JEE Main 2025 (Online) 24th January Evening Shift

Match List - I with List - II.

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Identify correct statement/s :
(A) $-\mathrm{OCH}_3$ and $-\mathrm{NHCOCH}_3$ are activating group.
(B) $\quad-\mathrm{CN}$ and -OH are meta directing group.
(C) -CN and $-\mathrm{SO}_3 \mathrm{H}$ are meta directing group.
(D) Activating g...

The hydrocarbon $(\mathrm{X})$ with molar mass $80 \mathrm{~g} \mathrm{~mol}^{-1}$ and $90 \%$ carbon has _______ degree of unsaturation.

The possible number of stereoisomers for 5-phenylpent-4-en-2-ol is ________.

In the given structure, number of sp and $\mathrm{sp}^2$ hybridized carbon atoms present respectively are :

Match List - I with List - II.

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Given below are two statements :
Statement (I) : Experimentally determined oxygen-oxygen bond lengths in the $\mathrm{O}_3$ are found to be same and the bond length is greater than that of a $\mathrm{O}=\mathrm{O}$ (double bond) but less th...

For the reaction,
\(\mathrm{H}_2(\mathrm{~g})+\mathrm{I}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{HI}(\mathrm{~g})\)
Attainment of equilibrium is predicted correctly by :

Consider a complex reaction taking place in three steps with rate constants $\mathrm{k}_1, \mathrm{k}_2$ and $\mathrm{k}_3$ respectively. The overall rate constant $k$ is given by the expression $k=\sqrt{\frac{k_1 k_3}{k_2}}$. If the activa...

Given below are two statements :
Statement (I) : is valid for first order reaction.
Statement (II) : is valid for first order reaction.
In the light of the above statements, choose the correct answer from the options given below :

For reaction

The correct order of set of reagents for the above conversion is :

When Ethane-1,2-diamine is added progressively to an aqueous solution of Nickel (II) chloride, the sequence of colour change observed will be:

The conditions and consequence that favours the $t_{2 \mathrm{~g}}{ }^3 \mathrm{e}_{\mathrm{g}}{ }^1$ configuration in a metal complex are :

Match List - I with List - II.

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Based on the data given below :
$$\begin{array}{ll}
\mathrm{E}_{\mathrm{Cr}_2 \mathrm{O}_7^{2-} / \mathrm{Cr}^{3+}}^{\circ}=1.33 \mathrm{~V} & \mathrm{E}_{\mathrm{Cl}_2 / \mathrm{Cl}^{(-)}}^{\circ}=1.36 \mathrm{~V} \\
\mathrm{E}_{\mathrm{Mn...

The structure of the major product formed in the following reaction is :

The observed and normal molar masses of compound $\mathrm{MX}_2$ are 65.6 and 164 respectively. The percent degree of ionisation of $\mathrm{MX}_2$ is __________%. (Nearest integer)

Given below are two statements :
Statement (I) : The first ionization energy of Pb is greater than that of Sn .
Statement (II) : The first ionization energy of Ge is greater than that of Si .
In the light of the above statements, choose the...

The successive 5 ionisation energies of an element are $800,2427,3658,25024$ and $32824 \mathrm{~kJ} / \mathrm{mol}$, respectively. By using the above values predict the group in which the above element is present :

In Carius method of estimation of halogen, 0.25 g of an organic compound gave 0.15 g of silver bromide ( AgBr ). The percentage of Bromine in the organic compound is ________ $\times 10^{-1} \%$ (Nearest integer).
(Given : Molar mass of Ag ...

$$
\begin{aligned}
&\text { Find the compound ' } \mathrm{A} \text { ' from the following reaction sequences. }\\
&\mathrm{A} \xrightarrow{\text { aqua-regia }} \mathrm{B} \xrightarrow[\text { (2) } \mathrm{AcOH}]{\text { (1) } \mathrm{KNO}...

The elemental composition of a compound is $54.2 \% \mathrm{C}, 9.2 \% \mathrm{H}$ and $36.6 \% \mathrm{O}$.
If the molar mass of the compound is $132 \mathrm{~g} \mathrm{~mol}^{-1}$, the molecular formula of the compound is :
[Given : The ...

For hydrogen atom, the orbital/s with lowest energy is/are :
(A) $\mathrm{4 s}$
(B) $3 \mathrm{p}_x$
(C) $3 \mathrm{~d}_{x^2-y^2}$
(D) $3 \mathrm{~d}_{z^2}$
(E) $4 \mathrm{p}_z$
Choose the correct answer from the options given below :

Which of the following mixing of 1 M base and 1 M acid leads to the largest increase in temperature?

$$\begin{aligned}
& \mathrm{S}(\mathrm{~g})+\frac{3}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{SO}_3(\mathrm{~g})+2 x \mathrm{kcal} \\
& \mathrm{SO}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{SO}_3(\math...

Let P be the image of the point $\mathrm{Q}(7,-2,5)$ in the line $\mathrm{L}: \frac{x-1}{2}=\frac{y+1}{3}=\frac{z}{4}$ and $\mathrm{R}(5, \mathrm{p}, \mathrm{q})$ be a point on $L$. Then the square of the area of $\triangle P Q R$ is ______...

Let $(2,3)$ be the largest open interval in which the function $f(x)=2 \log _{\mathrm{e}}(x-2)-x^2+a x+1$ is strictly increasing and (b, c) be the largest open interval, in which the function $\mathrm{g}(x)=(x-1)^3(x+2-\mathrm{a})^2$ is str...

The area of the region enclosed by the curves $y=\mathrm{e}^x, y=\left|\mathrm{e}^x-1\right|$ and $y$-axis is :

Suppose $A$ and $B$ are the coefficients of $30^{\text {th }}$ and $12^{\text {th }}$ terms respectively in the binomial expansion of $(1+x)^{2 \mathrm{n}-1}$. If $2 \mathrm{~A}=5 \mathrm{~B}$, then n is equal to:

Let $y=y(x)$ be the solution of the differential equation $2 \cos x \frac{\mathrm{~d} y}{\mathrm{~d} x}=\sin 2 x-4 y \sin x, x \in\left(0, \frac{\pi}{2}\right)$. If $y\left(\frac{\pi}{3}\right)=0$, then $y^{\prime}\left(\frac{\pi}{4}\right)...

Let $f:(0, \infty) \rightarrow \mathbf{R}$ be a function which is differentiable at all points of its domain and satisfies the condition $x^2 f^{\prime}(x)=2 x f(x)+3$, with $f(1)=4$. Then $2 f(2)$ is equal to :

The equation of the chord, of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$, whose mid-point is $(3,1)$ is :

The function $f:(-\infty, \infty) \rightarrow(-\infty, 1)$, defined by $f(x)=\frac{2^x-2^{-x}}{2^x+2^{-x}}$ is :

Let $\mathrm{H}_1: \frac{x^2}{\mathrm{a}^2}-\frac{y^2}{\mathrm{~b}^2}=1$ and $\mathrm{H}_2:-\frac{x^2}{\mathrm{~A}^2}+\frac{y^2}{\mathrm{~B}^2}=1$ be two hyperbolas having length of latus rectums $15 \sqrt{2}$ and $12 \sqrt{5}$ respectively...

If $\int \frac{2 x^2+5 x+9}{\sqrt{x^2+x+1}} \mathrm{~d} x=x \sqrt{x^2+x+1}+\alpha \sqrt{x^2+x+1}+\beta \log _{\mathrm{e}}\left|x+\frac{1}{2}+\sqrt{x^2+x+1}\right|+\mathrm{C}$, where $C$ is the constant of integration, then $\alpha+2 \beta$ ...

If $\alpha>\beta>\gamma>0$, then the expression $\cot ^{-1}\left\{\beta+\frac{\left(1+\beta^2\right)}{(\alpha-\beta)}\right\}+\cot ^{-1}\left\{\gamma+\frac{\left(1+\gamma^2\right)}{(\beta-\gamma)}\right\}+\cot ^{-1}\left\{\alpha+\frac{\left...

Let $[x]$ denote the greatest integer function, and let m and n respectively be the numbers of the points, where the function $f(x)=[x]+|x-2|,-2< x<3$, is not continuous and not differentiable. Then $\mathrm{m}+\mathrm{n}$ is equal to :

For some $a, b,$ let $f(x)=\left|\begin{array}{ccc}\mathrm{a}+\frac{\sin x}{x} & 1 & \mathrm{~b} \\ \mathrm{a} & 1+\frac{\sin x}{x} & \mathrm{~b} \\ \mathrm{a} & 1 & \mathrm{~b}+\frac{\sin x}{x}\end{array}\right|, x \neq 0, \lim \limits_{x ...

If the system of equations

$$ \begin{aligned} & x+2 y-3 z=2 \\ & 2 x+\lambda y+5 z=5 \\ & 14 x+3 y+\mu z=33 \end{aligned} $$

has infinitely many solutions, then $\lambda+\mu$ is equal to :

If the equation of the parabola with vertex $\mathrm{V}\left(\frac{3}{2}, 3\right)$ and the directrix $x+2 y=0$ is $\alpha x^2+\beta y^2-\gamma x y-30 x-60 y+225=0$, then $\alpha+\beta+\gamma$ is equal to :

Number of functions $f:\{1,2, \ldots, 100\} \rightarrow\{0,1\}$, that assign 1 to exactly one of the positive integers less than or equal to 98 , is equal to ________.

Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group $A$ and the remaining 3 from group $B$, is equal to :

Let $\mathrm{A}=\left[\mathrm{a}_{\mathrm{ij}}\right]$ be a square matrix of order 2 with entries either 0 or 1 . Let E be the event that A is an invertible matrix. Then the probability $\mathrm{P}(\mathrm{E})$ is :

The number of real solution(s) of the equation $x^2+3 x+2=\min \{|x-3|,|x+2|\}$ is :

In an arithmetic progression, if $\mathrm{S}_{40}=1030$ and $\mathrm{S}_{12}=57$, then $\mathrm{S}_{30}-\mathrm{S}_{10}$ is equal to :

If $7=5+\frac{1}{7}(5+\alpha)+\frac{1}{7^2}(5+2 \alpha)+\frac{1}{7^3}(5+3 \alpha)+\ldots \ldots \ldots \ldots \infty$, then the value of $\alpha$ is :

Let $\mathrm{A}=\left\{x \in(0, \pi)-\left\{\frac{\pi}{2}\right\}: \log _{(2 /\pi)}|\sin x|+\log _{(2 / \pi)}|\cos x|=2\right\}$ and $\mathrm{B}=\{x \geqslant 0: \sqrt{x}(\sqrt{x}-4)-3|\sqrt{x}-2|+6=0\}$. Then $\mathrm{n}(\mathrm{A} \cup ...

Let the points $\left(\frac{11}{2}, \alpha\right)$ lie on or inside the triangle with sides $x+y=11, x+2 y=16$ and $2 x+3 y=29$. Then the product of the smallest and the largest values of $\alpha$ is equal to :

Let $\overrightarrow{\mathrm{a}}=3 \hat{i}-\hat{j}+2 \hat{k}, \overrightarrow{\mathrm{~b}}=\overrightarrow{\mathrm{a}} \times(\hat{i}-2 \hat{k})$ and $\overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{b}} \times \hat{k}$. Then the project...

Let the position vectors of three vertices of a triangle be $4 \vec{p}+\vec{q}-3 \vec{r},-5 \vec{p}+\vec{q}+2 \vec{r}$ and $2 \vec{p}-\vec{q}+2 \vec{r}$. If the position vectors of the orthocenter and the circumcenter of the triangle are $\...