of drug in a bottle was $16 \mathrm{mg} / \mathrm{mL}$ which becomes $4 \mathrm{mg} / \mathrm{mL}$ in 12 months. The expiry time of the drug in months is _...

Which one of the following reaction sequences will give an azo dye?

Identify the homoleptic complexes with odd number of $d$ electrons in the central metal :
(A) $\left[\mathrm{FeO}_4\right]^{2-}$
(B) $\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3-}$
(C) $\left[\mathrm{Fe}(\mathrm{CN})_5 \mathrm{NO}\right]^{2-...

The calculated spin-only magnetic moments of $K_3[Fe(OH)_6]$ and $K_4[Fe(OH)_6]$ respectively are :

Consider the following low-spin complexes
$$ \mathrm{K}_3\left[\mathrm{Co}\left(\mathrm{NO}_2\right)_6\right], \mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right], \mathrm{K}_3\left[\mathrm{Fe}(\mathrm{CN})_6\right], \mathrm{Cu}_2\left[\mat...

Match List - I with List - II :

List - I (Applications)
List - II (Batteries/Cell)


(A) Transistors
(I) Anode - Zn/Hg; Cathode - HgO + C


(B) Hearing aids
(II) Hydrogen fuel cell


(C) Inverters
...

$\mathrm{O}_2$ gas will be evolved as a product of electrolysis of :
(A) an aqueous solution of $\mathrm{AgNO}_3$ using silver electrodes.
(B) an aqueous solution of $\mathrm{AgNO}_3$ using platinum electrodes.
(C) a dilute solution of $\ma...

Which among the following halides will generate the most stable carbocation in the nucleophilic substitution reaction?

Total number of sigma (σ) _______ and pi(π) ______ bonds respectively present in hex-1-en-4-yne are:

Isomeric hydrocarbons → negative Baeyer’s test(Molecular formula C9H12)The total number of isomers from above with four different non-aliphatic substitution sites is -

The type of oxide formed by the element among Li, Na, Be, Mg, B and Al that has the least atomic radius is :

First ionisation enthalpy values of first four group 15 elements are given below. Choose the correct value for the element that is a main component of apatite family :

Given below are two statements :
Statement (I): In partition chromatography, stationary phase is thin film of liquid present in the inert support.
Statement (II): In paper chromatography, the material of paper acts as a stationary phase.
In...

In the sulphur estimation, 0.20 g of a pure organic compound gave 0.40 g of barium sulphate. The percentage of sulphur in the compound is __________ $\times 10^{-1} \%$.
(Molar mass : $\mathrm{O}=16, \mathrm{~S}=32, \mathrm{Ba}=137$ in $\ma...

0.1 M solution of KI reacts with excess of $\mathrm{H}_2 \mathrm{SO}_4$ and $\mathrm{KIO}_3$ solutions. According to equation
\(5 \mathrm{I}^{-}+\mathrm{IO}_3^{-}+6 \mathrm{H}^{+} \rightarrow 3 \mathrm{I}_2+3 \mathrm{H}_2 \mathrm{O}\)
Ide...

Given below are two statements :
Statement (I): NaCl is added to the ice at 0°C, present in the ice cream box to prevent the melting of ice cream.
Statement (II): On addition of NaCl to ice at 0°C, there is a depression in freezing point.
I...

For hydrogen like species, which of the following graphs provides the most appropriate representation of E vs Z plot for a constant n?
[E : Energy of the stationary state, Z : atomic number, n = principal quantum number]

Given below are two statements :
Statement (I): It is impossible to specify simultaneously with arbitrary precision, both the linear momentum and the position of a particle.
Statement (II) : If the uncertainty in the measurement of position...

If $\quad C$ (diamond $) \rightarrow C$ (graphite) $+X \mathrm{~kJ} \mathrm{~mol}^{-1}$
C (diamond) $+\mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})+\mathrm{Y} \mathrm{kJ} \mathrm{mol}{ }^{-1}$
C (graphite) $+\mathrm{O}_2(...

Let a straight line $L$ pass through the point $P(2, -1, 3)$ and be perpendicular to the lines $ \frac{x - 1}{2} = \frac{y + 1}{1} = \frac{z - 3}{-2} $ and $ \frac{x - 3}{1} = \frac{y - 2}{3} = \frac{z + 2}{4} $. If the line $L$ intersects ...

Let P be the foot of the perpendicular from the point $(1,2,2)$ on the line $\mathrm{L}: \frac{x-1}{1}=\frac{y+1}{-1}=\frac{z-2}{2}$. Let the line $\vec{r}=(-\hat{i}+\hat{j}-2 \hat{k})+\lambda(\hat{i}-\hat{j}+\hat{k}), \lambda \in \mathbf{R...

Let the area enclosed between the curves $|y| = 1 - x^2$ and $x^2 + y^2 = 1$ be $\alpha$. If $9\alpha = \beta \pi + \gamma; \beta, \gamma$ are integers, then the value of $|\beta - \gamma|$ equals:

The remainder, when $7^{103}$ is divided by 23, is equal to:

Let a circle C pass through the points (4, 2) and (0, 2), and its centre lie on 3x + 2y + 2 = 0. Then the length of the chord, of the circle C, whose mid-point is (1, 2), is:

Let integers $\mathrm{a}, \mathrm{b} \in[-3,3]$ be such that $\mathrm{a}+\mathrm{b} \neq 0$. Then the number of all possible ordered pairs (a, b), for which $\left|\frac{z-\mathrm{a}}{z+\mathrm{b}}\right|=1$ and $\left|\begin{array}{ccc}z+1...

Let $f(x)=\int\limits_0^x \mathrm{t}\left(\mathrm{t}^2-9 \mathrm{t}+20\right) \mathrm{dt}, 1 \leq x \leq 5$. If the range of $f$ is $[\alpha, \beta]$, then $4(\alpha+\beta)$ equals :

If $ 24 \int\limits_0^{\frac{\pi}{4}} \bigg[\sin \left| 4x - \frac{\pi}{12} \right| + [2 \sin x] \bigg] dx = 2\pi + \alpha $, where $[\cdot]$ denotes the greatest integer function, then $\alpha$ is equal to ________.

If $\lim\limits _{t \rightarrow 0}\left(\int\limits_0^1(3 x+5)^t d x\right)^{\frac{1}{t}}=\frac{\alpha}{5 e}\left(\frac{8}{5}\right)^{\frac{2}{3}}$, then $\alpha$ is equal to ________________.

If for the solution curve $y=f(x)$ of the differential equation $\frac{d y}{d x}+(\tan x) y=\frac{2+\sec x}{(1+2 \sec x)^2}$, $x \in\left(\frac{-\pi}{2}, \frac{\pi}{2}\right), f\left(\frac{\pi}{3}\right)=\frac{\sqrt{3}}{10}$, then $f\left(\...

If $\alpha x+\beta y=109$ is the equation of the chord of the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$, whose mid point is $\left(\frac{5}{2}, \frac{1}{2}\right)$. then $\alpha+\beta$ is equal to :

If the domain of the function $ \log_5(18x - x^2 - 77) $ is $ (\alpha, \beta) $ and the domain of the function $ \log_{(x-1)} \left( \frac{2x^2 + 3x - 2}{x^2 - 3x - 4} \right) $ is $(\gamma, \delta)$, then $ \alpha^2 + \beta^2 + \gamma^2 $ ...

Let the function $f(x)=\left(x^2-1\right)\left|x^2-a x+2\right|+\cos |x|$ be not differentiable at the two points $x=\alpha=2$ and $x=\beta$. Then the distance of the point $(\alpha, \beta)$ from the line $12 x+5 y+10=0$ is equal to :

Let $A = [a_{ij}]$ be a $2 \times 2$ matrix such that $a_{ij} \in \{0, 1\}$ for all $i$ and $j$. Let the random variable $X$ denote the possible values of the determinant of the matrix $A$. Then, the variance of $X$ is:

Let $ \alpha, \beta \ (\alpha \neq \beta) $ be the values of $ m $, for which the equations $ x+y+z=1 $, $ x+2y+4z=m $ and $ x+4y+10z=m^2 $ have infinitely many solutions. Then the value of $ \sum\limits_{n=1}^{10} (n^{\alpha}+n^{\beta}) $ ...

Let $\mathrm{A}=\left[a_{i j}\right]$ be a matrix of order $3 \times 3$, with $a_{i j}=(\sqrt{2})^{i+j}$. If the sum of all the elements in the third row of $A^2$ is $\alpha+\beta \sqrt{2}, \alpha, \beta \in \mathbf{Z}$, then $\alpha+\beta$...

Let $y^2=12 x$ be the parabola and $S$ be its focus. Let $P Q$ be a focal chord of the parabola such that $(S P)(S Q)=\frac{147}{4}$. Let $C$ be the circle described taking $P Q$ as a diameter. If the equation of a circle $C$ is $64 x^2+64 ...

If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then the word at 440th position in this arrangement is :

Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains n white balls and 3 black balls. One ball is drawn randomly from Bag 1 and transferred to Bag 2. A ball is then drawn randomly from Bag 2. If the probability, that the ball ...

If the set of all $a \in \mathbf{R}$, for which the equation $2 x^2+(a-5) x+15=3 a$ has no real root, is the interval ( $\alpha, \beta$ ), and $X=|x \in Z ; \alpha < x < \beta|$, then $\sum\limits_{x \in X} x^2$ is equal to:

Let $a_1, a_2, \ldots, a_{2024}$ be an Arithmetic Progression such that $a_1+\left(a_5+a_{10}+a_{15}+\ldots+a_{2020}\right)+a_{2024}=2233$. Then $a_1+a_2+a_3+\ldots+a_{2024}$ is equal to _________.

Let $\mathrm{S}=\mathbf{N} \cup\{0\}$. Define a relation R from S to $\mathbf{R}$ by :
\(\mathrm{R}=\left\{(x, y): \log _{\mathrm{e}} y=x \log _{\mathrm{e}}\left(\frac{2}{5}\right), x \in \mathrm{~S}, y \in \mathbf{R}\right\} .\)
Then, th...

Let the line x + y = 1 meet the axes of x and y at A and B, respectively. A right angled triangle AMN is inscribed in the triangle OAB, where O is the origin and the points M and N lie on the lines OB and AB, respectively. If the area of th...

If $\sin x + \sin^2 x = 1$, $x \in \left(0, \frac{\pi}{2}\right)$, then $(\cos^{12} x + \tan^{12} x) + 3(\cos^{10} x + \tan^{10} x + \cos^8 x + \tan^8 x) + (\cos^6 x + \tan^6 x)$ is equal to:

Let $ \hat{a} $ be a unit vector perpendicular to the vectors $ \vec{b} = \hat{i} - 2\hat{j} + 3\hat{k} $ and $ \vec{c} = 2\hat{i} + 3\hat{j} - \hat{k} $, and $ \hat{a} $ makes an angle of $ \cos^{-1} \left( -\frac{1}{3} \right) $ with the ...