JEE Main 2026 · 08 Apr 2026 · Shift 2

Q1.A new unit ($\alpha$) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of $\alpha$ units if light takes 6 min. 40 s to cover this distance?

Q2.Consider the equation $H=\frac{x^p{ϵ}^q{E}^r}{t^s}$

Where $\mathrm{H}=$ magnetic field; $\mathrm{E}=$ electric field; $ϵ=$ permittivity, $\mathrm{x}=$ distance, $\mathrm{t}=$ time. The values of $p,q,r$ and $s$ respectively are :

Q3.A car moving with a speed of $54\mathrm{km}/\mathrm{h}$ takes a turn of radius 20 m. A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take …

Q4.A gas balloon is going up with a constant velocity of $10\mathrm{m}/\mathrm{s}$. When this balloon reached a height of 75 m, a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is
____ m …

Q5.A thin biconvex lens is prepared from the glass ($\mu =1.5$) both curved surfaces of which have equal radii of 20 cm each. Left side surface of the lens is silvered from outside to make it reflecting. To have the position of image and object at the same place, the object should …

Q6.Two identical bodies, projected with the same speed at two different angles cover the same horizontal range R. If the time of flight of these bodies are 5 s and 10 s, respectively, then the value of $R$ is ____ m. (Take $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$)

Q7.A solid cylinder having radius R and length L is slipping on a rough horizontal plane. At time $\mathrm{t}=0$ the cylinder has a translational velocity ${\mathrm{v}}_0=49\mathrm{m}/\mathrm{s}$, perpendicular to its axis and a rotational velocity …

Q8.A liquid of density $600\mathrm{kg}/{\mathrm{m}}^3$ flowing steadily in a tube of varying cross-section. The cross-section at a point A is $1.0{\mathrm{cm}}^2$ and that at B is $20{\mathrm{mm}}^2$. Both the points A and B are in same horizontal plane, the speed of t …

Q9.A spherical liquid drop of radius R acquires the terminal velocity ${\mathrm{v}}_1$ when falls through a gas of viscosity $\eta$. Now the drop is broken into 64 identical droplets and each droplet acquires terminal velocity ${\mathrm{v}}_2$ falling through the same gas. The …

Q10.One mole of diatomic gas having rotational modes only is kept is a cylinder with a piston system. The cross-section area of the cylinder is $4{\mathrm{cm}}^2$. The gas is heated slowly to raise the temperature by $1.2{}^{\circ }\mathrm{C}$ during which the piston moves by …

Q11.Initial pressure and volume of a monoatomic ideal gas are P and V. The change in internal energy of this gas in adiabatic expansion to volume ${\mathrm{V}}_{\text{final }}=27\mathrm{V}$ is ____ J.

Q12.The frequency of oscillation of a mass m suspended by spring is ${\mathrm{v}}_1$. If the length of the spring is cut to half, the same mass oscillates with frequency ${\mathrm{v}}_2$. The value of $\frac{{\mathrm{v}}_2}{{\mathrm{v}}_1}$ is ____.

Q13.A monochromatic source of light operating at 15 kW emits $2.5\times 10^{22}$ photons/s. The region of an electromagnetic spectrum to which the emitted electromagnetic radiation belongs to ______.
(Take $\mathrm{h}=6.6\times 10^{-34}\mathrm{J}$.s and …

Q14.A current carrying circular loop of radius 2 cm with unit normal $\hat{n}=\frac{\hat{k}+\hat{i}}{\sqrt{2}}$ is placed in a magnetic field, $\overrightarrow{\mathrm{B}}={\mathrm{B}}_0(3\hat{\mathrm{i}}+2\hat{\mathrm{k}})$. If ${\mathrm{B}}_0=4\times 10^{-3}\mathrm{T}$ and cur …

Q15.A 30 cm long solenoid has 10 turns per cm and area of $5{\mathrm{cm}}^2$. The current through the solenoid coil varies from 2 A to 4 A is 3.14 s. The e.m.f. induced in the coil is $\alpha \times 10^{-5}\mathrm{V}$. The value $\alpha$ is ______.

Q16.Two point charges ${\mathrm{q}}_1=3\mu \mathrm{C}$ and ${\mathrm{q}}_2=-4\mu \mathrm{C}$ are placed at points $(2\hat{i}+3\hat{j}+3\hat{k})$ and $(\hat{i}+\hat{j}+\hat{k})$ respectively. Force on charge ${\mathrm{q}}_2$ is ______ N.
(Take …

Q17.Light ray incident along a vector $\overrightarrow{\mathrm{AO}}(\overrightarrow{\mathrm{AO}}=2\hat{\mathrm{i}}-3\hat{\mathrm{j}})$ emerges out along vector $\overrightarrow{\mathrm{OB}}(\overrightarrow{\mathrm{OB}}=\mathrm{C}\hat{\mathrm{i}}-4\hat{\mathrm{j}})$ as shown in th …

Q18.${\mathrm{K}}_1$ and ${\mathrm{K}}_2$ be the maximum kinetic energies of photoelectrons emitted from a surface of a given material for the light of wavelength ${\lambda }_1$ and ${\lambda }_2$, respectively. If ${\lambda }_1=2{\lambda }_2$ then the work function of material is given …

Q19.Two radioactive substances A and B of mass numbers 200 and 212 respectively, shows spontaneous $\alpha$-decay with same Q value of 1 MeV . The ratio of energies of $\alpha$-rays produced by A and $B$ is ______.

Q20.The output Y for the given inputs A and B to the circuit is :

Q21.A parallel plate capacitor is having separation between plates 0.885 mm . It has a capacitance of $1\mu \mathrm{F}$ when the space between the plates is filled with an insulating material of resistivity $1\times 10^{13}\Omega \mathrm{m}$ and resistance …

Q22.Some distance star is to be observed by some telescope of diameter of objective lens a , at an angular resolution of $3.0\times 10^{-7}$ radian. If the wavelength of light from the star reaching the telescope is 500 nm , the minimum diameter of the objective lens of the telescop …

Q23.A 5 mg particle carrying a charge of $5\pi \times 10^{-6}\mathrm{C}$ is moving with velocity of $(3\hat{\mathrm{i}}+2\hat{\mathrm{k}})\times 10^{-2}\mathrm{m}/\mathrm{s}$ in a region having magnetic field …

Q24.The stored charge in the capacitor in steady state of the following circuit is ______ $\mu \mathrm{C}$.

Q25.Two masses of 3.4 kg and 2.5 kg are accelerated from an initial speed of $5\mathrm{m}/\mathrm{s}$ and $12\mathrm{m}/\mathrm{s}$, respectively. The distances traversed by the masses in the $5^{\text{th }}$ second are 104 m and 129 m, respectively. The ratio of their momen …

Q1.Which of the following are not correct ?
A. For water, magnitude of ${\mathrm{K}}_{\mathrm{b}}$ is more than the magnitude of ${\mathrm{K}}_{\mathrm{f}}$.
B. The elevation in boiling point of water when a non-volative solute is added to it is larger in magnitude than its depression i …

Q2.Consider the following reactions in which all the reactants and products are present in gaseous state
$2\mathrm{xy}\rightleftharpoons {\mathrm{x}}_2+{\mathrm{y}}_2$ ${\mathrm{K}}_1=2.5\times 10^5$
$\mathrm{xy}+\frac{1}{2}{\mathrm{z}}_2\rightleftharpoons \mathrm{xyz}$ …

Q3.Given at $298\mathrm{K}$: ${\mathrm{E}}_{{\mathrm{Fe}}^{2+}/\mathrm{Fe}}^{\ominus }=\mathrm{X}$ Volt
${\mathrm{E}}_{{\mathrm{Fe}}^{3+}/\mathrm{Fe}}^{\ominus }=\mathrm{Y}$ Volt

The ${\mathrm{E}}_{{\mathrm{Fe}}^{3+}/{\mathrm{Fe}}^{2+}}^{\ominus }$ in Volt at 298 K is given by :

Q4.Given below are two statements :
$\mathrm{R}=8.314\mathrm{J}{\mathrm{K}}^{-1}{\mathrm{mol}}^{-1}$ and $1\mathrm{cal}=4.2\mathrm{J}$

Statement I : When $\mathrm{Ea}=12.6\mathrm{kcal}/\mathrm{mol}$, the room temperature rate constant is doubled by a $10^{\circ }\mathrm{C}$ increase …

Q5.Match List-I with List-II.

List-I
Electronic configuration of neutral atom
(where $\mathbf{n}=2$)

A. ${\mathrm{ns}}^2$
B. ${\mathrm{ns}}^2{\mathrm{np}}^1$
C. ${\mathrm{ns}}^2{\mathrm{np}}^3$
D. ${\mathrm{ns}}^2{\mathrm{np}}^6$

List-II
First ionization enthalpy (kJ/mol)

I. 2 …

Q6.Find the correct statements related to group 15 hydrides.
A. Reducing nature increases from ${\mathrm{NH}}_3$ to ${\mathrm{BiH}}_3$
B. Tendency to donate lone pair of electrons decreases from ${\mathrm{NH}}_3$ to ${\mathrm{BiH}}_3$
C. The stability of hydrides decreases from …

Q7.Given below are two statements :

Statement I : The number of pairs among $[{\mathrm{Ti}}^{4+},{\mathrm{V}}^{2+}]$, $[{\mathrm{V}}^{2+},{\mathrm{Mn}}^{2+}]$, $[{\mathrm{Mn}}^{2+},{\mathrm{Fe}}^{3+}]$ and $[{\mathrm{V}}^{2+},{\mathrm{Cr}}^{2+}]$ in which both ions are coloured is 3.

Statemen …

Q8.Given below are two statements for catalytic properties of transition metals :

Statement I : First row transition metals which act as catalyst utilise their 3d electrons only for formation of bonds between reactant molecules and atoms on the surface of catalyst.

Statement II : …

Q9.Given below are two statements :

Statement I: Vapours of the liquid with higher boiling point condense before vapours of the liquid with lower boiling points in fractional distillation.

Statement II : The vapours rising up in the fractionating column become richer in high boili …

Q10.The major product of which of the following reaction is not obtained by rearrangement reaction?

Q11.The total number of aromatic compounds/species from the following is

Q12.n-Butane on monochlorination under photochemical conditions gives an optically active compound "P". "P" on further chlorination gives dichloro compounds.

The number of dichloro compounds obtained (ignore stereoisomers) is :

Q13.Given below are two statements :

Statement-I : Due to increase in van der Waals forces, the order of boiling points is ${\mathrm{CH}}_3{\mathrm{CH}}_2{\mathrm{CH}}_2\mathrm{I}>{\mathrm{CH}}_3{\mathrm{CH}}_2\mathrm{I}>{\mathrm{CH}}_3\mathrm{I}$.

Statement-II : As (see str …

Q14.Consider the following reaction.

(see reaction scheme)

The major product (P) formed is :

Q15.Which statements are True?
(A) In Hoffmann bromamide degradation, 4 moles of NaOH and 2 moles of ${\mathrm{Br}}_2$ are consumed per mole of an amide
(B) Hoffmann bromamide reaction is not given by alkyl amides.
(C) Primary amines can be synthesized by Hoffmann bromamide degradati …

Q16.The incorrect statement from the following with respect to carbohydrates is :

Q17.Which of the following amino acid will give violet coloured complex with neutral ferric chloride solution?

Q18.Number of paramagnetic complexes among the following is ____.
${\left[{\mathrm{MnBr}}_4\right]}^{2-}$, ${\left[{\mathrm{NiCl}}_4\right]}^{2-}$, ${\left[\mathrm{Ni}(\mathrm{CN}{)}_4\right]}^{2-}$, $\left[\mathrm{Ni}(\mathrm{CO}{)}_4\right]$, ${\left[{\mathrm{CoF}}_6\right]}^{3-}$, …

Q19.'x' is the product which is obtained from benzene by reacting it with carbon monoxide and hydrogen chloride in the presence of cuprous chloride. 'y' is the major product obtained from the benzene by reacting it with ethanoyl chloride in the presence of anhydrous …

Q20.Consider two radiations of wavelengths :

1. ${\lambda }_1=2000$ Å
2. ${\lambda }_2=6000$ Å

The ratio of the energies of these two radiations $\left(\frac{{\mathrm{E}}_1}{{\mathrm{E}}_2}\right)$ is ____. (Nearest integer)

Q21.Consider the reaction :
$2{\mathrm{H}}_2\mathrm{S}(\mathrm{g})+3{\mathrm{O}}_2(\mathrm{g})\to 2{\mathrm{H}}_2\mathrm{O}(\mathrm{l})+2{\mathrm{SO}}_2(\mathrm{g})$

The magnitude of enthalpy change for the reaction in $\mathrm{kJ}{\mathrm{mol}}^{-1}$ is ____. (Neares …

Q22.Solid carbon, CaO and ${\mathrm{CaCO}}_3$ are mixed and allowed to attain equilibrium at T K.

${\mathrm{CaCO}}_3\rightleftharpoons \mathrm{CaO}(\mathrm{s})+{\mathrm{CO}}_2(\mathrm{g})$ $K_{p_1}=0.08$ atm …

Q23.Match List-I (Mass of substance) with List-II (Number of atoms). [N_A = Avogadro number]

Q24.Given below are two statements. (Given: Molar mass of C, H, O, Cl are 12, 1, 16 and 35.5 g mol^-1 respectively.) Statement I: In 30% (w/w) solution of methanol in CCl4 (at T K), the mole fraction of CCl4 is equal to 0.33. Statement II: Mixture of methanol and CCl4 shows positive …

Q25.Bromine trifluoride autoionizes to form BrF2+ and BrF4-. The shapes of the cation and anion are respectively ____ and ____.

Q1.Consider the relation R on the set $\{-2,-1,0,1,2\}$ defined by $(\mathrm{a},\mathrm{b})\in \mathrm{R}$ if and only if $1+\mathrm{ab}>0$. Then among the statements:
I. The number of elements in R is 17
II. R is an equivalence relation

Q2.The number of values of $z\in \mathbb{C}$, satisfying the equations $|z-(4+8i)|=\sqrt{10}$ and $|z-(3+5i)|+|z-(5+11i)|=4\sqrt{5}$, is :

Q3.If the system of linear equations:
$x+y+z=6$,
$x+2y+5z=10$,
$2\mathrm{x}+3\mathrm{y}+\lambda \mathrm{z}=\mu$.
has infinitely many solutions, then the value of $\lambda +\mu$ equals.

Q4.Let $A=\left[\begin{array}{ccc}\alpha & 1& 2\\ 2& 3& 0\\ 0& 4& 5\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{ccc}1& 0& 0\\ 0& -5\alpha & 0\\ 0& 4\alpha & -2\alpha \end{array}\right]+\mathrm{adj}(\mathrm{A})$. If …

Q5.Let $\alpha =3+4+8+9+13+14+\dots$ upto 40 terms. If $(\tan \beta {)}^{\frac{\alpha }{1020}}$ is a root of the equation $x^2+x-2=0,\beta \in \left(0,\frac{\pi }{2}\right)$, then ${\sin }^2\beta +3{\cos }^2\beta$ is equal to :

Q6.A candidate has to go to the examination centre to appear in an examination. The candidate uses only one means of transportation for the entire distance out of bus, scooter and car. The probabilities of the candidate going by bus, scooter and car, respectively, are …

Q7.A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1. Then, the variance of all these 10 observations is equal to :

Q8.If $26\left(\frac{2^3}{3}\left({}^{12}{\mathrm{C}}_2\right)+\frac{2^5}{5}\left({}^{12}{\mathrm{C}}_4\right)+\frac{2^7}{7}\left({}^{12}{\mathrm{C}}_6\right)+\dots .+\frac{2^{13}}{13}\left({}^{12}{\mathrm{C}}_{12}\right)\right)=3^{13}-\alpha$, then $\alpha$ is equ …

Q9.A person has three different bags and four different books. The number of ways, in which he can put these books in the bags so that no bag is empty, is

Q10.If a straight line drawn through the point of intersection of the lines $4x+3y-1=0$ and $3x+4y-1=0$, meet the co-ordinate axes at the points P and Q, then the locus of the mid point of PQ is:

Q11.Let O be the vertex of the parabola ${\mathrm{y}}^2=4\mathrm{x}$ and its chords OP and OQ are perpendicular to each other. If the locus of the mid-point of the line segment PQ is a conic C, then the length of its latus rectum is :

Q12.Let $\alpha =3{\sin }^{-1}\left(\frac{6}{11}\right)$ and $\beta =3{\cos }^{-1}\left(\frac{4}{9}\right)$, where inverse trigonometric functions take only the principal values.

Given below are two statements:
Statement I : $\cos (\alpha +\beta )>0$
Statement II : …

Q13.For the function $\mathrm{f}(\mathrm{x})={\mathrm{e}}^{\sin |\mathrm{x}|}-|\mathrm{x}|,\mathrm{x}\in \mathbf{R}$, consider the following statements:

Statement I : f is differentiable for all $\mathrm{x}\in \mathbf{R}$.
Statement II : f is increasing in …

Q14.Let $\vec{a}=4\hat{i}-\hat{j}+3\hat{k},\vec{b}=10\hat{i}+2\hat{j}-\hat{k}$ and a vector $\vec{c}$ be such that $2(\vec{a}\times \vec{b})+3(\vec{b}\times \vec{c})=\overrightarrow{0}$. If $\vec{a}\cdot \vec{c}=15$, then …

Q15.Let the foot of perpendicular from the point $(\lambda ,2,3)$ on the line $\frac{x-4}{1}=\frac{y-9}{2}=\frac{z-5}{1}$ be the point $(1,\mu ,2)$. Then the distance between the lines $\frac{\mathrm{x}-1}{2}=\frac{\mathrm{y}-2}{3}=\frac{\mathrm{z}+4}{6}$ and …

Q16.The value of the integral
${\int }_0^2\frac{\sqrt{x\left(x^2+x+1\right)}}{(\sqrt{x+1})\left(\sqrt{x^4+x^2+1}\right)}dx$ is equal to :

Q17.Let $y=y(x)$ be the solution of the differential equation
$x\sqrt{1-x^2}dy+\left(y\sqrt{1-x^2}-x{\cos }^{-1}x\right)dx=0$,
$x\in (0,1),{\lim }_{x\to 1^{-}}y(x)=1$. Then $y\left(\frac{1}{2}\right)$ equals :

Q18.Let $\mathrm{f}:(1,\infty )\to \mathbf{R}$ be function defined as $\mathrm{f}(\mathrm{x})=\frac{\mathrm{x}-1}{\mathrm{x}+1}$. Let ${\mathrm{f}}^{\mathrm{i}+1}(\mathrm{x})=\mathrm{f}\left({\mathrm{f}}^{\mathrm{i}}(\mathrm{x})\right)$,
$\mathrm{i}=1,2,\dots ,25$, whe …

Q19.Let $f(x)=\{\begin{array}{lll}\frac{1}{3}& ,& x\le \pi /2\\ \frac{b(1-\sin x)}{(\pi -2x{)}^2}& ,& x>\pi /2\end{array}$, If $f$ is continuous at $\mathrm{x}=\pi /2$, then the value of …

Q20.Let $\frac{x^2}{f\left(a^2+7a+3\right)}+\frac{y^2}{f(3a+15)}=1$ represent an ellipse with major axis along y-axis, where $f$ is a strictly decreasing positive function on $\mathbf{R}$. If the set of all possible values of $a$ is $\mathbf{R}-[\alpha ,\beta ]$, the …

Q21.The sum of squares of all real solution of the equation
${\log }_{(x+1)}\left(2x^2+5x+3\right)=4-{\log }_{(2x+3)}\left(x^2+2x+1\right)$ is equal to ____.

Q22.If ${\int }_{\pi /6}^{\pi /4}\left(\cot \left(x-\frac{\pi }{3}\right)\cot \left(x+\frac{\pi }{3}\right)+1\right)dx=\alpha {\log }_e(\sqrt{3}-1)$,
then $9{\alpha }^2$ is equal to ____.

Q23.Let a line ${\mathrm{L}}_1$ pass through the origin and be perpendicular to the lines
$L_2:\vec{r}=(3+t)\hat{i}+(2t-1)\hat{j}+(2t+4)\hat{k}$ and …

Q24.Consider the circle $\mathrm{C}:{\mathrm{x}}^2+{\mathrm{y}}^2-6\mathrm{x}-8\mathrm{y}-11=0$.

Let a variable chord AB of the circle C subtend a right angle at the origin. If the locus of the foot of the perpendicular drawn from the origin on the chord AB is the circle …

Q25.Let f be a polynomial function such that

and $f(6)=37$. Then ${\sum }_{n=1}^{10}f(n)$ is equal to ____.