JEE Main 2026 · 22 Jan 2026 · Shift 2

Q1.If ε, E and t represent the free space permittivity, electric field and time respectively, then the unit of $\frac{\epsilon E}{t}$ will be :

Q2.Using a simple pendulum experiment g is determined by measuring its time period T. Which of the following plots represent the correct relation between the pendulum length L and time period T?

Q3.Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The molecular size of A is half of that of B and mass of molecule A is four times that of B. If the collision frequency in gas B is …

Q4.A uniform bar of length 12 cm and mass $20m$ lies on a smooth horizontal table. Two point masses m and $2m$ are moving in opposite directions with same speed of v and in the same plane as the bar, as shown in figure. These masses strike the bar simultaneously and get stuck to it. …

Q5.Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is :

Q6.In parallax method for the determination of focal length of a concave mirror, the object should always be placed :

Q7.The smallest wavelength of Lyman series is 91 nm. The difference between the largest wavelengths of Paschen and Balmer series is nearly $\_\_\_\_$ nm.

Q8.In an open organ pipe $v_3$ and $v_6$ are $3^{\text{rd}}$ and $6^{\text{th}}$ harmonic frequencies, respectively. If $v_6-v_3=2200$ Hz then length of the pipe is $\_\_\_\_$ mm. (Take velocity of sound in air is $330$ m/s.)

Q9.When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises upto certain height h. If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by $1\%$ each, then the height of the liquid in the tube …

Q10.An electric power line having total resistance of $2\Omega$, delivers 1 kW of power of 250 V. The percentage efficiency of transmission line is $\_\_\_\_$.

Q11.The wavelength of light, while it is passing through water is 540 nm. The refractive index of water is $\frac{4}{3}$. The wavelength of the same light when it is passing through a transparent medium having refractive index of $\frac{3}{2}$ is $\_\_\_\_$ nm.

Q12.Figure shows the circuit that contains three resistances ($9\Omega$ each) and two inductors (4 mH each). The reading of ammeter at the moment switch $K$ is turned ON, is ______ A.

Q13.Given below are two statements:
Statement I: A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth.
Statement II: The time period of revolution of the satellite is …

Q14.Given below are two statements:
Statement I: An object moves from position $r_1$ to position $r_2$ under a conservative force field $\vec{F}$. The work done by the force is $W=-{\int }_{r_1}^{r_2}\vec{F}\cdot \overrightarrow{dr}$.
Statement II: Any object moving from one l …

Q15.Five positive charges each having charge $q$ are placed at the vertices of a pentagon as shown in the figure. The electric potential ($V$) and the electric field ($\vec{E}$) at the center O of the pentagon due to these five positive charges are:

Q16.A laser beam has intensity of $4.0\times 10^{14}\mathrm{W}/{\mathrm{m}}^2$. The amplitude of magnetic field associated with beam is ______ T. (Take ${ϵ}_0=8.85\times 10^{-12}{\mathrm{C}}^2/{\mathrm{Nm}}^2$ and $\mathrm{c}=3\times 10^8\mathrm{m}/\mathrm{s}$)

Q17.Light is incident on a metallic plate having work function $110\times 10^{-20}\mathrm{J}$. If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is ______ $\mathrm{rad}/\mathrm{s}$. ( …

Q18.Given below are two statements:
Statement I: For a mechanical system of many particles total kinetic energy is the sum of kinetic energies of all the particles.
Statement II: The total kinetic energy can be the sum of kinetic energy of the center of mass w.r.t. to the origin and …

Q19.A conducting circular loop is rotated about its diameter at a constant angular speed of $100\mathrm{rad}/\mathrm{s}$ in a magnetic field of 0.5 T perpendicular to the axis of rotation. When the loop is rotated by $30^{\circ }$ from the horizontal position, the induced EMF is 15 …

Q20.Two masses m and 2m are connected by a light string going over a pulley (disc) of mass 30m with radius $r=0.1\mathrm{m}$. The pulley is mounted in a vertical plane and it is free to rotate about its axis. The 2m mass is released from rest and its speed when it has descended thr …

Q21.A capacitor $P$ with capacitance $10\times 10^{-6}\mathrm{F}$ is fully charged with a potential difference of 6.0 V and disconnected from the battery. The charged capacitor $P$ is connected across another capacitor $Q$ with capacitance $20\times 10^{-6}\mathrm{F}$. The char …

Q22.A cylindrical conductor of length 2 m and area of cross-section $0.2{\mathrm{mm}}^2$ carries an electric current of 1.6 A when its ends are connected to a 2 V battery. Mobility of electrons in the conductor is $\alpha \times 10^{-3}{\mathrm{m}}^2/\mathrm{V}$.s. The value of …

Q23.An insulated cylinder of volume $60{\mathrm{cm}}^3$ is filled with a gas at $27^{\circ }\mathrm{C}$ and 2 atmospheric pressure. Then the gas is compressed making the final volume as $20{\mathrm{cm}}^3$ while allowing the temperature to rise to $77^{\circ }\mathrm{C}$. The fin …

Q1.At $\mathrm{T}(\mathrm{K}),100\mathrm{g}$ of $98\%{\mathrm{H}}_2{\mathrm{SO}}_4(\mathrm{w}/\mathrm{w})$ aqueous solution is mixed with 100 g of $49\%{\mathrm{H}}_2{\mathrm{SO}}_4(\mathrm{w}/\mathrm{w})$ aqueous solution. What is the mole fraction of …

Q2.Consider the following reaction :

$\underset{\text{ (ii) }\text{ ↓ }-\mathrm{Br}}{\overset{\text{ (i) }{\mathrm{NaNH}}_2}{\to }}\mathrm{Y}$

The product Y formed is :

Q3.$\mathrm{A}+2\mathrm{B}⟶{\mathrm{AB}}_2$

36.0 g of 'A' (Molar mass : $60\mathrm{g}{\mathrm{mol}}^{-1}$ ) and 56.0 g of ' B ' (Molar mass : $80\mathrm{g}{\mathrm{mol}}^{-1}$ ) are allowed to react. Which of the following statements are correct?
(A) ' A …

Q4.Given below are two statements :

Statement-I : The first ionization enthalpy of Cr is lower than that of Mn.
Statement-II : The second and third ionization enthalpies of Cr are higher than those of Mn .

In the light of the above statements, choose the correct answer from the op …

Q5.The final product $[\mathrm{B}]$ is :

Q6.When 1 g of compound ( X ) is subjected to Kjeldahl's method for estimation of nitrogen, 15 $\mathrm{mL},1\mathrm{M}{\mathrm{H}}_2{\mathrm{SO}}_4$ was neutralized by ammonia evolved. The percentage of nitrogen in compound $(\mathrm{X})$ is :

Q7.Correct statements regarding Arrhenius equation among the following are :
(A) Factor $e^{-\mathrm{Ea}/\mathrm{RT}}$ corresponds to fraction of molecules having kinetic energy less than Ea.
(B) At a given temperature, lower the Ea, faster is the reaction.
(C) Increase in tempe …

Q8.The IUPAC name of the following comopound is :

Q9.Given below are two statements :

Statement-I : Element ' X ' and ${}^{\prime }\mathrm{Y}$ ' are the most and least electronegative elements, respectively among $\mathrm{N},\mathrm{As},\mathrm{Sb}$ and P . The nature of the oxides ${\mathrm{X}}_2{\mathrm{O}}_3$ and …

Q10.Match List-I with List-II.

List-I
Reaction of glucose with
A. Hydroxylamine
B. ${\mathrm{Br}}_2$ water
C. Excess acetic anhydride
D. Concentrated ${\mathrm{HNO}}_3$

List-II
Product formed
I. Glouconic acid
II. Glucose pentacetate
III. Saccharic acid
IV. Glucoxime

Choose th …

Q11.Among ${\mathrm{H}}_2\mathrm{S},{\mathrm{H}}_2\mathrm{O},{\mathrm{NF}}_3,{\mathrm{NH}}_3$ and ${\mathrm{CHCl}}_3$, identify the molecule $(\mathrm{X})$ with lowest dipole moment value. The number of lone pairs of electrons present on the central atom of the molecule …

Q12.Given below are two statements :

Statement-I : $\mathrm{C}<\mathrm{O}<\mathrm{N}<\mathrm{F}$ is the correct order in terms of first ionization enthalpy values.

Statement-II : $\mathrm{S}>\mathrm{Se}>\mathrm{Te}>\mathrm{Po}>\mathrm{O}$ is the correct order in terms of the ma …

Q13.Which of the following mixture gives a buffer solution with $\mathrm{pH}=9.25$ ?
Given : ${\mathrm{pK}}_{\mathrm{b}}\left({\mathrm{NH}}_4\mathrm{OH}\right)=4.75$

Q14.The energy of first (lowest) Balmer line of H atom is x J. The energy (in J) of second Balmer line of H atom is :

Q15.Identify the correct statements:
A. Hydrated salts can be used as primary standard.
B. Primary standard should not undergo any reaction with air.
C. Reactions of primary standard with another substance should be instantaneous and stoichiometric.
D. Primary standard should not be …

Q16.$[\mathrm{Ni}({\mathrm{PPh}}_3{)}_2{\mathrm{Cl}}_2]$ is a paramagnetic complex. Identify the INCORRECT statements about this complex.
A. The complex exhibits geometrical isomerism.
B. The complex is white in colour.
C. The calculated spin-only magnetic moment of the complex is 2. …

Q17.Consider the following reduction processes:
${\mathrm{Al}}^{3+}+3{\mathrm{e}}^{-}\to \mathrm{Al}(\mathrm{s}),{\mathrm{E}}^{\circ }=-1.66\mathrm{V}$
${\mathrm{Fe}}^{3+}+{\mathrm{e}}^{-}\to {\mathrm{Fe}}^{2+},{\mathrm{E}}^{\circ }=+0.77\mathrm{V}$ …

Q18.The compound A, ${\mathrm{C}}_8{\mathrm{H}}_8{\mathrm{O}}_2$ reacts with acetophenone to form a single product via cross-Aldol condensation. The compound A on reaction with conc. NaOH forms a substituted benzyl alcohol as

Q19.3,3-Dimethyl-2-butanol cannot be prepared by:
A.
B.
C.
D.
E.
Choose the correct answer from the options given below:

Q20.The dibromo compound [P] (molecular formula: ${\mathrm{C}}_9{\mathrm{H}}_{10}{\mathrm{Br}}_2$) when heated with excess sodamide followed by treatment with dilute HCl gives [Q]. On warming [Q] with mercuric sulphate and dilute sulphuric acid yield [R] which gives positive Iodoform t …

Q21.Consider the following electrochemical cell:
$\mathrm{Pt}|{\mathrm{O}}_2(\mathrm{g})(1\mathrm{bar})|\mathrm{HCl}(\mathrm{aq})||{\mathrm{M}}^{2+}(\mathrm{aq},1.0\mathrm{M})|\mathrm{M}(\mathrm{s})$
The pH above which, oxygen gas would start to evolve at anode is _____ (nearest inte …

Q22.If the enthalpy of sublimation of Li is $155{\mathrm{kJ}\mathrm{mol}}^{-1}$, enthalpy of dissociation of ${\mathrm{F}}_2$ is $150{\mathrm{kJ}\mathrm{mol}}^{-1}$, ionization enthalpy of Li is $520{\mathrm{kJ}\mathrm{mol}}^{-1}$, electron gain enthalpy of F is $-313{\mathrm{kJ}\mathrm{mol}}^{-1}$, standard enthalpy o …

Q23.Among the following oxides of 3d elements, the number of mixed oxides are _____. …

Q24.The mass of benzanilide obtained from the benzoylation reaction of 5.8 g of aniline, if yield of product is 82%, is _____ g (nearest integer).
(Given molar mass in ${\mathrm{g}\mathrm{mol}}^{-1}$ H: 1, C: 12, N: 14, O: 16)

Q25.Consider $\mathrm{A}\stackrel{k_1}{\to }\mathrm{B}$ and $\mathrm{C}\stackrel{k_2}{\to }\mathrm{D}$ are two reactions. If the rate constant $(k_1)$ of the $\mathrm{A}\to \mathrm{B}$ reaction can be expressed by the following equation …

Q1.Let n be the number obtained on rolling a fair die. If the probability that the system
$x-ny+z=6$
$x+(n-2)y+(n+1)z=8$
$(n-1)y+z=1$
has a unique solution is $\frac{k}{6}$, then the sum of k and all possible values of n is :

Q2.If the mean deviation about the median of the numbers $k,2k,3k,\dots ,1000k$ is 500, then $k^2$ is equal to :

Q3.The number of elements in the relation $R=\{(x,y):4x^2+y^2<52,x,y\in \mathbb{Z}\}$ is

Q4.Let $S=\{z\in \mathbb{C}:4z^2+\overline{z}=0\}$. Then ${\sum }_{z\in S}|z{|}^2$ is equal to :

Q5.If ${\lim }_{x\to 0}\frac{e^{(a-1)x}+2\cos bx+(c-2)e^{-x}}{x\cos x-{\log }_e(1+x)}=2$, then $a^2+b^2+c^2$ is equal to :

Q6.If $y=y(x)$ satisfies the differential equation
$16(\sqrt{x+9\sqrt{x}})(4+\sqrt{9+\sqrt{x}})\cos ydy=(1+2\sin y)dx$, $x>0$ and $y(256)=\frac{\pi }{2}$, $y(49)=\alpha$, then $2\sin \alpha$ is equal to :

Q7.Among the statements
(S1): If $A(5,-1)$ and $B(-2,3)$ are two vertices of a triangle, whose orthocentre is $(0,0)$, then its third vertex is $(-4,-7)$ and
(S2): If positive numbers $2a,b,c$ are three consecutive terms of an A.P., then the lines $ax+by+c=0$ are …

Q8.Let $\vec{a}=2\hat{i}-\hat{j}+\hat{k}$ and $\vec{b}=\lambda \hat{j}+2\hat{k}$, $\lambda \in \mathbb{Z}$ be two vectors. Let $\vec{c}=\vec{a}\times \vec{b}$ and $\vec{d}$ be a vector of magnitude 2 in yz-plane. If $|\vec{c}|=\sqrt{53}$, then the maximum p …

Q9.If $X=\left[\begin{array}{c}x\\ y\\ z\end{array}\right]$ is a solution of the system of equations $AX=B$, where $\text{adj }A=\left[\begin{array}{ccc}4& 2& 2\\ -5& 0& 5\\ 1& -2& 3\end{array}\right]$ and $B=\left[\begin{array}{c}4\\ 0\\ 2\end{array}\right]$, then $|x+y+z|$ is equal t …

Q10.Let L be the line $\frac{x+1}{2}=\frac{y+1}{3}=\frac{z+3}{6}$ and let S be the set of all points $(a,b,c)$ on L, whose distance from the line $\frac{x+1}{2}=\frac{y+1}{3}=\frac{z-9}{0}$ along the line L is 7. Then ${\sum }_{(a,b,c)\in S}(a+b+c)$ is equal to :

Q11.Let $P(10,2\sqrt{15})$ be a point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, whose foci are S and $S^{\prime }$. If the length of its latus rectum is 8, then the square of the area of $△PS{S}^{\prime }$ is equal to :

Q12.The area of the region
$A=\{(x,y):4x^2+y^2\le 8\text{ and }{y}^2\le 4x\}$ is :

Q13.Let $\alpha ,\beta$ be the roots of the quadratic equation $12{\mathrm{x}}^2-20\mathrm{x}+3\lambda =0,\lambda \in \mathbb{Z}$. If $\frac{1}{2}\le |\beta -\alpha |\le \frac{3}{2}$, then the sum of all possible values of $\lambda$ is :

Q14.Let the domain of the function
$\mathrm{f}(\mathrm{x})={\log }_3{\log }_5\left(7-{\log }_2\left({\mathrm{x}}^2-10\mathrm{x}+85\right)\right)+{\sin }^{-1}\left(\left|\frac{3\mathrm{x}-7}{17-\mathrm{x}}\right|\right)$ be $(\alpha ,\beta ]$. Then $\alpha +\beta$ is equal to :

Q15.Let $[\bullet ]$ denote the greatest integer function, and let $f(x)=\min \left\{\sqrt{2}x,x^2\right\}$. Let $S=\{x\in (-2,2):$ the function $\mathrm{g}(\mathrm{x})=|\mathrm{x}|\left[{\mathrm{x}}^2\right]$ is discontinuous at x$\}$.

Then ${\sum }_{x\in S}f(x)$ equa …

Q16.Let $S$ and $S^{\prime }$ be the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$ and $\mathrm{P}(\alpha ,\beta )$ be a point on the ellipse in the first quadrant. If …

Q17.Let the locus of the mid-point of the chord through the origin O of the parabola ${\mathrm{y}}^2=4\mathrm{x}$ be the curve S . Let P be any point on S . Then the locus of the point, which internally divides OP in the ratio $3:1$, is :

Q18.Let $f(x)=[x{]}^2-[x+3]-3,x\in \mathbb{R}$ where $[\bullet ]$ is the greatest integer function. Then

Q19.Let $f$ and $g$ be functions satisfying $f(\mathrm{x}+\mathrm{y})=f(\mathrm{x})f(\mathrm{y}),\mathrm{f}(\mathrm{l})=7$ and $\mathrm{g}(\mathrm{x}+\mathrm{y})=\mathrm{g}(\mathrm{xy})$, $\mathrm{g}(\mathrm{l})=1$, for all …

Q20.Let ${\mathrm{C}}_{\mathrm{r}}$ denote the coefficient of ${\mathrm{x}}^{\mathrm{r}}$ in the binomial expansion of $(1+\mathrm{x}{)}^{\mathrm{n}},\mathrm{n}\in \mathbb{N},0\le \mathrm{r}\le \mathrm{n}$.

If …

Q21.Let a vector $\vec{a}=\sqrt{2}\hat{i}-\hat{j}+\lambda \hat{k},\lambda >0$, make an obtuse angle with the vector $\vec{b}=-{\lambda }^2\hat{i}+4\sqrt{2}\hat{j}+4\sqrt{2}\hat{k}$ and an angle $\theta ,\frac{\pi }{6}<\theta <\frac{\pi }{2}$, with the positive $z$-axis. If …

Q22.Let $[\bullet ]$ be the greatest integer function. If $\alpha ={\int }_0^{64}\left({\mathrm{x}}^{1/3}-\left[{\mathrm{x}}^{1/3}\right]\right)\mathrm{dx}$, then …

Q23.Let $\cos (\alpha +\beta )=-\frac{1}{10}$ and $\sin (\alpha -\beta )=\frac{3}{8}$, where $0<\alpha <\frac{\pi }{3}$ and $0<\beta <\frac{\pi }{4}$.

If $\tan 2\alpha =\frac{3(1-r\sqrt{5})}{\sqrt{11}(s+\sqrt{5})},r,s\in \mathbb{N}$, then $r+s$ is equal to ______。

Q24.Suppose $\mathrm{a},\mathrm{b},\mathrm{c}$ are in A.P. and ${\mathrm{a}}^2,2{\mathrm{b}}^2,{\mathrm{c}}^2$ are in G.P. If $\mathrm{a}<\mathrm{b}<\mathrm{c}$ and $\mathrm{a}+\mathrm{b}+\mathrm{c}=1$, then $9\left({\mathrm{a}}^2+{\mathrm{b}}^2+c^2\right)$ is equa …

Q25.Let S be the set of the first 11 natural numbers. Then the number of elements in $A=\{B\subseteq S:n(B)\ge 2$ and the product of all elements of B is even $\}$ is