JEE Main 2026 (Online) 24th January Evening Shift

\(\text { From the following, how many compounds contain at least one secondary alcohol?}\)

Choose the correct answer from the options given below :

The unsaturated ether on acidic hydrolysis produces carbonyl compounds as shown below :-

Based on this, predict the solution/reagent that will help to distinguish "P" and "Q" obtained in the following reaction :-

Given below are two statements :
Statement I : Cross aldol condensation between two different aldehydes will always produce four different products.
Statement II : When semicarbazide reacts with a mixture of benzaldehyde and acetophenone un...

Grignard reagent $\mathrm{RMgBr}(\mathrm{P})$ reacts with water and forms a gas $(\mathrm{Q})$. One gram of Q occupies $1.4 \mathrm{dm}^3$ at STP. (P) on reaction with dry ice in dry ether followed by $\mathrm{H}_3 \mathrm{O}^{+}$forms a co...

Given below are two statements :
Statement I : There are several conformers for n -butane. Out of those conformers,

Statement II : As the dihedral angle increases, torsional strain decreases from (X) to $(\mathrm{Y})$.
In the light of the ...

Find out the statements which are not true.
A. Resonating structures with more number of covalent bonds and lesser charge separation are more stable.
B. In electromeric effect, an unsaturated system shows +E effect with nucleophile and -E e...

The number of possible tripeptides formed involving alanine (ala), glycine (gly) and valine (val), where no amino acid has been used more than once is:

Pair of species among the following having same bond order as well as paramagnetic character will be-

Consider the following gaseous equilibrium in a closed container of volume ' $V$ ' at $\mathrm{T}(\mathrm{K})$.
\(\mathrm{P}_2(\mathrm{~g})+\mathrm{Q}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{PQ}(\mathrm{~g})\)
2 moles each of $\mathrm...

The half-life of ${ }^{65} \mathrm{Zn}$ is 245 days. After $x$ days, $75 \%$ of original activity remained. The value of $x$ in days is $\_\_\_\_$ . (Nearest integer)
(Given: $\log 3=0.4771$ and $\log 2=0.3010$ )

A student has planned to prepare acetanilide from aniline using acetic anhydride.
The student has started from 9.3 g of aniline. However, the student has managed to obtain 11 g of dry acetanilide.
The % yield of this reaction is :-

Given below are two statements :
Statement I : The dipole moment of R-CN is greater than R-NC and R-NC can

Statement II : R-CN hydrolyses under acidic medium to produce a compound which on treatment with $\mathrm{SOCl}_2$, followed by the ...

\(\text { The wavelength of light absorbed for the following complexes are in the order }\)

A chromium complex with a formula $\mathrm{CrCl}_3 \cdot 6 \mathrm{H}_2 \mathrm{O}$ has a spin only magnetic moment value of 3.87 BM and its solution conductivity corresponds to $1: 2$ electrolyte. 2.75 g of the complex solution was initial...

Molar conductivity of a weak acid HQ of concentration 0.18 M was found to be $1 / 30$ of the molar conductivity of another weak acid HZ with concentration of 0.02 M . If $\lambda^{\circ} \mathrm{Q}^{-}$happened to be equal with $\lambda^{\c...

Choose the INCORRECT statement

" X " is an oxoanion of the lightest element of group 7 (in the periodic table). The metal is in +6 oxidation state in " X ". The color of the potassium salt of X is

The correct order of $\mathrm{C}, \mathrm{N}, \mathrm{O}$ and F in terms of second ionisation potential is

One mole of $\mathrm{Cl}_2(\mathrm{~g})$ was passed into 2 L of cold 2 M KOH solution. After the reaction, the concentrations of $\mathrm{Cl}^{-}, \mathrm{ClO}^{-}$and $\mathrm{OH}^{-}$are respectively (assume volume remains constant)

In the Group analysis of cations, $\mathrm{Ba}^{2+} $ & $\mathrm{Ca}^{2+}$ are precipitated respectively as

At 298 K , the mole percentage of $\mathrm{N}_2(\mathrm{~g})$ in air is $80 \%$. Water is in equilibrium with air at a pressure of 10 atm . What is the mole fraction of $\mathrm{N}_2(\mathrm{~g})$ in water at 298 K ? $\left(\mathrm{K}_{\mat...

Two liquids A and B form an ideal solution at temperature T K . At T K , the vapour pressures of pure A and B are 55 and $15 \mathrm{kN} \mathrm{m}^{-2}$ respectively. What is the mole fraction of A in solution of A and B in equilibrium wit...

0.25 g of an organic compound "A" containing carbon, hydrogen and oxygen was analysed using the combustion method. There was an increase in mass of $\mathrm{CaCl}_2$ tube and potash tube at the end of the experiment. The amount was found to...

The wavelength of spectral line obtained in the spectrum of $\mathrm{Li}^{2+}$ ion, when the transition takes place between two levels whose sum is 4 and difference is 2 , is

The heat of atomisation of methane and ethane are ' x ' $\mathrm{kJ} \mathrm{mol}^{-1}$ and ' y ' $\mathrm{kJ} \mathrm{mol}^{-1}$ respectively. The longest wavelength ( $\lambda$ ) of light capable of breaking the $\mathrm{C}-\mathrm{C}$ bo...

The sum of all values of $\alpha$, for which the shortest distance between the lines $\frac{x+1}{\alpha}=\frac{y-2}{-1}=\frac{z-4}{-\alpha}$ and $\frac{x}{\alpha}=\frac{y-1}{2}=\frac{z-1}{2 \alpha}$ is $\sqrt{2}$, is

Consider the following three statements for the function $f:(0, \infty) \rightarrow \mathbb{R}$ defined by $f(x)=\left|\log _e x\right|-|x-1|$ :
(I) $f$ is differentiable at all $x>0$.
(II) $f$ is increasing in $(0,1)$.
(III) $f$ is decreas...

Let $f(\alpha)$ denote the area of the region in the first quadrant bounded by $x=0, x=1, y^2=x$ and $y=|\alpha x-5|-|1-\alpha x|+\alpha x^2$. Then $(f(0)+f(1))$ is equal to

Let $z=(1+i)(1+2 i)(1+3 i) \ldots .(1+n i)$, where $i=\sqrt{-1}$. If $|z|^2=44200$, then $n$ is equal to $\_\_\_\_$

If $f(x)$ satisfies the relation $f(x)=e^x+\int_0^1\left(y+x e^x\right) f(y) d y$, then $e+f(0)$ is equal to $\_\_\_\_$ .

Let the length of the latus rectum of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,(a>b)$, be 30 . If its eccentricity is the maximum value of the function $f(t)=-\frac{3}{4}+2 t-t^2$, then $\left(a^2+b^2\right)$ is equal to

Let $(h, k)$ lie on the circle $\mathrm{C}: x^2+y^2=4$ and the point $(2 h+1,3 k+2)$ lie on an ellipse with eccentricity $e$. Then the value of $\frac{5}{e^2}$ is equal to $\_\_\_\_$ .

Let $f$ be a function such that $3 f(x)+2 f\left(\frac{m}{19 x}\right)=5 x, x \neq 0$, where $m=\sum\limits_{i=1}^9(i)^2$. Then $f(5)-f(2)$ is equal to

If the domain of the function $f(x)=\sin ^{-1}\left(\frac{1}{x^2-2 x-2}\right)$, is $(-\infty, \alpha] \cup[\beta, \gamma] \cup[\delta, \infty)$, then $\alpha+\beta+\gamma+\delta$ is equal to

Let $y=y(x)$ be a differentiable function in the interval $(0, \infty)$ such that $y(1)=2$, and $\lim\limits_{t \rightarrow x}\left(\frac{t^2 y(x)-x^2 y(t)}{x-t}\right)=3$ for each $x > 0$. Then $2 y(2)$ is equal to :

Let $[t]$ denote the greatest integer less than or equal to $t$. If the function
$$ f(x)=\left\{\begin{array}{cl} b^2 \sin \left(\frac{\pi}{2}\left[\frac{\pi}{2}(\cos x+\sin x) \cos x\right]\right), & x<0 \\ \frac{\sin x-\frac{1}{2} \sin 2 ...

Let $f(x)=\int \frac{7 x^{10}+9 x^8}{\left(1+x^2+2 x^9\right)^2} d x, x>0, \lim\limits_{x \rightarrow 0} f(x)=0$ and $f(1)=\frac{1}{4}$.
If $\mathrm{A}=\left[\begin{array}{ccc}0 & 0 & 1 \\ \frac{1}{4} & f^{\prime}(1) & 1 \\ \alpha^2 & 4 & 1...

Let $P=\left[p_{i j}\right]$ and $Q=\left[q_{i j}\right]$ be two square matrices of order 3 such that $q_{\mathrm{ij}}=2^{(\mathrm{i}+\mathrm{j}-1)} \mathrm{p}_{\mathrm{ij}}$ and $\operatorname{det}(\mathrm{Q})=2^{10}$. Then the value of $\...

Let the image of parabola $x^2=4 y$, in the line $x-y=1$ be $(y+a)^2=b(x-c)$, $a, b, c \in \mathrm{~N}$. Then $a+b+c$ is equal to

The letters of the word "UDAYPUR" are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word "UDAYPUR" is

The largest value of $n$, for which $40^n$ divides $60!$, is

Let S be a set of 5 elements and $\mathrm{P}(\mathrm{S})$ denote the power set of S . Let E be an event of choosing an ordered pair (A, B) from the set $\mathrm{P}(\mathrm{S}) \times \mathrm{P}(\mathrm{S})$ such that $\mathrm{A} \cap \mathr...

The smallest positive integral value of $a$, for which all the roots of $x^4-a x^2+9=0$ are real and distinct, is equal to

Let $a_1, a_2, a_3, a_4$ be an A.P. of four terms such that each term of the A.P. and its common difference $l$ are integers. If $a_1+a_2+a_3+a_4=48$ and $a_1 a_2 a_3 a_4+l^4=361$, then the largest term of the A.P. is equal to

$\left(\frac{1}{3}+\frac{4}{7}\right)+\left(\frac{1}{3^2}+\frac{1}{3} \times \frac{4}{7}+\frac{4^2}{7^2}\right)+\left(\frac{1}{3^3}+\frac{1}{3^2} \times \frac{4}{7}+\frac{1}{3} \times \frac{4^2}{7^2}+\frac{4^3}{7^3}\right)+\ldots$ upto infi...

Let $\mathrm{X}=\{x \in \mathrm{~N}: 1 \leq x \leq 19\}$ and for some $a, b \in \mathbb{R}, \mathrm{Y}=\{a x+b: x \in \mathrm{X}\}$. If the mean and variance of the elements of Y are 30 and 750 , respectively, then the sum of all possible v...

Let the angles made with the positive $x$-axis by two straight lines drawn from the point $\mathrm{P}(2,3)$ and meeting the line $x+y=6$ at a distance $\sqrt{\frac{2}{3}}$ from the point P be $\theta_1$ and $\theta_2$. Then the value of $\l...

The number of elements in the set $\left\{x \in\left[0,180^{\circ}\right]: \tan \left(x+100^{\circ}\right)=\tan \left(x+50^{\circ}\right) \tan x \tan \left(x-50^{\circ}\right)\right\}$ is $\_\_\_\_$ .

Let $\vec{a}=2 \hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}}, \vec{b}=\hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}}$ and $\vec{c}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}+3 \hat{\mathrm{k}}$. Let $\vec{v}$ be the vector in the plane ...

Let $\vec{a}=2 \hat{\mathrm{i}}-5 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}$ and $\vec{b}=\hat{\mathrm{i}}-\hat{\mathrm{j}}+3 \hat{\mathrm{k}}$. If $\vec{c}$ is a vector such that $2(\vec{a} \times \vec{c})+3(\vec{b} \times \vec{c})=\overrightarr...