JEE Main 2026 · 21 Jan 2026 · Shift 2

Q1.Consider two identical metallic spheres of radius $R$ each having charge $Q$ and mass $m$. Their centers have an initial separation of $4R$. Both the spheres are given an initial speed of $u$ towards each other. The minimum value of $u$, so that they can just touch e …

Q2.The charge stored by the capacitor C in the given circuit in the steady state is $\_\_\_\_$ $\mu \mathrm{C}$.

Q3.The total length of potentiometer wire AB is 50 cm in the arrangement as shown in figure. If P is the point where the galvanometer shows zero reading then the length AP is $\_\_\_\_$ cm .

Q4.A capacitor C is first charged fully with potential difference of ${\mathrm{V}}_0$ and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L . In t s $25\%$ of the initial energy in the capacitor is transferred to the induct …

Q5.The r.m.s speed of oxygen molecules at $47^{\circ }\mathrm{C}$ is equal to that of the hydrogen molecules kept at $\_\_\_\_$ ${}^{\circ }\mathrm{C}$. (Mass of oxygen molecule/mass of hydrogen molecule=32/2)

Q6.Two cars A and B each of mass $10^3\mathrm{kg}$ are moving on parallel tracks separated by a distance of 10 m , in same direction with speeds $72\mathrm{km}/\mathrm{h}$ and $36\mathrm{km}/\mathrm{h}$. The magnitude of angular momentum of car A with respect to ca …

Q7.The pulley shown in figure is made using a thin rim and two rods of length equal to diameter of the rim. The rim and each rod have a mass of M . Two blocks of mass of M and m are attached to two ends of a light string passing over the pulley, which is hinged to rotate freely in v …

Q8.The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of $176\mathrm{rad}/\mathrm{s}$. The frequency of this simple harmonic oscillator is___ Hz. $[$ take $\pi =\frac{22}{7}]$

Q9.Given below are two statements:
Statement I: In a Young's double slit experiment, the angular separation of fringes will increase as the screen is moved away from the plane of the slits
Statement II : In a Young's double slit experiment, the angular separation of fringes will inc …

Q10.A battery with EMF E and internal resistance $r$ is connected across a resistance $R$. The power consumption in R will be maximum when :

Q11.Keeping the significant figures in view, the sum of the physical quantities $52.01\mathrm{m},153.2\mathrm{m}$ and 0.123 m is :

Q12.A spherical body of radius $r$ and density $\sigma$ falls freely through a viscous liquid having density $\rho$ and viscosity $\eta$ and attains a terminal velocity ${\mathrm{v}}_0$. Estimated maximum error in the quantity $\eta$ is : (Ignore errors associated with …

Q13.Surface tension of two liquids (having same densities), ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$, are measured using capillary rise method utilizing two tubes with inner radii of $r_1$ and $r_2$ where $r_1>r_2$. The measured liquid heights in these tubes are …

Q14.A river of width 200 m is flowing from west to east with a speed of $18\mathrm{km}/\mathrm{h}$. A boat, moving with speed of $36\mathrm{km}/\mathrm{h}$ in still water, is made to travel one-round trip (bank to bank of the river). Minimum time taken by the boat for thi …

Q15.Two known resistance of $\mathrm{R}\Omega$ and $2\mathrm{R}\Omega$ and and one unknown resistance $\mathrm{X}\Omega$ are connected in a circuit as shown in the figure. If the equivalent resistance between points A and B in the circuit is $\mathrm{X}\Omega$, then the …

Q16.The energy of an electron in an orbit of the Bohr's atom is $-0.04{\mathrm{E}}_0\mathrm{eV}$ where ${\mathrm{E}}_0$ is the ground state energy. If L is the angular momentum of the electron in this orbit and h is the Planck's constant, then …

Q17.An infinitely long straight wire carrying current I is bent in a planer shape as shown in the diagram. The radius of the circular part is r . The magnetic field at the centre O of the circular loop is :

Q18.A large drum having radius R is spinning around its axis with angular velocity $\omega$, as shown in figure. The minimum value of $\omega$ so that a body of mass M remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mas …

Q19.A body of mass 2 kg is moving along x-direction such that its displacement as function of time is given by $\mathrm{x}(\mathrm{t})=\alpha {\mathrm{t}}^2+\beta \mathrm{t}+\gamma \mathrm{m}$, where $\alpha =1\mathrm{m}/{\mathrm{s}}^2$, $\beta =1\mathrm{m}/\mathrm{s}$ an …

Q20.As shown in the diagram, when the incident ray is parallel to base of the prism, the emergent ray grazes along the second surface.

If refractive index of the material of prism is $\sqrt{2}$, the angle $\theta$ of prism is.

Q21.An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, $\sigma =10\mathrm{mho}/\mathrm{m}$. The ratio of maximum conducting current density to maximum displacement current density is ____ .

$[$ Take …

Q22.The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is $20\mathrm{cm}/\mathrm{s}$. The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be
____ $\mathrm{cm}/\mathrm{s}$.

Q23.A particle having electric charge $3\times 10^{-19}\mathrm{C}$ and mass $6\times 10^{-27}\mathrm{kg}$ is accelerated by applying an electric potential of 1.21 V . Wavelength of the matter wave associated with the particle is $\alpha \times 10^{-12}\mathrm{m}$. The va …

Q24.In a Young's double slit experiment set up, the two slits are kept 0.4 mm apart and screen is placed at 1 m from slits. If a thin transparent sheet of thickness $20\mu \mathrm{m}$ is introduced in front of one of the slits then centre bring fringe shifts by 20 mm on the screen …

Q25.A diatomic gas $(\gamma =1.4)$ does 100 J of work when it is expanded isobarically. Then the heat given to the gas ______ J.

Q1.Consider the following spectral lines for atomic hydrogen:
A. First line of Paschen series
B. Second line of Balmer series
C. Third line of Paschen series
D. Fourth line of Bracket series

The correct arrangement of the above lines in ascending order of energy is:

Q2.Match List-I with List-II.

List-I (Pair of Compounds):
A. 2-Methylpropene and but-1-ene
B. Cis-but-2-ene and trans-but-2-ene
C. 2-Butanol and diethyl ether
D. But-1-ene and but-2-ene

List-II (Type of Isomers):
I. Stereoisomers
II. Position isomers
III. Chain isomers
IV. Functio …

Q3.Consider the above sequence of reactions. The number of bromine atom(s) in the final product (P) will be:

(1) ${\mathrm{Br}}_2/{\mathrm{FeBr}}_3/\Delta$
(2) $\mathrm{Sn}/\mathrm{HCl}/\Delta$
(3) pH neutralisation
(4) ${\mathrm{Br}}_2/{\mathrm{H}}_2\mathrm{O}$
(5) …

Q4.Aqueous HCl reacts with ${\mathrm{MnO}}_2(\mathrm{s})$ to form ${\mathrm{MnCl}}_2(\mathrm{aq})$, ${\mathrm{Cl}}_2(\mathrm{g})$ and ${\mathrm{H}}_2\mathrm{O}(l)$. What is the weight (in g) of ${\mathrm{Cl}}_2$ liberated when 8.7 g of ${\mathrm{MnO}}_2(\mathrm{s})$ is reacted w …

Q5.By usual analysis, 1.00 g of compound (X) gave 1.79 g of magnesium pyrophosphate. The percentage of phosphorus in compound (X) is: (nearest integer)
(Given, molar mass in $\mathrm{g}{\mathrm{mol}}^{-1}$: O=16, Mg=24, P=31)

Q6.Consider the following data:
${\Delta }_{\mathrm{f}}{\mathrm{H}}^{\Theta }$(methane, g)$=-\mathrm{X}\mathrm{kJ}{\mathrm{mol}}^{-1}$
Enthalpy of sublimation of graphite $=\mathrm{Y}\mathrm{kJ}{\mathrm{mol}}^{-1}$
Dissociation enthalpy of …

Q7.Match List-I with List-II.

List-I (Reaction Name - Involving aldehydes):
I. Etard Reaction
II. Rosenmund Reduction
III. Gatterman-Koch Reaction
IV. Stephen Reaction

List-II (Reagents):
A. ${\mathrm{H}}_2$, Pd-${\mathrm{BaSO}}_4$
B. ${\mathrm{SnCl}}_2$, HCl
C. …

Q8.Decomposition of A is a first order reaction at $\mathrm{T}(\mathrm{K})$ and is given by $\mathrm{A}(\mathrm{g})\to \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$. In a closed 1 L vessel, 1 bar $\mathrm{A}(\mathrm{g})$ is allowed to decompose at $\mathrm{T}(\mathrm{K})$. …

Q9.The correct order of reactivity of the following benzyl halides towards reaction with KCN is:

Q10.Given below are two statements:

Statement-I: The correct order in terms of atomic/ionic radii is $\mathrm{Al}>\mathrm{Mg}>{\mathrm{Mg}}^{2+}>{\mathrm{Al}}^{3+}$.

Statement-II: The correct order in terms of the magnitude of electron gain enthalpy is …

Q11.The correct statements are:
A. Activation energy for enzyme catalysed hydrolysis of sucrose is lower than that of acid catalysed hydrolysis.
B. During denaturation, secondary and tertiary structures of a protein are destroyed but primary structure remains intact.
C. Nucleotides a …

Q12.The correct order of the rate of the reaction for the following reaction with respect to nucleophiles is:
${\mathrm{CH}}_3\mathrm{Br}+{\mathrm{Nu}}^{\Theta }⟶{\mathrm{CH}}_3\mathrm{Nu}+{\mathrm{Br}}^{\Theta }$

Q13.Given below are two statements:

Statement I: Crystal Field Stabilization Energy (CFSE) of ${\left[\mathrm{Cr}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{2+}$ is greater than that of ${\left[\mathrm{Mn}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{2+}$.

Statement II: Pot …

Q14.The correct increasing order of $\mathrm{C}-\mathrm{H}(\mathrm{A})$, $\mathrm{C}-\mathrm{O}(\mathrm{B})$, $\mathrm{C}=\mathrm{O}(\mathrm{C})$ and $\mathrm{C}\equiv \mathrm{N}(\mathrm{D})$ bonds in terms of covalent bond length is:

Q15.Given below are four compounds:
(a) n-propyl chloride
(b) iso-propyl chloride
(c) sec-butyl chloride
(d) neo-pentyl chloride

Percentage of carbon in the one which exhibits optical isomerism is:

Q16.Given below are some of the statements about Mn and ${\mathrm{Mn}}_2{\mathrm{O}}_7$. Identify the correct statements
A. Mn forms the oxide ${\mathrm{Mn}}_2{\mathrm{O}}_7$ in which Mn is in its highest oxidation state.
B. Oxygen stabilizes the Mn in higher oxidation states by fo …

Q17.For a closed circuit Daniell cell, which of the following plots is the accurate one at a given temperature?

Q18.Given below are two statements:

Statement-I: Compound (X), shown below, dissolves in ${\mathrm{NaHCO}}_3$ solution and has two chiral carbon atoms

Statement-II: Compound (Y), shown below, has two carbons with ${\mathrm{sp}}^3$ hybridization, one carbon with ${\mathrm{sp}}^2$ an …

Q19.Given below are two statements:

Statement I: The correct order in terms of bond dissociation enthalpy is ${\mathrm{Cl}}_2>{\mathrm{Br}}_2>{\mathrm{F}}_2>{\mathrm{I}}_2$
Statement II: The correct trend in the covalent character of the metal halides is …

Q20.On heating a mixture of common salt and ${\mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7$ in equal amount along with concentrated ${\mathrm{H}}_2{\mathrm{SO}}_4$ in a test tube, a gas is evolved. Formula of the gas evolved and oxidation state of the central metal atom in the gas r …

Q21.The first and second ionization constants of ${\mathrm{H}}_2\mathrm{X}$ are $2.5\times 10^{-8}$ and $1.0\times 10^{-13}$ respectively. The concentration of ${\mathrm{X}}^{2-}$ in $0.1\mathrm{M}$ ${\mathrm{H}}_2\mathrm{X}$ solution is $\_\_\_\_$ $\times 10^{-15}\mathrm{M}$. (N …

Q22.The osmotic pressure of a living cell is 12 atm at 300 K. The strength of sodium chloride solution that is isotonic with the living cell at this temperature is $\_\_\_\_$ $\mathrm{g}{\mathrm{L}}^{-1}$. (Nearest integer)

Given: …

Q23.A substance 'X' (1.5 g) dissolved in 150 g of a solvent 'Y' (molar mass $=300\mathrm{g}{\mathrm{mol}}^{-1}$) led to an elevation of the boiling point by 0.5 K. The relative lowering in the vapour pressure of the solvent 'Y' is $\_\_\_\_$ $\times 10^{-2}$. (Nearest integer)
[Giv …

Q24.Identify the metal ions among ${\mathrm{Co}}^{2+}$, ${\mathrm{Ni}}^{2+}$, ${\mathrm{Fe}}^{2+}$, ${\mathrm{V}}^{3+}$ and ${\mathrm{Ti}}^{2+}$ having a spin-only magnetic moment value more than 3.0 BM. The sum of unpaired electrons present in the high spin octahedral complexes formed by thos …

Q25.MX is a sparingly soluble salt that follows the given solubility equilibrium at 298 K
$\mathrm{MX}(\mathrm{s})\rightleftharpoons {\mathrm{M}}^{+}(\mathrm{aq})+{\mathrm{X}}^{-}(\mathrm{aq})$; ${\mathrm{K}}_{\mathrm{sp}}=10^{-10}$
If the standard reduction potential for …

Q1.The positive integer n, for which the solutions of the equation

are two consecutive even integers, is :-

Q2.Let $f:\mathbf{R}\to \mathbf{R}$ be a twice differentiable function such that $f^{\prime \prime }(x)>0$ for all $x\in \mathbf{R}$ and $f^{\prime }(a-1)=0$, where a is real number. Let $g(x)=f\left({\tan }^{2}x-2\tan x+a\right)$, $0<x<\frac{\pi }{2}$.

Consider the following two statements:
(I) g i …

Q3.Let $f(x)=x^3+x^2{f}^{\prime }(1)+2x{f}^{\prime \prime }(2)+f^{\prime \prime \prime }(3)$, $x\in \mathbf{R}$. Then the value of $f^{\prime }(5)$ is :

Q4.In the line $\alpha x+4y=\sqrt{7}$, where $\alpha \in \mathbf{R}$, touches the ellipse $3x^2+4y^2=1$ at the point P in the first quadrant, then one of the focal distances of P is :

Q5.Let $y^2=12x$ be the parabola with its vertex at O. Let P be a point on the parabola and A be a point on the x-axis such that $\angle OPA=90^{\circ }$. Then the locus of the centroid of such triangles OPA is :

Q6.Let one end of a focal chord of the parabola $y^2=16x$ be (16, 16). If $P(\alpha ,\beta )$ divides this focal chord internally in the ratio $5:2$, then the minimum value of $\alpha +\beta$ is equal to :

Q7.Let the line L pass through the point $(-3,5,2)$ and make equal angles with the positive coordinate axes. If the distance of L from the point $(-2,r,1)$ is $\sqrt{\frac{14}{3}}$, then the sum of all possible values of $r$ is :

Q8.Let the line $L_1$ be parallel to the vector $-3\hat{i}+2\hat{j}+4\hat{k}$ and pass through the point $(2,6,7)$ and the line $L_2$ be parallel to the vector $2\hat{i}+\hat{j}+3\hat{k}$ and pass through the point $(4,3,5)$. If the line $L_3$ is parallel to the vector …

Q9.Let $\alpha$ and $\beta$ be the roots of equation $x^2+2ax+(3a+10)=0$ such that $\alpha <1<\beta$. Then the set of all possible values of $a$ is :

Q10.A random variable $X$ takes values $0,1,2,3$ with probabilities $\frac{2a+1}{30}$, $\frac{8a-1}{30}$, $\frac{4a+1}{30}$, b respectively, where $a,b\in \mathbf{R}$. Let $\mu$ and $\sigma$ respectively be the mean and standard deviation of X such that ${\sigma }^2+{\mu }^2=2$.
Then …

Q11.If the area of the region $\{(x,y):1-2x\le y\le 4-x^2,x\ge 0,y\ge 0\}$ is $\frac{\alpha }{\beta }$, $\alpha ,\beta \in \mathbf{N}$, $\gcd (\alpha ,\beta )=1$, then the value of $(\alpha +\beta )$ is :

Q12.Let $a_1,\frac{a_2}{2},\frac{a_3}{2^2},\dots ,\frac{a_{10}}{2^9}$ be a G.P. of common ratio $\frac{1}{\sqrt{2}}$. If $a_1+a_2+\dots +a_{10}=62$, then $a_1$ is equal to :

Q13.Let $\mathrm{A}=\left\{\mathrm{x}:\left|{\mathrm{x}}^2-10\right|\le 6\right\}$ and $\mathrm{B}=\{\mathrm{x}:|\mathrm{x}-2|>1\}$.

Then

Q14.For the matrices $\mathrm{A}=\left[\begin{array}{cc}3& -4\\ 1& -1\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{cc}-29& 49\\ -13& 18\end{array}\right]$, if …

Q15.For a triangle $ABC$, let $\vec{p}=\overrightarrow{BC},\vec{q}=\overrightarrow{CA}$ and $\overrightarrow{\mathrm{r}}=\overrightarrow{\mathrm{BA}}$. If $|\overrightarrow{\mathrm{p}}|=2\sqrt{3},|\overrightarrow{\mathrm{q}}|=2$ and $\cos \theta =\frac{1}{\sqrt{3}}$, where $\theta$ …

Q16.Let $y=y(x)$ be the solution of the differential equation $\sec x\frac{\mathrm{dy}}{\mathrm{dx}}-2\mathrm{y}=2+3\sin \mathrm{x},\mathrm{x}\in \left(-\frac{\pi }{2},\frac{\pi }{2}\right)$, $y(0)=-\frac{7}{4}$. Then $y\left(\frac{\pi }{6}\right)$ is equal to:

Q17.Let $\mathrm{A}=\{2,3,5,7,9\}$. Let R be the relation on A defined by x Ry if and only if $2\mathrm{x}\le 3\mathrm{y}$. Let $\ell$ be the number of elements in R, and m be the minimum number of elements required to be added in R to make it a symmetric relation. Then …

Q18.If the system of equations
$3\mathrm{x}+\mathrm{y}+4\mathrm{z}=3$
$2\mathrm{x}+\alpha \mathrm{y}-\mathrm{z}=-3$
$\mathrm{x}+2\mathrm{y}+\mathrm{z}=4$
has no solution, then the value of $\alpha$ is equal to:

Q19.Let z be the complex number satisfying $|\mathrm{z}-5|\le 3$ and having maximum positive principal argument.
Then $34{\left|\frac{5z-12}{5iz+16}\right|}^2$ is equal to:

Q20.The largest $\mathrm{n}\in \mathrm{N}$, for which $7^{\mathrm{n}}$ divides 101!, is:

Q21.Let $[\cdot ]$ denote the greatest integer function and $f(\mathrm{x})={\lim }_{\mathrm{n}\to \infty }\frac{1}{{\mathrm{n}}^3}{\sum }_{\mathrm{k}=1}^{\mathrm{n}}\left[\frac{{\mathrm{k}}^2}{3^{\mathrm{x}}}\right]$. Then $12{\sum }_{\mathrm{j}=1}^{\infty }f(\mathrm{j})$ is equal …

Q22.If ${\int }_0^{1}4{\cot }^{-1}\left(1-2\mathrm{x}+4{\mathrm{x}}^2\right)\mathrm{dx}=\mathrm{a}{\tan }^{-1}(2)-\mathrm{b}{\log }_{\mathrm{e}}(5)$, where $\mathrm{a},\mathrm{b}\in \mathbf{N}$, then $(2\mathrm{a}+\mathrm{b})$ is equal to ____.

Q23.Let the maximum value of ${\left({\sin }^{-1}\mathrm{x}\right)}^2+{\left({\cos }^{-1}\mathrm{x}\right)}^2$ for $x\in \left[-\frac{\sqrt{3}}{2},\frac{1}{\sqrt{2}}\right]$ be $\frac{m}{n}{\pi }^2$, where $\gcd (m,n)=1$.

Then $\mathrm{m}+\mathrm{n}$ is equal to ____.

Q24.If …

Q25.If P is a point on the circle $x^2+y^2=4$, Q is a point on the straight line $5x+y+2=0$ and $x-y+1=0$ is the perpendicular bisector of PQ, then 13 times the sum of abscissa of all such point P is ______.