JEE Advanced 2026 · 17 May 2026 · Paper 2

Q1.A metal wire of cross-sectional area $0.5{\mathrm{mm}}^2$ and length 100 m is connected across a battery of e.m.f. 2 V and internal resistance $1\Omega$. The density, atomic mass and electrical conductivity of the metal are …

Q2.A nuclear reactor starts producing a radioactive nuclide $X$ from $t=0$, at a constant rate of $\alpha$ per second. Each decay of $X$ produces energy $E_0$, which is utilized to heat a liquid of mass $m$ and specific heat $s$. Assuming no heat loss from the liquid …

Q3.A beam of polychromatic light passes through a thin prism of prism angle 6°. The refractive index of the material of the prism varies with wavelength $(\lambda )$ as $n(\lambda )=\alpha \lambda +\frac{\beta }{{\lambda }^2}$, where $\alpha =3\mu {\mathrm{m}}^{-1}$ and …

Q4.A particle of mass $m$, and angular momentum $\ell$ is moving in a circular orbit of radius $r_0$ 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 radially by a small dist …

Q5.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 mirror $M$. If …

Q6.In a vacuum chamber, a particle of charge $1\mu \mathrm{C}$ and mass 1 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 $1\hat{ı}{\mathrm{Vm}}^{-1}$. At $t=0.2\mathrm{s}$, the elec …

Q7.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 $a,b\ne 0$ and $m\ne 0,1$. If $V_1$ is the potential at a point in the $XY$ plane due to charge $Q_1$ and …

Q8.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 $\hat{ı}$. A uniform electric field $E\hat{j}$ is turned on at time $t=0$ and it …

Q9.Ten moles of an ideal monoatomic gas, initially in state $\mathbf{a}$ 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 suddenly compressed to state …

Q10.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 divisions on the circular scale (CS). …

Q11.In a single slit diffraction experiment, a slit of width $(0.016\pm 0.002)\mathrm{mm}$ is used to measure the wavelength of a monochromatic light source. In the diffraction pattern, the angular distance between the central maximum and first minimum is measured to be …

Q12.As shown in the figure, a ray $AB$ of unpolarized light enters from water of refractive index $n_w=4/3$ into a medium of refractive index $n_p=4/\sqrt{3}$ after passing through a glass plate of refractive index $n_g=1.5$ and a layer of water. At a particular inc …

Q13.As shown in the figure, the resistance of a galvanometer $G$ can be found by the half-deflection method. Here the resistance $R_2$ is adjusted such that when the key $K$ is closed the deflection in the galvanometer becomes half of the value as compared to when $K$ is op …

Q14.In a new system of units, the units of mass, length, time and current are 5 kg, 5 m, 5 s and 5 A, respectively. If ${\mu }_0$ and ${ϵ}_0$ are the permeability and permittivity of free space, respectively, then in this new system of units, the magnitude of one SI unit of …

Q15.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 container is partitioned into two eq …

Q16.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 container is partitioned into two eq …

Q17.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 $XY$ plane, as shown in the figure. Initially, when the disk is at rest, a particle of mass 20 g, travelling along negative $x$ direction …

Q18.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 $XY$ plane, as shown in the figure. Initially, when the disk is at rest, a particle of mass 20 g, travelling along negative $x$ direction …

Q1.At 300 K, the molar conductivities of the aqueous solutions of three salts at two different concentrations are given below:
| …

Q2.The correct order of ONO bond angle in the given species is:

Q3.Natural rubber on complete ozonolysis (${\text{O}}_3/\text{Zn}-{\text{H}}_2\text{O}$) gives compound $\mathbf{X}$ as the major product. X gives positive iodoform and Tollen's tests. X on heating with aqueous NaOH gives Y as the major product. Y is

Q4.A known artificial sweetener X is composed of 4-chloro-4-deoxy-α-D-galactose and 1,6-dichloro-1,6-dideoxy-β-D-fructose joined by a glycosidic linkage. Structure of D-galactose is given below:

The correct structure of $\mathbf{X}$ is:

Q5.For a first-order reaction $\mathbf{R}\to \mathbf{P}$ 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 $[\mathbf{R}]$ and $[\mathbf{P}]$, respectively. The …

Q6.Correct statement(s) about the compounds $\mathbf{P}$, $\mathbf{Q}$ and $\mathbf{R}$ is(are)

$\text{Xe}(g)+{\text{F}}_2(g)\stackrel{873\text{ K},7\text{ bar}}{\to }\mathbf{P}$ (1:5 ratio)

$\mathbf{P}+{\text{O}}_2{\text{F}}_2\stackrel{143\text{ K}}{\to }\mathbf{Q}+{\text{O}}_2$ …

Q7.The correct statement(s) regarding the periodic properties of elements is (are)

Q8.In the following reaction sequence, P, Q, S and T are the major products.

The correct statement(s) about $\mathbf{P}$, $\mathbf{Q}$, $\mathbf{S}$ and $\mathbf{T}$ is (are)

Q9.The correct statement(s) regarding sugars is (are)

Given: Specific rotations of L-(-)-glucose and L-(+)-fructose are -52.5° and +92.5°, respectively.

Q10.${\mathbf{X}}^{\mathbf{a}+}$ and ${\mathbf{Y}}^{\mathbf{b}+}$ 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 ${\mathbf{X}}^{\mathbf{a}+}$ is $\lambda$. The wavelength of light absorb …

Q11.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 isotherm,

If the …

Q12.In a solvent S, a compound B is partially dissociated into C and D as given below:

B, C and D are non-volatile in nature. The molar mass of B is 10 times the molar mass of S. The standard boiling point and the standard e …

Q13.Consider that the coordinating atoms of the ligands in cis-$[\text{Co}({\text{NH}}_3{)}_4{\text{Cl}}_2]\text{Cl}$ and mer-$[\text{Co}({\text{NH}}_3{)}_3{\text{Cl}}_3]$ octahedral complexes are at the vertices of an octahedron. The sum of total number of the triangular faces in both the compl …

Q14.In the following reaction sequence, major products $\mathbf{X}$ and $\mathbf{Y}$ are acyclic monomers. …

Q15.Two volatile liquids A and B form an ideal solution. Consider a 5 molal solution of B in A inside a closed container having a total vapour pressure of 100 mm Hg at 300 K. The vapour pressure of pure A at 300 K is 105 mm Hg. Assume that $\mathbf{A}$ and $\mathbf{B}$ behave as idea …

Q16.Two volatile liquids A and B form an ideal solution. Consider a 5 molal solution of B in A inside a closed container having a total vapour pressure of 100 mm Hg at 300 K. The vapour pressure of pure A at 300 K is 105 mm Hg. Assume that $\mathbf{A}$ and $\mathbf{B}$ behave as idea …

Q17.Consider the following reaction sequence in which J, K, L and M are the major products.

Given:
Atomic mass (in amu): H : 1, C : 12, N : 14, O : 16, S : 32, Br : 80, Ba : 137

The volume of 1 M aqueous ${\text{H}}_2{\text{SO}}_4$ required to completely neutralize the ammonia evolved …

Q18.Consider the following reaction sequence in which J, K, L and M are the major products.

Given:
Atomic mass (in amu): H : 1, C : 12, N : 14, O : 16, S : 32, Br : 80, Ba : 137

In sulphur estimation by Carius method, the amount of ${\text{BaSO}}_4$ formed from 3.79 g of $\mathbf{M}$ …

Q1.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 …

Q2.Let T be the tangent to the parabola ${\mathrm{y}}^2=16\mathrm{x}$ at the point (64, 32). Let L be the tangent to the same parabola at another point $\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)$ on the parabola. If L and T are perpendicular to each other, then the distance betwe …

Q3.Let $\mathrm{y}:(-\infty ,\infty )\to (0,\infty )$ be the solution of the differential equation

satisfying $\mathrm{y}(0)=\frac{1}{\sqrt{2}}$. Then the value of $\mathrm{y}\left({\log }_{\mathrm{e}}2\right)$ …

Q4.The value of the definite integral

Q5.Let $\mathbb{R}$ denote the set of all real numbers. Consider the polynomial function $\mathrm{f}:\mathbb{R}\to \mathbb{R}$ defined by …

Q6.Let a,b,c be positive integers in arithmetic progression such that the equation
${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0$
has only integer solutions.
Then which of the following statements is (are) TRUE ?
(A) $\mathrm{c}-\mathrm{b}$ is an integer multiple of a
(B) Both the roots …

Q7.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 $\mathrm{R}(4,-1,5)$ to the line L. Another line passing through R intersects L at a point T such that the point S divides the line segment PT intern …

Q8.Let $\mathrm{y}=f(\mathrm{x})$ be the real valued function defined on the interval $(0,\infty )$, satisfying $\mathrm{y}(1)=0$ and the differential equation

Then which of the following statements is (are) TRUE ?
(A) The function $f$ has a local minim …

Q9.Let $\mathbb{R}$ denote the set of all real numbers and let $\mathrm{i}=\sqrt{-1}$. Consider the matrices
$\mathrm{S}=\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]$ and $\mathrm{T}=\left[\begin{array}{ll}1& 1\\ 0& 1\end{array}\right]$.
Let …

Q10.Let $\mathbb{N}$ denote the set of all positive integers. Consider the sets

Let S be the set of all functions $f:\mathrm{A}\to \mathrm{B}$ such that $f(2)\ne 2$ and $f(4)\ne 4$. Consider the s …

Q11.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 number of Physics books chosen. If …

Q12.Consider a data consisting of 10 observations ${\mathrm{x}}_1,{\mathrm{x}}_2,\dots ,{\mathrm{x}}_{10}$, whose mean is 5 and variance is 7 . If the mean and the variance of the first 8 observations ${\mathrm{x}}_1,{\mathrm{x}}_2,\dots ,{\mathrm{x}}_8$ are 4 and 3.5, respective …

Q13.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 intersection of H and the parabola …

Q14.For a real number $\alpha$, let $[\alpha ]$ denote the greatest integer less than or equal to $\alpha$. For a finite set S , let $|\mathrm{S}|$ denote the number of elements in the set S .

Consider the functions $f:(-3,3)\to (-\infty ,\infty )$ and …

Q15.Consider the curve ${\mathrm{C}}_1$ given by

and the curve ${\mathrm{C}}_2$ given by

L …

Q16.Consider the curve ${\mathrm{C}}_1$ given by

and the curve ${\mathrm{C}}_2$ given by

L …

Q17.Consider the ellipses given by

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 at the point P , then the value of …

Q18.Consider the ellipses given by

If $\alpha$ is the area of the common region that lies inside both the given ellipses, then the value of $\cot \alpha$ is ____.