JEE Main 2026 (Online) 21st January Morning Shift

\(\text { Identify A in the following reaction. }\)

An organic compound " P " of molecular formula $\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_3$ gives positive Iodoform test but negative Tollen's test. When " P " is treated with dilute acid, it produces " Q ". " Q " gives positive Tollen's tes...

Identify correct statements from the following :
A. Propanal and propanone are functional isomers.
B. Ethoxyethane and methoxypropane are metamers.
C. But-2-ene shows optical isomerism.
D. But-1-ene and but-2-ene are functional isomers.
E. ...

\(\text { From the following, the least stable structure is : }\)

Identify the correct statements.
A. Arginine and Tryptophan are essential amino acids.
B. Histidine does not contain heterocyclic ring in its structure.
C. Proline is a six membered cyclic ring amino acid.
D. Glycine does not have chiral ce...

Given below are two statements :
Statement I :
The number of species among $\mathrm{SF}_4, \mathrm{NH}_4^{+},\left[\mathrm{NiCl}_4\right]^{2-}, \mathrm{XeF}_4,\left[\mathrm{PtCl}_4\right]^{2-}, \mathrm{SeF}_4$ and $\left[\mathrm{Ni}(\mathrm...

Pre-exponential factors of two different reactions of same order are identical. Let activation energy of first reaction exceeds the activation energy of second reaction by $20 \mathrm{~kJ} \mathrm{~mol}^{-1}$. If $\mathrm{k}_1$ and $\mathrm...

A hydrocarbon ' P ' $\left(\mathrm{C}_4 \mathrm{H}_8\right)$ on reaction with HCl gives an optically active compound ' Q ' $\left(\mathrm{C}_4 \mathrm{H}_9 \mathrm{Cl}\right)$ which on reaction with one mole of ammonia gives compound ' $\ma...

An organic compound $(\mathrm{P})$ on treatment with aqueous ammonia under hot condition forms compound $(\mathrm{Q})$ which on heating with $\mathrm{Br}_2$ and KOH forms compound $(\mathrm{R})$ having molecular formula $\mathrm{C}_6 \mathr...

Consider the following reaction sequence

The percentage of nitrogen in product ' T ' formed is $\_\_\_\_$ %. (Nearest integer) (Given molar mass in $\mathrm{g} \mathrm{mol}^{-1} \mathrm{H}: 1, \mathrm{C}: 12, \mathrm{~N}: 14, \mathrm{O}: 1...

Given below are two statements :
Statement I : Among $\left.\left[\mathrm{Cu}\left(\mathrm{NH}_3\right)_4\right]^{2+},\left[\mathrm{Ni}(\mathrm{en})_3\right)\right]^{2+},\left[\mathrm{Ni}\left(\mathrm{NH}_3\right)_6\right]^{2+}$ and $\left[...

$\mathrm{MnO}_4{ }^{2-}$, in acidic medium, disproportionates to :

Consider the following reactions :
$$ \begin{aligned} & \mathrm{NaCl}+\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7+\mathrm{H}_2 \mathrm{SO}_4 \rightarrow \mathrm{~A}+\mathrm{KHSO}_4+\mathrm{NaHSO}_4+\mathrm{H}_2 \mathrm{O} \\ & \mathrm{~A}+\math...

The pH and conductance of a weak acid $(\mathrm{HX})$ was found to be 5 and $4 \times 10^{-5} \mathrm{~S}$, respectively. The conductance was measured under standard condition using a cell where the electrode plates having a surface area of...

80 mL of a hydrocarbon on mixing with 264 mL of oxygen in a closed U-tube undergoes complete combustion. The residual gases after cooling to 273 K occupy 224 mL . When the system is treated with KOH solution, the volume decreases to 64 mL ....

Consider the following reactions.
$\underset{\text { (Hot solution) }}{\mathrm{PbCl}_2}+\mathrm{K}_2 \mathrm{CrO}_4 \rightarrow A+2 \mathrm{KCl}$
$$ \begin{aligned} & \mathrm{A}+\mathrm{NaOH} \rightleftharpoons \mathrm{~B}+\mathrm{Na}_2 \ma...

Given below are two statements :
Statement I : The number of pairs among $\left[\mathrm{SiO}_2, \mathrm{CO}_2\right],\left[\mathrm{SnO}, \mathrm{SnO}_2\right],\left[\mathrm{PbO}, \mathrm{PbO}_2\right]$ and $\left[\mathrm{GeO}, \mathrm{GeO}_...

Which of the following represents the correct trend for the mentioned property?A. F > P > S > B      - First Ionization EnergyB. Cl > F > S > P      - Electron AffinityC. K > Al > Mg > B      - Metallic characterD. K2O > Na2O > MgO > Al2O3 ...

In Carius method, 0.75 g of an organic compound gave 1.2 g of barium sulphate, find percentage of sulphur (molar mass $32 \mathrm{~g} \mathrm{~mol}^{-1}$ ). Molar mass of barium sulphate is $233 \mathrm{~g} \mathrm{~mol}^{-1}$.

Elements P and Q form two types of non-volatile, non-ionizable compounds PQ and $\mathrm{PQ}_2$. When 1 g of $P Q$ is dissolved in 50 g of solvent ' $A^{\prime}, \Delta T_b$ was 1.176 K while when 1 g of $P Q_2$ is dissolved in 50 g of solv...

14.0 g of calcium metal is allowed to react with excess HCl at 1.0 atm pressure and 273 K . Which of the following statements is incorrect?
[Given : Molar mass in $\mathrm{g} \mathrm{mol}^{-1}$ of $\mathrm{Ca}-40, \mathrm{Cl}-35.5, \mathrm{...

Given below are two statements :
Statement I : When an electric discharge is passed through gaseous hydrogen, the hydrogen molecules dissociate and the energetically excited hydrogen atoms produce electromagnetic radiation of discrete frequ...

For the reaction, $\mathrm{N}_2 \mathrm{O}_4 \rightleftharpoons 2 \mathrm{NO}_2$, graph is plotted as shown below. Identify correct statements.
A. Standard free energy change for the reaction is $-5.40 \mathrm{~kJ} \mathrm{~mol}^{-1}$.
B. A...

$$ \begin{aligned} &\text { Use the following data : }\\ &\begin{array}{|c|c|c|} \hline \text { Substance } & \frac{\Delta_f \mathrm{H}^{\ominus}(500 \mathrm{~K})}{\mathrm{kJ} \mathrm{~mol}^{-1}} & \frac{\mathrm{~S}^{\ominus}(500 \mathrm{~K...

Which of the following graphs between pressure ' p ' versus volume ' V ' represents the maximum work done?

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a twice differentiable function such that the quadratic equation $f(x) \mathrm{m}^2-2 f^{\prime}(x) \mathrm{m}+f^{\prime \prime}(x)=0$ in m , has two equal roots for every $x \in \mathbf{R}$. If...

The area of the region, inside the ellipse $x^2+4 y^2=4$ and outside the region bounded by the curves $y=|x|-1$ and $y=1-|x|$, is :

If the coefficient of $x$ in the expansion of $\left(a x^2+b x+c\right)(1-2 x)^{26}$ is -56 and the coefficients of $x^2$ and $x^3$ are both zero, then $\mathrm{a}+\mathrm{b}+\mathrm{c}$ is equal to :

Let PQ and MN be two straight lines touching the circle $x^2+y^2-4 x-6 y-3=0$ at the points $A$ and $B$ respectively. Let $O$ be the centre of the circle and $\angle A O B=\pi / 3$. Then the locus of the point of intersection of the lines P...

If $x^2+x+1=0$, then the value of $\left(x+\frac{1}{x}\right)^4+\left(x^2+\frac{1}{x^2}\right)^4+\left(x^3+\frac{1}{x^3}\right)^4+\ldots+\left(x^{25}+\frac{1}{x^{25}}\right)^4$ is:

The value of $\int\limits_{-\pi / 6}^{\pi / 6}\left(\frac{\pi+4 x^{11}}{1-\sin (|x|+\pi / 6)}\right) d x$ is equal to:

$6 \int_0^\pi|(\sin 3 x+\sin 2 x+\sin x)| d x$ is equal to $\_\_\_\_$ .

Let $y=y(x)$ be the solution curve of the differential equation $\left(1+x^2\right) \mathrm{d} y+\left(y-\tan ^{-1} x\right) d x=0, y(0)=1$. Then the value of $y(1)$ is :

Let the foci of a hyperbola coincide with the foci of the ellipse $\frac{x^2}{36}+\frac{y^2}{16}=1$. If the eccentricity of the hyperbola is 5 , then the length of its latus rectum is :

If the domain of the function $f(x)=\cos ^{-1}\left(\frac{2 x-5}{11-3 x}\right)+\sin ^{-1}\left(2 x^2-3 x+1\right)$ is the interval $[\alpha, \beta]$, then $\alpha+2 \beta$ is equal to :

Let $f: \mathbf{R} \rightarrow(0, \infty)$ be a twice differentiable function such that $f(3)=18, f^{\prime}(3)=0$ and $f^{\prime \prime}(3)=4$.
Then $\lim\limits _{x \rightarrow 1}\left(\log _e\left(\frac{f(2+x)}{f(3)}\right)^{\frac{18}{(...

For some $\alpha, \beta \in \mathbf{R}$, let $A=\left[\begin{array}{ll}\alpha & 2 \\ 1 & 2\end{array}\right]$ and $B=\left[\begin{array}{ll}1 & 1 \\ 1 & \beta\end{array}\right]$ be such that $A^2-4 A+2 I=B^2-3 B+I=O$. Then $\left(\operatorn...

Let O be the vertex of the parabola $x^2=4 y$ and Q be any point on it. Let the locus of the point P , which divides the line segment OQ internally in the ratio $2: 3$ be the conic C . Then the equation of the chord of $C$, which is bisecte...

The number of strictly increasing functions $f$ from the set $\{1,2,3,4,5,6\}$ to the set $\{1,2,3, \ldots ., 9\}$ such that $f(i) \neq i$ for $1 \leq i \leq 6$, is equal to :

Let $S=\{(m, n): m, n \in\{1,2,3, \ldots . ., 50\}\}$. If the number of elements $(m, n)$ in $S$ such that $6^m+9^n$ is a multiple of 5 is $p$ and the number of elements ( $m, n$ ) in $S$ such that $m+n$ is a square of a prime number is q ,...

Let the mean and variance of 7 observations $2,4,10, x, 12,14, y, x>y$, be 8 and 16 respectively. Two numbers are chosen from $\{1,2,3, x-4, y, 5\}$ one after another without replacement, then the probability, that the smaller number among ...

The sum of all the roots of the equation $(x-1)^2-5|x-1|+6=0$, is :

Let $a_1=1$ and for $n \geqslant 1, a_{n+1}=\frac{1}{2} a_n+\frac{n^2-2 n-1}{n^2(n+1)^2}$. Then $\left|\sum_{n=1}^{\infty}\left(a_n-\frac{2}{n^2}\right)\right|$ is equal to $\_\_\_\_$ .

Let $a_1, a_2, a_3, \ldots$ be a G.P. of increasing positive terms such that $a_2 \cdot a_3 \cdot a_4=64$ and $a_1+a_3+a_5=\frac{813}{7}$. Then $a_3+a_5+a_7$ is equal to :

The number of relations, defined on the set $\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}\}$, which are both reflexive and symmetric, is equal to:

Let a point A lie between the parallel lines $\mathrm{L}_1$ and $\mathrm{L}_2$ such that its distances from $\mathrm{L}_1$ and $\mathrm{L}_2$ are 6 and 3 units, respectively. Then the area (in sq. units) of the equilateral triangle ABC , wh...

The value of $\operatorname{cosec} 10^{\circ}-\sqrt{3} \sec 10^{\circ}$ is equal to :

Let $(\alpha, \beta, \gamma)$ be the co-ordinates of the foot of the perpendicular drawn from the point $(5,4,2)$ on the line $\overrightarrow{\mathrm{r}}=(-\hat{i}+3 \hat{j}+\hat{k})+\lambda(2 \hat{i}+3 \hat{j}-\hat{k})$.
Then the length o...

Let $\overrightarrow{\mathrm{a}}=-\hat{i}+2 \hat{j}+2 \hat{k}, \overrightarrow{\mathrm{~b}}=8 \hat{i}+7 \hat{j}-3 \hat{k}$ and $\overrightarrow{\mathrm{c}}$ be a vector such that $\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{c...

Let $\overrightarrow{\mathrm{c}}$ and $\overrightarrow{\mathrm{d}}$ be vectors such that $|\overrightarrow{\mathrm{c}}+\overrightarrow{\mathrm{d}}|=\sqrt{29}$ and $\overrightarrow{\mathrm{c}} \times(2 \hat{i}+3 \hat{j}+4 \hat{k})=(2 \hat{i}...