JEE Main 2025 (Online) 8th April Evening Shift

When undergoes intramolecular aldol condensation, the major product formed is :

Choose the correct option for structures of $A$ and $B$, respectively

Match the LIST-I with LIST-II
LIST-I LIST-II A. Carbocation I. Species that can supply a pair of electrons. B. C-Free radical II. Species that can receive a pair of electrons. C. Nucleophile III. sp2 hybridized carbon with empty ...

What is the correct IUPAC name of the compound?

The equilibrium constant for decomposition of $\text{H}_2\text{O(g)}$
$ \text{H}_2\text{O(g)} \rightleftharpoons \text{H}_2\text{(g)} + \frac{1}{2}\text{O}_2\text{(g)} \quad (\Delta G^\circ = 92.34 \, \text{kJ mol}^{-1}) $
is $8.0 \times 10...

In a first order decomposition reaction, the time taken for the decomposition of reactant to one fourth and one eighth of its initial concentration are $t_1$ and $t_2$ (s), respectively. The ratio $t_1/t_2$ will be:

$\mathrm{A} \xrightarrow[\text { (i) } \mathrm{H}_3 \mathrm{O}^{+}]{\text {(i) } \mathrm{NaH}} \mathrm{B} \xrightarrow[\text { (ii) } \mathrm{H}_2 \mathrm{SO}_4, \Delta]{\text { (i) } \mathrm{EOH}} \mathrm{C}$
' A ' shows positive Lassaign'...

Match the LIST-I with LIST-IItable {width: 100%;border-collapse: collapse;margin: 20px 0;}th {background-color: blue;color: white;border: 1px solid lightgrey;padding: 10px;}td {border: 1px solid lightgrey;padding: 10px;text-align: left;}LIS...

The number of species from the following that are involved in sp3d2 hybridization is :[Co(NH3)6]3+, SF6, [CrF6]3−, [CoF6]3−, [Mn(CN)6]3−, and [MnCl6]3−

Given below are two statements:Statement I: A homoleptic octahedral complex, formed using monodentate ligands, will not show stereoisomerism.Statement II: cis- and trans- platin are heteroleptic complexes of Pd.In the light of the above sta...

The correct decreasing order of spin only magnetic moment values (BM) of Cu+, Cu2+, Cr2+ and Cr3+ ions is :

Consider the following half cell reaction\(\text{Cr}_2\text{O}_7^{2-} \, (\text{aq}) + 6\text{e}^- + 14\text{H}^+ \, (\text{aq}) \rightarrow 2\text{Cr}^{3+} \, (\text{aq}) + 7\text{H}_2\text{O} \, (\ell)\)The reaction was conducted with ...

'P' is

Choose the correct set of reagents for the following conversion.

Which one of the following reactions will not lead to the desired ether formation in major proportion?
(iso- $\mathrm{Bu} \Rightarrow$ isobutyl, sec $-\mathrm{Bu} \Rightarrow$ sec-butyl, $\mathrm{nPr} \Rightarrow \mathrm{n}$-propyl, $$ { }^...

The atomic number of the element from the following with lowest 1st ionisation enthalpy is :

Given below are two statements:Statement I: H2Se is more acidic than H2TeStatement II: H2Se has higher bond enthalpy for dissociation than H2TeIn the light of the above statements, choose the correct answer from the options given below:

Match the LIST-I with LIST-IItable {width: 100%;border-collapse: collapse;margin: 20px 0;}th {background-color: blue;color: white;border: 1px solid lightgrey;padding: 10px;}td {border: 1px solid lightgrey;padding: 10px;text-align: left;}LIS...

$\mathrm{HA}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{A}^{-}(a q)$The freezing point depression of a 0.1 m aqueous solution of a monobasic weak acid HA is 0.20 °C. The dissociation constant for the acid isGiven: $K_f$(H2O) = 1.8 ...

Which of the following binary mixture does not show the behaviour of minimum boiling azeotropes?

On combustion 0.210 g of an organic compound containing C, H and O gave 0.127 g H2O and 0.307 g CO2. The percentages of hydrogen and oxygen in the given organic compound respectively are:

20 mL of sodium iodide solution gave 4.74 g silver iodide when treated with excess of silver nitrate solution. The molarity of the sodium iodide solution is _______ M. (Nearest Integer value) (Given : Na = 23, I = 127, Ag = 108, N = 14, O =...

Correct statements for an element with atomic number 9 are:A. There can be 5 electrons for which $m_s = +\frac{1}{2}$ and 4 electrons for which $m_s = -\frac{1}{2}$.B. There is only one electron in $p_z$ orbital.C. The last electron goes to...

The energy of an electron in the first Bohr orbit of the H-atom is -13.6 eV. The magnitude of energy value of an electron in the first excited state of Be3+ is ________ eV (nearest integer value).

Resonance in $\mathrm{X}_2 \mathrm{Y}$ can be represented as
The enthalpy of formation of $X_2Y$ $ \left(X = X(g) + \frac{1}{2} Y = Y(g) \rightarrow X_2Y(g) \right) $ is 80 kJ mol$^{-1}$. The magnitude of resonance energy of $X_2Y$ is __ kJ...

Let the values of $\lambda$ for which the shortest distance between the lines $\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4}$
and $\frac{x-\lambda}{3} = \frac{y-4}{4} = \frac{z-5}{5}$ is $\frac{1}{\sqrt{6}}$ be $\lambda_1$ and $\lambda_2$....

Let the area of the triangle formed by the lines $x+2=y-1=z, \frac{x-3}{5}=\frac{y}{-1}=\frac{z-1}{1}$ and $\frac{x}{-3}=\frac{y-3}{3}=\frac{z-2}{1}$ be $A$. Then $A^2$ is equal to ________.

Let the function $ f(x) = \frac{x}{3} + \frac{3}{x} + 3, x \neq 0 $ be strictly increasing in $(-\infty, \alpha_1) \cup (\alpha_2, \infty)$ and strictly decreasing in $(\alpha_3, \alpha_4) \cup (\alpha_4, \alpha_5)$. Then $ \sum\limits_{i=1...

Let the area of the bounded region $\left\{(x, y): 0 \leq 9 x \leq y^2, y \geq 3 x-6\right\}$ be $A$. Then $6 A$ is equal to _________.

The number of integral terms in the expansion of $ \left( {5^\frac{1}{2}} + 7^\frac{1}{8} \right)^{1016} $ is:

The product of the last two digits of $(1919)^{1919}$ is

Let $ A = \left\{ \theta \in [0, 2\pi] : 1 + 10\operatorname{Re}\left( \frac{2\cos\theta + i\sin\theta}{\cos\theta - 3i\sin\theta} \right) = 0 \right\} $. Then $ \sum\limits_{\theta \in A} \theta^2 $ is equal to

The integral $\int\limits_{-1}^{\frac{3}{2}} \left(| \pi^2 x \sin(\pi x) \right|) dx$ is equal to:

Let f(x) be a positive function and $I_{1} = \int\limits_{-\frac{1}{2}}^{1} 2x \, f(2x(1-2x)) \, dx$ and $I_{2} = \int\limits_{-1}^{2} f(x(1-x)) \, dx$. Then the value of $\frac{I_{2}}{I_{1}}$ is equal to ________

Let $f(x) = x - 1$ and $g(x) = e^x$ for $x \in \mathbb{R}$. If $\frac{dy}{dx} = \left( e^{-2\sqrt{x}} g\left(f(f(x))\right) - \frac{y}{\sqrt{x}} \right)$, $y(0) = 0$, then $y(1)$ is

Let the ellipse $3x^2 + py^2 = 4$ pass through the centre $C$ of the circle $x^2 + y^2 - 2x - 4y - 11 = 0$ of radius $r$. Let $f_1, f_2$ be the focal distances of the point $C$ on the ellipse. Then $6f_1f_2 - r$ is equal to

Let the domain of the function $f(x)=\cos ^{-1}\left(\frac{4 x+5}{3 x-7}\right)$ be $[\alpha, \beta]$ and the domain of $g(x)=\log _2\left(2-6 \log _{27}(2 x+5)\right)$ be $(\gamma, \delta)$.
Then $|7(\alpha+\beta)+4(\gamma+\delta)|$ is equ...

The value of $ \cot^{-1} \left( \frac{\sqrt{1 + \tan^2(2)} - 1}{\tan(2)} \right) - \cot^{-1} \left( \frac{\sqrt{1 + \tan^2\left(\frac{1}{2}\right)} + 1}{\tan\left(\frac{1}{2}\right)} \right) $ is equal to

Given below are two statements:
Statement I: $ \lim\limits_{x \to 0} \left( \frac{\tan^{-1} x + \log_e \sqrt{\frac{1+x}{1-x}} - 2x}{x^5} \right) = \frac{2}{5} $
Statement II: $ \lim\limits_{x \to 1} \left( x^{\frac{2}{1-x}} \right) = \frac{...

Let α be a solution of $x^2 + x + 1 = 0$, and for some a and b in $R, \begin{bmatrix} 4 & a & b \end{bmatrix} \begin{bmatrix} 1 & 16 & 13 \\ -1 & -1 & 2 \\ -2 & -14 & -8 \end{bmatrix} = \begin{bmatrix} 0 & 0 & 0 \end{bmatrix}$. If $\frac{4}...

Let $ A = \begin{bmatrix} 2 & 2+p & 2+p+q \\ 4 & 6+2p & 8+3p+2q \\ 6 & 12+3p & 20+6p+3q \end{bmatrix} $.
If $ \det(\text{adj}(\text{adj}(3A))) = 2^m \cdot 3^n $, $ m, n \in \mathbb{N} $, then $ m + n $ is equal to

Let $r$ be the radius of the circle, which touches $x$ - axis at point $(a, 0), a<0$ and the parabola $\mathrm{y}^2=9 x$ at the point $(4,6)$. Then $r$ is equal to ______.

There are 12 points in a plane, no three of which are in the same straight line, except 5 points which are collinear. Then the total number of triangles that can be formed with the vertices at any three of these 12 points is

If A and B are two events such that $P(A) = 0.7$, $P(B) = 0.4$ and $P(A \cap \overline{B}) = 0.5$, where $\overline{B}$ denotes the complement of B, then $P\left(B \mid (A \cup \overline{B})\right)$ is equal to

The sum of the squares of the roots of $ |x-2|^2 + |x-2| - 2 = 0 $ and the squares of the roots of $ x^2 - 2|x-3| - 5 = 0 $, is

If $ \frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + \ldots \infty= \frac{\pi^4}{90} $, $\frac{1}{1^4} + \frac{1}{3^4} + \frac{1}{5^4} + \ldots \infty= \alpha $, $ \frac{1}{2^4} + \frac{1}{4^4} + \frac{1}{6^4} + \ldots \infty= \beta $, then...

Let A = {0, 1, 2, 3, 4, 5}. Let R be a relation on A defined by (x, y) ∈ R if and only if max{x, y} ∈ {3, 4}. Then among the statements (S1): The number of elements in R is 18, and (S2): The relation R is symmetric but neither reflexive nor...

Let a be the length of a side of a square OABC with O being the origin. Its side OA makes an acute angle \(\alpha\) with the positive x-axis and the equations of its diagonals are $(\sqrt{3}+1)x+(\sqrt{3}-1)y=0$ and $(\sqrt{3}-1)x-(\sqrt{3...

A line passing through the point P($a$, 0) makes an acute angle \(\alpha\) with the positive x-axis. Let this line be rotated about the point P through an angle $\frac{\alpha}{2}$ in the clockwise direction. If in the new position, the slo...

Let $ \vec{a} = \hat{i} + 2\hat{j} + \hat{k} $ and $ \vec{b} = 2\hat{i} + \hat{j} - \hat{k} $. Let $ \hat{c} $ be a unit vector in the plane of the vectors $ \vec{a} $ and $ \vec{b} $ and be perpendicular to $ \vec{a} $. Then such a vector ...