JEE Main 2026 · 05 Apr 2026 · Shift 2

Q1.Match List-I with List-II.

List-I
List-II
(A) Meter (L)
I. $\sqrt{\frac{hc}{\mathrm{G}}}$
(B) Second (S)
II. $\sqrt{\frac{Gh}{{\mathrm{c}}^5}}$
(C) Kilogram (M)
III. $\sqrt{\frac{{\mathrm{K}}^2{\mathrm{L}}^2{\mathrm{c}}^3}{\mathrm{G}h}}$
(D) Kelvin (K)
IV. …

Q2.In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as 10 V and 5 A, respectively. The least counts of voltmeter and ammeter are 500 mV and 200 mA, respectively. The estimated error in the resistance measureme …

Q3.A mass of 1 kg kept in a inclined plane with $30^{\circ }$ inclination with respect to horizontal plane and it is at rest initially. Then the whole assembly is moved up with constant velocity of $4\text{m/s}$. The work done by the frictional force in time 2 s is ______ J.
(T …

Q4.The velocity $(v)$ versus time $(t)$ plot of a particle is shown in the figure, for a time interval of 40s. The total distance travelled by the particle and the average velocity during this period are, respectively ______

Q5.A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle ${\theta }_1$ and in the next 2 s it rotates through an angle ${\theta }_2$. The ratio $\frac{{\theta }_2}{{\theta }_1}$ is ______.

Q6.An object of uniform density rolls up the curved path with the initial velocity $v_0$ as shown in the figure. If the maximum height attained by an object is $\frac{7v_0^2}{10g}$ ($g=$ acceleration due to gravity), the object is a ______.

Q7.A body of mass $m$ is taken from the surface of earth to a height equal to twice the radius of earth ($R_e$). The increase in potential energy will be ______.
($g$ is acceleration due to gravity at the surface of earth)

Q8.Eight mercury drops, each of radius $r$, coalesce to form a bigger drop. The surface energy released in this process is ______. (S is the surface tension of mercury).

Q9.An ideal gas at pressure $P$ and temperature $T$ is expanding such that $P{T}^3=$ constant. The coefficient of volume expansion of the gas is ______.

Q10.A metal rod of length $L$ rotates about on end at origin with a uniform angular velocity $\omega$. The magnetic field radially falls off as $B(r)=B_o{e}^{-\lambda r}$; $\lambda$ being a positive constant. The emf induced (neglecting the centripetal force on electrons in th …

Q11.Under steady state condition the potential difference across the capacitor in the circuit is ______ V.

Q12.A particle of charge $q$ and mass $m$ is projected from origin with an initial velocity $\vec{v}=\left(\frac{v_0}{\sqrt{2}}\hat{\mathrm{x}}+\frac{v_0}{\sqrt{2}}\hat{\mathrm{y}}\right)$. There exists a uniform magnetic field $\vec{B}=B_0\hat{\mathrm{z}}$ and a spa …

Q13.Given below are two statements: one is labelled as Assertion (A): and the other is labelled as Reason (R).

Assertion (A): The electromagnetic wave exerts pressure on the surface on which they are allowed to fall.

Reason (R): There is no mass associated with the electromagnetic …

Q14.A thin convex lens and a thin concave lens are kept in contact and are co-axial. Which of the following statements is correct for this combination of two lenses?

Q15.An object AB is placed 15 cm on the left of a convex lens P of focal length 10 cm. Another convex lens Q is now placed 15 cm right of lens P. If the focal length of lens Q is 15 cm, the final image is ______

Q16.The maximum intensity in a Young's double slit experiment is ${\mathrm{I}}_0$. Distance between the slits (d) is $5\lambda$, where $\lambda$ is the wavelength of light used. The intensity of the fringe, exactly opposite to one of the slits on the screen, placed at …

Q17.An electron is travelling with a velocity $v$ in free space and when it enters a medium, its velocity is reduced by $20\%$. The de Broglie wavelength of electron in the medium is $\alpha {\lambda }_0$, where ${\lambda }_0$ is its de Broglie wavelength in free space. The va …

Q18.Assuming the experimental mass of ${}_6^{12}\mathrm{C}$ as 12 u, the mass defect of ${}_6^{12}\mathrm{C}$ atom is ______ $\mathrm{MeV}/{\mathrm{c}}^2$. (Mass of proton $=1.00727\mathrm{u}$. mass of neutron …

Q19.In a semiconductor p-n diode, the doping concentrations on p-side and n-side are $10^{15}$ atoms/${\mathrm{cm}}^3$ and $10^{18}$ atoms $/{\mathrm{cm}}^3$, respectively. Which one of the following statement is true?

Q20.A copper wire of length 3 m is stretched by 3 mm by applying an external force. The volume of the wire is $600\times 10^{-6}{\mathrm{m}}^3$. The elastic potential energy stored in the wire in stretched condition would be ______ J. (Given Young modulus of copper …

Q21.The heat extracted out of x gram of water initially at $50^{\circ }\mathrm{C}$ to cool it down to $0^{\circ }\mathrm{C}$ is sufficient to evaporate ($1000-\mathrm{x}$) gram of water also initially at $50^{\circ }\mathrm{C}$. The value of x (closest integer) is ______. (Ta …

Q22.A series LCR circuit with R $=20\Omega ,\mathrm{L}=1.6\mathrm{H}$ and $\mathrm{C}=40\mu \mathrm{F}$ is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is ______ $\Omega$.

Q23.When an external resistance of $5\Omega$ is connected across terminals of a cell, a current of 0.25 A flows through it. When the $5\Omega$ resistor is replaced by a $2\Omega$ resistor, a current of 0.5 A flows through it. The internal resistance of the cell is ______ …

Q24.A circular loop of radius 20 cm and resistance $2\Omega$ is placed in a time varying magnetic field $\overrightarrow{\mathrm{B}}=\left(2{\mathrm{t}}^2+2\mathrm{t}+3\right)\mathrm{T}$. At $\mathrm{t}=0$, for the plane of the loop being perpendicular to the magnetic field …

Q1.What volume of hydrogen gas at STP would be liberated by action of 50 mL of ${\mathrm{H}}_2{\mathrm{SO}}_4$ of $50\%$ purity (density $=1.3\mathrm{g}{\mathrm{mL}}^{-1}$ ) on 20 g of zinc?

Given : Molar mass of H, O, S, Zn are 1, 16, 32, 65 …

Q2.Which of the following statement(s) is/are true ?
(A) If two orbitals have the same value of ( $\mathrm{n}+l$ ), the orbital with lower value of $n$ will have lower energy.
(B) Energies of the orbitals in the same subshell increase with increase in atomic number.
(C) The size …

Q3.The covalent radii of atoms A and B are ${\mathrm{r}}_{\mathrm{A}}$ and ${\mathrm{r}}_{\mathrm{B}}$, respectively. The covalent bond length and total length of AB molecule are respectively :

Q4.Consider the following data for the reaction
${\mathrm{X}}_2(\mathrm{g})+{\mathrm{Y}}_2(\mathrm{g})\rightleftharpoons 2\mathrm{XY}(\mathrm{g})$
at $600\mathrm{K}$. The ${\Delta }_{\mathrm{r}}{\mathrm{G}}^{\ominus }$ (in $\mathrm{kJ}{\mathrm{mol}}^{-1}$) for the reaction i …

Q5.The correct order of molar heat capacities measured at 298 K and 1 bar is :

Q6.The reaction $\mathrm{A}(\mathrm{g})\rightleftharpoons \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$ was initiated with the amount ' a ' of $\mathrm{A}(\mathrm{g})$. At equilibrium it is found that the amount of $\mathrm{A}(\mathrm{g})$ remaining is …

Q7.One half cell in a voltaic cell is constructed by dipping silver rod in ${\mathrm{AgNO}}_3$ solution of unknown concentration, other half cell is Zn rod dipped in 1 molar solution of ${\mathrm{ZnSO}}_4$.
A voltage of 1.60 V is measured at 298 K for this cell. What is the conc …

Q8.Given below are two statements :

Statement-I : The number of pairs among …

Q9.Given below are two statements :

Statement-I : Aluminium upon reaction with NaOH forms ${\left[\mathrm{Al}(\mathrm{OH}{)}_6\right]}^{3-}$ ion.
Statement-II : The geometry of ${\mathrm{ICl}}_4^{-},{\mathrm{ClO}}_3^{-}$and ${\mathrm{IBr}}_2^{-}$is square planar, pyramidal and …

Q10.Given below are two statements :

Statement-I : Presence of large number of unpaired electrons in transition metal atoms results in higher enthalpies of their atomisation.

Statement-II : …

Q11.Identify the correct statements from the following:
(A) ${\left[\mathrm{Fe}{\left({\mathrm{C}}_2{\mathrm{O}}_4\right)}_3\right]}^{3-}$ is the most stable complex among …

Q12.IUPAC name of the some alkenes are given below :

Find out the correct stability order.
A. 2-Methylbut-2-ene
B. cis-But-2-ene
C. 2,3-Dimethylbut-2-ene
D. Prop-1-ene

Choose the correct answer from the options given below:

Q13.Identify the correct IUPAC name of hydrocarbon (x) containing three primary carbon atoms and with molar mass 72 g mol⁻¹.

Q14.Complete the following reaction sequence and give the name of major product 'P'.

Q15.Given below are two statements :

Statement-I : The condensation reaction between CH₃-CH=O and (see structure) under optimum pH will produce (see structure)

Statement-II : The molecule, (see structure) will generate Ph-CH=O in the presence of dilute acid.

In the light of the ab …

Q16.Given below are two statements :

Statement-I : Heating benzamide with bromine in an ethanolic solution of sodium hydroxide will give benzylamine.

Statement-II : Nitration of aniline with HNO₃/H₂SO₄ at 288 K produces m-nitroaniline in higher amount than o-nitroaniline ( pH adjus …

Q17.Identify the incorrect statement about tertiary structure of proteins.

Q18.Given below are two statements :

Statement-I : (see structures) and (see structure) are two anomers of D-(+)-glucose.

Statement-II : The open chain forms of D-glucose and D-fructose contain three similar chiral carbons at C₃, C₄ and C₅.

In the light of the above statements, ch …

Q19.A paper dipped in a dil. H₂SO₄ solution of 'X' upon treatment with SO₂ gas turns into green. The compound 'X' is :

Q20.The total number of unpaired electrons present in the d³, d⁴ (low spin) d⁵ (high spin), d⁶ (high spin) and d⁷ (low spin) octahedral complex systems is ____.

Q21.RMgI when treated with ice cold water liberated a gas which occupied 1.4 dm³/g at STP. The gas produced is further reacted with iodine in presence of HIO₃ to give compound (X). Compound (X) in presence of Na and dry ether produced compound (Y). Molar mass of compound (Y) is ____ …

Q22.20 g hemoglobin in a 1 L aqueous solution (A) at 300 K is separated from pure water by semi permeable membrane. At equilibrium the height of solution in a tube dipped in a solution (A) is found to be 80.0 mm higher than the tube dipped in water.

The molar mass of hemoglobin is _ …

Q23.At 298 K, the molar conductivity of x %(w/w) MX solution (aqueous) is 123.5 S cm² mol⁻¹. The conductance of same solution is 1.9 × 10⁻³ S. The value of x is ____ × 10⁻².
(Given : cell constant =1.3 cm⁻¹; molar mass of MX is 75 g mol⁻¹, density of aqueous solution of MX at 298 K i …

Q24.For a reaction $\mathrm{A}\to \mathrm{P}$ at TK, the half life $({\mathrm{t}}_{1/2})$ is plotted as a function of initial concentration $[\mathrm{A}{]}_0$ of A as given below:

The value of x in the given figure is _____ s
(Nearest integer)

Q1.Let $\alpha ,\beta$ be the roots of the equation ${\mathrm{x}}^2-\mathrm{x}+\mathrm{p}=0$ and $\gamma ,\delta$ be the roots the equation ${\mathrm{x}}^2-4\mathrm{x}+\mathrm{q}=0$; $\mathrm{p},\mathrm{q}\in \mathrm{Z}$. If $\alpha ,\beta ,\gamma ,\delta$ are in G.P. …

Q2.Let ${\mathrm{z}}_1,{\mathrm{z}}_2\in \mathrm{C}$ be the distinct solutions of the equation $z^2+4z-(1+12i)=0$. Then ${\left|z_1\right|}^2+{\left|z_2\right|}^2$ is equal to :

Q3.If $\mathrm{f}:\mathrm{N}\to \mathrm{Z}$ is defined by
$f(n)=\left|\begin{array}{ccc}n& -1& -5\\ -2n^2& 3(2k+1)& 2k+1\\ -3n^3& 3k(2k+1)& 3k(k+2)+1\end{array}\right|,k\in N$, and ${\sum }_{n=1}^{k}f(n)=98$, then $k$ is equal to:

Q4.Let M be a $3\times 3$ matrix such that
$\mathrm{M}\left(\begin{array}{l}1\\ 0\\ 0\end{array}\right)=\left(\begin{array}{l}1\\ 2\\ 3\end{array}\right),\mathrm{M}\left(\begin{array}{l}0\\ 1\\ 0\end{array}\right)=\left(\begin{array}{l}0\\ 1\\ 2\end{array}\right)$ and …

Q5.If the sum of the first 10 terms of the series $\frac{1}{1+1^4\times 4}+\frac{2}{1+2^4\times 4}+\frac{3}{1+3^4\times 4}+\frac{4}{1+4^4\times 4}+\dots$ is $\frac{\mathrm{m}}{\mathrm{n}},\gcd (\mathrm{m},\mathrm{n})=1$, then $\mathrm{m}+\mathrm{n}$ …

Q6.Let ${\mathrm{A}}_1,{\mathrm{A}}_2,{\mathrm{A}}_3,\dots \dots ..,{\mathrm{A}}_{39}$ be 39 arithmetic means between the numbers 59 and 159. Then the mean of ${\mathrm{A}}_{25},{\mathrm{A}}_{28},{\mathrm{A}}_{31}$ and ${\mathrm{A}}_{36}$ is equal to:

Q7.The coefficient of $x^2$ in the expansion of ${\left(2{\mathrm{x}}^2+\frac{1}{\mathrm{x}}\right)}^{10},\mathrm{x}\ne 0$, is :

Q8.The probabilities that players A and B of a team are selected for the captaincy for a tournament are 0.6 and 0.4 , respectively. If A is selected the captain, the probability that the team wins the tournament is 0.8 and if B is selected the captain, the probability that the team …

Q9.A box contains 5 blue, 6 yellow and 4 red balls. The number of ways, of drawing 8 balls containing at least two balls of each colour, is:

Q10.A variable $X$ takes values $0,0,2,6,12,20,\dots$. $\mathrm{n}(\mathrm{n}-1)$ with frequencies ${}^{\mathrm{n}}{\mathrm{C}}_0,{}^{\mathrm{n}}{\mathrm{C}}_1,{}^{\mathrm{n}}{\mathrm{C}}_2,{}^{\mathrm{n}}{\mathrm{C}}_3,{}^{\mathrm{n}}{\mathrm{C}}_4$, …

Q11.Let the point P be the vertex of the parabola $y=x^2-6x+12$. If a line passing through the point $P$ intersects the circle $x^2+y^2-2x-4y+3=0$ at the points R and S , then the maximum value of $(\mathrm{PR}+\mathrm{PS}{)}^2$ is:

Q12.Let the directrix of the parabola $P:y^2=8x$, cut x -axis at the point A . Let $\mathrm{B}(\alpha ,\beta ),\alpha >1$, be a point on P such that the slope of AB is $3/5$. If BC is a focal chord of P , then six times the area of $△\mathrm{ABC}$ is:

Q13.Let the eccentricity e of a hyperbola satisfy the equation $6{\mathrm{e}}^2-11\mathrm{e}+3=0$. If the foci of the hyperbola are $(3,5)(3,-4)$, then the length of its latus rectum is:

Q14.Let a triangle PQR be such that P and Q lie on the line $\frac{x+3}{8}=\frac{y-4}{2}=\frac{z+1}{2}$ and are at a distance of 6 units from $\mathrm{R}(1,2,3)$. If $(\alpha ,\beta ,\gamma )$ is the centroid of $\Delta \mathrm{PQR}$, then $\alpha +\beta +\gamma$ is equal to:

Q15.If the distance of the point $(a,2,5)$ from the image of the point $(1,2,7)$ in the line $\frac{x}{1}=\frac{y-1}{1}=\frac{z-2}{2}$ is 4, then the sum of all possible values of a is equal to:

Q16.Let O be the origin, $\overrightarrow{\mathrm{OP}}=\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{OQ}}=\overrightarrow{\mathrm{b}}$. If $R$ is the point on $\overrightarrow{\mathrm{OP}}$ such that $\overrightarrow{\mathrm{OP}}=5\overrightarrow{\mathrm{OR}}$, …

Q17.Let $f(x)={\lim }_{y\to 0}\frac{(1-\cos (xy))\tan (xy)}{y^3}$. Then the number of solutions of the equation $f(\mathrm{x})=\sin \mathrm{x}$, $x\in R$ is:

Q18.Let $\left(2^{1-\mathrm{a}}+2^{1+\mathrm{a}}\right),f(\mathrm{a}),\left(3^{\mathrm{a}}+3^{-\mathrm{a}}\right)$ be a A. P. and $\alpha$ be the minimum value of $f(\mathrm{a})$. Then the value of the integral …

Q19.Let $\mathrm{f}:[1,\infty )\to \mathrm{R}$ be a differentiable function defined as $f(x)={\int }_1^{x}f(t)dt+(1-x)\left({\log }_{e}x-1\right)+e$. Then the value of $\mathrm{f}(\mathrm{f}(1))$ is:

Q20.Let $\mathrm{f}(\mathrm{x})$ and $\mathrm{g}(\mathrm{x})$ be twice differentiable functions satisfying ${\mathrm{f}}^{\prime \prime }(\mathrm{x})={\mathrm{g}}^{\prime \prime }(\mathrm{x})$ for all $\mathrm{x}\in \mathrm{R}$, $f^{\prime }(1)=2g^{\prime }(1)=4$ and …

Q21.Let $\mathrm{A}=\{1,4,7\}$ and $\mathrm{B}=\{2,3,8\}$. Then the number of elements, in the relation $\mathrm{R}=\{(\left({\mathrm{a}}_1,{\mathrm{b}}_1\right)$, …

Q22.From the point $(-1,-1)$, two rays are sent making angles of $45^{\circ }$ with the line $\mathrm{x}+\mathrm{y}=0$. These rays get reflected from the mirror $x+2y=1$. If the equations of the reflected rays are $ax+by=9$ and …

Q23.If $S=\left\{\theta \in [-\pi ,\pi ]:\cos \theta \cos \frac{5\theta }{2}=\cos 7\theta \cos \frac{7\theta }{2}\right\}$, then $\mathrm{n}(\mathrm{S})$ is equal to

Q24.Let $\mathrm{f}:\mathrm{R}\to \mathrm{R}$ be a function such that $\mathrm{f}(\mathrm{x})+3\mathrm{f}\left(\frac{\pi }{2}-\mathrm{x}\right)=\sin \mathrm{x},\mathrm{x}\in \mathrm{R}$. Let maximum value of $f$ on $R$ be $\alpha$. If the area of the region boun …

Q25.Let $y=y(x)$ be the solution of the differential equation $(\tan x{)}^{1/2}dy=({\sec }^{3}x-(\tan x{)}^{3/2}y)dx$, $0<x<\frac{\pi }{2}$, $y\left(\frac{\pi }{4}\right)=\frac{6\sqrt{2}}{5}$. If $y\left(\frac{\pi }{3}\right)=\frac{4}{5}\alpha$, then ${\alpha }^4$ equals ______