JEE Main 2026 · 05 Apr 2026 · Shift 1

Q1.In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and $7^{\text{th}}$ Vernier division coincides with a main scale reading. If the value of 1 main scale division is 1 mm and there are 10 Vernier sca …

Q2.L, C and R represents physical quantities inductance, capacitance and resistance respectively.

The dimensional formula ${\mathrm{ML}}^2{\mathrm{T}}^{-4}{\mathrm{A}}^{-2}$ corresponds to ______.

Q3.When one moves from a point 16 km below the earth's surface to a point 16 km above the earth's surface. The change in g is approximately $\alpha \%$. The value of $\alpha$ is ______.
(Take radius of the earth $=6400$ km.)

Q4.Three masses ${\mathrm{m}}_1=4$ kg, ${\mathrm{m}}_2=4$ kg and ${\mathrm{m}}_3=6$ kg are suspended from a fixed smooth frictionless pully as shown in the figure below. The value of ${\mathrm{T}}_1/{\mathrm{T}}_2$ is ______. (take $\mathrm{g}=10$ m/s${}^2$)

Q5.A wedge Y with mass of 10 kg and all frictionless surfaces and the inclined surface making $37^{\circ }$ with horizontal. A block X with mass 2 kg is placed at the highest point of the wedge as shown in figure is at rest. At $\mathrm{t}=0$ wedge (Y) is pulled toward right with con …

Q6.The Young's modulus of steel wire of radius $r$ and length L is Y. If the radius r and length L of the wire are doubled then the value of Y

Q7.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Statement I: Change in internal energy of a system containing $n$ mole of ideal gas can be written as …

Q8.Consider the following statements:

A. Zeroth law of thermodynamics gives concept of temperature

B. First law of thermodynamics gives concept of internal energy

C. In isothermal expansion of ideal gas, $\Delta \mathrm{Q}\ne \Delta \mathrm{W}$

D. Product of intensive and exte …

Q9.Refer to the figure given below. The values of ${\mathrm{I}}_1$, ${\mathrm{I}}_2$ and ${\mathrm{I}}_3$ are ______.

Q10.An electron of mass $m$ is moving in an electric field $\overrightarrow{\mathrm{E}}=-2{\mathrm{E}}_0\hat{\mathrm{i}}$ (${\mathrm{E}}_0=$ constant $>0$), with an initial velocity $\overrightarrow{\mathrm{V}}={\mathrm{v}}_{\mathrm{o}}\hat{\mathrm{i}}$ (${\mathrm{v}}_0=$ constant …

Q11.In the hydrogen atom, the electron makes a transition from the higher orbit (i) to a lower orbit (f). The ratio of the radius of the orbits in given by ${\mathrm{r}}_{\mathrm{i}}:{\mathrm{r}}_f=16:4$. The wavelength of photon emitted due to this transition is ______ nm. (Given Ry …

Q12.A displacement current of 4.0 A can be set up in the space between two parallel plates of $6\mu \mathrm{F}$ capacitor. The rate of change of potential difference across the plates of the capacitor is nearly $\alpha \times 10^6$ V/s. The value of $\alpha$ is ______.

Q13.Refer to the figure given below, current between terminals A and B is ______ A.

Q14.In Young's double slit experiment, the fringe width of the interference pattern produced on the screen is $2.4\mu$m. If the experiment is carried out in another medium having refractive index 1.2, the fringe width will be ______ $\mu$m.

Q15.A ray of light passing through an equilateral prism is having velocity $2.12\times 10^8$ m/s in the prism material, then the minimum angle of deviation is ______ degrees.

Q16.Light source having wavelength 331 nm is used to generate photo-electrons whose stopping potential is 0.2 V. The work function of the used metal in the experiment is $\alpha \times 10^{-19}$ J. The value of $\alpha$ is ______.
($h=6.62\times 10^{-34}$ J·s, …

Q17.A compound microscope is designed with two symmetric biconvex lenses. The objective lens is cut vertically, creating two identical plano-convex lenses. One of them is used in place of original objective lens. To retain same magnification keeping the object distance unchanged, the …

Q18.Two wires as shown in the figure below, made of steel and have breaking stress of $12\times 10^8$ N/m${}^2$. Area of cross-section of upper wire is $0.008$ cm${}^2$ and of lower wire is $0.004$ cm${}^2$. The maximum mass that can be added to pan without breaking any wire is ______ k …

Q19.An a.c. source of angular frequency $\omega$ is connected across a resistor R and a capacitor C in series. The current is observed as I. Now the frequency of the source is changed to $\omega /4$, (keeping the voltage unchanged) the current is found to be $I/3$. The ratio of resist …

Q20.For the given logic circuit, which of the following inputs combination will make both LED-1 and LED-2 to glow?

Q21.A cube has side length 5 cm and modulus of rigidity $10^5$ N/m${}^2$. The displacement produced by a force of 10 N in the upper face of cube is ______ mm.

Q22.From 18 m height above the ground a ball is dropped from rest. The height above the ground at which the magnitude of velocity equal to the magnitude of acceleration (in the same set of units) due to gravity is ______ m.
(Take $g=10$ m/s${}^2$ and neglect the air resistance)

Q23.A transverse wave on a string is described by $y=3\sin (36t+0.018x+\pi /4)$. Where $x,y$ are in cm and $t$ in seconds. The least distance between the two successive crests in the wave is ______ cm.
(Nearest integer) ($\pi =3.14$)

Q24.The charged particle moving in a uniform magnetic field of $(3\hat{i}+2\hat{j})$ T has an acceleration $\left(4\hat{i}-\frac{x}{2}\hat{j}\right)$ m/s${}^2$. The value of $x$ is ______.

Q25.In the given circuit below inductance values of ${\mathrm{L}}_1$, ${\mathrm{L}}_2$ and ${\mathrm{L}}_3$ are same. The magnetic energy stored in the entire circuit is $({\mathrm{U}}_{\mathrm{t}})$ and that stored in the ${\mathrm{L}}_2$ inductor is $({\mathrm{U}}_l)$. …

Q1.How many grams of residue is obtained by heating 2.76 g of silver carbonate?
(Given : Molar mass of $\mathrm{C},\mathrm{O}$ and Ag are 12, 16 and $108\mathrm{g}{\mathrm{mol}}^{-1}$ respectively)

Q2.Arrange the following atomic orbitals of multi electron atoms in order of increasing energy.
(A) $\mathrm{n}=3,\ell =2,\mathrm{m}=+1$
(B) $n=4,\ell =0,m=0$
(C) $\mathrm{n}=6,\ell =1,\mathrm{m}=0$
(D) $\mathrm{n}=5,\ell =1,\mathrm{m}=+1$
(E) …

Q3.Identify the correct statements from the following :
A. Heisenberg uncertainty principle is applicable to electron.
B. The size of $2p_x$ orbital is less than the size of $3p_x$ orbital.
C. The energy of 2s orbital of H atom is equal to the energy of 2s orbital of Li.
D …

Q4.What is the mole fraction of water in $10\%$ by weight $(\mathrm{w}/\mathrm{w})$ of aqueous urea solution ?
[Given : Molar mass of H, O, C and N are 1, 16, 12 and $14\mathrm{g}{\mathrm{mol}}^{-1}$ respectively]

Q5.${\mathrm{M}}_3{\mathrm{A}}_2$ is a sparingly soluble salt of molar mass y $\mathrm{g}{\mathrm{mol}}^{-1}$ and solubility $\times \mathrm{g}{\mathrm{L}}^{-1}$. The ratio of the molar concentration of the anion ( ${\mathrm{A}}^{3-}$ ) to the solubility product of the salt i …

Q6.Arrange the following resultant mixtures in increasing order of their pH values
A. $10\mathrm{mL}0.2\mathrm{M}\mathrm{Ca}(\mathrm{OH}{)}_2+25\mathrm{mL}0.1\mathrm{M}\mathrm{HCl}$
B. …

Q7.First order gas phase reaction
$\mathrm{A}\to \mathrm{B}+\mathrm{C}$
$p_i=$ initial pressure of gas $A,p_t=$ total pressure of the reaction mixture at time t
Expression of rate constant ( k ) is

Q8.Statement I : The correct order of electronegativity of fluorine, oxygen nitrogen is $\mathrm{F}>\mathrm{O}>\mathrm{N}$.
Statement II : The oxidation state of oxygen in ${\mathrm{OF}}_2$ is +2 and in ${\mathrm{Na}}_2\mathrm{O}$ is -2 .
In the light of the above statements, …

Q9.Correct statements from the following are :
A. Nitrogen in oxidation states from +1 to +4 disproportionates in acid medium.
B. Nitrogen has the ability of form $\mathrm{d}\pi -\mathrm{p}\pi$ multiple bonds with itself and other elements with small size and high electronegativi …

Q10.Which of the following is NOT a physical or chemical characteristics of interstitial compounds?

Q11.The correct statements about metal carbonyls are
A. The metal-carbon bonds in metals carbonyls possess both $\sigma$ and $\pi$-character.
B. Due to synergic bonding interactions between metals and CO ligand the metal-carbon bond becomes weak.
C. The metal-carbon $\sigma$ bo …

Q12.Given below are two statements :
Statement I : Each electron in ${\mathrm{e}}_{\mathrm{g}}$ orbitals destabilizes the orbitals by $+0.6{\Delta }_0$ and each electron in the $t_{2g}$ orbitals stabilizes the orbitals by $-0.4{\Delta }_0$ in an octahedral field on the b …

Q13.Given below are two statements :

Statement I: On the basis of inductive effect, the order of stability of alkyl carbanions is ${\mathrm{CH}}_3^{-}>{\mathrm{CH}}_3-{\mathrm{CH}}_2^{-}>({\mathrm{CH}}_3{)}_2{\mathrm{CH}}^{-}>({\mathrm{CH}}_3{)}_3{\mathrm{C}}^{-}$.
Statement II : All …

Q14."P" is hydrocarbon of molecular formula : ${\mathrm{C}}_8{\mathrm{H}}_{14}$. On ozonolysis, "P" forms "Q". "Q" on treatment with alkali under reflux condition produces. "R", which on treatment with ${\mathrm{I}}_2/\mathrm{NaOH}$ gives a yellow precipitate. Acidification of the s …

Q15.For the following Friedel Craft's alkylation reaction, which of the statements are correct?

(see reaction)

A. Major product is n -propyl benzene.
B. iso-propyl carbocation intermediate is also generated
C. Multiple substitution is inevitable.
D. Introducing electron-donating su …

Q16.Benzyl isocyanide can be obtained from
(A) (see structure)
(B) (see structure)
(C) (see structure)
(D) (see structure)
(E) (see structure)

Choose the correct answer from the options given below :

Q17.Consider compounds $\mathrm{A},\mathrm{B}$ and C with following structural formulae
$\mathrm{A}={\mathrm{CH}}_3-{\mathrm{CH}}_2-{\mathrm{CH}}_2-{\mathrm{CH}}_2-{\mathrm{CH}}_2-\mathrm{OH}$
$\mathrm{B}={\mathrm{CH}}_2=\mathrm{CH}-{\mathrm{CH}}_2-{\mathrm{CH}}_2-{\mathrm{CH}}_3$ …

Q18.Identify the incorrect statements :
A. (see structure) is a stronger base than (see structure)
B. (see structure) can be synthesized by Gabriel phthalimide synthesis.
C. (see reaction)
D. (see structure) will dissolve in NaOH

Choose the correct answer from the options given belo …

Q19.Identify the correct statements
A. Glucose exist in two anomeric forms.
B. Anomers of glucose differ in configuration at C -1 in cyclic hemiacetal structure.
C. Melting point of $\alpha$-anomer of glucose is greater than $\beta$-anomer.
D. Specific rotation of $\alpha$-anomer is …

Q20.Statement I : Sodium dichromate and potassium dichromate are classified as primary standard in titrimetric analysis .

Statement II : Phenolphthalein is a weak base, therefore it dissociates in acidic medium.

In the light of the above statements, choose the correct answer from t …

Q21.Consider the following species


Number of species having sp ${}^{3}d$ hybrid …

Q22.In an estimation of sulphur by Carius method 0.2 g of the substance gave 0.6 g of ${\mathrm{BaSO}}_4$. The percentage of sulphur in the substance is ____ %.
(Given molar mass in $\mathrm{g}{\mathrm{mol}}^{-1}\mathrm{S}:32,{\mathrm{BaSO}}_4:231$ )

Q23.One mole of phenol is treated with dilute ${\mathrm{HNO}}_3$ at 298 K to give a mixture of products. The mixture is separated by steam distillation. The seam volatile compound ( X ) is separated. The increase in percentage of oxygen in (X) with respect to phenol is ____ $10^{-1}$ …

Q24.The values of pressure equilibrium constant recorded at different temperatures for the following equilibrium reaction have been given below:
$\mathrm{A}(\mathrm{g})\rightleftharpoons \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$

| $\frac{1}{\mathrm{T}}({\mathrm{K}}^{-1})$ | …

Q25.If the half life of a first order reaction is 6.93 minutes then the time required for completion of $99\%$ of the reaction will be $\_\_\_\_$ minutes.
(Given : $\log 2=0.3010$ )

Q1.Let $\mathrm{a},\mathrm{b}\in \mathrm{C}$. Let $\alpha ,\beta$ be the roots of the equation ${\mathrm{x}}^2+\mathrm{ax}+\mathrm{b}=0$. If $\beta -\alpha =\sqrt{11}$ and ${\beta }^2-{\alpha }^2=3\mathrm{i}\sqrt{11}$, then ${\left({\beta }^3-{\alpha }^3\right)}^2$ is equa …

Q2.Let the sum of the first $n$ terms of an A.P. be $3n^2+5n$. Then the sum of squares of the first 10 terms of the A.P. is :

Q3.Let A be a $3\times 3$ matrix such that …

Q4.Consider the system of linear equations in $\mathrm{x},\mathrm{y},\mathrm{z}$ :
$\mathrm{x}+2\mathrm{y}+\mathrm{tz}=0$,
$6\mathrm{x}+\mathrm{y}+5\mathrm{tz}=0$,
$3\mathrm{x}+{\mathrm{t}}^2\mathrm{y}+\mathrm{f}(\mathrm{t})\mathrm{z}=0$,
Where …

Q5.${\sum }_{\mathrm{n}=1}^{10}\left(\frac{528}{\mathrm{n}(\mathrm{n}+1)(\mathrm{n}+2)}\right)$ is equal to :

Q6.Let $\tan \mathrm{A},\tan \mathrm{B}$, where $\mathrm{A},\mathrm{B}\in \left(-\frac{\pi }{2},\frac{\pi }{2}\right)$, be the roots of the quadratic equation ${\mathrm{x}}^2-2\mathrm{x}-5=0$. Then $20{\sin }^2\left(\frac{A+B}{2}\right)$ is equal to :

Q7.A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the the envelope just two consecutive letters AN are visible. The probability, that the letter came from ANANTPUR, is :

Q8.The mean deviation about the mean for the data

is equal to :

Q9.Let a focus of the ellipse $E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ be $S(4,0)$ and its eccentricity be $\frac{4}{5}$. If the point $\mathrm{P}(3,\alpha )$ lies on E and O is the origin, then the area of $△\mathrm{POS}$ is equal to :

Q10.Let P be a moving point on the circle


Then, the maximum distance of P from the vertex of the parabola $x^2+6x+y+13=0$ is equal to :

Q11.In an equilateral triangle PQR , let the vertex P be at $(3,5)$ and the side QR be along the line $x+y=4$. If the orthocentre of the triangle $PQR$ is $(\alpha ,\beta )$, then $9(\alpha +\beta )$ is equal to :

Q12.The sum of all the integral values of $p$ such that the equation $3{\sin }^{2}x+12\cos x-3=p,x\in R$, has at least one solution, is :

Q13.The square of the distance of the point $\mathrm{P}(5,6,7)$ from the line $\frac{x-2}{2}=\frac{y-5}{3}=\frac{z-2}{4}$ is equal to :

Q14.Let $\vec{a}=\sqrt{7}\hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=\hat{j}+2\hat{k}$. If $\vec{r}$ is a vector such that $\overrightarrow{\mathrm{r}}\times \overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{a}}\times \overrightarrow{\mathrm{b}}=\overrightarrow{0}$ and …

Q15.The square of the distance of the point of intersection of the line $\vec{r}=(\hat{i}+\hat{j}-\hat{k})+\lambda (\hat{a}-\hat{j})$, $\mathrm{a}\ne 0$ and $\overrightarrow{\mathrm{r}}=(4\hat{\mathrm{i}}-\hat{\mathrm{k}})+\mu (2\hat{\mathrm{i}}+\mathrm{a}\hat{\mathrm{k}})$ from t …

Q16.The area of the region
$\mathrm{R}=\left\{(\mathrm{x},\mathrm{y}):\mathrm{xy}\le 27,1\le \mathrm{y}\le {\mathrm{x}}^2\right\}$ is equal to :

Q17.The product of all possible values of $\alpha$, for which ${\lim }_{x\to 0}\left(\frac{1-\cos (\alpha x)\cos ((\alpha +1)x)\cos ((\alpha +2)x)}{{\sin }^2((\alpha +1)x)}\right)=2$, is :

Q18.The value of the integral ${\int }_0^{\infty }\frac{{\log }_e(\mathrm{x})}{{\mathrm{x}}^2+4}\mathrm{dx}$ is:

Q19.Let $\mathrm{f}:\mathrm{R}\to \mathrm{R}$ be a differentiable function such that $f\left(\frac{x+y}{3}\right)=\frac{f(x)+f(y)}{3}$ for all $x,y\in R$ and $f^{\prime }(0)=3$. Then the minimum value of the function …

Q20.The value of the integral ${\int }_{\frac{\pi }{6}}^{\frac{\pi }{3}}\left(\frac{4-{\mathrm{cosec}}^{2}x}{{\cos }^{4}x}\right)dx$ is :

Q21.Let $\mathrm{A}=\{1,2,3,4,5,6\}$. The number of one-one functions $\mathrm{f}:\mathrm{A}\to \mathrm{A}$ such that $\mathrm{f}(1)\ge 3,\mathrm{f}(3)\le 4$ and $f(2)+f(3)=5$, is ______.

Q22.Two players A and B play a series of games of badminton. The player, who wins 5 games first, wins the series. Assuming that no game ends in a draw, the number of ways, in which player A wins the series is ______.

Q23.If the sum of the coefficients of $x^7$ and $x^{14}$ in the expansion of ${\left(\frac{1}{x^3}-x^4\right)}^n,x\ne 0$, is zero, then the value of $n$ is ______.

Q24.If $\frac{\pi }{4}+{\sum }_{p=1}^{11}{\tan }^{-1}\left(\frac{2^{p-1}}{1+2^{2p-1}}\right)=\alpha$, then $\tan \alpha$ is equal to ______.

Q25.Let $y=y(x)$ be the solution of the differential equation
$x\sin \left(\frac{y}{x}\right)dy=\left(y\sin \left(\frac{y}{x}\right)-x\right)dx,y(1)=\frac{\pi }{2}$ and let $\alpha =\cos \left(\frac{y\left(e^{12}\right)}{e^{12}}\right)$. Then the number of integral value of $p$, f …