JEE Main 2026 · 23 Jan 2026 · Shift 2

Q1.The internal energy of a monoatomic gas is 3 nRT. One mole of helium is kept in a cylinder having internal cross section area of $17{\mathrm{cm}}^2$ and fitted with a light movable frictionless piston. The gas is heated slowly by suppling 126 J heat. If the temperature rises …

Q2.A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses in the ratio $2:2:3$. The two pieces of equal masses fly off perpendicular to each other with a speed of $18\mathrm{m}/\mathrm{s}$ each. The velocity of the heavier fragment is _\ …

Q3.A block is sliding down on an inclined plane of slope $\theta$ and at an instant $t=0$ this block is given an upward momentum so that it starts moving up on the inclined surface with velocity $u$. The distance $(S)$ travelled by the block before its velocity become zero, …

Q4.The current passing through a conducting loop in the form of equilateral triangle of side $4\sqrt{3}\mathrm{cm}$ is 2A. The magnetic field at its centroid is $\alpha \times 10^{-5}\mathrm{T}$. The value of $\alpha$ is ____.
(Given : …

Q5.A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts deaccelerating with $3\mathrm{m}/{\mathrm{s}}^2$. At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is …

Q6.Two shorts dipoles $(A,B)$, A having charges $\pm 2\mu \mathrm{C}$ and length 1 cm and $B$ having charges $\pm 4\mu \mathrm{C}$ and length 1 cm are placed with their centres 80 cm apart as shown in the figure. The electric field at a point $P$, equi-distant from the …

Q7.Two charges $7\mu \mathrm{C}$ and $-2\mu \mathrm{C}$ are placed at $(-9,0,0)\mathrm{cm}$ and $(9,0,0)\mathrm{cm}$ respectively in an external field $E=\frac{\mathrm{A}}{{\mathrm{r}}^2}\hat{\mathrm{r}}$, where …

Q8.A bead $P$ sliding on a frictionless semi-circular string $(ACB)$ and it is at point $S$ at $\mathrm{t}=0$ and at this instant the horizontal component of its velocity is $v$. Another bead $Q$ of the same mass as $P$ is ejected from point $A$ at $\mathrm{t}=0$ …

Q9.A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws $25\%$ more charge from the battery. The dielectric con …

Q10.An air bubble of volume $2.9{\mathrm{cm}}^3$ rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is $17^{\circ }\mathrm{C}$. The volume of the bubble when it reaches the surface, where the water temperature is …

Q11.Which of the following pair of nuclei are isobars of the element?

Q12.For the given logic gate circuit, which of the following is the correct truth table?

Q13.One mole of an ideal diatomic gas expands from volume V to 2V isothermally at a temperature $27^{\circ }\mathrm{C}$ and does W joule of work. If the gas undergoes same magnitude of expansion adiabatically from $27^{\circ }\mathrm{C}$ doing the same amount of work W, then its final …

Q14.A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s. The EMF induced in the loop is $\_\_\_\_$ mV.

Q15.Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a current $I=10\sin (\omega t)$ A, where $\omega =1000$ rad./s. A circular conducting loop (B) of radius 1 cm coaxially slided through the solenoid at a speed $v=1$ cm/s. The r.m.s. curr …

Q16.The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant $k=3$ and permeability of $\mu =2{\mu }_0$, is (${\mu }_0=$ permeability of vacuum)

Q17.When an unpolarized light falls at a particular angle on a glass plate (placed in air), it is observed that the reflected beam is linearly polarized. The angle of refracted beam with respect to the normal is $\_\_\_\_$.
(${\tan }^{-1}(1.52)=57.7^{\circ }$, refractive indices of air a …

Q18.A small metallic sphere of diameter 2 mm and density $10.5$ g/cm³ is dropped in glycerine having viscosity 10 Poise and density $1.5$ g/cm³ respectively. The terminal velocity attained by the sphere is $\_\_\_\_$ cm/s.
($\pi =\frac{22}{7}$ and $g=10$ m/s²)

Q19.The average energy released per fission for the nucleus of ${}_{92}^{235}\mathrm{U}$ is 190 MeV. When all the atoms of 47 g pure ${}_{92}^{235}\mathrm{U}$ undergo fission process, the energy released is $\alpha \times 10^{23}$ MeV. The value of $\alpha$ is $\_\_\_\_$.
(Avogadro Numbe …

Q20.The size of the images of an object, formed by a thin lens are equal when the object is placed at two different positions 8 cm and 24 cm from the lens. The focal length of the lens is $\_\_\_\_$ cm.

Q21.A ball of radius r and density $\rho$ dropped through a viscous liquid of density $\sigma$ and viscosity $\eta$ attains its terminal velocity at time t, given by $t=A{\rho }^a{r}^b{\eta }^c{\sigma }^d$, where A is a constant and a, b, c and d are integers. The value of $\frac{b+c}{a+d}$ …

Q22.Suppose there is a uniform circular disc of mass M kg and radius r m shown in figure. The shaded regions are cut out from the disc. The moment of inertia of the remainder about the axis A of the disc is given by $\frac{X}{256}M{r}^2$. The value of x is $\_\_\_\_$.

Q23.The velocity of sound in air is doubled when the temperature is raised from $0^{\circ }\mathrm{C}$ to ${\alpha }^{\circ }\mathrm{C}$. The value of $\alpha$ is ______.

Q24.A prism of angle 75° and refractive index 5/3 is coated with a thin film of refractive index 1.5 only at the back exit surface. To have total internal reflection at the back exit surface, the incident angle must be _______. (sin 15° = 0.25 and sin 25° = 0.43)

Q1.It is noticed that ${\mathrm{Pb}}^{2+}$ is more stable than ${\mathrm{Pb}}^{4+}$ but ${\mathrm{Sn}}^{2+}$ is less stable than ${\mathrm{Sn}}^{4+}$. Observe the following reactions …

Q2.Consider the above electrochemical cell where a metal electrode (M) is undergoing redox reaction by forming ${\mathrm{M}}^{+}$ ($\mathrm{M}\to {\mathrm{M}}^{+}+\mathrm{e}$). The cation ${\mathrm{M}}^{+}$ is present in two different concentrations ${\mathrm{c}}_1$ and …

Q3.Both human DNA and RNA are chiral molecules. The chirality in DNA and RNA arises due to the presence of

Q4.Identify the CORRECT set of details from the following:
A. ${\left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_6\right]}^{3+}$: Inner orbital complex; ${\mathrm{d}}^2{\mathrm{sp}}^3$ hybridized
B. ${\left[{\mathrm{MnCl}}_6\right]}^{3-}$: Outer orbital complex; …

Q5.Elements X and Y belong to Group 15. The difference between the electronegativity values of 'X' and phosphorus is higher than that of the difference between phosphorus and 'Y'. 'X' & 'Y' are respectively

Q6.Given below are two statements:

Statement I: ${\left({\mathrm{CH}}_3\right)}_3\stackrel{\oplus }{\mathrm{C}}$ is more stable than $\stackrel{\oplus }{\mathrm{C}}{\mathrm{H}}_3$ as nine hyperconjugation interactions are possible in …

Q7.Iodoform test can differentiate between
A. Methanol and Ethanol
B. ${\mathrm{CH}}_3\mathrm{COOH}$ and ${\mathrm{CH}}_3{\mathrm{CH}}_2\mathrm{COOH}$
C. Cyclohexene and cyclohexanone
D. Diethyl ether and Pentan-3-one
E. Anisole and acetone

Choose the correct answer from the …

Q8.Given below are two statements:

Statement I: The second ionisation enthalpy of Na is larger than the corresponding ionisation enthalpy of Mg.

Statement II: The ionic radius of ${\mathrm{O}}^{2-}$ is larger than that of ${\mathrm{F}}^{-}$.

In the light of the above statements, …

Q9.Identify (P)

Q10.Observe the following reactions at T(K).
I. A → products.
II. 5Br⁻(aq) + BrO₃⁻(aq) + 6H⁺(aq) → 3Br₂(aq) + 3H₂O(l)
Both the reactions are started at 10:00 am. The rates of these reactions at 10:10 am are the same. The value of −Δ[Br⁻]/Δt at 10:10 am is 2 × 10⁻⁴ mol L⁻¹ min⁻¹. The …

Q11.Which of the following statements are TRUE about Haloform reaction?
A. Sodium hypochlorite reacts with KI to give KOI.
B. KOI is a reducing agent.
C. $\alpha ,\beta$-unsaturated methylketone will give iodoform reaction.
D. Isopropyl alcohol will not give iodoform test.
E. Metha …

Q12.Which statements are NOT TRUE about ${\mathrm{XeO}}_2{\mathrm{F}}_2$?
A. It has a see-saw shape.
B. Xe has 5 electron pairs in its valence shell in ${\mathrm{XeO}}_2{\mathrm{F}}_2$.
C. The $\mathrm{O}-\mathrm{Xe}-\mathrm{O}$ bond angle is close to $180^{\circ }$.
D. Th …

Q13.Identify the INCORRECT statements from the following:
A. Notation ${}_{12}^{24}\mathrm{Mg}$ represents 24 protons and 12 neutrons.
B. Wavelength of a radiation of frequency $4.5\times 10^{15}{\mathrm{s}}^{-1}$ is $6.7\times 10^{-8}\mathrm{m}$.
C. One radiation has wave …

Q14.In Carius method 0.2425 g of an organic compound gave 0.5253 g silver chloride. The percentage of chlorine in the organic compound is

Q15.A mixed ether ( P ), when heated with excess of hot concentrated hydrogen iodide produces two different alkyl iodides which when treated with aq. NaOH give compounds (Q) and (R). Both (Q) and (R) give yellow precipitate with NaOI. Identify the mixed ether (P):

Q16.The oxidation state of chromium in the final product formed in the reaction between KI and acidified ${\mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7$ solution is:

Q17.The work functions of two metals ( ${\mathrm{M}}_{\mathrm{A}}$ and ${\mathrm{M}}_{\mathrm{B}}$ ) are in the $1:2$ ratio. When these metals are exposed to photons of energy 6 eV , the kinetic energy of liberated electrons of $M_A:M_B$ is in the ratio of 2.642 : 1. The wo …

Q18.Given below are two statements:

Statement I:
(see structure)
can be synthesized from
(see structure)
using simpler reagents in the order i) Acidic ${\mathrm{KMnO}}_4$, ii) Ammonia, iii) Bromine and alkali

Statement II :
(see structure)
can be converted into
(see structure)
us …

Q19.A student has been given a compound " x " of molecular formula $-{\mathrm{C}}_6{\mathrm{H}}_7\mathrm{N}$. ' x ' is sparingly soluble in water. However, on addition of dilute mineral acid , ' x ' becomes soluble in water. ' x ' when treated with ${\mathrm{CHCl}}_3$ and KOH …

Q20.${\mathrm{X}}_2(\mathrm{g})+{\mathrm{Y}}_2(\mathrm{g})\rightleftharpoons 2\mathrm{Z}(\mathrm{g})$
${\mathrm{X}}_2(\mathrm{g})$ and ${\mathrm{Y}}_2(\mathrm{g})$ are added to a 1 L flask and it is found that the system attains the above equilibrium at …

Q21.Two liquids A and B form an ideal solution. At 320 K , the vapour pressure of the solution, containing 3 mol of A and 1 mol of B is 500 mm Hg. At the same temperature, if 1 mol of A is further added to this solution, vapour pressure of the solution increases by 20 mm Hg . Vapour …

Q22.200 cc of $\mathrm{x}\times 10^{-3}\mathrm{M}$ potassium dichromate is required to oxidise 750 cc of 0.6 M

Mohr's salt solution in acidic medium.
Here $\mathrm{x}=$

Q23.Total number of unpaired electrons present in the central metal atoms/ions of
$\left[\mathrm{Ni}(\mathrm{CO}{)}_4\right],{\left[{\mathrm{NiCl}}_4\right]}^{2-},\left[{\mathrm{PtCl}}_2{\left({\mathrm{NH}}_3\right)}_2\right],{\left[\mathrm{Ni}\left({\mathrm{CN}}_4\right)\right]}^{2-}$ …

Q1.If $f(x)=\{\begin{array}{cl}\frac{a|x|+x^2-2(\sin |x|)(\cos |x|)}{x}& ,x\ne 0\\ b& ,x=0\end{array}$
is continuous at $\mathrm{x}=0$, then $\mathrm{a}+\mathrm{b}$ is equal to :

Q2.Let $\frac{\pi }{2}<\theta <\pi$ and $\cot \theta =-\frac{1}{2\sqrt{2}}$. Then the value of $\sin \left(\frac{15\theta }{2}\right)(\cos 8\theta +\sin 8\theta )+\cos \left(\frac{15\theta }{2}\right)(\cos 8\theta -\sin 8\theta )$ is equal to :

Q3.Let $\vec{a}=\hat{i}-2\hat{j}+3\hat{k},\vec{b}=2\hat{i}+\hat{j}-\hat{k},\vec{c}=\lambda \hat{i}+\hat{j}+\hat{k}$ and $\vec{v}=\vec{a}\times \vec{b}$. If $\vec{v}\cdot \vec{c}=11$ and the length of the projection of $\vec{b}$ on $\vec{c}$ is $p$, then …

Q4.Let $\mathrm{A}(1,2)$ and $\mathrm{C}(-3,-6)$ be two diagonally opposite vertices of a rhombus, whose sides AD and BC are parallel to the line $7\mathrm{x}-\mathrm{y}=14$. If $\mathrm{B}(\alpha ,\beta )$ and $\mathrm{D}(\gamma ,\delta )$ are the other two vertices, then …

Q5.Consider two sets $\mathrm{A}=\{\mathrm{x}\in \mathrm{Z}:|(|\mathrm{x}-3|-3)|\le 1\}$ and $B=\left\{x\in \mathbb{R}-\{1,2\}:\frac{(x-2)(x-4)}{x-1}{\log }_e(|x-2|)=0\right\}$.

Then the number of onto functions $f:\mathrm{A}\to \mathrm{B}$ is equal to :

Q6.The system of linear equations
$x+y+z=6$
$2\mathrm{x}+5\mathrm{y}+\mathrm{az}=36$
$x+2y+3z=b$
has

Q7.The sum of all the real solutions of the equation ${\log }_{(x+3)}\left(6x^2+28x+30\right)=5-2{\log }_{(6x+10)}\left(x^2+6x+9\right)$ is equal to :

Q8.If the points of intersection of the ellipses $x^2+2y^2-6x-12y+23=0$ and $4x^2+2y^2-20x-12y+35=0$ lie on a circle of radius r and centre $(\mathrm{a},\mathrm{b})$, then the value of $\mathrm{ab}+18{\mathrm{r}}^2$ is

Q9.Let PQ be a chord of the hyperbola $\frac{{\mathrm{x}}^2}{4}-\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1$, perpendicular to the x-axis such that OPQ is an equilateral triangle, $O$ being the centre of the hyperbola. If the eccentricity of the hyperbola is $\sqrt{3}$, then the a …

Q10.Let $\vec{a},\vec{b},\vec{c}$ be three vectors such that $\overrightarrow{\mathrm{a}}\times \overrightarrow{\mathrm{b}}=2(\overrightarrow{\mathrm{a}}\times \overrightarrow{\mathrm{c}})$. If …

Q11.Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked up from the bag B and mixed up with the balls in the bag A. Then a ball is randomly drawn from the bag A. If the probability, that the ball drawn is white, is …

Q12.The area of the region enclosed between the circles $x^2+y^2=4$ and $x^2+(y-2{)}^2=4$ is :

Q13.The least value of $\left({\cos }^2\theta -6\sin \theta \cos \theta +3{\sin }^2\theta +2\right)$ is

Q14.Let $\mathrm{I}(\mathrm{x})=\int \frac{3\mathrm{dx}}{(4\mathrm{x}+6)\left(\sqrt{4{\mathrm{x}}^2+8\mathrm{x}+3}\right)}$ and $\mathrm{I}(0)=\frac{\sqrt{3}}{4}+20$. If $\mathrm{I}\left(\frac{1}{2}\right)=\frac{\mathrm{a}\sqrt{2}}{\mathrm{b}}+\mathrm{c}$, where …

Q15.The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is

Q16.Let $\mathrm{A}=\{0,1,2,\dots .9)$. Let R be a relation on A defined by $(\mathrm{x},\mathrm{y})\in \mathrm{R}$ if and only if $|\mathrm{x}-\mathrm{y}|$ is a multiple of 3.
Given below are two statements:
Statement I: $n(R)=36$
Statement II: $R$ is an equivalence re …

Q17.If $\mathrm{z}=\frac{\sqrt{3}}{2}+\frac{\mathrm{i}}{2},\mathrm{i}=\sqrt{-1}$, then ${\left({\mathrm{z}}^{201}-\mathrm{i}\right)}^8$ is equal to

Q18.If the mean and the variance of the data

\begin{tabular}{|l|c|c|c|c|}
\hline Class & $4-8$ & $8-12$ & $12-16$ & $16-20$ \\
\hline Frequency & 3 & $\lambda$ & 4 & 7 \\
\hline
\end{tabular}

are $\mu$ and 19 respectively, then the value of $\lambda +\mu$ is

Q19.An equilateral triangle OAB is inscribed in the parabola ${\mathrm{y}}^2=4\mathrm{x}$ with the vertex O at the vertex of the parabola. Then the minimum distance of the circle having AB as a diameter from the origin is

Q20.Let ${\sum }_{\mathrm{k}=1}^{\mathrm{n}}{\mathrm{a}}_{\mathrm{k}}=\alpha {\mathrm{n}}^2+\beta \mathrm{n}$. If ${\mathrm{a}}_{10}=59$ and ${\mathrm{a}}_6=7{\mathrm{a}}_1$ then $\alpha +\beta$ is equal to

Q21.If the solution curve $y=f(x)$ of the differential equation $\left(x^2-4\right)y^{\prime }-2xy+2x{\left(4-x^2\right)}^2=0,x>2$, passes through the point (3,15), then the local maximum value of f is

Q22.If the image of the point $\mathrm{P}(\mathrm{a},2,\mathrm{a})$ in the line $\frac{\mathrm{x}}{2}=\frac{\mathrm{y}+\mathrm{a}}{1}=\frac{\mathrm{z}}{1}$ is Q and the image of Q in the line $\frac{x-2b}{2}=\frac{y-a}{1}=\frac{z+2b}{-5}$ is P, then $a+b$ is equal to

Q23.The number of elements in the set $S=\left\{x:x\in [0,100]\text{ and }{\int }_0^x{t}^2\sin (x-t)dt=x^2\right\}$ is

Q24.Let $\mathrm{A}=\left[\begin{array}{ccc}0& 2& -3\\ -2& 0& 1\\ 3& -1& 0\end{array}\right]$ and B be a matrix such that $\mathrm{B}(\mathrm{I}-\mathrm{A})=\mathrm{I}+\mathrm{A}$. Then the sum of the diagonal elements of $B^{T}B$ is equal to

Q25.Let S denote the set of 4-digit numbers abcd such that $a>b>c>d$ and P denote the set of 5-digit numbers having product of its digits equal to 20. Then $n(S)+n(P)$ is equal to...........