JEE Main 2026 · 24 Jan 2026 · Shift 1

Q1.Match the List-I with List-II

Choose the correct answer from the options given below:
(1) A-IV,B-III,C-I,D-II
(2) A-III,B-IV,C-II,D-I
(3) A-I,B-III,C-IV,D-II
(4) A-III,B-IV,C-I,D-II

Q2.Three charges $+2\mathrm{q}$, $+3\mathrm{q}$ and $-4\mathrm{q}$ are situated at $(0,-3\mathrm{a})$, $(2\mathrm{a},0)$ and $(-2\mathrm{a},0)$ respectively in the xy plane. The resultant dipole moment about origin is

Q3.A cylindrical block of mass M and area of cross section A is floating in a liquid of density $\rho$ and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is

Q4.Density of water at $4^{\circ }\mathrm{C}$ and $20^{\circ }\mathrm{C}$ are $1000\mathrm{kg}/{\mathrm{m}}^3$ and $998\mathrm{kg}/{\mathrm{m}}^3$ respectively. The increase in internal energy of 4 kg water when it is heated from $4^{\circ }\mathrm{C}$ to …

Q5.Two resistors of $100\Omega$ each are connected in series with a 9 V battery. A voltmeter of $400\Omega$ resistance is connected to measure the voltage drop across one of the resistors. The voltmeter reading is ______ V.

Q6.The exit surface of a prism with refractive index $n$ is coated with a material having refractive index $\frac{\mathrm{n}}{2}$. When this prism is set for minimum angle of deviation it exactly meets the condition of critical angle. The prism angle is

Q7.Two electrons are moving in orbits of two hydrogen like atoms with speeds $3\times 10^5\mathrm{m}/\mathrm{s}$ and $2.5\times 10^5\mathrm{m}/\mathrm{s}$ respectively. If the radii of these orbits are nearly same then the possible order of energy states are ______ res …

Q8.In a microscope of tube length 10 cm two convex lenses are arranged with focal length of 2 cm and 5 cm. Total magnification obtained with this system for normal adjustment is $(5{)}^{\mathrm{k}}$. The value of k is

Q9.For the series LCR circuit connected with 220 V, 50 Hz a.c source as shown in the figure, the power factor is $\frac{\alpha }{10}$. The value of $\alpha$ is

Q10.Match the List-I with List-II

Choose the correct answer from the options given below:
(1) A-II,B-IV,C-III,D-I
(2) A-IV,B-III,C-I,D-II
(3) A-IV,B-I,C-II,D-III
(4) A-IV,B-II,C-I,D-III

Q11.A spring of force constant $15\mathrm{N}/\mathrm{m}$ is cut into two pieces. If the ratio of their length is $1:3$, then the force constant of smaller piece is ______ $\mathrm{N}/\mathrm{m}$

Q12.Two resistors $2\Omega$ and $3\Omega$ are connected in the gaps of bridge as shown in figure. The null point is obtained with the contact of jockey at some point on wire XY. When an unknown resistor is connected in parallel with $3\Omega$ resistor, the null point is shifted by …

Q13.Given below are two statements:

Statement I : For all elements, greater the mass of the nucleus, greater is the binding energy per nucleon.

Statement II : For all elements, nuclei with less binding energy per nucleon transforms to nuclei with greater binding energy per nucleon. …

Q14.A brass wire of length 2 m and radius 1 mm at $27^{\circ }\mathrm{C}$ is held taut between two rigid supports. Initially it was cooled to a temperature of $-43^{\circ }\mathrm{C}$ creating a tension T in the wire. The temperature to which the wire has to be cooled in order to inc …

Q15.The electrostatic potential in a charged spherical region of radius $r$ varies as $V=a{r}^3+b$, where $a$ and $b$ are constants. The total charge in the sphere of unit radius is $\alpha \times \pi \mathrm{a}{ϵ}_0$. The value of $\alpha$ is ______.
(permittivity of vacuum …

Q16.Two masses 400 g and 350 g are suspended from the ends of a light string passing over a heavy pulley of radius 2 cm. When released from rest the heavier mass is observed to fall 81 cm in 9 s. The rotational inertia of the pulley is ______ $\mathrm{kg}.{\mathrm{m}}^2$.
( …

Q17.An unpolarised light is incident at an interface of two dielectric media having refractive indices of 2 (incident medium) and $2\sqrt{3}$ (medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is …

Q18.A boy thrown a ball into air at $45^{\circ }$ from the horizontal to land it on a roof of a building of height H. If the ball attains maximum height in 2 s and lands on the building in 3 s after launch, then value of H is ______ m.
($\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$)

Q19.There are three co-centric conducting spherical shells A, B and C of radii a, b and c respectively. The potential of the spheres A, B and C respectively, are:

Q20.Three masses 200 kg, 300 kg and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m. They are rearranged on the vertices of a bigger triangle of side 25 m and with the same centre. The work done in this process ______ J.
(Gravitational constant …

Q21.A short bar magnet placed with its axis at $30^{\circ }$ with an external field of 800 Gauss, experiences a torque of 0.016 N.m. The work done in moving it from most stable to most unstable position is $\alpha \times 10^{-3}\mathrm{J}$. The value of $\alpha$ is ______.

Q22.A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature $50^{\circ }\mathrm{C}$. The gas is now heated to double its temperature. The modified pressure is ______ Pa.

Q23.A voltage regulating circuit consisting of Zener diode, having break-down voltage of 10 V and maximum power dissipation of 0.4 W, is operated at 15 V. The approximate value of protective resistance in this circuit is ______ $\Omega$.

Q24.In the given figure the blocks A, B and C weigh 4 kg, 6 kg and 8 kg respectively. The co-efficient of sliding friction between any two surfaces is 0.5. The force $\overrightarrow{\mathrm{F}}$ required to slide the block C with constant speed is ______ N. (Used …

Q25.Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of $10\mathrm{cm}/\mathrm{s}$ coalesce to form a bigger drop. The terminal velocity of bigger drop is ______ $\mathrm{cm}/\mathrm{s}$.

Q1.Given below are two statements :

Statement-I Hybridisation, shape and spin only magnetic moment of ${\mathrm{K}}_3\left[\mathrm{Co}{\left({\mathrm{CO}}_3\right)}_3\right]$ is ${\mathrm{sp}}^3{\mathrm{d}}^2$, octahedral and 4.9 BM respectively.

Statement-II Geometry, hybri …

Q2.$\mathrm{A}\to \mathrm{D}$ is an endothermic reaction occurring in three steps (elementary).
(i) $\mathrm{A}\to \mathrm{B}\Delta {\mathrm{H}}_{\mathrm{i}}=+\mathrm{ve}$
(ii) $\mathrm{B}\to \mathrm{C}\Delta {\mathrm{H}}_{\mathrm{ii}}=-\mathrm{ve}$
(i …

Q3.Arrange the following alkenes in decreasing order of stability.
I. (see structure)
II. (see structure)
III. (see structure)
IV. (see structure)

Choose the correct answer from the options given below :

Q4.Given below are statements about some molecules/ions.

Identify the CORRECT statements.
A. The dipole moment value of ${\mathrm{NF}}_3$ is higher than that of ${\mathrm{NH}}_3$.
B. The dipole moment value of ${\mathrm{BeH}}_2$ is zero.
C. The bond order of …

Q5.A solution is prepared by dissolving 0.3 g of a nonvolatile non-electrolyte solute ' A ' of molar mass $60\mathrm{g}{\mathrm{mol}}^{-1}$ and 0.9 g of a non-volatile nonelectrolyte solute ' B ' of molar mass $180\mathrm{g}{\mathrm{mol}}^{-1}$ in …

Q6.Among the following, the CORRECT combinations are :
A. ${\mathrm{IF}}_3\to$ T-shaped ( ${\mathrm{sp}}^3\mathrm{d}$ )
B. ${\mathrm{IF}}_5\to$ Square pyramidal ( ${\mathrm{sp}}^3{\mathrm{d}}^2$ )
C. ${\mathrm{IF}}_7\to$ Pentagonal bipyramida …

Q7.The correct stability order of the following diazonium salts is
(A) (see structure)
(B) (see structure)
(C) (see structure)
(D) (see structure)

Q8.Consider a mixture ' X ' which is made by dissolving 0.4 mol of $\left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_5{\mathrm{SO}}_4\right]\mathrm{Br}$ and 0.4 mol of $\left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_5\mathrm{Br}\right]{\mathrm{SO}}_4$ in water to make 4 L of …

Q9.Given below are two statements

Statements-I : The number of paramagnetic species among ${\left[{\mathrm{CoF}}_6\right]}^{3-},{\left[{\mathrm{TiF}}_6\right]}^{3-},{\mathrm{V}}_2{\mathrm{O}}_5$ and ${\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right]}^{3-}$ is 3 .
Statement-II …

Q10.Consider three metal chlorides $\mathrm{x},\mathrm{y}$ and z , where x is water soluble at room temperature, $y$ is sparingly soluble in water at room temperature and z is soluble in hot water. $\mathrm{x},\mathrm{y}$ and z are respectively

Q11.' W ' g of a non-volatile electrolyte solid solute of molar mass ' M ' $\mathrm{g}{\mathrm{mol}}^{-1}$ when dissolved in 100 mL water, decreases vapour pressure of water from 640 mm Hg to 600 mm Hg . If aqueous solution of the electrolyte boils at 375 K and …

Q12.Match the List-I with List-II

List-I (Isothermal process for ideal gas system) | List-II Work done (${\mathbf{V}}_{\mathbf{f}}>{\mathbf{V}}_{\mathbf{i}}$)

Choose the correct answer from the options given below :

Q13.A student is given one compound among the following compounds that gives positive test with Tollen's reagent.

The compound is :

Q14.A hydroxy compound (X) with molar mass 122 g ${\mathrm{mol}}^{-1}$ is acetylated with acetic anhydride, using a large excess of the reagent ensuring complete acetylation of all hydroxyl groups. The product obtained has a molar mass of $290\mathrm{g}{\mathrm{mol}}^{-1}$. The numbe …

Q15.At $27^{\circ }\mathrm{C}$ in presence of a catalyst, activation energy of a reaction is lowered by $10\mathrm{kJ}{\mathrm{mol}}^{-1}$. The logarithm ratio of $\frac{\mathrm{k}\text{ (catalysed) }}{\mathrm{k}\text{ (uncatalysed) }}$ is ....
(Consider that the frequency factor …

Q16.Given below are two statements :
Statement I: 'C-Cl' bond is stronger in ${\mathrm{CH}}_2=\mathrm{CH}-\mathrm{Cl}$ than ${\mathrm{CH}}_3-{\mathrm{CH}}_2-\mathrm{Cl}$
Statement II : The given optically active molecule, (see structure) on hydrolysis gives a solution that can rotate …

Q17.Consider the following two reactions A and B .
(A) (see structure)
(B) (see structure)

Numerical value of [molar mass of $\mathrm{x}+$ molar mass of y ] is ______。

Q18.Arrange the following carbanions in the decreasing order of stability
I. $p-\mathrm{Br}-{\mathrm{C}}_6{\mathrm{H}}_4-\stackrel{\ominus }{\mathrm{C}}{\mathrm{H}}_2$
II. ${\mathrm{C}}_6{\mathrm{H}}_5-\stackrel{\ominus }{\stackrel{\ominus }{\mathrm{C}}}{\mathrm{H}}_2$
III. …

Q19.Given below are two statements :
Statement I: $\mathrm{K}>\mathrm{Mg}>\mathrm{Al}>\mathrm{B}$ is the correct order in terms of metallic character.
Statement II : Atomic radius is always greater than the ionic radius for any element.
In the light of the above statements, choose th …

Q20.Electricity is passed through an acidic solution of ${\mathrm{Cu}}^{2+}$ till all the ${\mathrm{cu}}^{2+}$ was exhausted, leading to the deposition of 300 mg of Cu metal. However, a current of 600 mA was continued to pass through the same solution for another 28 minutes by keeping th …

Q21.Consider two Group IV metal ions ${\mathrm{X}}^{2+}$ and ${\mathrm{Y}}^{2+}$.

A solution containing $0.01{\mathrm{MX}}^{2+}$ and $0.01{\mathrm{MY}}^{2+}$ is saturated with ${\mathrm{H}}_2\mathrm{S}$. The pH at which the metal sulphide YS will form as a precipitate is ______
(Nearest …

Q22.The hydrogen spectrum consists of several spectral lines in Lyman series $({\mathrm{L}}_1,{\mathrm{L}}_2,{\mathrm{L}}_3\dots .;{\mathrm{L}}_1$ has lowest energy among Lyman series). Similarly it consists of several spectral lines in Balmer series ( …

Q23.In Dumas method for estimation of nitrogen, 0.50 g of an organic compound gave 70 mL of nitrogen collected at 300 K and 715 mm pressure. The percentage of nitrogen in the organic compound is ______ %
(Aqueous tension at 300 K is 15 mm ).

Q24.X and Y are the number of electrons involved, respectively during the oxidation of ${\mathrm{I}}^{-}$ to ${\mathrm{I}}_2$ and ${\mathrm{S}}^{2-}$ to S by acidified ${\mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7$. The value of $\mathrm{X}+\mathrm{Y}$ is ____.

Q1.If the function $\mathrm{f}(\mathrm{x})=\frac{e^x\left(e^{\tan x-x}-1\right)+{\log }_e(\sec x+\tan x)-x}{\tan x-x}$ is Continuous at $\mathrm{x}=0$, then the value of $\mathrm{f}(0)$ is equal to

Q2.Let a circle of radius 4 pass through the origin O , the points $\mathrm{A}(-\sqrt{3}\mathrm{a},0)$ and $\mathrm{B}(0,-\sqrt{2}\mathrm{b})$, where a and b are real parameters and $\mathrm{ab}\ne 0$. Then the locus of the centroid of $△\mathrm{OAB}$ is a cir …

Q3.Let the lines $L_1:\vec{r}=\hat{i}+2\hat{j}+3\hat{k}+\lambda (2\hat{i}+3\hat{j}+4\hat{k})$, $\lambda \in \mathbb{R}$ and $L_2:\vec{r}=(4\hat{i}+\hat{j})+\mu (5\hat{i}+2\hat{j}+\hat{k}),\mu \in \mathbb{R}$, intersect at the point R . Let P and Q be the points ly …

Q4.Let $729,81,9,1,\dots$ be a sequence and ${\mathrm{P}}_{\mathrm{n}}$ denote the product of the first $n$ terms of this sequence.

If $2{\sum }_{n=1}^{40}{\left(P_n\right)}^{\frac{1}{n}}=\frac{3^{\alpha }-1}{3^{\beta }}$ and $\gcd (\alpha ,\beta )=1$, then …

Q5.Let $\vec{a}=2\hat{i}+\hat{j}-2\hat{k},\vec{b}=\hat{i}+\hat{j}$ and $\vec{c}=\vec{a}\times \vec{b}$. Let $\overrightarrow{\mathrm{d}}$ be a vector such that …

Q6.If the domain of the function
$f(x)={\log }_{\left(10x^2-17x+7\right)}\left(18x^2-11x+1\right)$
is $(-\infty ,a)\cup (b,c)\cup (d,\infty )-\{e\}$, then
$90(\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}+\mathrm{e})$ equals:

Q7.Let each of the two ellipses ${\mathrm{E}}_1:\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}+\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1,(\mathrm{a}>\mathrm{b})$ and ${\mathrm{E}}_2:\frac{{\mathrm{x}}^2}{{\mathrm{A}}^2}+\frac{{\mathrm{y}}^2}{{\mathrm{B}}^2}=1,(\mathrm{A}<\mathrm{B})$ …

Q8.The value of $\frac{\sqrt{3}\mathrm{cosec}20^{\circ }-\sec 20^{\circ }}{\cos 20^{\circ }\cos 40^{\circ }\cos 60^{\circ }\cos 80^{\circ }}$ is equal to

Q9.Let $\mathrm{S}=\{\mathrm{z}\in \mathbb{C}:\left|\frac{\mathrm{z}-6\mathrm{i}}{\mathrm{z}-2\mathrm{i}}\right|=1$ and $\left|\frac{\mathrm{z}-8+2\mathrm{i}}{\mathrm{z}+2\mathrm{i}}\right|=\frac{3}{5}\}$.

Then …

Q10.If $\cot x=\frac{5}{12}$ for some $x\in \left(\pi ,\frac{3\pi }{2}\right)$, then
$\sin 7x\left(\cos \frac{13x}{2}+\sin \frac{13x}{2}\right)+$
$\cos 7x\left(\cos \frac{13x}{2}-\sin \frac{13x}{2}\right)$ is equal to

Q11.Let $\mathrm{f}(\mathrm{t})=\int \left(\frac{1-\sin \left({\log }_{\mathrm{e}}\mathrm{t}\right)}{1-\cos \left({\log }_{\mathrm{e}}\mathrm{t}\right)}\right)\mathrm{dt},\mathrm{t}>1$.

If $\mathrm{f}\left({\mathrm{e}}^{\pi /2}\right)=-{\mathrm{e}}^{\pi /2}$ and …

Q12.Let R be a relation defined on the set $\{1,2,3,4\}\times \{1,2,3,4\}$ by
$\mathrm{R}=\{((\mathrm{a},\mathrm{b}),(\mathrm{c},\mathrm{d})):2\mathrm{a}+3\mathrm{b}=3\mathrm{c}+4\mathrm{d}\}$.
Then the number of elements in R is

Q13.Let $A(1,0),B(2,-1)$ and $C\left(\frac{7}{3},\frac{4}{3}\right)$ be three points. If the equation of the bisector of the angle ABC is $\alpha x+\beta y=5$, then the value of ${\alpha }^2+{\beta }^2$ is

Q14.Let $\mathrm{S}=\frac{1}{25!}+\frac{1}{3!23!}+\frac{1}{5!21!}+\dots$ up to 13 terms.

If $13\mathrm{S}=\frac{2^{\mathrm{k}}}{\mathrm{n}!},\mathrm{k}\in \mathrm{N}$, then $\mathrm{n}+\mathrm{k}$ is equal to

Q15.Consider an A.P.: ${\mathrm{a}}_1,{\mathrm{a}}_2,\dots .,{\mathrm{a}}_{\mathrm{n}};{\mathrm{a}}_1>0$. If ${\mathrm{a}}_2-{\mathrm{a}}_1=\frac{-3}{4},{\mathrm{a}}_{\mathrm{n}}=\frac{1}{4}{\mathrm{a}}_1$, and …

Q16.Let $\alpha ,\beta \in \mathbb{R}$ be such that the function
$f(\mathrm{x})=\{\begin{array}{ll}2\alpha \left({\mathrm{x}}^2-2\right)+2\beta \mathrm{x}& ,\mathrm{x}<1\\ (\alpha +3)\mathrm{x}+(\alpha -\beta )& ,\mathrm{x}\ge 1\end{array}$
be differentiable at all …

Q17.From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of getting at least 7 defective bulbs is :-

Q18.The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observation $\alpha$ in this data is replaced by $\beta$, then the mean and variance become 10.1 and 1.99, respectively. Then $\alpha +\beta$ equals.

Q19.Let ${\mathrm{A}}_1$ be the bounded area enclosed by the curves $y=x^2+2,x+y=8$ and $y$-axis that lies in the first quadrant. Let ${\mathrm{A}}_2$ be the bounded area enclosed by the curves $y=x^2+2,y^2=x,x=2$, and $y$-axis that lies in the first quadrant. Th …

Q20.The number of the real solutions of the equation :
$x|x+3|+|x-1|-2=0$ is

Q21.Let a differentiable function $f$ satisfy the equation ${\int }_0^{36}f\left(\frac{\mathrm{tx}}{36}\right)\mathrm{dt}=4\alpha f(\mathrm{x})$.

If $\mathrm{y}=f(\mathrm{x})$ is a standard parabola passing through the points $(2,1)$ and $(-4,\beta )$,

Then …

Q22.Let a line L passing through the point $\mathrm{P}(1,1,1)$ be perpendicular to the lines $\frac{x-4}{4}=\frac{y-1}{1}=\frac{z-1}{1}$ and $\frac{\mathrm{x}-17}{1}=\frac{\mathrm{y}-71}{1}=\frac{\mathrm{z}}{0}$. Let the line L intersect the yz-plane at the point Q. Another lin …

Q23.The number of numbers greater than 5000, less than 9000 and divisible by 3, that can be formed using the digits $0,1,2,5,9$, if the repetition of the digits is allowed, is ______

Q24.Let $(2\alpha ,\alpha )$ be the largest interval in which the function $f(t)=\frac{|t+1|}{t^2},t<0$, is strictly decreasing. Then the local maximum value of the function
$g(x)=2{\log }_e(x-2)+\alpha x^2+4x-\alpha ,x>2$, is ______

Q25.The number of $3\times 2$ matrices A, which can be formed using the elements of the set $\{-2,-1,0,1,2\}$ such that the sum of all the diagonal elements of $A^{T}A$ is 5, is ______