JEE Main 2026 (Online) 2nd April Evening Shift

An organic compound “x” where molar ratio of C, O and H are equal, on treatment with 50% KOH under reflux followed by acidification produced “y”. The most likely structure of “y” is: [Molar mass of ‘x’ is 58 g mol−1]

A molecule (X) with following structure under mild acidic condition is hydrolysed to produce (Y) and (Z). Identify the correct statements about (Y) and (Z).A. Both (Y) and (Z) have same molar mass.B. (Y) and (Z) can be distinguished from ea...

Identify compounds A and E in the following reaction sequence.

Given below are two statements : Statement I : In , the carbocation is stabilised by +R effect of –OCH3 group. Statement II : In , the carbanion is stabilised by –R effect of –NO2 group. In the light of the above statements, choose the corr...

Identify the correct pair having amino acid (A) and the hormone (B) that is iodinated derivative of the amino acid (A).(T and Y represent one letter code for amino acids)

SF$_4$ is isostructural with :A. BrF$_4^\ominus$B. CH$_4$C. IF$_4^{\oplus}$D. XeF$_4$E. XeO$_2$F$_2$Choose the correct answer from the options given below :

Consider the reaction aX → bY, for which the rate constant at 30°C is $1 \times 10^{-3}\ \text{mol}^{-1}\ \text{L}\ \text{s}^{-1}$. Which of the following statements are true?
A. When concentration of ‘X’ is increased to four times, the rat...

Consider the following gas phase reaction being carried out in a closed vessel at $25 ^\circ$C.\(2A(g) \longrightarrow 4B(g) + C(g)\)table {width: 100%;border-collapse: collapse;margin: 20px 0;}th {background-color: blue;color: white;border...

Given below are two statements : Statement I : Among Zn, Mn, Sc and Cu, the energy required to remove the third valence electron is highest for Zn and lowest for Sc. Statement II : The correct order of the following complexes in terms of CF...

Which of the following complexes will show coordination isomerism?A. $[\mathrm{Ag(NH}_3)_2][\mathrm{Ag(CN)}_2]$B. $[\mathrm{Co(NH}_3)_6][\mathrm{Cr(CN)}_6]$C. $[\mathrm{Co(NH}_3)_6][\mathrm{Co(CN)}_6]$D. $[\mathrm{Fe(NH}_3)_6][\mathrm{Co(CN...

Among $Fe^{2+}$, $Fe^{3+}$, $Cr^{2+}$ and $Zn^{2+}$, the ion that shows positive borax bead test and with highest ionisation enthalpy is :

Number of paramagnetic ions among the following d- and f-block metal ions is __________.Mn2+, Cu2+, Zn2+, Yb2+, Sc3+, La3+, Gd3+, Lu3+, Ti4+, Ce4+(Atomic number of Mn = 25, Cu = 29, Zn = 30, Yb = 70, Sc = 21, La = 57, Gd = 64, Lu = 71, Ti =...

Consider the following two half-cell reactions along with the standard reduction potential given :
$\mathrm{CO}_2 + 6\mathrm{H}^+ + 6e^- \longrightarrow \mathrm{CH}_3\mathrm{OH} + \mathrm{H}_2\mathrm{O}\qquad E_{\text{red}}^{\circ} = 0.02\ ...

Correct statements regarding alkyl halides (R–X) among the following are : A. Alcohol being less polar solvent as compared to water, alcoholic KOH favours elimination reaction with R–X. B. Order of reactivity towards SN1 mechanism is C6H5–C...

The compound (X) on(i) on heating in the presence of anhydrous AlCl3 and HCl gas gives 2,4-dimethyl pentane(ii) aromatization gives toluene and(iii) cyclisation gives methyl cyclohexaneThe correct name of compound (X) is:

The first and second ionization constants of a weak dibasic acid H2A are $8.1 \times 10^{-8}$ and $1.0 \times 10^{-13}$ respectively. 0.1 mol of H2A was dissolved in 1 L of 0.1 M HCl solution. The concentration of HA- in the resultant solut...

At 25°C, 20.0 mL of 0.2 M weak monoprotic acid HX is titrated against 0.2 M NaOH. The pH of the solution (a) at the start of the titration (when NaOH has not been added) and (b) when 10 mL of NaOH is added respectively, are :Given :$K_a = 5...

Given below are two statements :Statement I: The second ionization enthalpy of B, Al and Ga is in the order of B > Al > Ga.Statement II: The correct order in terms of first ionization enthalpy is Si < Ge < Pb < Sn.In the light of the above ...

The correct set that contains all kinds (basic, acidic, amphoteric and neutral) of oxides is :

Complete combustion of $X$ g of an organic compound gave $0.25$ g of $CO_2$ and $0.12$ g of $H_2O$. If the % of carbon is $25\%$ and of hydrogen is $4.89\%$, then $X = \underline{\phantom{xxx}} \times 10^{-3}$ g. (Nearest integer) (Molar ma...

Consider the following reactions sequenceWhen the product (P) is subjected to Carius analysis using AgNO3, 1.0 g of the product (P) will produce _________ g of the precipitate of AgBr. (Nearest Integer)(Given : molar mass in g mol-1 C : 12,...

Solution A is prepared by dissolving 1 g of a protein (molar mass = 50,000 g mol-1) in 0.5 L of water at 300 K. Its osmotic pressure is $x$ bar. Solution B is made by dissolving 2 g of the same protein in 1 L of water at 300 K. Osmotic pres...

The ratio of mass percentage (w/w) of C : H in a hydrocarbon is 12 : 1. It has two carbon atoms. The weight (in g) of CO2(g) formed when 3.38 g of this hydrocarbon is completely burnt in oxygen is : (Given : Molar mass in g mol–1 C : 12, H...

The surface of sodium metal is irradiated with radiation of wavelength $x$ nm. The kinetic energy of ejected electrons is $2.8 \times 10^{-20}\ \text{J}$. The work function of sodium is $2.3$ eV. The value of $x$ is ________ $\times 10^2$ n...

Gas 'A' undergoes change from state 'X' to state 'Y'. In this process, the heat absorbed and work done by the gas is 10 J and 18 J respectively. Now gas is brought back to state 'X' by another process during which 6 J of heat is evolved. In...

Let the point A be the foot of perpendicular drawn from the point P$(a, b, 0)$ on the line\(\frac{x-1}{2} = \frac{y-2}{1} = \frac{z-\alpha}{3}.\)If the midpoint of the line segment PA is \(\left(0, \frac{3}{4}, -\frac{1}{4}\right),\) then t...

Let $f(x)$ be a polynomial of degree 5, and have extrema at $x = 1$ and $x = -1$. If $\lim\limits_{x \to 0} \left( \frac{f(x)}{x^3} \right) = -5$, then $f(2) - f(-2)$ is equal to:

If the area of the region bounded by $16x^2 - 9y^2 = 144$ and $8x - 3y = 24$ is $A$, then $3(A + 6 \log_e(3))$ is equal to ________.

If for $3 \leq r \leq 30$, $\left({^{30}C_{30-r}}\right) + 3\left({^{30}C_{31-r}}\right) + 3\left({^{30}C_{32-r}}\right) + \left({^{30}C_{33-r}}\right) = {^mC_r}$, then m equals :

Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines $x + (k-1)y + 3 = 0$ and $2x + k^2y - 4 = 0$. If the line $x - y + 2 = 0$ intersects the circle at the points A and B, then...

Let the circles $C_1:|z| = r$ and $C_2:|z - 3 - 4i| = 5$, $z \in \mathbb{C}$, be such that $C_2$ lies within $C_1$.If $z_1$ moves on $C_1$, $z_2$ moves on $C_2$ and $\min |z_1 - z_2| = 2$, then $\max |z_1 - z_2|$ is equal to :

The value of $\int\limits_{0}^{20\pi} (\sin^4 x + \cos^4 x) dx$ is equal to:

Let $x = x(y)$ be the solution of the differential equation $2y^2 \frac{dx}{dy} - 2xy + x^2 = 0$, $y > 1$, $x(e) = e$.Then $x(e^2)$ is equal to:

Let A be the point (3, 0) and circles with variable diameter AB touch the circle $x^2 + y^2 = 36$ internally. Let the curve C be the locus of the point B. If the eccentricity of C is $e$, then $72e^2$ is equal to ________.

Let O be the origin, and P and Q be two points on the rectangular hyperbola $xy = 12$ such that the midpoint of the line segment PQ is $\left( \frac{1}{2}, -\frac{1}{2} \right)$. Then the area of the triangle OPQ equals :

Let $f(x) = \int \left( \frac{16x + 24}{x^2 + 2x - 15} \right) dx$. If $f(4) = 14 \log_e(3)$ and $f(7) = \log_e(2^\alpha \cdot 3^\beta)$, $\alpha, \beta \in \mathbb{N}$, then $\alpha + \beta$ is equal to :

The number of points in the interval $[2, 4]$, at which the function $f(x) = \left[ x^2 - x - \frac{1}{2} \right]$, where $[ \cdot ]$ denotes the greatest integer function, is discontinuous, is ________.

If the system of equations $x + 5y + 6z = 4$ $2x + 3y + 4z = 7$ $x + 6y + az = b$ has infinitely many solutions, then the point $(a, b)$ lies on the line

Consider the matrices $A = \begin{bmatrix} 2 & -2 \\ 4 & -2 \end{bmatrix}$ and $B = \begin{bmatrix} 3 & 9 \\ 1 & 3 \end{bmatrix}$. If matrices $P$ and $Q$ are such that $PA = B$ and $AQ = B$, then the absolute value of the sum of the diagon...

Let the parabola $y = x^2 + px + q$ passing through the point $(1, -1)$ be such that the distance between its vertex and the $x$-axis is minimum. Then the value of $p^2 + q^2$ is :

Let $p_n$ denote the total number of triangles formed by joining the vertices of an $n$-side regular polygon.If $p_{n+1} - p_n = 66$, then the sum of all distinct prime divisors of $n$ is :

A man throws a fair coin repeatedly. He gets 10 points for each head he throws and 5 points for each tail he throws. If the probability that he gets exactly 30 points is $\frac{m}{n}$, gcd $(m, n) = 1$, then m + n is equal to :

Let $\alpha, \beta$ be the roots of the equation $x^2 - 3x + r = 0$, and $\frac{\alpha}{2}, 2\beta$ be the roots of the equation $x^2 + 3x + r = 0$.If the roots of the equation $x^2 + 6x = m$ are $2\alpha + \beta + 2r$ and $\alpha - 2\beta ...

Let $a_1, a_2, a_3, \ldots$ be an A.P. and $g_1 = a_1, g_2, g_3, \ldots$ be an increasing G.P. If $a_1 = a_2 + g_2 = 1$ and $a_3 + g_3 = 4$, then $a_{10} + g_5$ is equal to:

The sum $\frac{1^3}{1} + \frac{1^3 + 2^3}{1 + 3} + \frac{1^3 + 2^3 + 3^3}{1 + 3 + 5} + \ldots$ up to 8 terms, is :

Let $A = \{2, 3, 4, 5, 6\}$. Let $R$ be a relation on the set $A \times A$ given by $(x, y)R(z, w)$ if and only if $x$ divides $z$ and $y \leq w$. Then the number of elements in $R$ is _________.

The mean and variance of n observations are 8 and 16, respectively. If the sum of the first (n − 1) observations is 48 and the sum of squares of the first (n − 1) observations is 496, then the value of n is :

Let $P = \{ \theta \in [0, 4\pi] : \tan^2 \theta \neq 1 \}$ and $S = \{ a \in \mathbb{Z} : 2(\cos^8 \theta - \sin^8 \theta) \sec 2 \theta = a^2, \theta \in P \}$. Then $n(S)$ is:

Let the vectors $\vec{a} = -\hat{i} + \hat{j} + 3\hat{k}$ and $\vec{b} = \hat{i} + 3\hat{j} + \hat{k}$. For some $\lambda, \mu \in \mathbb{R}$, let $\vec{c} = \lambda \vec{a} + \mu \vec{b}$.If $\vec{c} \cdot (3\hat{i} - 6\hat{j} + 2\hat{k})...

Two adjacent sides of a parallelogram PQRS are given by $\overrightarrow{PQ} = \hat{j} + \hat{k}$ and $\overrightarrow{PS} = \hat{i} - \hat{j}$. If the side PS is rotated about the point P by an acute angle $\alpha$ in the plane of the para...