JEE Main 2026 — 2 April, Morning Shift

The diameter of a wire measured by a screw gauge of least count 0.001 cm is 0.08 cm. The length measured by a scale of least count 0.1 cm is 150 cm. When a weight of 100 N is applied to the wire, the extension in length is 0.5 cm, measured by a micrometer of least count 0.001 cm. The error in the measured Young's modulus is $\alpha \times 10^{9}\mathrm{N} / \mathrm{m}^{2}$ . The value of $\alpha$ is _____

The velocity of a particle is given as $\vec{\mathrm{v}} = -\mathrm{x}\hat{\mathrm{i}} +2\mathrm{y}\hat{\mathrm{j}} -\mathrm{z}\hat{\mathrm{k}}\mathrm{m} / \mathrm{s}$ The magnitude of acceleration at point (1, 2, 4) is m/s2.

The position of an object having mass $0.1\mathrm{kg}$ as a function of time t is given as $\vec{\mathrm{r}} = \left(10\mathrm{t}^{2}\vec{\mathrm{i}} +5\mathrm{t}^{3}\vec{\mathrm{j}}\right)\mathrm{m}.$ At $\mathrm{t} = 1\mathrm{~s~}$ , which of the following statements are correct? A. The linear momentum $\vec{\mathrm{p}} = \left(2\vec{\mathrm{i}} +1.5\vec{\mathrm{j}}\right)\mathrm{kg}\cdot \mathrm{m} / \mathrm{s}.$ B. The force acting on the object $\vec{\mathrm{F}} = \left(2\vec{\mathrm{i}} +3\vec{\mathrm{j}}\right)\mathrm{N}.$ C. The angular momentum of the object about its origin $\vec{\mathrm{L}} = 15\vec{\mathrm{k}}\mathrm{J}\mathrm{s}.$ D. The torque acting on the object about its origin $\vec{\mathrm{r}} = 20\vec{\mathrm{k}}\mathrm{N}\mathrm{m}.$ Choose the correct answer from the option given below.

A planet $(\mathrm{P}_{1})$ is moving around the star of mass 2M in the orbit of radius R. Another planet $(\mathrm{P}_{2})$ is moving around another star of mass 4M in a orbit of radius 2R. Ratio of time periods of revolution of $\mathrm{P}_{2}$ and $\mathrm{P}_{1}$ is

A particle is rotating in a circular path and at any instant its motion can be described as $\theta = \frac{5\mathrm{t}^{4}}{40} -\frac{\mathrm{t}^{3}}{3}$ The angular acceleration of the particle after 10 seconds is rad/s2.

Heat is supplied to a diatomic gas at constant pressure. Then the ratio of $\Delta \mathrm{Q}:\Delta \mathrm{U}:\Delta \mathrm{W}$ is

Two charged conducting spheres $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ of radii $8\mathrm{cm}$ and $18\mathrm{cm}$ are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ spheres are $\mathrm{E}_{\mathrm{S1}}$ and $\mathrm{E}_{\mathrm{S2}}$ respectively. The value of $\frac{\mathrm{E}_{\mathrm{S1}}}{\mathrm{E}_{\mathrm{S2}}}$ is

The equation of a plane progressive wave is given by $\mathrm{y} = 5\cos \pi \left(200\mathrm{t} - \frac{\mathrm{x}}{150}\right)$ where $\mathbf{x}$ and $\mathbf{y}$ are in cm and t is in second. The velocity of the wave is m/s

Two short electric dipoles A and B having dipole moment $\mathbf{p}_1$ and $\mathbf{p}_2$ respectively are placed with their axis mutually perpendicular as shown in the figure. The resultant electric field at a point $\mathbf{x}$ is making an angle of $60^{\circ}$ with the line joining points O and $\mathbf{x}$ . The ratio of the dipole moments $\mathbf{p}_2 / \mathbf{p}_1$ is ______.

When a coil is placed in a time dependent magnetic field the power dissipated in it is P. The number of turns, area of the coil and radius of the coil wire are N, A and r respectively. For a second coils number of turns, area of the coil and radius of the coil wire are 2N, 2A and 3r respectively. When the first coil is replaced with second coil the power dissipated in it is $\sqrt{2}\alpha \mathrm{P}$ . The value of $\alpha$ is

For a thin symmetric prism made of glass (refractive index 1.5), the ratio of incident angle and minimum deviation will be

For a certain metal, when monochromatic light of wavelength $\lambda$ is incident, the stopping potential for photoelectrons is $3\mathrm{V}_{\mathrm{o}}$ . When the same metal is illuminated by light of wavelength $2\lambda$ , then the stopping potential becomes $\mathrm{V}_{\mathrm{o}}$ . The threshold wavelength for photoelectric emission for the given metal is $\alpha \lambda$ . The value of $\alpha$ is

An electromagnetic wave travelling in x- direction is described by field equation $\mathrm{E}_{\mathrm{y}} = 300 \sin \omega \left(\mathrm{t} - \frac{\mathrm{x}}{\mathrm{c}}\right)$ . If the electron is restricted to move in y- direction only with speed of $1.5 \times 10^{6} \mathrm{~m} / \mathrm{s}$ then ratio of maximum electric and magnetic forces acting on the electron is

Angular momentum of an electron in a hydrogen atom is $\frac{3h}{\pi}$ , then the energy of the electron is $\mathrm{eV}$ .

In single slit diffraction pattern, the wavelength of light used is $628\mathrm{nm}$ and slit width is $0.2\mathrm{mm}$ , the angular width of central maximum is $\alpha \times 10^{-2}$ degrees. The value of $\alpha$ is ______.

A vessel contains $0.15\mathrm{m}^3$ of a gas at pressure 8 bar and temperature $140^{\circ}\mathrm{C}$ with $\mathrm{c}_{\mathrm{p}} = 3\mathrm{R}$ and $\mathrm{c}_{\mathrm{v}} = 2\mathrm{R}$ . It is expanded adiabatically till pressure falls to 1 bar. The work done during this process is ______ kJ. (R is gas constant)

1 μC charge moving with velocity $\bar{\nu} = (\hat{\mathrm{i}} - 2\hat{\mathrm{j}} + 3\hat{\mathrm{k}})\mathrm{m / s}$ in the region of magnetic field $\bar{\mathrm{B}} = (2\hat{\mathrm{i}} + 3\hat{\mathrm{j}} - 5\hat{\mathrm{k}})\mathrm{T}$ . The magnitude of force acting on it is $\sqrt{\alpha}\times 10^{- 6}\mathrm{N}$ . The value of $\alpha$ is

A uniform wire of length $l$ of weight w is suspended from the roof with a weight of W at the other end. The stress in the wire at $\frac{l}{3}$ distance from the top is $\left(\frac{W}{A} +\frac{2w}{\gamma A}\right)$ , where, A is the cross sectional area of the wire. The value of $\gamma$ is

A tube is filled with water and a wooden cube $10\mathrm{cm}\times 10\mathrm{cm}\times 10\mathrm{cm}$ is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged part is increased by $3.87\mathrm{cm}$ . The mass of the metal coin is gram. (Take water density as $1\mathrm{g / cm}^3$ and density of wood as $0.4\mathrm{g / cm}^3$)

Let $\alpha ,\alpha +2,\alpha \in \mathbf{Z}$ be the roots of the quadratic equation $\mathbf{x}(\mathbf{x} + 2) + (\mathbf{x} + 1)(\mathbf{x} + 3) + (\mathbf{x} + 2)(\mathbf{x} + 4) + \ldots +(\mathbf{x} + \mathbf{n} - 1)(\mathbf{x} + \mathbf{n} + 1) = 4\mathbf{n}$ for some $\mathbf{n}\in \mathbf{N}$ . Then $(\mathbf{n} + \alpha)$ is equal to:

Let $\mathbf{x}$ and $\mathbf{y}$ be real number such that $50\left(\frac{2\mathbf{x}}{1 + 3\mathbf{i}} -\frac{\mathbf{y}}{1 - 2\mathbf{i}}\right) = 31 + 17\mathbf{i},\mathbf{i} = \sqrt{-1}$. value of $10(\mathbf{x} - 3\mathbf{y})$ is :

Let $\alpha ,\beta \in \mathbf{R}$ be such that the system of linear equations $\mathbf{x} + 2\mathbf{y} + \mathbf{z} = 5$, $2\mathbf{x} + \mathbf{y} + \alpha \mathbf{z} = 5$, $8\mathbf{x} + 4\mathbf{y} + \beta \mathbf{z} = 18$ has no solution. Then $\frac{\beta}{\alpha}$ is equal to :

Let $\mathbf{A} = \left[ \begin{array}{ll}1 & 2\\ 1 & \alpha \end{array} \right]$ and $\mathbf{B} = \left[ \begin{array}{ll}3 & 3\\ \beta & 2 \end{array} \right]$. If $\mathbf{A}^2 - 4\mathbf{A} + \mathbf{I} = \mathbf{O}$ and $\mathbf{B}^2 - 5\mathbf{B} - 6\mathbf{I} = \mathbf{O}$ then among the two statements :

(S1) : $\left[(\mathbf{B} - \mathbf{A})(\mathbf{B} + \mathbf{A})\right]^{\mathrm{T}} = \left[ \begin{array}{ll}13 & 15\\ 7 & 10 \end{array} \right]$ and

(S2) : det (adj(A + B)) = -5,

Let A be the set of first 101 terms of an A.P., whose first term is 1 and the common difference is 5 and let B be the set of first 71 terms of an A.P., whose first term is 9 and the common difference is 7. Then the number of elements in A $\cap$ B, which are divisible by 3, is :

The number of seven-digit numbers, that can be formed by using the digits 1, 2, 3, 5 and 7 such that each digit is used at least once, is….

If the mean of the data

is 21, then k is one of the roots of the equation :

Two vertices of a triangle are $(0,2)$ and $(4,3)$. If its orthocentre is at the origin, then its third vertex lies in which quadrant?

Let an ellipse $\frac{\mathrm{x}^{2}}{\mathrm{a}^{2}} +\frac{\mathrm{y}^{2}}{\mathrm{b}^{2}} = 1$ , a < b, pass through the point (4, 3) and have eccentricity $\frac{\sqrt{5}}{3}$ . Then the length of its latus rectum is :

If $\sin \left(\frac{\pi}{18}\right)\sin \left(\frac{5\pi}{18}\right)\sin \left(\frac{7\pi}{18}\right) = \mathrm{K}$ , then the value of $\sin \left(\frac{10\mathrm{K}\pi}{3}\right)$ is :

Let $\mathrm{S} = \{\mathrm{x}\in [-\pi ,\pi ]:\sin \mathrm{x}(\sin \mathrm{x} + \cos \mathrm{x}) = \mathrm{a}, \mathrm{a}\in \mathbf{Z}\}$ . Then $\mathrm{n}(\mathrm{S})$ is equal to :

If the point of intersection of the lines $\frac{\mathrm{x} + 1}{3} = \frac{\mathrm{y} + \mathrm{a}}{5} = \frac{\mathrm{z} + \mathrm{b} + 1}{7}$ and $\frac{\mathrm{x} - 2}{1} = \frac{\mathrm{y} - \mathrm{b}}{4} = \frac{\mathrm{z} - 2\mathrm{a}}{7}$ lies on xy- plane, then the value of a + b is :

If $\bar{\mathbf{a}}$ and $\bar{\mathbf{b}}$ are two vectors such that $|\bar{\mathbf{a}} | = 2$ and $|\bar{\mathbf{b}} | = 3$ , then the maximum value of $3\left|(3\bar{\mathbf{a}} +2\bar{\mathbf{b}})\right| + 4\left|(3\bar{\mathbf{a}} -2\bar{\mathbf{b}})\right|$ is :

If $\lim_{x\to 2}\frac{\sin(x^3 - 5x^2 + ax + b)}{(\sqrt{x - 1} - 1)\log_{\mathrm{e}}(x - 1)} = \mathbf{m}$ , then $\mathbf{a} + \mathbf{b} + \mathbf{m}$ is equal to:

If the curve y = f(x) passes through the point (1, e) and satisfies the differential equation dy = y (2 + log_e x) dx, x > 0, then f(e) is equal to :

The number of critical points of the function $f(x) = \begin{cases} \frac{\sin x}{x}, & x \neq 0 \\ 1, & x=0 \end{cases}$ in the interval $(-2\pi, 2\pi)$ is equal to:

Let y = y(x) be the solution curve of the differential equation (1 + sin x) $\frac{dy}{dx}$ + (y + 1) cos x = 0, y(0) = 0. If the curve y = y(x) passes through the point $\left(\alpha, -\frac{1}{2}\right)$, then a value of α is :

If the domain of the function $f(x) = \log_{0.6}\left(\frac{2x-5}{x^2-4}\right)$ is $(-\infty, a] \cup \{b\} \cup [c,d) \cup (e,\infty)$, then the value of a + b + c + d + e is _____.

Let a, b, c ∈ {1,2,3,4}. If the probability that ax^2 + 2√2 bx + c > 0 for all x ∈ R, is m/n, gcd(m,n)=1, then m+n is equal to ______.

Let a circle C have its centre in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal intercepts from the coordinate axes. If the length of the chord of C on the line $x + y = 1$ is $\sqrt{14},$ then the square of the radius of C is _____.

Let $P(x)$ be a real polynomial of degree 3 which vanishes at $x=-3$. Let $P(x)$ have local minima at $x=1$,

local maxima at $x=-1$ and $\int_{-1}^{1} P(x) d x=18$, then the sum of all the coefficients of the polynomial $P(x)$ is equal to $\_\_\_\_\_\_$ .

The mass of iron converted into $\mathrm{Fe}_{3} \mathrm{O}_{4}$ by the action of 18 g of steam is : (Given : Molar mass of H, O and Fe are 1, 16 and $56 \mathrm{~g} \mathrm{~mol}^{-1}$ respectively)

Assume iron is present in excess :

What is the energy (in J atom ${ }^{-1}$ ) required for the following process? $\mathrm{Li}^{2+}(\mathrm{g}) \rightarrow \mathrm{Li}^{3+}(\mathrm{g})+\mathrm{e}^{-}$ (Take the ionization energy for the H atom in the ground state as $2.18 \times 10^{-18} \mathrm{~J}^{-1}$ atom ${ }^{-1}$ )

Consider the following data (i) $2 \mathrm{Al}(\mathrm{s})+6 \mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{Al}_{2} \mathrm{Cl}_{6}(\mathrm{aq})+3 \mathrm{H}_{2}(\mathrm{~g})+ 1200 \mathrm{~kJ} / \mathrm{mol}$. (ii) $\mathrm{H}_{2}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{HCl}(\mathrm{g})+164 \mathrm{~kJ} / \mathrm{mol}$. (iii) $\mathrm{HCl}(\mathrm{g})+\mathrm{aq} \rightarrow \mathrm{HCl}(\mathrm{aq})+83 \mathrm{~kJ} / \mathrm{mol}$. (iv) $\mathrm{Al}_{2} \mathrm{Cl}_{6}(\mathrm{~s})+\mathrm{aq} \rightarrow \mathrm{Al}_{2} \mathrm{Cl}_{6}(\mathrm{aq})+663 \mathrm{~kJ} / \mathrm{mol}$.

The enthalpy of formation of anhydrous solid $\mathrm{Al}_{2} \mathrm{Cl}_{6}$ is :

19.5 g of fluoro acetic acid (molar mass $=78 \mathrm{~g} \mathrm{~mol}^{-1}$ ) is dissolved in 500 g of water at 298 K . The depression in the freezing point of water was $1^{\circ} \mathrm{C}$. What is $\mathrm{K}_{\mathrm{a}}$ of fluoro acetic acid ? (For water, $\mathrm{K}_{\mathrm{f}}=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$ ). Assume molarity and molality to have same values

The solubility product constants of $\mathrm{Ag}_{2} \mathrm{CrO}_{4}$ and AgBr are 32x and 4y respectively at 298 K .

The value of $\left(\frac{\text { molarity of } \mathrm{Ag}_{2} \mathrm{CrO}_{4}}{\text { molarity of } \mathrm{AgBr}}\right)$ can be expressed as :

An electrochemical cell is constructed using half cells in the direction of spontaneous change $\mathrm{Fe}(\mathrm{OH})_{2}(\mathrm{~s})+2 \mathrm{e}^{-} \rightarrow \mathrm{Fe}(\mathrm{s})+2 \mathrm{OH}(\mathrm{aq}) \quad \mathrm{E}^{0}=-0.88 \mathrm{~V}$ and $\operatorname{AgBr}(\mathrm{s})+\mathrm{e}^{-} \rightarrow \operatorname{Ag}(\mathrm{s})+\operatorname{Br}^{-}(\mathrm{aq}) \mathrm{E}^{0}=+0.07 \mathrm{~V}$ Which of the following option is correct?

Given below are two statements :

Statement (I) : The first ionisation enthalpy of the elements $\mathrm{Na}, \mathrm{Mg}, \mathrm{Cl}$ and Ar follows the order $\mathrm{Na}>\mathrm{Mg}>\mathrm{Cl}>\mathrm{Ar}$

Statement (II) : Among $\mathrm{Ca}, \mathrm{Al}, \mathrm{Fe}$ and B , the third ionisation enthalpy is very high for Ca .

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

Given below are two statements :

Statement (I) : Oxidising power of halogens decreases in the order $\mathrm{F}_{2}>\mathrm{Cl}_{2}>\mathrm{Br}_{2}>\mathrm{I}_{2}$, which is the basis of Layer test.

Statement (II): Layer test to identify $\mathrm{Br}_{2}$ and $\mathrm{I}_{2}$ in aqueous solution involves the oxidation of bromide or iodide into $\mathrm{Br}_{2}$ or $\mathrm{I}_{2}$ respectively with $\mathrm{Cl}_{2}$, which is a type of displacement redox reaction.

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

Which of the following sets includes all the species that will change the orange colour of $\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}$ in acidic medium?

Match List - I with List - II.

Choose the correct answer from the options given below:

Given below are two statements :

Statement (I) : 1,2,3-Trihydroxypropane can be separated from water by simple distillation.

Statement (II) : An azotropic mixture cannot be separated by fractional distillation.

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

Given below are two statements :

Statement (I) : Benzyl chloride reacts faster in $\mathrm{S}_{\mathrm{N}} 1$ mechanism than ethyl chloride.

Statement (II) : Ethyl carbocation intermediate is less stabilized by hyperconjugation than benzyl carbocation by resonance.

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

In IUPAC nomenclature, the correct order of decreasing priority of functional group is :

Match List-I with List-II.

Choose the correct answer from the options given below :

Match List-I with List-II.

Choose the correct answer from the options given below:

A salt with few drops of conc. HCl gives apple green colour in flame test. The group precipitate of the salt is dissolved in acetic acid and treated with $\mathrm{K}_{2} \mathrm{CrO}_{4}$ to give yellow precipitate. When the sodium carbonate extract of the salt solution is heated with conc. $\mathrm{HNO}_{3}$ and ammonium molybdate, it resulted a canary yellow precipitate. The cation and anion present in the salt are respectively.

5.33 g of $\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}$, which is a $1: 3$ electrolyte, is dissolved in water and is passed through a cation exchanger. The chloride ions in the eluted solution, on treatment with $\mathrm{AgNO}_{3}$, results in 8.61 g of AgCl . The ratio of moles of complex reacted and moles of AgCl formed is $\_\_\_\_$ $\times 10^{-2}$. (Nearest integer) [Molar mass in $\mathrm{g} \mathrm{mol}^{-1} \mathrm{Cr}: 52, \mathrm{Ag}: 108, \mathrm{Cl}: 35.5$, $\mathrm{H}: 1, \mathrm{O}: 16]$

One mole of an alkane (x) requires 8 mole oxygen for complete combustion. Sum of number of carbon and hydrogen atoms in the alkane ( x ) is $\_\_\_\_$ .

For reaction $\mathrm{A} \rightarrow \mathrm{P}$, rate constant $\mathrm{k}=1.5 \times 10^{3} \mathrm{~s}^{-1}$ at $27^{\circ} \mathrm{C}$. If activation energy for the above reaction is $60 \mathrm{~kJ} \mathrm{~mol}^{-1}$, then the temperature (in ${ }^{\circ} \mathrm{C}$ ) at which rate constant, $\mathrm{k}=4.5 \times 10^{3} \mathrm{~s}^{-1}$ is $\_\_\_\_$ . (Nearest integer) Given : $\log 2=0.30, \log 3=0.48, \mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$, $\ln 10=2.3$

At the transition temperature $\mathrm{T}, \mathrm{A} \rightleftharpoons \mathrm{B}$ and $\Delta \mathrm{G}^{0}=105-35 \log \mathrm{~T}$ where A and B are two states of substance X . The transition temperature in ${ }^{\circ} \mathrm{C}$ when pressure is 1 atm is $\_\_\_\_$ . (Nearest integer)

Let the mid points of the sides of a triangle ABC be $\left(\frac{5}{2},7\right),\left(\frac{5}{2},3\right)$ and (4,5). If its incentive is (h, k), then $3\mathrm{h} + \mathrm{k}$ is equal to: