JEE Main 2026 · 04 Apr 2026 · Shift 2

Q1.Two cars A and B are moving in the same direction along a straight line with speeds $100\mathrm{km}/\mathrm{h}$ and $80\mathrm{km}/\mathrm{h}$, respectively such that car A is moving ahead of car B . A person in car B throws a stone with a speed v so that it hits the car …

Q2.At $t=0$, a body of mass 100 g starts moving under the influence of a force $(5\hat{\mathrm{i}}+10\hat{\mathrm{j}})\mathrm{N}$. After 2 s its position is $(2x\hat{\mathrm{i}}+5y\hat{\mathrm{j}})\mathrm{m}$. The ratio $\mathrm{x}:\mathrm{y}$ is $\_\_\_\_$ .

Q3.If x and y coordinates of a projectile as a function of time $(t)$ are given as $24t$ and $43.6t-4.9t^2$, respectively, then the angle (in degrees) made by the projectile with horizontal when $\mathrm{t}=2\mathrm{s}$ is $\_\_\_\_$ .

Q4.The height in terms of radius of the earth $(R)$, at which the acceleration due to gravity becomes $\frac{\mathrm{g}}{9}$, where $g$ is acceleration due to gravity on earth's surface, is $\_\_\_\_$ .

Q5.A metal string A is suspended from a rigid support and its free end is attached to a block of mass M. Second block having mass 2 M is suspended at the bottom of the first block using a string B . The area of cross sections of strings A and B are same. The ratio of lengths of stri …

Q6.A water spray gun is attached to a hose of cross sectional area $30{\mathrm{cm}}^2$. The gun comprises of 10 perforations each of cross sectional area of $15{\mathrm{mm}}^2$. If the water flows in the hose with the speed of $50\mathrm{cm}/\mathrm{s}$, calculate the speed …

Q7.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: If the average kinetic energy of ${\mathrm{H}}_2$ and ${\mathrm{O}}_2$ molecules, kept in two different sized containers are same, then their temperatures will be sa …

Q8.The temperature of a metal strip having coefficient of linear expansion $\alpha$ is increased from ${\mathrm{T}}_1$ to ${\mathrm{T}}_2$ resulting in increase of its length by $\Delta {\mathrm{L}}_1$. The temperature is further increased from ${\mathrm{T}}_2$ to ${\mathrm{T}}_3$ s …

Q9.A uniform disc of radius R and mass M is free to oscillate about the axis A as shown in the figure. For small oscillations the time period is $\_\_\_\_$ . (g is acceleration due to gravity)

Q10.A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field ${\overrightarrow{\mathrm{E}}}_1={\mathrm{E}}_0\hat{\mathrm{x}}$. If another electric field …

Q11.From the circuit given below, the capacitance between terminals A and B shown in the circuit is
$\_\_\_\_$ $\mu \mathrm{F}$. (take ${\mathrm{C}}_1={\mathrm{C}}_2={\mathrm{C}}_3=1\mu \mathrm{F}$ and ${\mathrm{C}}_4=2\mu \mathrm{F}$.)

Q12.Given below are two statements: one is labelled as
Assertion A and the other is labelled as Reason R
Assertion A : In electrostatics, a conductor does not store any net charge inside.
Reason R: Inside the capacitor (with no dielectric medium), the free charge carriers, if placed …

Q13.A solenoid has a core made of material with relative permeability 400. The magnetic field produced in the interior of solenoid is 1.0 T. The magnetic intensity is SI units is $\alpha \times 10^5$. The value of $\alpha$ is ______. (Free space permeability …

Q14.A magnetic field vector in an electromagnetic wave is represented by, $\overrightarrow{\mathrm{B}}={\mathrm{B}}_0\sin \left(2\pi \mathrm{vt}-\frac{2\pi \mathrm{x}}{\lambda }\right)\hat{\mathrm{j}}$. Its associated electric field vector is ______ .

Q15.A convex lens is made from glass material having refractive index of 1.4 with same radius of curvature on both sides. The ratio of its focal length and radius of curvature is ______ .

Q16.An unpolarized light of certain intensity passes through a combination of two polarizers whose transmission axes are at $30^{\circ }$ and $90^{\circ }$, respectively, with respect to the horizontal axis. A third polarizer with its transmission axis at $60^{\circ }$ with the horizont …

Q17.In Rutherford's alpha-particle scattering experiment, only a few alpha particles rebound back because
(A)The size of gold nucleus is very small as compared to the size of gold atom.
(B) Alpha particle and gold nucleus have equal charge.
(C) The impact parameter is minimum for a f …

Q18.The de Broglie wavelength associated with an electron accelerated through a potential difference V is ${\lambda }_{\mathrm{e}}$ and the de Broglie wavelength associated with a proton accelerated through the same potential difference is ${\lambda }_{\mathrm{p}}$. If their corresponding …

Q19.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : A diode under reverse- biased condition provides very small current which is nearly independent of voltage until a critical limit at which the current increases dras …

Q20.A diode has Zener voltage of 10 V and maximum power dissipation of 0.5 W , then the minimum resistance to be used in series with this diode for safety when it is connected to a 25 V power supply is ______ $\Omega$.

Q21.A gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is 6.4 m . The speed of the bullets from the gun is ______ $\mathrm{m}/\mathrm{s}$. (take $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$)

Q22.Two identical small bar magnets each of dipole moment $3\sqrt{5}\mathrm{J}/\mathrm{T}$ are placed at a center to center separation of 10 cm , with their axes perpendicular to each other as shown in figure. The value of magnetic field at the point P midway between the magnets …

Q23.A circular coil of radius 2 cm and 125 turns carries a current of 1 A . The coil is placed in a uniform magnetic field of magnitude 0.4 T. The axis of the coil makes an angle of $30^{\circ }$ with the direction of the magnetic field. The torque acting on the coil is …

Q24.In a double slit experiment, when one of the slits is covered by a transparent mica sheet of refractive index 1.56, the central fringe shifts to the position of $7^{\text{th}}$ bright fringe, obtained with both slits uncovered. If the light source wavelength is 450 nm, the thic …

Q1.The correct order of total number of atoms of present in
(A) 2 moles of cyclohexane
(B) 684 g of sucrose
(C) 90.8 L of dihydrogen at STP

Q2.The species having identical radii according to the Bohr's theory are:
A. H (first orbit)
B. He⁺ (first orbit)
C. He⁺ (second orbit)
D. Li²⁺ (first orbit)
E. Be³⁺ (Second orbit)

Choose the correct answer from the options given below:

Q3.Which of the following pictorial diagram most correctly represents the π* (π-antibonding) molecular orbital between two atoms if the internuclear axis is taken to be in the z-direction (→ z-axis)?

Q4.At 27°C, 0.1 M, 1 L K₄[Fe(CN)₆] aqueous solution and 0.1 M, 1 L FeCl₃ aqueous solution are placed in a container separated by a semi permeable membrane AB. Assume complete dissociation of both the solutes. Which of the following statement is correct?

Q5.20 mL of a solution of acetic acid required 28.4 mL of 0.1 M NaOH for its neutralization. A solution (X) was prepared by mixing 20 mL of the above acetic acid and 14.2 mL of 0.1 M NaOH solution. What is the pH of the solution (X)? (pKₐ value of acetic acid is 4.75).

Q6.The 1st ionization enthalpy for Mg is +737 kJ/mol. The most probable estimated value of the 2nd ionization enthalpy of Mg is

Q7.The electronegativity of a group 13 element 'E' is same as that of Ge (on Pauling scale and upto one decimal point). The CORRECT statements about E³⁺ are
A. It can act as a reducing agent.
B. It can act as an oxidizing agent.
C. E³⁺ is more stable than E⁺.
D. The standard electro …

Q8.Pairs of elements with the same number of electrons in their respective 4f orbital are
[Atomic number, Eu-63, Gd-64, Dy-66, Ho-67, Tm-69, Yb-70, Lu-71, Hf-72]
A. (Eu and Gd)
B. (Dy and Ho)
C. (Yb and Hf)
D. (Lu and Tm)

Choose the correct answer from the options given below:

Q9.Consider the metal complexes [Ni(en)₃]²⁺ (A), [NiCl₄]²⁻ (B) and [Ni(NH₃)₆]²⁺ (C). Choose the CORRECT option by considering the number of unpaired electron present in (A), (B) and (C) respectively and the order of frequency of absorption.

Q10.Consider the following molecules/species:

The correct order of carbon-oxygen double bond length is:

Q11.Consider |x| is the difference in oxidation states of Mn in highest manganese fluoride and highest manganese oxide. The ions with |x| number of unpaired electrons from the following are:
A. Sc³⁺
B. Zn²⁺
C. V²⁺
D. Fe²⁺
E. Co²⁺

Choose the correct answer from the options given belo …

Q12.Consider the given graph showing variation of reactant concentration with time.
Three different reactions were started with identical initial concentration of reactants. Which of the following statement is correct?

Q13.Compound (X) is subjected to the sequence of reactions as shown above. Molar mass of the major product (Y) formed is _____ ${\mathrm{gmol}}^{-1}$.
(Given molar mass in ${\mathrm{g}\mathrm{mol}}^{-1}$ C: 12, H: 1, O: 16)

Q14.The following structures are

Q15.The descending order of acidity among the following compounds is
A. (see structure)
B. (see structure)
C. (see structure)
D. (see structure)
E. (see structure)
Choose the correct answer from the option given below options

Q16.The strongest conjugate acid will result from

Q17.A D-aldotetrose on oxidation with concentrated ${\mathrm{HNO}}_3$ resulted in optically inactive dicarboxylic acid. The structure of the D-aldotetrose is:

Q18.Among ${\mathrm{Fe}}^{3+}$, ${\mathrm{Pb}}^{2+}$, ${\mathrm{Cu}}^{2+}$ and ${\mathrm{Mn}}^{2+}$, identify the one that gets precipitated out while passing ${\mathrm{H}}_2\mathrm{S}$ in presence of ${\mathrm{NH}}_4\mathrm{OH}$ as group reagent. The highest possible oxidation state of the …

Q19.If 3.365 g of ethanol ($l$) burnt completely in a bomb calorimeter at 298.15 K, the heat produced is 99.472 kJ. The $|\Delta {\mathrm{H}}_{\mathrm{f}}^{\circ }|$ of ethanol at 298.15 K is _____ $\times 10^2{\mathrm{kJ}\mathrm{mol}}^{-1}$. (Nearest integer)
Given:
Standard enthalpy of comb …

Q20.For the following reaction at 50°C and at 2 atm pressure,
2 N₂O₅(g) ⇌ 2 N₂O₄(g) + O₂(g)
N₂O₅ is 50% dissociated.
The magnitude of standard free energy change at this temperature is x.
x = _____ J mol⁻¹ [Nearest integer].
Given: R = 8.314 J mol⁻¹ K⁻¹, log 2 = 0.30, log 3 = 0.48, l …

Q21.An electrochemical cell consist of the following two redox couples,
${\mathrm{M}}^{\times +}(\mathrm{aq})/\mathrm{M}(\mathrm{s})$ $[{\mathrm{E}}_{\text{red}}^{\ominus }=+0.15\mathrm{V}]$ and
${\mathrm{Fe}}^{3+}(\mathrm{aq})/\mathrm{Fe}(\mathrm{s})$ …

Q22.For a first order reaction $\mathrm{A}\to \mathrm{B}$

$\mathrm{x}=$ _____ min. (Nearest integer)

Q23.In sulphur estimation, $2.0\times 10^{-3}\mathrm{mol}$ of an organic compound (X) (molar mass $76{\mathrm{g}\mathrm{mol}}^{-1}$) gave 0.4813 g of barium sulphate (molar mass $233{\mathrm{gmol}}^{-1}$). The percentage of sulphur in the compound (X) is _____ $\times 10^{-1}\%$ (Nearest in …

Q1.For the function $f:[1,\infty )\to [1,\infty )$ defined by $f(\mathrm{x})=(\mathrm{x}-1{)}^4+1$, among the two statements :
(I) The set $\mathrm{S}=\left\{\mathrm{x}\in [1,\infty ):f(\mathrm{x})=f^{-1}(\mathrm{x})\right\}$ contains exactly two elements, and
(II) Th …

Q2.Let $\mathrm{S}=\left\{\mathrm{z}\in \mathbb{C}:{\mathrm{z}}^2+4\mathrm{z}+16=0\right\}$.

Then ${\sum }_{\mathrm{z}\in \mathrm{S}}|\mathrm{z}+\sqrt{3}\mathrm{i}{|}^2$ is equal to :

Q3.If the system of equations :
$x+y+z=5$
$x+2y+3z=9$
$x+3y+\lambda z=\mu$
has infinitely many solutions, then the value of $\lambda +\mu$ is :

Q4.If $\alpha =1$ and $\beta =1+\mathrm{i}\sqrt{2}$, where $i=\sqrt{-1}$ are two roots of the equation
${\mathrm{x}}^3+{\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0,\mathrm{a},\mathrm{b},\mathrm{c}\in \mathbb{R}$, then ${\int }_{-1}^1\left(x^3+a{x}^2+bx+c\right)dx$ is e …

Q5.If the quadratic equation $(\lambda +2){\mathrm{x}}^2-3\lambda \mathrm{x}+4\lambda =0$, $\lambda \ne -2$, has two positive roots, then the number of possible integral values of $\lambda$ is :

Q6.Let $\mathrm{A}=\left[\begin{array}{ccc}1& 2& 7\\ 4& -2& 8\\ 3& 8& -7\end{array}\right]$ and $\det (\mathrm{A}-\alpha \mathrm{I})=0$, where $\alpha$ is a real number. If the largest possible value of $\alpha$ is $p$, then the circle …

Q7.Let $\alpha =\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\dots \infty$ and
$\beta =\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\dots \infty$. Then the value of $(0.2{)}^{{\log }_{\sqrt{5}}(\alpha )}+(0.04{)}^{{\log }_5(\beta )}$ is equal to :

Q8.For 10 observations ${\mathrm{x}}_1,{\mathrm{x}}_2,\dots .,{\mathrm{x}}_{10}$, if ${\sum }_{\mathrm{i}=1}^{10}{\left({\mathrm{x}}_{\mathrm{i}}+2\right)}^2=180$ and ${\sum }_{\mathrm{i}=1}^{10}{\left({\mathrm{x}}_{\mathrm{i}}-1\right)}^2=90$, then their standard deviation is :

Q9.In the expansion of ${\left(9x-\frac{1}{3\sqrt{x}}\right)}^{18},x>0$, if the term independent of x is $(221)\mathrm{k}$. then k is equal to:

Q10.Let $P(3\cos \alpha ,2\sin \alpha ),\alpha \ne 0$, be a point on the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1,Q$ be a point on the circle $x^2+y^2-14x-14y+82=0$ and $R$ be a point on the line $x+y=5$ such that the centroid of the triangle PQR is …

Q11.Let $\mathrm{H}:\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}-\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1$ be a hyperbola such that the distance between its foci is 6 and the distance between its directrices is $\frac{8}{3}$. If the line $\mathrm{x}=\alpha$ intersects the hyperbola H …

Q12.${\max }_{0\le x\le \pi }\left(16\sin \left(\frac{x}{2}\right){\cos }^3\left(\frac{x}{2}\right)\right)$ is equal to :

Q13.The shortest distance between the lines

and …

Q14.If $(2\alpha +1,{\alpha }^2-3\alpha ,\frac{\alpha -1}{2})$ is the image of $(\alpha ,2\alpha ,1)$ in the line $\frac{\mathrm{x}-2}{3}=\frac{\mathrm{y}-1}{2}=\frac{\mathrm{z}}{1}$, then the possible value(s) of $\alpha$ is(are) :

Q15.Let $\hat{u}$ and $\hat{v}$ be unit vectors inclined at an acute angle such that $|\hat{\mathrm{u}}\times \hat{\mathrm{v}}|=\frac{\sqrt{3}}{2}$. If

Then $\lambda$ …

Q16.Let for some $\alpha \in \mathbb{R},f:\mathbb{R}\to \mathbb{R}$ be a function satisfying $f(\mathrm{x}+\mathrm{y})=f(\mathrm{x})+2{\mathrm{y}}^2+\mathrm{y}+\alpha \mathrm{xy}$ for all $\mathrm{x},\mathrm{y}\in \mathbb{R}$. If $f(0)=-1$ and $f(1)=2$, then the value o …

Q17.Let $\mathrm{A}=\{(\mathrm{a},\mathrm{b},\mathrm{c}):\mathrm{a},\mathrm{b},\mathrm{c}$ are non-negative integers and $\mathrm{a}+\mathrm{b}+2\mathrm{c}=22\}$.
The $\mathrm{n}(\mathrm{A})$ is equal to :

Q18.The area of the region bounded by the curves
$x+3y^2=0$ and $x+4y^2=1$ is equal to :

Q19.Let $y=y(x)$ be the solution of the differential equation :

$\mathrm{x}\in (-1,2)$, satisfying $\mathrm{y}(0)=\frac{3}{2}$.
If …

Q20.The integral ${\int }_0^1{\cot }^{-1}\left(1+\mathrm{x}+{\mathrm{x}}^2\right)\mathrm{dx}$ is equal to :

Q21.From a month of 31 days, 3 different dates are selected at random. If the probability that these dates are in an increasing A.P. is equal to $\frac{\mathrm{a}}{\mathrm{b}}$, where $\mathrm{a},\mathrm{b}\in \mathrm{N}$ and $\gcd (\mathrm{a},\mathrm{b})=1$, then …

Q22.Let $f(\mathrm{x})=\{\begin{array}{cc}{\mathrm{e}}^{\mathrm{x}-1}& ,\mathrm{x}<0\\ {\mathrm{x}}^2-5\mathrm{x}+6& ,\mathrm{x}\ge 0\end{array}$ and
$g(\mathrm{x})=f(|\mathrm{x}|)+|f(\mathrm{x})|$. If the number of points where g is not continuous and is not differ …

Q23.Let $\mathrm{A},\mathrm{B}$ be points on the two half-lines $x-\sqrt{3}|y|=\alpha ,\alpha >0$ at a distance of $\alpha$ from their point of intersection P . The line segment AB meets the angle bisector of the given half-lines at the point Q . If $\mathrm{PQ}=\frac{9}{2}$ and R is …

Q24.Let $\mathrm{A},\mathrm{B}$ and C be the vertices of a variable right angled triangle inscribed in the parabola ${\mathrm{y}}^2=16\mathrm{x}$. Let the vertex B containing the right angle be $(4,8)$ and the locus of the centroid of $△\mathrm{ABC}$ be a conic …

Q25.Let $f$ be a twice differentiable function such that
$f(\mathrm{x})={\int }_0^{\mathrm{x}}\tan (\mathrm{t}-\mathrm{x})\mathrm{dt}-{\int }_0^{\mathrm{x}}f(\mathrm{t})\tan \mathrm{tdt},\mathrm{x}\in \left(-\frac{\pi }{2},\frac{\pi }{2}\right)$
Then …