JEE Main 2026 · 22 Jan 2026 · Shift 1

Q1.A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10 kg and radius 20 cm. The moment of inertia of this pair of spheres about the tangent passing through the point of contact is ______ kg.m².

Q2.7.9 MeV α-particle scatters from a target material of atomic number 79. From the given data the estimated diameter of nuclei of the target material is (approximately) ______ m.
[$\frac{1}{4\pi {ϵ}_0}=9\times 10^9$ Nm²/C² and electron charge $=1.6\times 10^{-19}$ C]

Q3.Six point charges are kept 60° apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the centre of the circle is ______.
(${ϵ}_0$ is permittivity of free space)

Q4.XPQY is a vertical smooth long loop having a total resistance R where PX is parallel to QY and separation between them is $l$. A constant magnetic field B perpendicular to the plane of the loop exists in the entire space. A rod CD of length L ($L>l$) and mass $m$ is made to sli …

Q5.The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, is ______ m/s.

Q6.A meter bridge with two resistances $R_1$ and $R_2$ as shown in figure was balanced (null point) at 40 cm from the point P. The null point changed to 50 cm from the point P, when $16\Omega$ resistance is connected in parallel to $R_2$. The values of resistances $R_1$ and $R_2$ ar …

Q7.A projectile is thrown upward at an angle $60^{\circ }$ with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is $45^{\circ }$ with the horizontal. The initial speed of the projectile is ______ m/s.

Q8.Given below are two statements:
Statement I: Pressure of fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid.
Statement II: Excess potential energy of the molecules on the surface of a liquid, when compared to inter …

Q9.Find the correct combination of A, B, C and D inputs which can cause the LED to glow.

Q10.Net gravitational force at the centre of a square is found to be $F_1$ when four particles having mass $M,2M,3M$ and $4M$ are placed at the four corners of the square as shown in figure and it is $F_2$ when the positions of $3M$ and $4M$ are interchanged. The ratio …

Q11.The minimum frequency of photon required to break a particle of mass 15.348 amu into $4\alpha$ particles is ______ kHz.
[mass of He nucleus = 4.002 amu, $1$ amu $=1.66\times 10^{-27}$ kg, $h=6.6\times 10^{-34}$ J.s and $c=3\times 10^8$ m/s]

Q12.A cylindrical tube $AB$ of length $l$, closed at both ends contains an ideal gas of 1 mol having molecular weight $M$. The tube is rotated in a horizontal plane with constant angular velocity $\omega$ about an axis perpendicular to $AB$ and passing through the edge at end A, as s …

Q13.Rods $x$ and $y$ of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points $A$ and $F$ are maintained at $100^{\circ }\mathrm{C}$ and $40^{\circ }\mathrm{C}$ respectively. Given the thermal conductivity of rod x is three …

Q14.Consider an equilateral prism (refractive index $\sqrt{2}$ ). A ray of light is incident on its one surface at a certain angle $i$. If the emergent ray is found to graze along the other surface then the angle of refraction at the incident surface is close to ____ .

Q15.The volume of an ideal gas increases 8 times and temperature becomes $(1/4{)}^{\text{th }}$ of initial temperature during a reversible change. If there is no exchange of heat in this process ( $\Delta \mathrm{Q}=0$ ) then identify the gas from the following options (Assuming …

Q16.Electric field in a region is given by $\vec{E}=Ax\hat{i}+By\hat{j}$, where $A=10\mathrm{V}/{\mathrm{m}}^2$ and $B=5\mathrm{V}/{\mathrm{m}}^2$. If the electric potential at a point $(10,20)$ is 500 V , then the electric potential at origin is ____ V.

Q17.A simple pendulum has a bob with mass $m$ and charge q . The pendulum string has negligible mass. When a uniform and horizontal electric field $\vec{E}$ is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium positi …

Q18.Three identical coils ${\mathrm{C}}_1,{\mathrm{C}}_2$ and ${\mathrm{C}}_3$ are closely placed such that they share a common axis. ${\mathrm{C}}_2$ is exactly midway. ${\mathrm{C}}_1$ carries current $I$ in anti-clockwise direction while ${\mathrm{C}}_3$ carries curre …

Q19.Two loudspeakers ( $L_1$ and $L_2$ ) are placed with a separation of 10 m , as shown in figure. Both speakers are fed with an audio input signal of same frequency with constant volume. A voice recorder, initially at point $A$, at equidistance to both loud speakers, is m …

Q20.The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by,
${\mathrm{E}}_{\mathrm{y}}=20\sin \left(3\times 10^6\mathrm{x}-4.5\times 10^{14}\mathrm{t}\right)\mathrm{V}/\mathrm{m}$
(where $\mathrm{x},\mathrm{t}$ and ot …

Q21.A parallel beam of light travelling in air (refractive index 1.0) is incident on a convex spherical glass surface of radius of curvature 50 cm . Refractive index of glass is 1.5 . The rays converge to a point at a distance x cm from the centre of the curvature of the spherical su …

Q22.A circular disc has radius $R_1$ and thickness $T_1$. Another circular disc made of the same material has radius $R_2$ and thickness $T_2$. If the moment of inertia of both discs are same and $\frac{R_1}{R_2}=2$ then $\frac{T_1}{T_2}=\frac{1}{\alpha }$. …

Q23.Inductance of a coil with $10^4$ turns is 10 mH and it is connected to a dc source of 10 V with internal resistance of $10\Omega$. The energy density in the inductor when the current reaches $\left(\frac{1}{\mathrm{e}}\right)$ of its maximum value is …

Q1.Consider the transition metal ions ${\mathrm{Mn}}^{3+},{\mathrm{Cr}}^{3+},{\mathrm{Fe}}^{3+}$ and ${\mathrm{Co}}^{3+}$ and all form low spin octahedral complexes. The correct decreasing order of unpaired electrons in their respective d-orbitals of the complexes is

Q2.The formal changes on the atoms marked as (1) to (4) in the Lewis representation of ${\mathrm{HnO}}_3$ molecule respectively are

Q3.Given below are two statements :

Statement I: Phenol on treatment with ${\mathrm{CHCl}}_3/$ aq. KOH under refluxing condition, followed by acidification produces $p$-hydroxy benzladehyde as the major product and $o$-hydroxy benzaldehyde as the minor product.

Statement II …

Q4.The energy required by electrons, present in the first Bohr orbit of hydrogen atom to be excited to second Bohr orbit is ____ $\mathrm{J}{\mathrm{mol}}^{-1}$.

Given : ${\mathrm{R}}_{\mathrm{H}}=2.18\times 10^{-11}\mathrm{ergs}$.

Q5.A 'p'-block element (E) and hydrogen form a binary cation ${\left({\mathrm{EH}}_{\mathrm{x}}\right)}^{+}$, while ${\mathrm{EH}}_3$ on treatment with ${\mathrm{K}}_2{\mathrm{HgI}}_4$ in alkaline medium gives a precipitate of basic mercury(II)amido-iodine. Given below are first …

Q6.In the reaction,
$2\mathrm{Al}(\mathrm{s})+6\mathrm{HCl}(\mathrm{aq})\to 2{\mathrm{Al}}^{3+}(\mathrm{aq})+6{\mathrm{Cl}}^{-}(\mathrm{aq})+3{\mathrm{H}}_2(\mathrm{g})$

Q7.Consider a solution of ${\mathrm{CO}}_2(\mathrm{g})$ dissolved in water in a closed container.

Which one of the following plots correctly represents variation of log (partial pressure of CO2 in vapour phase above water) [y-axis] with log (mole fraction of ${\mathrm{CO}}_2$ …

Q8.A first row transition metla (M) does not liberate ${\mathrm{H}}_2$ gas from dilute HCl .1 mol of aqueous solution of ${\mathrm{MSO}}_4$ is treated with excess of aqueous KCN and then ${\mathrm{H}}_2\mathrm{S}(\mathrm{g})$ is passed through the solution. The amount of MS …

Q9.The correct order of reactivity of ${\mathrm{CH}}_3\mathrm{Br}$ in methanol with the following nucleophiles is ${\mathrm{F}}^{-},{\mathrm{I}}^{-},{\mathrm{C}}_2{\mathrm{H}}_5{\mathrm{O}}^{-}$and ${\mathrm{C}}_6{\mathrm{H}}_5{\mathrm{O}}^{-}$

Q10.Given below are two statements :

Statement I : Benzene is nitrated to give nitrobenzene, which on further treatment with
${\mathrm{CH}}_3\mathrm{COCl}/{\mathrm{AlCl}}_3$ will give

Q11.A → products (First order reaction).

Three sets of experiment were performed for a reaction under similar experimental conditions.
Run $1\Rightarrow 100\mathrm{mL}$ of 10 M solution of reactant A
Run $2\Rightarrow 200\mathrm{mL}$ of 10 M solution of reactant A
Run …

Q12.Given below are two statements :

Statement I: The halogen that makes longest bond with hydrogen in HX, has the smallest covalent radius in its group.

Statement II : A group 15 element's hydride ${\mathrm{EH}}_3$ has the lowest boiling point among corresponding hydrides of oth …

Q13.Given below are two statements:

Statement I: Sucrose is dextrorotatory. However sucrose upon hydrolysis gives a solution having mixture of products. This solution shows laevorotation.

Statement II : Hydrolysis of sucrose gives glucose and fructose. Since the laevorotation of gl …

Q14.'A' is a neutral organic compound (M. F : ${\mathrm{C}}_8{\mathrm{H}}_9\mathrm{ON}$ ). On treatment with aqueous ${\mathrm{Br}}_2/{\mathrm{HO}}^{(-)}$, 'A' forms a compound ' B ' which is soluble in dilute acid. ' B ' on treatment with aqueous …

Q15.The correct order of the rate of reaction of the following reactants with nucleophile by ${\mathrm{S}}_{\mathrm{N}}1$ mechanism is :
(Given : Structure I and II are rigid)

Q16.Two p-block elements X and Y form fluroides of the type ${\mathrm{EF}}_3$. The fluoride compound ${\mathrm{XF}}_3$ is a Lewis acid and ${\mathrm{YF}}_3$ is a Lewis base. The hybridization of the central atoms of ${\mathrm{XF}}_3$ and ${\mathrm{YF}}_3$ respectively are

Q17.As compared with chlorocyclohexane, which of the following statements correctly apply to chlorobenzene?
A. The magnitude of negative charge is more on chlorine atoms
B. The $\mathrm{C}-\mathrm{Cl}$ bond has partial double bond character
C. $\mathrm{C}-\mathrm{Cl}$ bond is les …

Q18.Given below are two statements:

Statement I: The Henry's law constant ${\mathrm{K}}_{\mathrm{H}}$ is constant with respect to variations in solution's concentration over the range for which the solutions is ideally dilute.
Statement II : ${\mathrm{K}}_{\mathrm{H}}$ does not diff …

Q19.The cycloalkane ( X ) on bromination consumes one mole of bromine per mole of ( X ) and gives the product ( Y ) in which $\mathrm{C}:\mathrm{Br}$ ratio is $3:1$. The percentage of bromine in the product $(\mathrm{Y})$ is
____ %. (Nearest integer)
(Given : Molar mass …

Q20.Consider the following electrochemical cell at 298 K
$\mathrm{Pt}\left|{\mathrm{HSnO}}_2^{-}(\mathrm{aq})\right|\mathrm{Sn}(\mathrm{OH}{)}_6{}^{2-}(\mathrm{aq})\left|{\mathrm{Bi}}_2{\mathrm{O}}_3(\mathrm{s})\right|\mathrm{Bi}(\mathrm{s})$.
If the reaction quotient at a giv …

Q21.The temperature at which the rate constants of the given below two gaseous reactions become equal is
____ K. (Nearest integer).
$\mathrm{X}⟶\mathrm{Y}{\mathrm{k}}_1=10^6{\mathrm{e}}^{\frac{-30000}{\mathrm{T}}}$ …

Q22.Sodium fusion extract of an organic compound (Y) with ${\mathrm{CHCl}}_3$ and chlorine water gives violet color to the ${\mathrm{CHCl}}_3$ layer. 0.15 g of $(\mathrm{Y})$ gave 0.12 g of the silver halide precipitate in Carius method. Percentage of halogen in the compound …

Q23.Dissociation of a gas ${\mathrm{A}}_2$ takes place according to the following chemical reactions. At equilibrium, the total pressure is 1 bar at 300 K.
${\mathrm{A}}_2(\mathrm{g})\rightleftharpoons 2\mathrm{A}(\mathrm{g})$
The standard Gibbs energy of formation of the involv …

Q1.Let $\overrightarrow{AB}=2\hat{i}+4\hat{j}-5\hat{k}$ and $\overrightarrow{\mathrm{AD}}=\hat{\mathrm{i}}+2\hat{\mathrm{j}}+\lambda \hat{k},\lambda \in \mathbb{R}$. Let the projection of the vector …

Q2.Let the relation R on the set $\mathrm{M}=\{1,2,3,\dots ,16\}$ be given by
$\mathrm{R}=\{(\mathrm{x},\mathrm{y}):4\mathrm{y}=5\mathrm{x}-3,\mathrm{x},\mathrm{y}\in \mathrm{M}\}$.
Then the minimum number of elements required to be added in R, in order to make the relation …

Q3.Let the line $\mathrm{x}=-1$ divide the area of the region $\left\{(x,y):1+x^2\le y\le 3-x\right\}$ in the ratio $m:n,\gcd (\mathrm{m},\mathrm{n})=1$. Then $\mathrm{m}+\mathrm{n}$ is equal to

Q4.Two distinct numbers a and b are selected at random from $1,2,3,\dots ,50$. The probability, that their product ab is divisible by 3, is

Q5.Let $f(x)=x^{2025}-x^{2000},x\in [0,1]$ and the minimum value of the function $\mathrm{f}(\mathrm{x})$ in the interval $[0,1]$ be $(80{)}^{80}(\mathrm{n}{)}^{-81}$. Then n is equal to

Q6.Let $\mathrm{P}(\alpha ,\beta ,\gamma )$ be the point on the line
$\frac{\mathrm{x}-1}{2}=\frac{\mathrm{y}+1}{-3}=\mathrm{z}$ at a distance $4\sqrt{14}$ from the point $(1,-1,0)$ and nearer to the origin. Then the shortest distance, between the lines …

Q7.If a random variable $x$ has the probability distribution

then …

Q8.The number of distinct real solutions of the equation $x|x+4|+3|x+2|+10=0$ is

Q9.Let $f:[1,\infty )\to \mathbb{R}$ be a differentiable function. If $6{\int }_1^{x}f(t)dt=3xf(x)+x^3-4$ for all $\mathrm{x}\ge 1$, then the value of $f(2)-f(3)$ is

Q10.If the line $\alpha x+2y=1$, where $\alpha \in \mathbb{R}$, does not meet the hyperbola $x^2-9y^2=9$, then a possible value of $\alpha$ is:

Q11.If the image of the point $\mathrm{P}(1,2,a)$ in the line $\frac{\mathrm{x}-6}{3}=\frac{\mathrm{y}-7}{2}=\frac{7-\mathrm{z}}{2}$ is $\mathrm{Q}(5,\mathrm{b},\mathrm{c})$, then ${\mathrm{a}}^2+{\mathrm{b}}^2+{\mathrm{c}}^2$ is equal to

Q12.Let the set of all values of r, for which the circles $(x+1{)}^2+(y+4{)}^2=r^2$ and $x^2+y^2-4x-2y-4=0$ intersect at two distinct points be the interval ($\alpha$, $\beta$). Then $\alpha \beta$ is equal to

Q13.If $\mathrm{A}=\left[\begin{array}{ll}2& 3\\ 3& 5\end{array}\right]$, then the determinant of the matrix $({\mathrm{A}}^{2025}-3{\mathrm{A}}^{2024}+{\mathrm{A}}^{2023})$ is

Q14.If the domain of the function $f(x)={\sin }^{-1}\left(\frac{5-x}{3+2x}\right)+\frac{1}{{\log }_e(10-x)}$ is $(-\infty ,\alpha ]\cup [\beta ,\gamma )-\{\delta \}$, then $6(\alpha +\beta +\gamma +\delta )$ is equal to

Q15.The value of ${\int }_{-\frac{\pi }{2}}^{\frac{\pi }{2}}\left(\frac{1}{[\mathrm{x}]+4}\right)\mathrm{dx}$, where [•] denotes the greatest integer function, is

Q16.The coefficient of $x^{48}$ in $(1+x)+2(1+x{)}^2+3(1+x{)}^3+\dots +100(1+x{)}^{100}$ is equal to:

Q17.If the chord joining the points ${\mathrm{P}}_1\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)$ and ${\mathrm{P}}_2\left({\mathrm{x}}_2,{\mathrm{y}}_2\right)$ on the parabola $y^2=12x$ subtends a right angle at the vertex of the parabola, then $x_1{x}_2-y_1{y}_2$ is equal t …

Q18.The number of solutions of ${\tan }^{-1}4\mathrm{x}+{\tan }^{-1}6\mathrm{x}=\frac{\pi }{6}$, where $-\frac{1}{2\sqrt{6}}<x<\frac{1}{2\sqrt{6}}$ is equal to

Q19.Let the solution curve of the differential equation $xdy-ydx=\sqrt{x^2+y^2}dx,x>0,y(1)=0$, be $y=y(x)$. Then $y(3)$ is equal to

Q20.If the sum of the first four terms of an A.P. is 6 and the sum of its first six terms is 4, then the sum of its first twelve terms is

Q21.Let $\alpha =\frac{-1+i\sqrt{3}}{2}$ and $\beta =\frac{-1-i\sqrt{3}}{2},i=\sqrt{-1}$. If $(7-7\alpha +9\beta {)}^{20}+(9+7\alpha -7\beta {)}^{20}+(-7+9\alpha +7\beta {)}^{20}+(14+7\alpha +7\beta {)}^{20}={\mathrm{m}}^{10}$, then m is

Q22.Let A be a $3\times 3$ matrix such that $\mathrm{A}+{\mathrm{A}}^{\mathrm{T}}=\mathrm{O}$. If …

Q23.If …

Q24.If $\frac{{\cos }^{2}48^{\circ }-{\sin }^{2}12^{\circ }}{{\sin }^{2}24^{\circ }-{\sin }^2{6}^{\circ }}=\frac{\alpha +\beta \sqrt{5}}{2}$, where $\alpha ,\beta \in \mathbb{N}$, then $\alpha +\beta$ is equal to

Q25.Let ABC be a triangle. Consider four points ${\mathrm{p}}_1,{\mathrm{p}}_2$, ${\mathrm{p}}_3,{\mathrm{p}}_4$ on the side AB , five points ${\mathrm{p}}_5,{\mathrm{p}}_6,{\mathrm{p}}_7,{\mathrm{p}}_8,{\mathrm{p}}_9$ on the side BC and four points …