JEE Main 2025 (Online) 28th January Evening Shift

The total number of compounds from below when treated with hot KMnO4, giving benzoic acid is:

Given below are two statements:Statement I: and are isomeric compounds.Statement II: and are functional group isomers.In the light of the above statements, choose the correct answer from the options given below:

Match List-I with List-II.

List - I (Saccharides)
List - II (Glycosidic-linkages found)


(A) Sucrose
(I) α 1 $-$ 4


(B) Maltose
(II) α 1 $-$ 4 and α 1 $-$ 6


(C) Lactose
(III) α 1 $-$ β 2
...

Identify correct conversion during acidic hydrolysis from the following :
(A) starch gives galactose.
(B) cane sugar gives equal amount of glucose and fructose.
(C) milk sugar gives glucose and galactose.
(D) amylopectin gives glucose and f...

Consider an elementary reaction
\(\mathrm{A}(\mathrm{~g})+\mathrm{B}(\mathrm{~g}) \rightarrow \mathrm{C}(\mathrm{~g})+\mathrm{D}(\mathrm{~g})\)
If the volume of reaction mixture is suddenly reduced to $\frac{1}{3}$ of its initial volume, ...

For bacterial growth in a cell culture, growth law is very similar to the law of radioactive decay. Which of the following graphs is most suitable to represent bacterial colony growth ? Where N - Number of Bacteria at any time, $\mathrm{N}_...

Identify correct statements :
(A) Primary amines do not give diazonium salts when treated with $\mathrm{NaNO}_2$ in acidic condition.
(B) Aliphatic and aromatic primary amines on heating with $\mathrm{CHCl}_3$ and ethanolic KOH form carbyla...

Match List - I with List - II.

List - I (Complex)
List - II (Hybridisation of central metal ion)


(A) [CoF6]3-
(I) d2sp3


(B) [NiCl4]2-
(II) sp3


(C) [Co(NH3)6]3+
(III) sp3d2


(D) ...

The spin only magnetic moment ( $\mu$ ) value (B.M.) of the compound with strongest oxidising power among $\mathrm{Mn}_2 \mathrm{O}_3, \mathrm{TiO}$ and VO is ____________ B.M. (Nearest integer).

Total number of molecules/species from following which will be paramagnetic is __________. $\mathrm{O}_2, \mathrm{O}_2^{+}, \mathrm{O}_2^{-}, \mathrm{NO}, \mathrm{NO}_2, \mathrm{CO}, \mathrm{K}_2\left[\mathrm{NiCl}_4\right],\left[\mathrm{Co...

The amphoteric oxide among $\mathrm{V}_2 \mathrm{O}_3, \mathrm{~V}_2 \mathrm{O}_4$ and $\mathrm{V}_2 \mathrm{O}_5$, upon reaction with alkali leads to formation of an oxide anion. The oxidation state of V in the oxide anion is :

Electrolysis of 600 mL aqueous solution of NaCl for 5 min changes the pH of the solution to 12 . The current in Amperes used for the given electrolysis is ___________ . (Nearest integer).

The major product of the following reaction is:

The product B formed in the following reaction sequence is:

Identify product [A], [B] and [C] in the following reaction sequence.
$\mathrm{CH}_3-\mathrm{C} \equiv \mathrm{CH} \xrightarrow[\mathrm{H}_2]{\mathrm{Pd} / \mathrm{C}}[\mathrm{A}] \xrightarrow[\text { (ii) } \mathrm{Zn}, \mathrm{H}_2 \mathr...

Arrange the following in increasing order of solubility product :
$\mathrm{Ca}(\mathrm{OH})_2, \mathrm{AgBr}, \mathrm{PbS}, \mathrm{HgS}$

The purification method based on the following physical transformation is :$\underset{(X)}{\text { Solid }} \xrightarrow[]{\text { Heat }} \underset{(X)}{\text { Vapour }} \xrightarrow{\text { Cool }} \underset{(X)}{\text { Solid }}$

A group 15 element forms $\mathrm{d} \pi-\mathrm{d} \pi$ bond with transition metals. It also forms hydride, which is a strongest base among the hydrides of other group members that form $d \pi-d \pi$ bond. The atomic number of the element ...

Given below are two statements :Statement I : According to the Law of Octaves, the elements were arranged in the increasing order of their atomic number.Statement II : Meyer observed a periodically repeated pattern upon plotting physical pr...

Identify the inorganic sulphides that are yellow in colour :(A) $(NH_4)_2S$(B) $PbS$(C) $CuS$(D) $As_2S_3$(E) $As_2S_5$Choose the correct answer from the options given below :

Assume a living cell with 0.9% (w/w) of glucose solution (aqueous). This cell is immersed in another solution having equal mole fraction of glucose and water. (Consider the data upto first decimal place only) The cell will :

Concentrated nitric acid is labelled as $75 \%$ by mass. The volume in mL of the solution which contains 30 g of nitric acid is ______________.
Given : Density of nitric acid solution is $1.25 \mathrm{~g} / \mathrm{mL}$.

Which of the following is/are not correct with respect to energy of atomic orbitals of hydrogen atom?(A) 1s < 2p < 3d < 4s(B) 1s < 2s = 2p < 3s = 3p(C) 1s < 2s < 2p < 3s < 3p(D) 1s < 2s < 4s < 3dChoose the correct answer from the options gi...

An ideal gas undergoes a cyclic transformation starting from the point A and coming back to the same point by tracing the path A→B→C→D→A as shown in the three cases above.Choose the correct option regarding ΔU :

Consider the following data :
Heat of formation of $\mathrm{CO}_2(\mathrm{g})=-393.5 \mathrm{~kJ} \mathrm{~mol}{ }^{-1}$
Heat of formation of $\mathrm{H}_2 \mathrm{O}(\mathrm{l})=-286.0 \mathrm{~kJ} \mathrm{~mol}{ }^{-1}$
Heat of combustion...

The square of the distance of the point $ \left( \frac{15}{7}, \frac{32}{7}, 7 \right) $ from the line $ \frac{x + 1}{3} = \frac{y + 3}{5} = \frac{z + 5}{7} $ in the direction of the vector $ \hat{i} + 4\hat{j} + 7\hat{k} $ is:

The area of the region bounded by the curves $x(1+y^2)=1$ and $y^2=2x$ is:

Let the coefficients of three consecutive terms $T_r$, $T_{r+1}$ and $T_{r+2}$ in the binomial expansion of $(a + b)^{12}$ be in a G.P. and let $p$ be the number of all possible values of $r$. Let $q$ be the sum of all rational terms in the...

If $\alpha + i\beta$ and $\gamma + i\delta$ are the roots of $x^2 - (3 - 2i)x - (2i - 2) = 0$, $i = \sqrt{-1}$, then $\alpha \gamma + \beta \delta$ is equal to:

Let $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$ be a twice differentiable function such that $f(2)=1$. If $\mathrm{F}(\mathrm{x})=\mathrm{x} f(\mathrm{x})$ for all $\mathrm{x} \in \mathrm{R}$, $\int\limits_0^2 x F^{\prime}(x) d x=6$ and...

Let $f$ be a real valued continuous function defined on the positive real axis such that $g(x)=\int\limits_0^x t f(t) d t$. If $g\left(x^3\right)=x^6+x^7$, then value of $\sum\limits_{r=1}^{15} f\left(r^3\right)$ is :

If $y=y(x)$ is the solution of the differential equation,
$\sqrt{4-x^2} \frac{\mathrm{~d} y}{\mathrm{~d} x}=\left(\left(\sin ^{-1}\left(\frac{x}{2}\right)\right)^2-y\right) \sin ^{-1}\left(\frac{x}{2}\right),-2 \leq x \leq 2, y(2)=\frac{\pi...

If the midpoint of a chord of the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ is $(\sqrt{2}, 4 / 3)$, and the length of the chord is $\frac{2 \sqrt{\alpha}}{3}$, then $\alpha$ is :

Let $f:[0,3] \rightarrow$ A be defined by $f(x)=2 x^3-15 x^2+36 x+7$ and $g:[0, \infty) \rightarrow B$ be defined by $g(x)=\frac{x^{2025}}{x^{2025}+1}$, If both the functions are onto and $S=\{ x \in Z ; x \in A$ or $x \in B \}$, then $n(S)...

If $f(x)=\int \frac{1}{x^{1 / 4}\left(1+x^{1 / 4}\right)} \mathrm{d} x, f(0)=-6$, then $f(1)$ is equal to :

Let [x] denote the greatest integer less than or equal to x. Then the domain of $ f(x) = \sec^{-1}(2[x] + 1) $ is:

Let $f(x)=\lim \limits_{n \rightarrow \infty} \sum\limits_{r=0}^n\left(\frac{\tan \left(x / 2^{r+1}\right)+\tan ^3\left(x / 2^{r+1}\right)}{1-\tan ^2\left(x / 2^{r+1}\right)}\right)$ Then $\lim\limits_{x \rightarrow 0} \frac{e^x-e^{f(x)}}{(...

Let $\mathrm{A}=\left[\begin{array}{cc}\frac{1}{\sqrt{2}} & -2 \\ 0 & 1\end{array}\right]$ and $\mathrm{P}=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right], \theta>0$. If $\mathrm{B}=\mathrm{P...

Let $A$ and $B$ be the two points of intersection of the line $y+5=0$ and the mirror image of the parabola $y^2=4 x$ with respect to the line $x+y+4=0$. If $d$ denotes the distance between $A$ and $B$, and a denotes the area of $\triangle S...

The number of natural numbers, between 212 and 999, such that the sum of their digits is 15, is _______.

Bag $B_1$ contains 6 white and 4 blue balls, Bag $B_2$ contains 4 white and 6 blue balls, and Bag $B_3$ contains 5 white and 5 blue balls. One of the bags is selected at random and a ball is drawn from it. If the ball is white, then the pro...

Let S be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set S, one word is selected at random. The probability that the selected word will NOT have vowels in alphabetical order is:

Let $f: \mathbf{R}-\{0\} \rightarrow(-\infty, 1)$ be a polynomial of degree 2 , satisfying $f(x) f\left(\frac{1}{x}\right)=f(x)+f\left(\frac{1}{x}\right)$. If $f(\mathrm{~K})=-2 \mathrm{~K}$, then the sum of squares of all possible values o...

For positive integers $n$, if $4 a_n=\left(n^2+5 n+6\right)$ and $S_n=\sum\limits_{k=1}^n\left(\frac{1}{a_k}\right)$, then the value of $507 S_{2025}$ is :

The interior angles of a polygon with n sides, are in an A.P. with common difference 6°. If the largest interior angle of the polygon is 219°, then n is equal to _______.

Two equal sides of an isosceles triangle are along $ -x + 2y = 4 $ and $ x + y = 4 $. If $ m $ is the slope of its third side, then the sum, of all possible distinct values of $ m $, is:

If A and B are the points of intersection of the circle $x^2 + y^2 - 8x = 0$ and the hyperbola $\frac{x^2}{9} - \frac{y^2}{4} = 1$ and a point P moves on the line $2x - 3y + 4 = 0$, then the centroid of $\Delta PAB$ lies on the line :

If $\sum\limits_{r=1}^{13}\left\{\frac{1}{\sin \left(\frac{\pi}{4}+(r-1) \frac{\pi}{6}\right) \sin \left(\frac{\pi}{4}+\frac{r \pi}{6}\right)}\right\}=a \sqrt{3}+b, a, b \in Z$, then $a^2+b^2$ is equal to :

If the components of $\vec{a}=\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k}$ along and perpendicular to $\vec{b}=3 \hat{i}+\hat{j}-\hat{k}$ respectively, are $\frac{16}{11}(3 \hat{i}+\hat{j}-\hat{k})$ and $\frac{1}{11}(-4 \hat{i}-5 \hat{j}-17...

Let $A, B, C$ be three points in xy-plane, whose position vector are given by $\sqrt{3} \hat{i}+\hat{j}, \hat{i}+\sqrt{3} \hat{j}$ and $a \hat{i}+(1-a) \hat{j}$ respectively with respect to the origin O . If the distance of the point C from...