JEE Advanced 2026 Paper 2 Online

Natural rubber on complete ozonolysis $\left(\mathrm{O}_3 / \mathrm{Zn}-\mathrm{H}_2 \mathrm{O}\right)$ gives compound $\mathbf{X}$ as the major product. $\mathbf{X}$ gives positive iodoform and Tollen's tests. $\mathbf{X}$ on heating with ...

A known artificial sweetener $\mathbf{X}$ is composed of 4-chloro-4-deoxy- $\alpha$-D-galactose and 1,6-dichloro-1,6-dideoxy- $\beta$-D-fructose joined by a glycosidic linkage. Structure of D-galactose is given below :

The correct structur...

The correct statement(s) regarding sugars is(are) :

The correct order of ONO bond angle in the given species is :

For a first-order reaction $\mathbf{R} \rightarrow \mathbf{P}$ at a given temperature, $k$ is the rate constant. For this reaction, at the given temperature, the concentrations of $\mathbf{R}$ and $\mathbf{P}$ at a time $t$ are $[\mathbf{R}...

In the following reaction sequence, P, Q, S and T are the major products. The correct statement(s) about P, Q, S and T is(are) :

Consider that the coordinating atoms of the ligands in cis- $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}_2\right] \mathrm{Cl}$ and mer- $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_3 \mathrm{Cl}_3\right]$ octahedral complexes ...

At 300 K , the molar conductivities of the aqueous solutions of three salts at two different concentrations are given below :


Salt
Concentration (M)
Molar conductivity (S cm2 mol−1)


NaNO3
0.01
111


...

Correct statement(s) about the compounds P, Q and R is(are)

The correct statement(s) regarding the periodic properties of elements is(are) :

In the following reaction sequence, major products $\mathbf{X}$ and $\mathbf{Y}$ are acyclic monomers.

500 mol of $\mathbf{X}$ completely reacts with 500 mol of $\mathbf{Y}$ to give 1 mol of a single biodegradable acyclic copolymer $\mathb...

Consider the following reaction sequence in which $\mathbf{J}, \mathbf{K}, \mathbf{L}$ and $\mathbf{M}$ are the major products.

Given:
Atomic mass (in amu) : $\mathrm{H}: 1, \mathrm{C}: 12, \mathrm{~N}: 14, \mathrm{O}: 16, \mathrm{~S}: 32,...

Consider the following reaction sequence in which $\mathbf{J}, \mathbf{K}, \mathbf{L}$ and $\mathbf{M}$ are the major products.

Given :
Atomic mass (in amu) : $\mathrm{H}: 1, \mathrm{C}: 12, \mathrm{~N}: 14, \mathrm{O}: 16, \mathrm{~S}: 32...

In a solvent $\mathbf{S}$, a compound $\mathbf{B}$ is partially dissociated into $\mathbf{C}$ and $\mathbf{D}$ as given below :
\(\mathbf{B} \rightleftharpoons 2 \mathbf{C}+2 \mathbf{D}\)
$\mathbf{B}, \mathbf{C}$ and $\mathbf{D}$ are non-...

Two volatile liquids $\mathbf{A}$ and $\mathbf{B}$ form an ideal solution. Consider a 5 molal solution of $\mathbf{B}$ in $\mathbf{A}$ inside a closed container having a total vapour pressure of 100 mm Hg at 300 K . The vapour pressure of p...

Two volatile liquids $\mathbf{A}$ and $\mathbf{B}$ form an ideal solution. Consider a 5 molal solution of $\mathbf{B}$ in $\mathbf{A}$ inside a closed container having a total vapour pressure of 100 mm Hg at 300 K . The vapour pressure of p...

$\mathbf{X}^{\boldsymbol{a}+}$ and $\mathbf{Y}^{\boldsymbol{b}+}$ are hydrogen-like species. The wavelength of light absorbed during the transition between the states with principal quantum numbers $n=1$ and $n=2$ of $\mathbf{X}^{\boldsymbo...

At a given temperature, 0.45 g of acetic acid in 50 mL of water is shaken with 1.0 g of charcoal and the pH of the resulting solution is 3.0 . Assume, the adsorption of acetic acid from the aqueous solution by charcoal follows Freundlich is...

Let L be the straight line joining the points P(1, 2, –1) and Q(2, 3, 1). Let S be the foot of the perpendicular drawn from the point R(4, –1, 5) to the line L. Another line passing through R intersects L at a point T such that the point S ...

Consider the curve $C_1$ given by
\(y=e^{-x} \quad \text { for } x \in[0,10 \pi],\)
and the curve $C_2$ given by
\(y=e^{-x}(\sin x+\cos x) \quad \text { for } x \in[0,10 \pi] .\)
Let $n$ be the total number of points of intersection of ...

Consider the ellipses given by
\(x^2+4 y^2=1 \quad \text { and } \quad 4 x^2+y^2=1 .\)
If $\alpha$ is the area of the common region that lies inside both the given ellipses, then the value of $\cot \alpha$ is $\_\_\_\_$ .

Let $\mathbb{R}$ denote the set of all real numbers and let $i=\sqrt{-1}$. Consider the matrices
$$ S=\left[\begin{array}{rr} 0 & -1 \\ 1 & 0 \end{array}\right] \quad \text { and } \quad T=\left[\begin{array}{ll} 1 & 1 \\ 0 & 1 \end{array}\...

The value of the definite integral\(\int\limits_{0}^{2} \frac{1}{3^x + 3} dx\)is

Let $y : (-\infty, \infty) \to (0, \infty)$ be the solution of the differential equation
\(\frac{dy}{dx} = \frac{e^{5x} y^3 + y^3}{e^x + e^x y^4},\)
satisfying $y(0) = \frac{1}{\sqrt{2}}$. Then the value of $y(\log_e 2)$ is

Let $y = f(x)$ be the real valued function defined on the interval $(0, \infty)$, satisfying $y(1) = 0$ and the differential equation\(x \frac{dy}{dx} = y - x^3.\)Then which of the following statements is (are) TRUE?

Let $\mathbb{R}$ denote the set of all real numbers. Consider the polynomial function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined by
$$ f(x)=\frac{d^{10}}{d x^{10}}\left(\left(x^2-1\right)^{10}\right), \quad \text { for all } x \in \math...

Consider the ellipses given by
\(x^2+4 y^2=1 \quad \text { and } \quad 4 x^2+y^2=1\)
Let $P$ be the point in the first quadrant where the given ellipses intersect. If $\theta$ is the acute angle between the tangents to the given ellipses ...

Let $\mathbb{N}$ denote the set of all positive integers. Consider the sets
\(A=\{1,2,3,4,5\} \text { and } B=\{1,2,3,4,5,6,7\} .\)
Let $S$ be the set of all functions $f: A \rightarrow B$ such that $f(2) \neq 2$ and $f(4) \neq 4$. Consid...

Consider the ellipse $E$ given by $\frac{x^2}{18}+\frac{y^2}{12}=1$. Let $H$ be the hyperbola whose eccentricity is the reciprocal of the eccentricity of $E$ and whose foci are the same as that of $E$. Let $P$ and $Q$ be the points of inter...

For a real number $\alpha$, let $[\alpha]$ denote the greatest integer less than or equal to $\alpha$. For a finite set $S$, let $|S|$ denote the number of elements in the set $S$.
Consider the functions $f:(-3,3) \rightarrow(-\infty, \inft...

Let T be the tangent to the parabola $y^2 = 16x$ at the point $(64, 32)$. Let L be the tangent to the same parabola at another point $(x_1, y_1)$ on the parabola. If L and T are perpendicular to each other, then the distance between the poi...

A bookshelf contains 6 distinct books of Mathematics and 5 distinct books of Physics. From these 11 books, 6 books are chosen at random. Let $X$ be the absolute value of the difference between the number of Mathematics books chosen and the ...

Let a, b, c be positive integers in arithmetic progression such that the equation\(ax^2 + bx + c = 0\)has only integer solutions.Then which of the following statements is (are) TRUE?

Consider a data consisting of 10 observations $x_1, x_2, \ldots, x_{10}$, whose mean is 5 and variance is 7 . If the mean and the variance of the first 8 observations $x_1, x_2, \ldots, x_8$ are 4 and 3.5 , respectively, and $x_9 < x_{10}$,...

Consider the curve $C_1$ given by
\(y=e^{-x} \quad \text { for } x \in[0,10 \pi],\)
and the curve $C_2$ given by
\(y=e^{-x}(\sin x+\cos x) \quad \text { for } x \in[0,10 \pi] .\)
Let $n$ be the total number of points of intersection of ...

Let $ \vec{a}, \vec{b} $ be two vectors, and let P, Q and R be the points with position vectors $ \vec{a}, \vec{b} $ and $ \vec{a} + \vec{b} $, respectively, with respect to the origin O. If $ |\vec{a} + \vec{b}| = \sqrt{21} $, $ |\vec{a} -...

A nuclear reactor starts producing a radioactive nuclide X from t = 0, at a constant rate of α per second. Each decay of X produces energy E0, which is utilized to heat a liquid of mass m and specific heat s. Assuming no heat loss from the ...

A container of height 2 m , length 2 m and breadth 1 m is made of insulating vertical walls and two large area horizontal metal plates ( $\mathrm{M}_1$ and $\mathrm{M}_2$ ) which extend far beyond the vertical walls in all directions. The c...

A metal wire of cross-sectional area 0.5 mm2 and length 100 m is connected across a battery of e.m.f. 2 V and internal resistance 1 Ω. The density, atomic mass and electrical conductivity of the metal are 6.35 × 103 kg m−3, 63.5 gm/mole and...

As shown in the figure, the resistance of a galvanometer G can be found by the half-deflection method. Here the resistance R2 is adjusted such that when the key K is closed the deflection in the galvanometer becomes half of the value as com...

Two charges $Q_1 = q$ and $Q_2 = mq$ are placed at the points $P_1(a, b)$ and $P_2(ma, mb)$, respectively, in the $XY$ plane, where $a, b \neq 0$ and $m \neq 0, 1$. If $V_1$ is the potential at a point in the $XY$ plane due to charge $Q_1$ ...

Consider an electric dipole comprising two charges $+q$ and $-q$ each with mass $m$, separated by a fixed distance $d$ and initially at rest with its dipole moment pointing along $\hat{\imath}$. A uniform electric field $E \hat{\jmath}$ is ...

A beam of polychromatic light passes through a thin prism of prism angle $6^{\circ}$. The refractive index of the material of the prism varies with wavelength $(\lambda)$ as $n(\lambda) = \alpha \lambda + \frac{\beta}{\lambda^2}$, where $\a...

Consider two isosceles prisms 1 and 2 with prism angles $A_1$ and $A_2$ and refractive indices $n_1$ and $n_2$, respectively, as shown in the figure. The faces $a_1 b_1$ and $a_2 b_2$ are parallel to each other and perpendicular to the mirr...

A particle of mass m, and angular momentum ℓ is moving in a circular orbit of radius r0 under the influence of an attractive force $\vec{F}(r)=-\frac{k}{r^2} \hat{r}$. Keeping its angular momentum unchanged, the particle is displaced radial...

Ten moles of an ideal monoatomic gas, initially in state $\boldsymbol{a}$ at atmospheric pressure and temperature $T_a=27^{\circ} \mathrm{C}$, is enclosed in a metal cylinder of volume $V_0$ fitted with a frictionless piston. The gas is sud...

In a vacuum chamber, a particle of charge $1\ \mu C$ and mass $1\ \mathrm{mg}$ is projected with a velocity $(\hat{i} + 2\hat{j})\ \mathrm{ms}^{-1}$ from the $XZ$ plane at time $t = 0$ in an electric field of $1\hat{i}\ \mathrm{Vm}^{-1}$. A...

Two thin wires, Wire-1 of diameter 0.650 mm and Wire-2 of unknown diameter d are given. To obtain the value of d, the diameters of the two wires are measured with a screw gauge. The screw gauge has a pitch of 0.5 mm and there are 100 divisi...

A container of height 2 m , length 2 m and breadth 1 m is made of insulating vertical walls and two large area horizontal metal plates ( $\mathrm{M}_1$ and $\mathrm{M}_2$ ) which extend far beyond the vertical walls in all directions. The c...

A uniform circular disk of radius 0.2 m and mass 1 kg is pivoted at its top point $C$ such that it can rotate freely around $C$ in the $X Y$ plane, as shown in the figure. Initially, when the disk is at rest, a particle of mass 20 g , trave...