JEE Main 2026 · 21 Jan 2026 · Shift 1

Q1.Potential energy ($V$) versus distance ($x$) is given by the graph, Rank various regions as per the magnitudes of the force (F) acting on a particle from high to low.

Q2.A gas based geyser heats water flowing at the rate of 5.0 litres per minute from $27^{\circ }\mathrm{C}$ to $87^{\circ }\mathrm{C}$.
The rate of consumption of the gas is ____ g/s.
(Take heat of combustion of gas $=5.0\times 10^4\mathrm{J}/\mathrm{g}$) specific h …

Q3.A conducting circular loop of area $1.0{\mathrm{m}}^2$ is placed perpendicular to a magnetic field which varies as $\mathrm{B}=\sin (100\mathrm{t})$ Tesla. If the resistance of the loop is $100\Omega$, then the average thermal energy dissipated in the loop in one period …

Q4.Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at $A$ and $B$ are $6{\mathrm{cm}}^2$ and $3{\mathrm{cm}}^2$ respectively.
The rate of flow will b …

Q5.In an experiment the values of two spring constants were measured as ${\mathrm{k}}_1=(10\pm 0.2)\mathrm{N}/\mathrm{m}$ and ${\mathrm{k}}_2=(20\pm 0.3)\mathrm{N}/\mathrm{m}$. If these springs are connected in parallel, then the percentage error in equivalent spring con …

Q6.A 4 kg mass moves under the influence of a force $\vec{F}=\left(4t^3\hat{i}-3t\hat{j}\right)N$ where $t$ is the time in second.
If mass starts from origin at $\mathrm{t}=0$, the velocity and position after $\mathrm{t}=2\mathrm{s}$ will be :

Q7.Consider a modified Bernoulli equation.

If t has the dimension of time then the dimensions of A and B are ____ , ___\ …

Q8.A current carrying is placed vertically and a particle of mass m with charge Q is released from rest. The particle moves along the axis of solenoid. If g is acceleration due to gravity then the acceleration (a) of the charged particle will satisfy :

Q9.A parallel plate capacitor has capacitance C , when there is vacuum within the parallel plates.
A sheet having thickness ${\left(\frac{1}{3}\right)}^{\text{rd }}$ of the separation between the plates and relative permittivity K is introduced between the plates. The new capacitan …

Q10.The electric field a plane electromagnetic wave is given by :
${\mathrm{E}}_{\mathrm{y}}=69\sin \left[0.6\times 10^3\mathrm{x}-1.8\times 10^{11}\mathrm{t}\right]\mathrm{V}/\mathrm{m}$.
The expression for magnetic field associated with this electromagnetic wave is ___ …

Q11.In a double slit experiment the distance between the slits is 0.1 cm and the screen is placed at 50 cm from the slits plane. When one slit is covered with a transparent sheet having thickness $t$ and refractive index $\mathrm{n}(=1.5)$, the central fringe shifts by 0.2 cm . T …

Q12.A light wave described by $\mathrm{E}=60\sin \left(3\times 10^{15}\right)\mathrm{t}+\sin \left(12\times 10^{15}\right)$ t] (in SI units) falls on a metal surface of work function 2.8 eV . The maximum kinetic energy of ejected photoelectron is (approximately)
____ eV. …

Q13.If an alpha particle with energy 7.7 MeV is bombarded on a thin gold foil, the closest distance from nucleus it can reach is ______ m.
(Atomic number of gold $=79$ and $\frac{1}{4\pi {ϵ}_0}=9\times 10^9$ in SI units)

Q14.A uniform rod of mass m and length $l$ suspended by means of two identical inextensible light strings as shown in figure. Tension in one string immediately after the other string is cut, is ______. (g acceleration due to gravity)

Q15.An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at $30^{\circ }\mathrm{C}$. The coefficient of linear expansion of aluminium and steel are $24\times 10^{-6}/{}^{\circ }\mathrm{C}$ and …

Q16.A 1 m long metal rod AB completes the circuit as shown in figure. The area of circuit is perpendicular to the magnetic field of 0.10 T. If the resistance of the total circuit is $2\Omega$ then the force needed to move the rod towards right with constant speed (v) of …

Q17.The given circuit works as :

Q18.Two strings (A, B) having linear densities ${\mu }_{\mathrm{A}}=2\times 10^{-4}\mathrm{kg}/\mathrm{m}$ and ${\mu }_{\mathrm{B}}=4\times 10^{-4}\mathrm{kg}/\mathrm{m}$ and lengths ${\mathrm{L}}_{\mathrm{A}}=2.5\mathrm{m}$ and ${\mathrm{L}}_{\mathrm{B}}=1.5\mathrm{m}$ respectiv …

Q19.Initially a satellite of 100 kg is in a circular orbit of radius $1.5{\mathrm{R}}_{\mathrm{E}}$. This satellite can be moved to a circular orbit of radius $3{\mathrm{R}}_{\mathrm{E}}$ by supplying $\alpha \times 10^6\mathrm{J}$ of energy. The value of $\alpha$ is ______.
(Take …

Q20.A point charge of $10^{-8}\mathrm{C}$ is placed at origin. The work done in moving a point charge $2\mu \mathrm{C}$ from point $\mathrm{A}(4,4,2)\mathrm{m}$ to $\mathrm{B}(2,2,1)\mathrm{m}$ is ______ J.
($\frac{1}{4\pi {ϵ}_0}=9\times 10^9$ in SI units)

Q21.A collimated beam of light of diameter 2 mm is propagating along x-axis. The beam is required to be expanded in a collimated beam of diameter 14 mm using a system of two convex lenses. If first lens has focal length 40 mm, then the focal length of second lens is ______ mm.

Q22.The heat generated in 1 minute between points A and B in the given circuit, when a battery of 9 V with internal resistance of $1\Omega$ is connected across these points is ______ J.

Q23.Two identical thin rods of mass M kg and length L m are connected as shown in figure. Moment of inertia of the combined rod system about an axis passing through point P and perpendicular to the plane of the rods is $\frac{X}{12}M{L}^2\mathrm{kg}{\mathrm{m}}^2$. The value of …

Q24.10 mole of oxygen is heated at constant volume from $30^{\circ }\mathrm{C}$ to $40^{\circ }\mathrm{C}$. The change in the internal energy of the gas is ______ cal. (The molecular specific heat of oxygen at constant pressure, …

Q25.In a microscope the objective is having focal length $f_0=2\mathrm{cm}$ and eye-piece is having focal length $f_{\mathrm{e}}=4\mathrm{cm}$. The tube length is 32 cm. The magnification produced by this microscope for normal adjustment is ______.

Q1.Consider the following reactions.
${\mathrm{PbCl}}_2+{\mathrm{K}}_2{\mathrm{CrO}}_4\to \mathrm{A}+2\mathrm{KCl}$ (Hot solution)
$\mathrm{A}+\mathrm{NaOH}\rightleftharpoons \mathrm{B}+{\mathrm{Na}}_2{\mathrm{CrO}}_4$ …

Q2.Which of the following represents the correct trend for the mentioned property?
A. $\mathrm{F}>\mathrm{P}>\mathrm{S}>\mathrm{B}$ - First Ionization Energy
B. $\mathrm{Cl}>\mathrm{F}>\mathrm{S}>\mathrm{P}$ - Electron Affinity
C. …

Q3.Identify A in the following reaction.

Q4.A hydrocarbon 'P' $\left({\mathrm{C}}_4{\mathrm{H}}_8\right)$ on reaction with HCl gives an optically active compound 'Q' $\left({\mathrm{C}}_4{\mathrm{H}}_9\mathrm{Cl}\right)$ which on reaction with one mole of ammonia gives compound 'R' …

Q5.Given below are two statements:

Statement I: The number of pairs among [${\mathrm{SiO}}_2,{\mathrm{CO}}_2$], $\left[\mathrm{SnO},{\mathrm{SnO}}_2\right],\left[\mathrm{PbO},{\mathrm{PbO}}_2\right]$ and $\left[\mathrm{GeO},{\mathrm{GeO}}_2\right]$, which contain oxides t …

Q6.80 mL of a hydrocarbon on mixing with 264 mL of oxygen in a closed U-tube undergoes complete combustion. The residual gases after cooling to 273 K occupy 224 mL. When the system is treated with KOH solution, the volume decreases to 64 mL. The formula of the hydrocarbon is:

Q7.14.0 g of calcium metal is allowed to react with excess HCl at 1.0 atm pressure and 273 K.
Which of the following statements is incorrect?
[Given: Molar mass in $\mathrm{g}{\mathrm{mol}}^{-1}$ of $\mathrm{Ca}-40,\mathrm{Cl}-35.5,\mathrm{H}-1$]

Q8.In Carius method, 0.75 g of an organic compound gave 1.2 g of barium sulphate, find percentage of sulphur (molar mass $32\mathrm{g}{\mathrm{mol}}^{-1}$). Molar mass of barium sulphate is $233\mathrm{g}{\mathrm{mol}}^{-1}$.

Q9.Elements P and Q form two types of non-volatile, non-ionizable compounds PQ and ${\mathrm{PQ}}_2$. When 1 g of PQ is dissolved in 50 g of solvent 'A', $\Delta {\mathrm{T}}_{\mathrm{b}}$ was 1.176 K while when 1 g of ${\mathrm{PQ}}_2$ is dissolved in 50 g of solvent 'A', …

Q10.An organic compound (P) on treatment with aqueous ammonia under hot condition forms compound (Q) which on heating with ${\mathrm{Br}}_2$ and KOH forms compound (R) having molecular formula ${\mathrm{C}}_7{\mathrm{H}}_9\mathrm{N}$. Names of $\mathrm{P},\mathrm{Q}$ and R …

Q11.An organic compound "P" of molecular formula ${\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_3$ gives positive iodoform test but negative Tollen's test. When "P" is treated with dilute acid, it produces "Q". "Q" gives positive Tollen's test and also iodoform test. The structure of …

Q12.From the following, the least stable structure is:

Q13.${\mathrm{MnO}}_4^{2-}$, in acidic medium, disproportionates to :

Q14.Given below are two statements:

Statement I: The number of species among ${\mathrm{SF}}_4$, ${\mathrm{NH}}_4^{+}$, $[{\mathrm{NiCl}}_4]$, ${\mathrm{XeF}}_4$, $[{\mathrm{PtCl}}_4{]}^{2-}$, ${\mathrm{SeF}}_4$ and $[\mathrm{Ni}(\mathrm{CN}{)}_4{]}^{2-}$, that have tetrahedral geometry …

Q15.Given below are two statements:

Statement I: Among $[\mathrm{Cu}({\mathrm{NH}}_3{)}_4{]}^{2+}$, $[\mathrm{Ni}(\mathrm{en}{)}_3{]}^{2+}$, $[\mathrm{Ni}({\mathrm{NH}}_3{)}_6{]}^{2+}$ and $[\mathrm{Mn}({\mathrm{H}}_2\mathrm{O}{)}_6{]}^{2+}$, …

Q16.Identify correct statement from the following:

A. Propanal and propanone are functional isomers.
B. Ethoxyethane and methoxypropane are metamers.
C. But-2-ene shows optical isomerism.
D. But-1-ene and but-2-ene are functional isomers.
E. Pentane and 2, 2-dimethyl propane are cha …

Q17.Identify the correct statements.

A. Arginine and Tryptophan are essential amino acids.
B. Histidine does not contain heterocyclic ring in its structure.
C. Proline is a six membered cyclic ring amino acid.
D. Glycine does not have chiral centre.
E. Cysteine has characteristic fe …

Q18.Which of the following graphs between pressure 'P' versus volume 'V' represent the maximum work done?

Q19.For the reaction, ${\mathrm{N}}_2{\mathrm{O}}_4\rightleftharpoons 2{\mathrm{NO}}_2$, graph is plotted as shown below. Identify correct statements.

A. Standard free energy change for the reaction is $-5.40\mathrm{kJ}{\mathrm{mol}}^{-1}$.
B. As $\Delta G^{\ominus }$ in graph i …

Q20.Given below are two statements:

Statement I: When an electric discharge is passed through gaseous hydrogen, the hydrogen molecules dissociate and the energetically excited hydrogen atoms produce electromagnetic radiation of discrete frequencies.

Statement II: The frequency of s …

Q21.Pre-exponential factors of two different reactions of same order are identical. Let activation energy of first reaction exceeds the activation energy of second reaction by $20\mathrm{kJ}{\mathrm{mol}}^{-1}$. If ${\mathrm{k}}_1$ and ${\mathrm{k}}_2$ are the rate constants of fir …

Q22.The pH and conductance of a weak acid (HX) was found to be 5 and $4\times 10^{-5}\mathrm{S}$, respectively. The conductance was measured under standard condition using a cell where the electrode plates having a surface area of $1{\mathrm{cm}}^2$ were at a distance of 15 cm a …

Q23.Use the following data:
| …

Q24.Consider the following reaction sequence

The percentage of nitrogen in product 'T' formed is _____ %. (Nearest integer)

(Given molar mass in $\mathrm{g}{\mathrm{mol}}^{-1}$ H: 1, C: 12, N: 14, O: 16)

Q25.Consider the following reactions:
$\mathrm{NaCl}+{\mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7+{\mathrm{H}}_2{\mathrm{SO}}_4\to \mathrm{A}+{\mathrm{KHSO}}_4+{\mathrm{NaHSO}}_4+{\mathrm{H}}_2\mathrm{O}$ …

Q1.If the domain of the function $f(x)={\cos }^{-1}\left(\frac{2x-5}{11-3x}\right)+{\sin }^{-1}\left(2x^2-3x+1\right)$ is the interval $[\alpha ,\beta ]$, then $\alpha +2\beta$ is equal to :

Q2.The area of the region, inside the ellipse $x^2+4y^2=4$ and outside the region bounded by the curves $\mathrm{y}=|\mathrm{x}|-1$ and $\mathrm{y}=1-|\mathrm{x}|$, is :

Q3.The number of relations, defined on the set $\{\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}\}$, which are both reflexive and symmetric, is equal to:

Q4.Let a point A lie between the parallel lines ${\mathrm{L}}_1$ and ${\mathrm{L}}_2$ such that its distances from ${\mathrm{L}}_1$ and ${\mathrm{L}}_2$ are 6 and 3 units, respectively. Then the area (in sq. units) of the equilateral triangle ABC , where the points B and C l …

Q5.Let $\vec{a}=-\hat{i}+2\hat{j}+2\hat{k},\vec{b}=8\hat{i}+7\hat{j}-3\hat{k}$ and $\vec{c}$ be a vector such that $\overrightarrow{\mathrm{a}}\times \overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{b}}$. If …

Q6.Let ${\mathrm{a}}_1,{\mathrm{a}}_2,{\mathrm{a}}_3,\dots$. be a G.P. of increasing positive terms such that $a_2\cdot a_3\cdot a_4=64$ and $a_1+a_3+a_5=\frac{813}{7}$.

Then ${\mathrm{a}}_3+{\mathrm{a}}_5+{\mathrm{a}}_7$ is equal to :

Q7.Let $\overrightarrow{\mathrm{c}}$ and $\overrightarrow{\mathrm{d}}$ be vectors such that $|\overrightarrow{\mathrm{c}}+\overrightarrow{\mathrm{d}}|=\sqrt{29}$ and …

Q8.Let $y=y(x)$ be the solution curve of the differential equation $\left(1+x^2\right)dy+\left(y-{\tan }^{-1}x\right)dx=0$, $y(0)=1$. Then the value of $y(1)$ is :

Q9.The number of strictly increasing functions f from the set $\{1,2,3,4,5,6\}$ to the set $(1,2,3,\dots ,9)$ such that $\mathrm{f}(\mathrm{i})\ne \mathrm{i}$ for $1\le \mathrm{i}\le 6$, is equal to :

Q10.Let $f:\mathrm{R}\to (0,\infty )$ be a twice differentiable function such that $\mathrm{f}(3)=18,{\mathrm{f}}^{\prime }(3)=0$ and ${\mathrm{f}}^{\prime \prime }(3)=4$.
Then …

Q11.Let the foci of hyperbola coincide with the foci of the ellipse $\frac{x^2}{36}+\frac{y^2}{16}=1$. If the eccentricity of the hyperbola is 5 , then the length of its latus rectum is:

Q12.The value of ${\int }_{-\pi /6}^{\pi /6}\left(\frac{\pi +4x^{11}}{1-\sin (|x|+\pi /6)}\right)dx$ is equal to

Q13.Let the mean and variance of 7 observations $2,4,10,x,12,14,y,x>y$, be 8 and 16 respectively. Two numbers are chosen from $\{1,2,3,\mathrm{x}-4,\mathrm{y},5\}$ one after another without replacement, then the probability, that the smaller number among the two chosen num …

Q14.Let $(\alpha ,\beta ,\gamma )$ be the co-ordinates of the foot of the perpendicular drawn from the point $(5,4,2)$ on the line $\vec{r}=(-\hat{i}+3\hat{j}+\hat{k})+\lambda (2\hat{i}+3\hat{j}-\hat{k})$.
Then the length of the projection of the vector …

Q15.Let PQ and MN be two straight lines touching the circle $x^2+y^2-4x-6y-3=0$ at the points A and B respectively. Let O be the centre of the circle and $\angle \mathrm{AOB}=\pi /3$. Then the locus of the point of intersection of the lines PQ and MN is:

Q16.If the coefficient of $x$ in the expansion of $\left(a{x}^2+bx+c\right)(1-2x{)}^{26}$ is -56 and the coefficients of ${\mathrm{x}}^2$ and ${\mathrm{x}}^3$ are both zero, then $\mathrm{a}+\mathrm{b}+\mathrm{c}$ is equal to

Q17.If $x^2+x+1=0$, then the value of ${\left(x+\frac{1}{x}\right)}^4+{\left(x^2+\frac{1}{x^2}\right)}^4+{\left(x^3+\frac{1}{x^3}\right)}^4+\dots +{\left(x^{25}+\frac{1}{x^{25}}\right)}^4$ is :

Q18.The value of $\mathrm{cosec}10^{\circ }-\sqrt{3}\sec 10^{\circ }$ is equal to:

Q19.The sum of all the roots of the equation $(\mathrm{x}-1{)}^2-5|\mathrm{x}-1|+6=0$, is:

Q20.Let O be the vertex of the parabola $x^2=4y$ and Q be any point on it. Let the locus of the point P , which divides the line segment OQ internally in the ratio 2: 3 be the conic C . Then the equation of the chord of C, which is bisected at the point $(1,2)$, is:

Q21.Let $f:R\to R$ be a twice differentiable function such that the quadratic equation $\mathrm{f}(\mathrm{x}){\mathrm{m}}^2-2{\mathrm{f}}^{\prime }(\mathrm{x})\mathrm{m}+{\mathrm{f}}^{\prime }(\mathrm{x})=0$ in m , has two equal roots for every …

Q22.Let ${\mathrm{a}}_1=1$ and for $\mathrm{n}\ge 1,{\mathrm{a}}_{\mathrm{n}+1}=\frac{1}{2}{a}_n+\frac{n^2-2n-1}{n^2(n+1{)}^2}$. Then $\left|{\sum }_{n=1}^{\infty }\left(a_n-\frac{2}{n^2}\right)\right|$ is equal to

Q23.Let $\mathrm{S}=\{(\mathrm{m},\mathrm{n}):\mathrm{m},\mathrm{n}\in \{1,2,3,\dots ..,50\}\}$. If the number of elements ( $\mathrm{m},\mathrm{n}$ ) in S such that $6^{\mathrm{m}}+9^{\mathrm{n}}$ is a multiple of 5 is p and the number of elements …

Q24.For some $\alpha ,\beta \in R$, let $A=\left[\begin{array}{ll}\alpha & 2\\ 1& 2\end{array}\right]$ and $B=\left[\begin{array}{ll}1& 1\\ 1& \beta \end{array}\right]$ be such that $A^2-4A+2I=B^2-3B+I=O$. Then …

Q25.$6{\int }_0^{\pi }|(\sin 3x+\sin 2x+\sin x)|dx$ is equal to.......