JEE Main 2026 · 06 Apr 2026 · Shift 2

Q1.The percentage error in the calculated volume of a sphere, if there is $2\%$ error in its diameter measurement, is ______.

Q2.A solid sphere (A) of mass, 5 m and spherical shell (B) of mass $m$, both having same radius, are placed on a rough surface. When a force of same magnitude is applied tangentially at the highest points of A and B, they start rolling without slipping with an acceleration of …

Q3.A body of mass 1 kg moves along a straight line with a velocity $v=2x^2$. The work done by the body during displacement from $x=0$ to 5 m is ______ J.

Q4.A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same $P,V,T$. Heating is started from left side until pressure changes to …

Q5.For an electromagnetic wave propagating through vacuum, $\overrightarrow{k}$, $\overrightarrow{E}$ and $\omega$ represent propagation vector, electric field and angular frequency, respectively. The magnetic field associated with this wave is represented by:

Q6.Two identical bodies A and B of equal masses have initial velocities ${\overrightarrow{v}}_1=4\hat{i}$ m/s and ${\overrightarrow{v}}_2=4\hat{j}$ m/s respectively. The body A has acceleration ${\overrightarrow{a}}_1=6\hat{i}+6\hat{j}$ m/s${}^2$ while the acceleration of th …

Q7.Figure represents the extension ($\Delta l$) of a wire of length 1 meter, suspended from the ceiling of the room at one end with load W connected to the other end. If the cross-sectional area of the wire is $10^{-5}$ m${}^2$ then the Young's modulus of the wire is ______ N/ …

Q8.A cylindrical vessel of 40 cm radius is completely filled with water and its capacity is $528$ dm${}^3$ (dm: decimeter). The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at 70 cm below the top of water level, then horizontal rang …

Q9.If 2 mole of an ideal monoatomic gas at temperature T, is mixed with 6 mole of another ideal monoatomic gas at temperature 2T then the temperature of mixture is:

Q10.A spring stretches by 2 mm when it is loaded with a mass of 200 g. From equilibrium position the mass is further pulled down by 2 mm and released. The frequency associated with the system and maximum energy in the spring are ______ Hz and ______ J, respectively. (Take $g=10$ m/ …

Q11.The electric potential as a function of $x,y$ is given by $V=5(x^2-y^2)$ V. The electric field at a point $(2,3)$ m is ______ V/m.

Q12.A current of 30 A each flows in opposite directions in two conducting wires, placed parallel to each other at a distance of 8 cm. The magnetic field at the mid point between the two wires is ______ $\mu \mathrm{T}$. …

Q13.A square loop of side 2 cm is placed in a time varying magnetic field with magnitude as $\mathrm{B}=0.4\sin (300\mathrm{t})$ Tesla. The normal to the plane of loop makes an angle of $60^{\circ }$ with the field. The maximum induced emf produced in the loop is ______ mV.

Q14.A sphere of capacitance 100 pF is charged to a potential of 100 V. Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is $\alpha \times 10^{-7}\mathrm{J}$. The valu …

Q15.The energy released if hydrogen atoms are combined to form $\frac{4}{2}\mathrm{He}$ is ______.
(Take binding energies per nucleon of ${}_1^2\mathrm{H}$ and ${}_2^4\mathrm{He}$ as 1.1 MeV and 7.2 MeV, respectively).

Q16.Angle of minimum deviation is equal to the half of the angle of prism in an equilateral prism. The refractive index of the prism is ______.

Q17.Refer to the logic circuit given below. For two inputs ($\mathrm{A}=1,\mathrm{B}=1$) and ($\mathrm{A}=0,\mathrm{B}=1$), output (Y) will be ______.

Q18.The velocity at which 6 kg mass (shown in figure) strikes the ground when it is released from a height of 6 m above the ground is ______ $\mathrm{m}/\mathrm{s}$. Assume pulley is massless and string is light and inextensible (Take $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$).

Q19.In a Young double slit experiment, the wavelength of incident light is $6000\text{ A˚}$, the separation between slits ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ is 5 cm, the distance between slits plane and screen is 50 cm, as shown in the figure below. If the resultant intensity at P …

Q20.A block takes $t$ time to slide down a plane inclined at $45^{\circ }$ to the horizontal. If the surface is made smooth (frictionless), the block takes time $\frac{\mathrm{t}}{2}$ to slide down the plane. The coefficient of friction between the block and the inclined plane is …

Q21.The de Broglie wavelength for an electron accelerated through the potential difference $V_1$ volt is ${\lambda }_1$. When the potential difference is changed to ${\mathrm{V}}_2$ volt, the associated de Broglie wavelength is increased by $50\%$. If …

Q22.A moving coil of a galvanometer when shunted with $2\Omega$ resistance gives a full scale deflection for a current of 500 mA. When a resistance of $470\Omega$ is connected in series it gives a full scale deflection for 10 V potential applied on it. The value of resistance of ga …

Q23.Two cells of emfs 1 V and 2 V and internal resistance $2\Omega$ and $1\Omega$, respectively connected in parallel, gave current of 1 A through an external resistance. If the polarity of one cell is reversed, then value of current through the external resistance will be …

Q24.A concave mirror of focal length 10 cm forms an image which is double the size of object when the object is placed at two different positions. The distance between the two positions of the object is ______ cm.

Q1.Which of the following contain the same number of atoms?
(Given : Molar mass in $\mathrm{g}{\mathrm{mol}}^{-1}$ of $\mathrm{H},\mathrm{He},\mathrm{O}$ and S are $1,4,16$ and 32 respectively)
A. 2 g of ${\mathrm{O}}_2$ gas
B. 4 g fo ${\mathrm{SO}}_2$ gas
C. 1400 mL of …

Q2.The Bohr radius of a hydrogen like species is 70.53 pm . The species and the stationary state(n) are respectively
(Given: Hydrogen atom Bohr radius is 52.9 pm )

Q3.Given below are two statements:

Statement I: The number of compounds among ${\mathrm{SO}}_2,{\mathrm{SO}}_3,{\mathrm{SF}}_4,{\mathrm{SF}}_6$ and ${\mathrm{H}}_2\mathrm{S}$ in which sulphur does not obey the Octet rule is 3 .

Statement II : Among …

Q4.Match List-I with List-II

Given $V_1$ and $V_2$ are initial and final volumes respectively:

Q5.Given below are two statements :

Statement I : ${\mathrm{H}}_2\mathrm{O}$ molecules move from the chamber 1 to chamber 2.
Statement II : The osmotic pressure of a solution prepared by dissolving 50 mg of potassium sulphate (molar mass $=174\mathrm{g}/\mathrm{mol}$ ) in …

Q6.Given is a concentrated solution of a weak electrolyte ${\mathrm{A}}_{\mathrm{x}}{\mathrm{B}}_{\mathrm{y}}$ of concentration ' c ' and dissociation constant ' K '. the degree of dissociation is given by:

Q7.For a general redox reaction

Anode ${\mathrm{Red}}_1\to {\mathrm{Ox}}_1{}^{{\mathrm{n}}_1^{+}}+{\mathrm{n}}_1{\mathrm{e}}^{-}$
Cathode ${\mathrm{Ox}}_2+{\mathrm{n}}_2{\mathrm{e}}^{-}\to {\mathrm{Red}}_2{}^{{\mathrm{n}}_2-}$
Which of the fo …

Q8.In a period, the first ionisation enthalpy of the element at extreme left and the negative electron gain enthalpy of the extreme right element, except noble gases, are respectively.

Q9.Given below are two statements :

Statement I: ${\mathrm{F}}_2\mathrm{O}<{\mathrm{H}}_2\mathrm{O}<{\mathrm{Cl}}_2\mathrm{O}$ is the correct trend in terms of bond angle.
Statement II : ${\mathrm{SiF}}_4,{\mathrm{SnF}}_4$ and ${\mathrm{PbF}}_4$ are ionic in nature.
In th …

Q10.The correct order of first $({\Delta }_{\mathrm{i}}{\mathrm{H}}_1)$ and second $({\Delta }_{\mathrm{i}}{\mathrm{H}}_2)$ ionisation enthalpy values of cr and Mn are :
A. ${\Delta }_{\mathrm{i}}{\mathrm{H}}_1:\mathrm{Cr}>\mathrm{Mn}$
B. …

Q11.Which of the following sequence of hybridisation, geometry and magnetic nature are correct for the given coordination compounds ?
A. $[{\mathrm{NiCl}}_4{]}^{2-}-{\mathrm{sp}}^3$, tetrahedral, paramagnetic
B. …

Q12.Given below are two statements :

Statement I: A mixture of ${\mathrm{C}}_{12}{\mathrm{H}}_{22}{\mathrm{O}}_{11}$ (sugar) and NaCl can be separated by dissolving sugar in alcohol, due to differential solubility
Statement II : Rose essence from rose petals is separated by steam dist …

Q13.Shown below is the structure of methyl acetate with three different α, β and γ carbon-oxygen bonds.

(see structure)

The correct order of bond length of these bonds is :

Q14.'x' is the product which is obtained by the hydrolysis of prop-1-yne in the presence of mercuric sulphate under dilute acidic medium at 333 K. 'y' is the product which is obtained by the reaction of ethane nitrile with methyl magnesium bromide in dry ether followed by hydrolysis. …

Q15.An optically active alkyl bromide C₄H₉Br, reacts with ethanolic KOH to form major compound [A] which reacts with bromine to give compound [B]. Compound [B] reacts with ethanolic KOH and sodamide to give compound [C]. One molecule of water adds to compound [C] on warming with merc …

Q16.Consider the following reaction.

(see structure)

Statement I: In the above reaction, product formed will be a mixture of benzyl alcohol and iodobenzene.
Statement II: In the above reaction, the -O-CH₂- bond is cleaved to give the product.

In the light of the above statements, …

Q17.Consider the following organic reaction sequence. Choose the final product (X) from the following (consider the major product in all intermediate reactions)

(see structure)

Q18.The number of compounds from the following which can undergo reaction with Br₂/KOH/(alcoholic) to give respective products and these respective products can also be obtained separately by Gabriel phthalimide reaction is:

(see structures)

Q19.Consider the following reactions. Total number of electrons in the π bonds and lone pair of electrons in the product (X) is:

(see structure)

Q20.Treatment of a gas 'X' with a freshly prepared ferrous sulphate solution gives a compound 'Y' as a brown ring. The compounds X and Y are.

Q21.An excess of AgNO₃ is added to 100 mL of a 0.05 M solution of tetraaquadichloridochromium (III) chloride. The number of moles of AgCl precipitated will be _____ × 10⁻³. (Nearest integer)

Q22.An alkane (Y) requires 8 moles of oxygen for complete combustion and on chlorination with Cl₂/hν, (Y) gives only one monochlorinated product (Z). The total number of primary carbon atoms in (Y) is _____.

Q23.500 mL of 0.2 M MnO₄⁻ solution in basic medium when mixed with 500 mL of 1.5 M KI solution, oxidises iodide ions to liberate molecular iodine. This liberated iodine is then titrated with a standard x M thiosulphate solution in presence of starch till the end point. If 300 mL of t …

Q24.In a closed flask at 600 K, one mole of X₂Y₄(g) attains equilibrium as given below:

X₂Y₄(g) ⇌ 2XY₂(g)

At equilibrium, 75% X₂Y₄(g) was dissociated and the total pressure is 1 atm. The magnitude of ΔᵣG° (in kJ mol⁻¹) at this temperature is _____. (Nearest Integer)

(Given: R = 8. …

Q25.Decomposition of a hydrocarbon follows the equation $k=(5.5\times 10^{11}{\mathrm{s}}^{-1})e^{\frac{-28000\mathrm{K}}{T}}$. The activation energy of reaction is $\_\_\_\_$ ${\mathrm{kJ}\mathrm{mol}}^{-1}$. (Nearest Integer)
Given : $R=8.3{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}$

Q1.Let $f:\mathrm{R}\to \mathrm{R}$ be defined as $f(\mathrm{x})=\frac{2{\mathrm{x}}^2-3\mathrm{x}+2}{3{\mathrm{x}}^2+\mathrm{x}+3}$. Then $f$ is :

Q2.Consider the quadratic equation $({\mathrm{n}}^2-2\mathrm{n}+2){\mathrm{x}}^2-3\mathrm{x}+({\mathrm{n}}^2-2\mathrm{n}+2{)}^2=0,\mathrm{n}\in \mathrm{R}$. Let $\alpha$ be the minimum value of the product of its roots and $\beta$ be the maximum value of the sum of its r …

Q3.Let $S=\{z\in \mathbb{C}:z^2+\sqrt{6}iz-3=0\}$. Then ${\sum }_{z\in S}{z}^8$ is equal to :

Q4.The sum of all possible values of $\theta \in [0,2\pi ]$, for which the system of equations :

has a non-trivial solution, is equal to:

Q5.Let $\mathrm{A}=\left[\begin{array}{lll}1& 0& 0\\ 3& 1& 0\\ 9& 3& 1\end{array}\right]$ and $\mathrm{B}=\left[{\mathrm{b}}_{\mathrm{ij}}\right],1\le \mathrm{i},\mathrm{j}\le 3$.

If $B=A^{99}-I$, then the value of $\frac{b_{31}-b_{21}}{b_{32}}$ is:

Q6.The sum $1+\frac{1}{2}\left(1^2+2^2\right)+\frac{1}{3}\left(1^2+2^2+3^2\right)+\dots \dots$. upto 10 terms is equal to :

Q7.A building has ground floor and 10 more floors. Nine persons enter in a lift at the ground floor. The lift goes up to the $10^{\text{th }}$ floor. The number of ways, in which any 4 persons exit at a floor and the remaining 5 persons exit at a different floor, if the lift does …

Q8.Let the mean and the variance of seven observations $2,4,\alpha ,8,\beta ,12,14,\alpha <\beta$, be 8 and 16 respectively. Then the quadratic equation whose roots are $3\alpha +2$ and $2\beta +1$ is :

Q9.A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue and one green ball is :

Q10.Let C be a circle having centre in the first quadrant and touching the x -axis at a distance 3 units from the origin. If the circle C has an intercept of length $6\sqrt{3}$ on $y$-axis, then the length of the chord of the circle $C$ on the line $x-y=3$ is :

Q11.The eccentricity of an ellipse E with centre at the origin $O$ is $\frac{\sqrt{3}}{2}$ and its directrices are $x=\pm \frac{4\sqrt{6}}{3}$. Let $H:\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be a hyperbola whose eccentricity is equal to the length of semi-major axis of …

Q12.Let $x=9$ be a directrix of an ellipse $E$, whose centre is at the origin and eccentricity is $\frac{1}{3}$. Let $\mathrm{P}(\alpha ,0),\alpha >0$, be a focus of E and AB be a chord passing through P . Then the locus of the mid point of AB is :

Q13.If $\sin \left({\tan }^{-1}(\mathrm{x}\sqrt{2})\right)=\cot \left({\sin }^{-1}\sqrt{1-{\mathrm{x}}^2}\right),\mathrm{x}\in (0,1)$, then the value of x is :

Q14.The shortest distance between the lines $\frac{x-4}{1}=\frac{y-3}{2}=\frac{z-2}{-3}$ and $\frac{x+2}{2}=\frac{y-6}{4}=\frac{z-5}{-5}$ is:

Q15.Let $\vec{a}=2\hat{i}+3\hat{j}+3\hat{k}$ and $\vec{b}=6\hat{i}+3\hat{j}+3\hat{k}$. Then the square of the area of the triangle with adjacent sides determined by the vectors $(2\vec{a}+3\vec{b})$ and $(\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}})$ is :

Q16.Let ${\lim }_{x\to 2}\frac{(\tan (x-2))\left(r^2+(p-2)x-2p\right)}{(x-2{)}^2}=5$ for some $\mathrm{r},\mathrm{p}\in \mathrm{R}$. If the set of all possible values of q , such that the roots of the equation ${\mathrm{rx}}^2-\mathrm{px}+\mathrm{q}=0$ lie in ( 0,2 ), b …

Q17.Let $\mathrm{A}=\left|\begin{array}{ccc}1& 3& -1\\ 2& 1& \alpha \\ 0& 1& -1\end{array}\right|$ be a singular matrix. Let $f(x)={\int }_0^x\left(t^2+2t+3\right)dt,x\in [1,\alpha ]$. If $M$ and $m$ are respectively the maximum and the minimum values of $f$ in …

Q18.Let $f:R\to R$ be such that $f(xy)=f(x)f(y)$, for all $x,y\in R$ and $f(0)\ne 0$. Let $g:[1,\infty )\to R$ be a differentiable function such that
$x^{2}g(x)={\int }_1^x\left(t^{2}f(t)-\mathrm{tg}(t)\right)dt$
Then $\mathrm{g}(2)$ is equal to :

Q19.The area of the region $\left\{(x,y):x^2-8x\le y\le -x\right\}$ is:

Q20.The value of the integral ${\int }_{-1}^1\left(\frac{x^3+|x|+1}{x^2+2|x|+1}\right)dx$ is equal to

Q21.Let $\mathrm{R}=\left\{(\mathrm{x},\mathrm{y})\in \mathrm{N}\times \mathrm{N}:{\log }_{\mathrm{e}}(\mathrm{x}+\mathrm{y})\le 2\right\}$. Then the minimum number of elements, required to be added in R to make it a transitive relation, is

Q22.If ${\left(1-x^3\right)}^{10}={\sum }_{r=0}^{10}{a}_r{x}^r(1-x{)}^{30-2r}$, then $\frac{9a_9}{a_{10}}$ is equal to

Q23.Let the line $\mathrm{x}-\mathrm{y}=4$ intersect the circle
$\mathrm{C}:(\mathrm{x}-4{)}^2+(\mathrm{y}+3{)}^2=9$ at the points Q and R . If $\mathrm{P}(\alpha ,\beta )$ is a point on C such that $\mathrm{PQ}=\mathrm{PR}$, then $(6\alpha +8\beta {)}^2$ is equal to

Q24.Let the image of the point $\mathrm{P}(0,-5,0)$ in the line $\frac{\mathrm{x}-1}{2}=\frac{\mathrm{y}}{1}=\frac{\mathrm{z}+1}{-2}$ be the point R and the image of the point $\mathrm{Q}\left(0,\frac{-1}{2},0\right)$ in the line $\frac{x-1}{-1}=\frac{y+9}{4}=\frac{z+1}{1}$ be the …

Q25.Let $f(x)=\{\begin{array}{ll}{x}^3+8& x<0\\ x^2-4& x\ge 0\end{array}$ and
$\mathrm{g}(\mathrm{x})=\{\begin{array}{ll}(\mathrm{x}-8{)}^{1/3};& \mathrm{x}<0\\ (\mathrm{x}+4{)}^{1/2};& \mathrm{x}\ge 0\end{array}$
Then the number of points, where the function …