JEE Main 2026 — 5 April, Evening Shift

Match List-I with List-II.

where h = Planck's constant, G = gravitational constant, c = speed of light in vacuum as fundamental units.

In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as 10V and 5 A, respectively. The least counts of voltmeter and ammeter are $500 \mathrm{mV}$ and $200 \mathrm{mA}$, respectively. The estimated error in the resistance measurement is $\Omega$

A mass of $1\mathrm{kg}$ kept in an 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 $4\mathrm{m/s}$. The work done by the frictional force in time $2\mathrm{s}$ is J.

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

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

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

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

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).

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

Match List-I with List-II.

Choose the correct answer from the options given below.

A metal rod of length L rotates about one end at origin with a uniform angular velocity $\omega$. The magnetic field radially falls off as $B(r) = B_0 e^{-\lambda r}$ $\lambda$ being a positive constant. The emf induced (neglecting the centripetal force on electrons in the rod) is:

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

A particle of charge $q$ and mass $m$ is projected from origin with an initial velocity $\bar{v} = \left(\frac{v_0}{\sqrt{2}}\hat{x} + \frac{v_0}{\sqrt{2}}\hat{y}\right)$. There exists a uniform magnetic field $\vec{B} = B_0\hat{z}$ and a space varying electric field $\vec{E} = E_0 e^{-\lambda x}$ within the region $0\le x\le L$. After travelling a distance such that x-coordinate has changed from $x=0$ to $x=L$, the change in the kinetic energy is

Assertion (A): The electromagnetic wave exerts pressure on the surface on which they are allowed to fall.\nReason (R): There is no mass associated with the electromagnetic waves.

An object AB is placed $15\mathrm{cm}$ on the left of a convex lens P of focal length $10\mathrm{cm}$. Another convex lens Q is now placed $15\mathrm{cm}$ right of lens P. If the focal length of lens Q is $15\mathrm{cm}$, the final image is

The maximum intensity in a Young's double slit experiment is $I_0$. 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 $D = 10d$ is

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 value of $\alpha$ is

Assuming the experimental mass of $^{12}_{6}\mathrm{C}$ as $12\mathrm{u}$ the mass defect of $^{12}_{6}\mathrm{C}$ atom is MeV/c². (Mass of proton = 1.00727u, mass of neutron = 1.00866u, $1\mathrm{u} = 931.5\mathrm{MeV}/c^2$)

In a semiconductor p-n diode, the doping concentrations on p-side and n-side are $10^{15}$ atoms/cm³ and $10^{18}$ atoms/cm³, respectively. Which one of the following statement is true?

A copper wire of length $3\mathrm{m}$ is stretched by $3\mathrm{mm}$ 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 = $1.1\times 10^{11}\mathrm{N/m}^2$)

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 $(1000 - x)$ gram of water also initially at $50^{\circ}\mathrm{C}$. The value of $x$ (closest integer) is. (Take latent heat of water $2256\mathrm{kJ/kg}$, specific heat capacity of water $4200\mathrm{J/kg.K}$)

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

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

A circular loop of radius $20\mathrm{cm}$ and resistance $2\Omega$ is placed in a time varying magnetic field $B = (2t^2+2t+3)\mathrm{T}$. At $t=0$, for the plane of the loop being perpendicular to the magnetic field, the induced current in the loop at $t=3\mathrm{s}$ is $\frac{\alpha}{50}\mathrm{A}$. The value of $\alpha$ is (Take $\pi = 22/7$)

Let $α, β$ be the roots of the equation $x² - x + p = 0$ and $γ, δ$ be the roots the equation $x² - 4x + q = 0, p, q ∈ Z$. If $α, β, γ, δ$ are in $G.P.$, then $|p + q|$ equals :

Let $z_1, z_2 ∈ C$ be the distinct solutions of the equation $z² + 4z - (1 + 12i) = 0.$ Then $|z₁|² + |z₂|²$ is equal to:

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

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 $\mathrm{M}\left(\begin{array}{l}0\\ 0\\ 1\end{array}\right)=\left(\begin{array}{c}-1\\ 1\\ 1\end{array}\right)$. If $\mathrm{M}\left(\begin{array}{l}\mathrm{x} \\ \mathrm{y} \\\mathrm{z}\end{array}\right)=\left(\begin{array}{c}1\\ 7\\ 11\end{array}\right)$, then $\mathrm{x}+\mathrm{y}+\mathrm{z}$ equals:

If the sum of the first $10$ terms of the series $\frac{1}{1+1^{4} \times 4}+\frac{2}{1+2^{4} \times 4}+\frac{3}{1+3^{4} \times 4}+\frac{4}{1+4^{4} \times 4}+\ldots$ is $\frac{\mathrm{m}}{\mathrm{n}}, \operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$, then $\mathrm{m}+\mathrm{n}$ is equal to :

Let $\mathrm{A}_{1}, \mathrm{~A}_{2}, \mathrm{~A}_{3}, \ldots \ldots . ., \mathrm{A}_{39}$ 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 :

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

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 wins the tournament is $0.7.$ Then the probability that the team wins the tournament is :

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:

A variable X takes values $0, 0, 2, 6, 12, 20, ..., n(n-1)$ with frequencies $ⁿC₀, ⁿC₁, ⁿC₂, ⁿC₃, ⁿC₄, ⁿC₅, ..., ⁿCₙ$ respectively. If the mean of this data is $60,$ then its median is:

Let the point P be the vertex of the parabola y = x² - 6x + 12. If a line passing through the point P intersects the circle x² + y² - 2x - 4y + 3 = 0 at the points R and S, then the maximum value of (PR + PS)² is:

Let the directrix of the parabola $P: y² = 8x$ cut x-axis at point A. Let $B(α,β) α>1$ 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 $ΔABC$ is :

Let the eccentricity $e$ of a hyperbola satisfy the equation $6e² - 11e + 3 = 0.$ If the foci of the hyperbola are $(3,5)$ and $(3,-4)$, then the length of its latus rectum is:

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 $R(1,2,3).$ If $(α,β,γ)$ is the centroid of $ΔPQR,$ then $α+β+γ$ is equal to:

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

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 $\overrightarrow{\mathrm{OP}}=5 \overrightarrow{\mathrm{OR}}$, and M is the point such that $\overrightarrow{\mathrm{OQ}}=5 \overrightarrow{\mathrm{RM}}$, then $\overrightarrow{\mathrm{PM}}$ is equal to:

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

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 $\int_{\log _{\mathrm{e}}(\alpha-1)}^{\log _{\mathrm{e}}(\alpha)} \frac{\mathrm{dx}}{\left(\mathrm{e}^{2 \mathrm{x}}-\mathrm{e}^{-2 \mathrm{x}}\right)}$ is:

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 $\mathrm{x} \in \mathrm{R}$, $\mathrm{f}^{\prime}(1)=2 \mathrm{~g}^{\prime}(1)=4$ and $\mathrm{g}(2)=3 \mathrm{f}(2)=9$. Then $\mathrm{f}(25)-\mathrm{g}(25)$ is equal to :

Let $A = {1,4,7}$ and $B = {2,3,8}.$ Then the number of elements in the relation $R = ((a₁,b₁),(a₂,b₂)) ∈ (A×B)×(A×B) : a_1 + b_2$ divides $a_2 + b_1$ is ______.

From the point $(-1,-1)$, two rays are sent making angles of $45°$ with the line $x+y=0$.. These rays get reflected from the mirror $x+2y=1.$ If the equations of the reflected rays are $ax+by=9$ and $cx+dy=7, a,b,c,d∈Z,$ then the value of $ad+bc$ is _____.

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

Let $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$ 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 bounded by the curves $\mathrm{g}(\mathrm{x})=\mathrm{x}^{2}$ and $\mathrm{h}(\mathrm{x})=\beta \mathrm{x}^{3}$, $\beta>0$, is $\alpha^{2}$, then $30 \beta^{3}$ is equal to $\_\_\_\_$

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

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 $\mathrm{g} \mathrm{mol}^{-1}$ respectively.

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 of $2 p_{x}$ orbital is less than the size of $3 \mathrm{p}_{\mathrm{x}}$ orbital. (D) Among 5f,6s, 4d, 5p and 5d orbitals, none of the orbitals have 2 radial nodes. Choose the correct answer from the options given below:

The covalent radii of atoms $A$ and $B$ are $r_{A}$ and $r_{B}$, respectively. The covalent bond length and total length of AB molecule are respectively :

Consider the following data for the reaction $\mathrm{X}_{2}(\mathrm{~g})+\mathrm{Y}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{XY}(\mathrm{g})$ at $600 \mathrm{~K}_{\text {. The } \Delta_{\mathrm{r}} \mathrm{G}^{\ominus}}\left(\mathrm{in} \mathrm{kJ} \mathrm{mol}^{-1}\right)$ for the reaction is:

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

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 $(\mathrm{a}-\mathrm{x})$ at a total pressure of p. The equilibrium constant $\mathrm{K}_{\mathrm{p}}$ of the reaction can be calculated from the expression :

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 concentration of $\mathrm{Ag}^{+}$ions used in terms of $\log \mathrm{x}\left(\mathrm{x}=\left[\mathrm{Ag}^{+}\right]\right)$? $\mathrm{E}_{\mathrm{Zn}^{2+} / \mathrm{Zn}}^{\Theta}=-0.76 \mathrm{~V}, \mathrm{E}_{\mathrm{Ag}^{+} / \mathrm{Ag}}^{\Theta}=+0.80 \mathrm{~V}$, $\frac{2.303 \mathrm{RT}}{\mathrm{F}}=0.059 \mathrm{~V}$

Given below are two statements :

Statement-I : The number of pairs among $\left[\mathrm{Al}_{2} \mathrm{O}_{3}\right.$, $\left.\mathrm{Cr}_{2} \mathrm{O}_{3}\right],\left[\mathrm{Cl}_{2} \mathrm{O}_{7}, \mathrm{Mn}_{2} \mathrm{O}_{7}\right],\left[\mathrm{Na}_{2} \mathrm{O}, \mathrm{V}_{2} \mathrm{O}_{3}\right]$ and $[\mathrm{CO}$, $\left.\mathrm{N}_{2} \mathrm{O}\right]$ that contain oxides of same nature (acidic, basic, neutral or amphoteric) is 4.

Statement-II : Among $\mathrm{Na}_{2} \mathrm{O}, \mathrm{Al}_{2} \mathrm{O}_{3}, \mathrm{CO}$ and $\mathrm{Cl}_{2} \mathrm{O}_{7}$, the most basic and acidic oxides are $\mathrm{Na}_{2} \mathrm{O}$ and $\mathrm{Cl}_{2} \mathrm{O}_{7}$, respectively.

In the light of the above statements, choose the correct answer from the options given below:

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 linear respectively.

In the light of the above statements, choose the correct answer from the options given below:

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 $\left[\mathrm{Fe}(\mathrm{OH})_{6}\right]^{3-},\left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-}$ and $\left[\mathrm{Fe}(\mathrm{SCN})_{6}\right]^{3-}$ (B) The stability of $\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}$ is greater than that of $\left[\mathrm{Cu}(\mathrm{en})_{2}\right]^{2+}$ (C) The hybridization of Fe in $\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]$ is $\mathrm{d}^{2} \mathrm{sp}^{3}$ (D) $\left[\mathrm{Fe}\left(\mathrm{NO}_{2}\right)_{3} \mathrm{Cl}_{3}\right]^{3-}$ exhibits linkage isomerism (E) $\mathrm{NO}_{2}^{-}$and $\mathrm{SCN}^{-}$ligands are NOT ambidentate ligands Choose the correct answer from the options given below :

Match List-I with List-II.

Choose the correct answer from the options given below :

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

Identify the correct IUPAC name of hydrocarbon (x) containing three primary carbon atoms and with molar mass $72 \mathrm{~g} \mathrm{~mol}^{-1}$.

Given below are two statements:

Statement-I : The condensation reaction between $\mathrm{CH}_{3}-\mathrm{CH}=\mathrm{O}$ and

Statement-II : The molecule, will generate $\mathrm{Ph}-\mathrm{CH}=\mathrm{O}$ in the presence of dilute acid.

In the light of the above statements, choose the correct answer from the options given below :

Identify the incorrect statement about tertiary structure of proteins.

Given below are two statements : Statement-I :

and

are two anomers of D-(+)-glucose. Statement-II : The open chain forms of D-glucose and D-fructose contain three similar chiral carbons at $\mathrm{C}_{3}, \mathrm{C}_{4}$ and $\mathrm{C}_{5}$. In the light of the above statements, choose the correct answer from the options given below :

A paper dipped in a dil. $\mathrm{H}_{2} \mathrm{SO}_{4}$ solution of ' X ' upon treatment with $\mathrm{SO}_{2}$ gas turns into green. The compound ' X ' is :

The total number of unpaired electrons present in the $\mathrm{d}^{3}, \mathrm{~d}^{4}$ (low spin) $\mathrm{d}^{5}$ (high spin), $\mathrm{d}^{6}$ (high spin) and $\mathrm{d}^{7}$ (low spin) octahedral complex systems is $\_\_\_\_$ .

RMgI when treated with ice cold water liberated a gas which occupied $1.4 \mathrm{dm}^{3} / \mathrm{g}$ at STP. The gas produced is further reacted with iodine in presence of $\mathrm{HIO}_{3}$ to give compound (X). Compound (X) in presence of Na and dry ether produced compound $(\mathrm{Y})$. Molar mass of compound $(\mathrm{Y})$ is $\_\_\_\_$ $\mathrm{g} \mathrm{mol}^{-1}$. (Nearest integer)

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 $\_\_\_\_$ $\mathrm{kg} \mathrm{mol}^{-1}$. (Nearest integer) (Given : $\mathrm{g}=10 \mathrm{~ms}^{-2}, \mathrm{R}=8.3 \mathrm{kPa} \mathrm{dm}^{3} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$, density of solution $=1000 \mathrm{~kg} \mathrm{~m}^{-3}$ )

At 298 K , the molar conductivity of $\mathrm{x} \%(\mathrm{w} / \mathrm{w})$ MX solution (aqueous) is $123.5 \mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}$. The conductance of same solution is $1.9 \times 10^{-3} \mathrm{~S}$. The value of $x$ is $\_\_\_\_$ $\times 10^{-2}$. (Given : cell constant $=1.3 \mathrm{~cm}^{-1}$; molar mass of MX is $75 \mathrm{~g} \mathrm{~mol}^{-1}$, density of aqueous solution of MX at 298 K is $1.0 \mathrm{~g} \mathrm{~mL}^{-1}$ )

For a reaction $\mathrm{A} \rightarrow \mathrm{P}$ at TK , the half life $\left(\mathrm{t}_{1 / 2}\right)$ 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)