JEE Main 2026 · 28 Jan 2026 · Shift 2

Q1.A nucleus has mass number $\alpha$ and radius $R_{\alpha }$. Another nucleus has mass number $\beta$ and radius ${\mathrm{R}}_{\beta }$. If $\beta =8\alpha$ then $R_{\alpha }/R_{\beta }$ is :

Q2.A plane electromagnetic wave is moving in free space with velocity c $=3\times 10^8\mathrm{m}/\mathrm{s}$ and its electric field is given as $\overrightarrow{\mathrm{E}}=54\sin (\mathrm{kz}-\omega \mathrm{t})\hat{\mathrm{j}}\mathrm{V}/\mathrm{m}$, where …

Q3.A biconvex lens is formed by using two thin planoconvex lenses, as shown in the figure. The refractive index and radius of curved surfaces are also mentioned in figure. When an object is placed on the left side of lens at a distance of 30 cm from the biconvex lens, the magnificat …

Q4.The mean free path of a molecule of diameter $5\times 10^{-10}\mathrm{m}$ at the temperature $41^{\circ }\mathrm{C}$ and pressure $1.38\times 10^5\mathrm{Pa}$, is given as ______ m.
(Given ${\mathrm{k}}_{\mathrm{B}}=1.38\times 10^{-23}\mathrm{J}/\mathrm{K}$ ).

Q5.Two p-n junction diodes ${\mathrm{D}}_1$ and ${\mathrm{D}}_2$ are connected as shown in figure. A and B are input signals and C is the output. The given circuit will function as a ______.

Q6.A wheatstone bridge is initially at room temperature and all arms of the bridge have same value of resistances $\left(R_1=R_2=R_3=R_4\right)$. When $R_3$ resistance is heated to some temperature, its resistance value has gone up by $10\%$. The potential differenc …

Q7.In an experiment, a set of reading are obtained -1.24 mm, 1.25 mm, 1.23 mm, 1.21 mm. The expected least count of the instrument used in recording these readings is ______ mm .

Q8.A particle starts moving from time $\mathrm{t}=0$ and its coordinate is given as $\mathrm{x}(\mathrm{t})=4{\mathrm{t}}^3-3\mathrm{t}$.
A. The particle returns to its original position (origin) 0.866 units later
B. The particle is 1 unit away from origin at its turning point …

Q9.The speed of a longitudinal wave in a metallic bar is $400\mathrm{m}/\mathrm{s}$. If the density and Young's modulus of the bar material are increased by $0.5\%$ and $1\%$ respectively then the speed of the wave is changed approximately to ______ …

Q10.Identify the correct statements :
A. Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination.
B. When a dielectric medium is placed between the charged plates of a capacitor, displacement of c …

Q11.Number of photons of equal energy emitted per second by a 6 mW laser source operating at 663 nm is ______.
(Given : $\mathrm{h}=6.63\times 10^{-34}$ J.s and $\mathrm{c}=3\times 10^8\mathrm{m}/\mathrm{s}$ )

Q12.When the position vector $\vec{r}=x\hat{i}+y\hat{j}+z\hat{k}$ changes sign as $-\overrightarrow{\mathrm{r}}$, which one of the following vector will not flip under sign change ?

Q13.Which one of the following is not a measurable quantity?

Q14.A long cylindrical conductor with large cross section carries an electric current distributed uniformly over its cross-section. Magnetic field due to this current is :
A. maximum at either ends of the conductor and minimum at the midpoint
B. maximum at the axis of the conductor
C …

Q15.A small block of mass $m$ slides down from the top of a frictionless inclined surface, while the inclined plane is moving towards left with constant acceleration ${\mathrm{a}}_0$. The angle between the inclined plane and ground is $\theta$ and its base length is L . Assuming that …

Q16.Identify the correct statements :
A. Electrostatic field lines form closed loops.
B. The electric field lines point radially outward when charge is greater than zero.
C. The Gauss-Law is valid only for inverse-square force.
D. The workdone in moving a charged particle in a static …

Q17.As shown in the figure, a spring is kept in a stretched position with some extension by holding the masses 1 kg and 0.2 kg with a separation more than spring natural length and are released. Assuming the horizontal surface to be frictionless, the angular frequency (in SI unit) of …

Q18.For a transparent prism, if the angle of minimum deviation is equal to its refracting angle, the refractive index $n$ of the prism satisfies.

Q19.The time period of a simple harmonic oscillator is $\mathrm{T}=2\pi \sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$. The measured value of mass (m) of the object is 10 g with an accuracy of 10 mg , and time for 50 oscillations of the spring is found to be 60 s using a watch of 2 s resolut …

Q20.Two tuning forks A and B are sounded together giving rise to 8 beats in 2 s . When fork A is loaded with wax, the beat frequency is reduced to 4 beats in 2 s . If the original frequency of tuning fork B is 380 Hz , then the original frequency of tuning fork A is ______ Hz.

Q21.A thermodynamic system is taken through the cyclic process ABC as shown in the figure. The total work done by the system during the cycle ABC is ______ J.

Q22.An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 50 Hz flows through it. The ratio of inductive reactance to its resistance is ______ .
( $\pi =3.14$ )

Q23.A beam of light consisting of wavelengths 650 nm and 550 nm illuminates the Young's double slits with separation of 2 mm such that the interference fringes are formed on a screen, placed at a distance of 1.2 m from the slits. The least distance of a point from the central maximum …

Q24.A fly wheel having mass 3 kg and radius 5 m is free to rotate about a horizontal axis. A string having negligible mass is wound around the wheel and the loose end of the string is connected to a 3 kg mass. The mass is kept at rest initially and released. Kinetic energy of the whe …

Q1.Identify the correct statements :

The presence of $-{\mathrm{NO}}_2$ group in benzene ring
A. activates the ring towards electrophilic substitutions.
B. deactivates the ring towards electrophilic substitutions.
C. activates the ring towards nucleophilic substitutions.
D. deact …

Q2.Given below are two statements :

Statement I : The increasing order of boiling point of hydrogen halides is $\mathrm{HCl}<\mathrm{HBr}<\mathrm{HI}<\mathrm{HF}$.
Statement II : The increasing order of melting point of hydrogen halides is …

Q3.Consider the elements $\mathrm{N},\mathrm{P},\mathrm{O},\mathrm{S},\mathrm{Cl}$ and F . The number of valence electrons present in the elements with most and least metallic character from the above list is respectively.

Q4.Observe the following equilibrium in a 1 L flask.


At $\mathrm{T}(\mathrm{K})$, the equilibrium concentrations of A and B are 0.5 M and 0.375 M respectively. 0.1 moles of A is added into the flask and heated to $\mathrm{T}(\mathrm{K})$ to es …

Q5.The plot of ${\log }_{10}\mathrm{K}$ vs $\frac{1}{\mathrm{T}}$ gives a straight line. The intercept and slope respectively are (where K is equilibrium constant).

Q6.The reactions which produce alcohol as the product area :
A. ${\mathrm{CH}}_4+{\mathrm{O}}_2\underset{\Delta }{\overset{{\mathrm{Mo}}_2{\mathrm{O}}_3}{\to }}$
B. …

Q7.Consider the following statements about manganate and permanganate ions. Identify the correct statements :
A. The geometry of both manganate and permanganate ions is tetrahedral.
B. The oxidation states of Mn in manganate and permanganate are +7 and +6 , respectively.
C. Oxidatio …

Q8.Which of the following reaction is NOT correctly represented?

Q9.The wavelength of photon ' $A$ ' is 400 nm . The frequency of photon ' B ' is $10^{16}{\mathrm{s}}^{-1}$. The wave number of photon ' C ' is $10^4{\mathrm{cm}}^{-1}$. The correct order of energy of these photons is :

Q10.The cyclic cations having the same number of hyperconjugation are :
A. (see structure)
B. (see structure)
C. (see structure)
D. (see structure)

Choose the correct answer from the options given below :

Q11.Structures of four disaccharides are given below. Among the given disaccharides, the non-reducing sugar is :

Q12.Match List-I with List-II according to shape.

List-I
A. ${\mathrm{XeO}}_3$
B. ${\mathrm{XeF}}_2$
C. ${\mathrm{XeO}}_2{\mathrm{F}}_2$
D. ${\mathrm{XeOF}}_4$

List-II
I. ${\mathrm{BrF}}_5$
II. ${\mathrm{NH}}_3$
III. $\left[{\mathrm{I}}_3\right]$
IV. …

Q13.A student performed analysis of aliphatic organic compound 'X' which on analysis gave $\mathrm{C}=61.01\%$, $\mathrm{H}=15.25\%$, $\mathrm{N}=23.74\%$.
This compound, on treatment with ${\mathrm{HNO}}_2/{\mathrm{H}}_2\mathrm{O}$ produced another compound 'Y' which did not contain …

Q14.Consider the following aqueous solutions.
I. 2.2 g Glucose in 125 mL of solution.
II. 1.9 g Calcium chloride in 250 mL of solution.
III. 9.0 g Urea in 500 mL of solution.
IV. 20.5 g Aluminium sulphate in 750 mL of solution.
The correct increasing order of boiling point of these s …

Q15.The correct order of acidic strength of the major products formed in the given reactions, is:
A. …

Q16.Total number of alkali insoluble solid sulphonamides obtained by reaction of given amines with Hinsberg's reagent is
Aniline, N-Methylaniline, Methanamine, N,N-Dimethylmethanamine, N-Methyl methanamine, Phenylmethanamine, N-propylaniline, N-phenylaniline, N,N-Dimethylaniline, All …

Q17.Consider the following reactions.
${\mathrm{Na}}_2{\mathrm{B}}_4{\mathrm{O}}_7\stackrel{\Delta }{\to }2\mathrm{X}+\mathrm{Y}$
${\mathrm{CuSO}}_4+\mathrm{Y}\stackrel{\text{Non-Luminous flame}}{\to }\mathrm{Z}+{\mathrm{SO}}_3$
$2\mathrm{Z}+2\mathrm{X}+$ Carbon …

Q18.For the given reaction;
${\mathrm{CaCO}}_3+2\mathrm{HCl}\to {\mathrm{CaCl}}_2+{\mathrm{H}}_2\mathrm{O}+{\mathrm{CO}}_2$
If $90\mathrm{g}{\mathrm{CaCO}}_3$ is added to 300 mL of HCl which contains $38.55\%$ HCl by mass and has density …

Q19.The correct increasing order of spin-only magnetic moment values of the complex ions
$[{\mathrm{MnBr}}_4{]}^{2-}$(A), $[\mathrm{Cu}({\mathrm{H}}_2\mathrm{O}{)}_6{]}^{2+}$(B), $[\mathrm{Ni}({\mathrm{CN}}_4){]}^{2-}$(C) and $[\mathrm{Ni}({\mathrm{H}}_2\mathrm{O}{)}_6{]}^{2+}$(D) is:

Q20.A student has been given 0.314 g of an organic compound and asked to estimate Sulphur. During the experiment, the student has obtained 0.4813 g of barium sulphate. The percentage of sulphur present in the compound is ______.
(Given Molar mass in $\mathrm{g}{\mathrm{mol}}^{-1}$ S: …

Q21.Two positively charged particles ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ have been accelerated across the same potential difference of 200 keV as shown below.

[Given mass of ${\mathrm{m}}_1=1$ amu and ${\mathrm{m}}_2=4$ amu]
The deBroglie wavelength of ${\mathrm{m}}_1$ will be x t …

Q22.$\mathrm{A}\to \mathrm{B}$ (first reaction)
$\mathrm{C}\to \mathrm{D}$ (second reaction)
Consider the above two first-order reactions. The rate constant for first reaction at 500 K is double of the same at 300 K. At 500 K, 50% of the reaction becomes complete in 2 h …

Q23.For strong electrolyte ${\Lambda }_{\mathrm{m}}$ increases slowly with dilution and can be represented by the equation ${\Lambda }_{\mathrm{m}}={\Lambda }_{\mathrm{m}}^{\circ }-\mathrm{A}{c}^{1/2}$
Molar conductivity values of the solutions of strong electrolyte AB at $18^{\circ }\mathrm{C}$ …

Q24.A volume of x mL of $5\mathrm{M}{\mathrm{NaHCO}}_3$ solution was mixed with 10 mL of $2\mathrm{M}{\mathrm{H}}_2{\mathrm{CO}}_3$ solution to make an electrolytic buffer. If the same buffer was used in the following electrochemical cell to record a cell potential of 235.3 m …

Q25.The number of isoelectronic species among ${\mathrm{Sc}}^{3+}$, ${\mathrm{Cr}}^{2+}$, ${\mathrm{Mn}}^{3+}$, ${\mathrm{Co}}^{3+}$ and ${\mathrm{Fe}}^{3+}$ is 'n'. If 'n' moles of AgCl is formed during the reaction of complex with formula ${\mathrm{CoCl}}_3(\mathrm{en}{)}_2{\mathrm{NH}}_3$ w …

Q1.Given below two statements :

Statement I : $25^{13}+20^{13}+8^{13}+3^{13}$ is divisible by 7.
Statement II : The integral part of $(7+4\sqrt{3}{)}^{25}$ is an odd number.

In the light of the above statements, choose the correct answer from the options given below :

Q2.The sum of the coefficients of $x^{499}$ and $x^{500}$ in $(1+x{)}^{1000}+x(1+x{)}^{999}+x^2(1+x{)}^{998}+\dots \dots +x^{1000}$ is

Q3.Let A be the focus of the parabola ${\mathrm{y}}^2=8\mathrm{x}$. Let the line $\mathrm{y}=\mathrm{mx}+\mathrm{c}$ intersect the parabola at two distinct points B and C . If the centroid of the triangle ABC is $\left(\frac{7}{3},\frac{4}{3}\right)$, then …

Q4.The probability distribution of a random variable X is given below :
| X | 4 k | $\frac{30}{7}\mathrm{k}$ | $\frac{32}{7}\mathrm{k}$ | $\frac{34}{7}\mathrm{k}$ | $\frac{36}{7}\mathrm{k}$ | $\frac{38}{7}\mathrm{k}$ | $\frac{40}{7}\mathrm{k}$ | 6 k || P(X) | …

Q5.Let $f(x)={\lim }_{\theta \to 0}\left(\frac{\cos \pi x-x^{\left(\frac{2}{\theta }\right)}\sin (x-1)}{1+x^{\left(\frac{2}{\theta }\right)}(x-1)}\right),x\in R$.

Consider the following two statements :
(I) $\mathrm{f}(\mathrm{x})$ is discontinous at $\mathrm{x}=1$.
(I …

Q6.Considering the principal values of inverse trigonometric functions, the value of the expression $\tan \left(2{\sin }^{-1}\left(\frac{2}{\sqrt{13}}\right)-2{\cos }^{-1}\left(\frac{3}{\sqrt{10}}\right)\right)$ is equal to :

Q7.Let the arithmetic mean of $\frac{1}{\mathrm{a}}$ and $\frac{1}{\mathrm{b}}$ be $\frac{5}{16},\mathrm{a}>2$.

If $\alpha$ is such that $\mathrm{a},4,\alpha ,\mathrm{b}$ are in A.P., then the equation $\alpha x^2-ax+2(\alpha -2b)=0$ has:

Q8.Given below are two statements :

Statement I: The function $\mathrm{f}:\mathbf{R}\to \mathbf{R}$ defined by $\mathrm{f}(\mathrm{x})=\frac{\mathrm{x}}{1+|\mathrm{x}|}$ is one-one.

Statement II : The function $\mathrm{f}:\mathbf{R}\to \mathbf{R}$ defined …

Q9.An ellipse has its center at $(1,-2)$, one focus at $(3,-2)$ and one vertex at $(5,-2)$. Then the length of its latus rectum is :

Q10.Let the ellipse $\mathrm{E}:\frac{{\mathrm{x}}^2}{144}+\frac{{\mathrm{y}}^2}{169}=1$ and the hyperbola $\mathrm{H}:\frac{{\mathrm{x}}^2}{16}-\frac{{\mathrm{y}}^2}{{\lambda }^2}=-1$ have the same foci. If e and L respectively denote the eccentricity and the length of the latu …

Q11.Let $P_1:y=4x^2$ and $P_2:y=x^2+27$ be two parabolas. If the area of the bounded region enclosed between ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$ is six times the area of the bounded region enclosed between the line $\mathrm{y}=\alpha \mathrm{x},\alpha >0$ and …

Q12.Let the circle $x^2+y^2=4$ intersect $x$-axis at the points $\mathrm{A}(\mathrm{a},0),\mathrm{a}>0$ and $\mathrm{B}(\mathrm{b},0)$. Let $\mathrm{P}(2\cos \alpha ,2\sin \alpha ),0<\alpha <\frac{\pi }{2}$ and $\mathrm{Q}(2\cos \beta ,2\sin \beta )$ be two points …

Q13.Let [ • ] denote the greatest integer function. Then ${\int }_{-\frac{\pi }{2}}^{\frac{\pi }{2}}\left(\frac{12(3+[x])}{3+[\sin x]+[\cos x]}\right)dx$ is equal to:

Q14.Let $\mathrm{y}=\mathrm{y}(\mathrm{x})$ be the solution of the differential equation $x\frac{dy}{dx}-y=x^2\cot x,x\in (0,\pi )$.
If $y\left(\frac{\pi }{2}\right)=\frac{\pi }{2}$, then $6y\left(\frac{\pi }{6}\right)-8y\left(\frac{\pi }{4}\right)$ is equal to :

Q15.The sum of all the elements in the range of $f(x)=\mathrm{Sgn}(\sin x)+\mathrm{Sgn}(\cos x)+\mathrm{Sgn}(\tan x)+\mathrm{Sgn}(\cot x)$, $\mathrm{x}\ne \frac{\mathrm{n}\pi }{2},\mathrm{n}\in \mathbf{Z}$,
where …

Q16.Let $\mathrm{Q}(\mathrm{a},\mathrm{b},\mathrm{c})$ be the image of the point $\mathrm{P}(3,2,1)$ in the line $\frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1}$. Then the distance of $Q$ from the line $\frac{x-9}{3}=\frac{y-9}{2}=\frac{z-5}{-2}$ is

Q17.Let P be a point in the plane of the vector $\overrightarrow{\mathrm{AB}}=3\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{AC}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}+3\hat{\mathrm{k}}$ such that P is equidistant from the lines AB and AC . If …

Q18.Let
$A=\{z\in \mathbb{C}:|z-2|\le 4\}$ and
$\mathrm{B}=\{\mathrm{z}\in \mathbb{C}:|\mathrm{z}-2|+|\mathrm{z}+2|=5\}$.
Then the max $\{\left|{\mathrm{z}}_1-{\mathrm{z}}_2\right|:{\mathrm{z}}_1\in \mathrm{A}$ and …

Q19.Let $\mathrm{f}(\mathrm{x})=\int \frac{\mathrm{dx}}{{\mathrm{x}}^{\left(\frac{2}{3}\right)}+2{\mathrm{x}}^{\left(\frac{1}{2}\right)}}$ be such that $\mathrm{f}(0)=-26+24{\log }_{\mathrm{e}}(2)$. If $\mathrm{f}(1)=\mathrm{a}+\mathrm{b}{\log }_{\mathrm{e}}(3)$, where …

Q20.$\frac{6}{3^{26}}+\frac{10.1}{3^{25}}+\frac{10.2}{3^{24}}+\frac{10.2^2}{3^{23}}+\dots +\frac{10.2^{24}}{3}$ is equal to

Q21.If ${\sum }_{\mathrm{r}=1}^{25}\left(\frac{\mathrm{r}}{{\mathrm{r}}^4+{\mathrm{r}}^2+1}\right)=\frac{\mathrm{p}}{\mathrm{q}}$, where p and q are positive integers such that $\gcd (p,q)=1$, then $p+q$ is equal to ______。

Q22.Three persons enter in a lift at the ground floor. The lift will go upto $10^{\text{th }}$ floor. The number of ways, in which the three persons can exit the lift at three different floors, if the lift does not stop at first, second and third floors, is equal to ______。

Q23.Let f be a differentiable function satisfying
$\mathrm{f}(\mathrm{x})=1-2\mathrm{x}+{\int }_0^{\mathrm{x}}{\mathrm{e}}^{(\mathrm{x}-\mathrm{t})}\mathrm{f}(\mathrm{t})\mathrm{dt},\mathrm{x}\in \mathbf{R}$ and let …

Q24.If the distance of the point $\mathrm{P}(43,\alpha ,\beta ),\beta <0$, from the line $\overrightarrow{\mathrm{r}}=4\hat{\mathrm{i}}-\hat{\mathrm{k}}+\mu (2\hat{\mathrm{i}}+3\hat{\mathrm{k}}),\mu \in \mathbf{R}$ along a line with direction ratios $3,-1,0$ is …

Q25.Let $\mathrm{A}=\left[\begin{array}{ll}3& -4\\ 1& -1\end{array}\right]$ and B be two matrices such that $A^{100}=100B+I$. Then the sum of all the elements of ${\mathrm{B}}^{100}$ is ______ .