JEE Main-2026 , 8th April 2nd shift

Which of the following are not correct ?

A. For water, magnitude of K_b is more than the magnitude of K_f.

B. The elevation in boiling point of water when a non-volatile solute is added to it is larger in magnitude than its depression in freezing point.

C. Osmotic pressure measurement is preferred over any other colligative property to determine molar mass of proteins and polymers.

D. The dimerised form of benzoic acid in benzene is C₆H₅—C(=O)—OH .... O=C(OH)—C₆H₅.

Two point charges q₁ = 3μC and q₂ = −4μC are placed at points (2î + 3ĵ + 3k̂) and (î + ĵ + k̂) respectively. Force on charge q₂ is __________ N. (Take 1/4πε₀ = 9 × 10⁹ SI Units)

Match List-I with List-II.

Let a line L₁ pass through the origin and be perpendicular to the lines

$\text{If }(a,b,c),a\in \mathbb{Z}$

is the point on L₃ at a distance of 17 from the point of intersection of L₁ and L₂ , then (a + b + c)² is equal to _______.

A parallel plate capacitor is having separation between plates 0.885 mm. It has a capacitance of 1 μF when the space between the plates is filled with an insulating material of resistivity 1 × 10¹³ Ωm and resistance 17.7 × 10¹⁴ Ω. Relative permittivity of the insulating material is α × 10⁷. The value of α is __________.

(Take permittivity of free space = 8.85 × 10^–12 F/m)

Match List-I with List-II.

Let f be a polynomial function such that

${\log }_3\left(1+\frac{f(x)}{f\left(\frac{1}{x}\right)}\right)$ , x > 0 , f(6) = 37

then

${\sum }_{n=1}^{10}f(n)\text{ is equal to }\underline{}.$

Consider the reaction :

$2H_{2}S(g)+3O_2(g)\to 2H_{2}O(l)+2S{O}_2(g)$

The magnitude of enthalpy change for the reaction in kJ mol^-1 is ________. (Nearest integer)

Given:

${\Delta }_f{H}^{\circ }(H_{2}S)=-20.1\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$

${\Delta }_f{H}^{\circ }(H_{2}O)=-286.0\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$

${\Delta }_f{H}^{\circ }(S{O}_2)=-297.0\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$

Let the foot of the perpendicular from the point (λ,2,3) on the line $\frac{x-4}{1}=\frac{y-9}{2}=\frac{z-5}{1}$ be the point (1,μ,2). Then the distance between the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z+4}{6}$ and $\frac{x-\lambda }{2}=\frac{y-\mu }{3}=\frac{z+5}{6}$ is equal to:

Let $\alpha =3+4+8+9+13+14+\cdots (upto40terms)$.

If $(\tan \beta {)}^{\frac{\alpha }{1020}}$ is a root of the equation $x^2+x-2=0$, $\beta \in \left(0,\frac{\pi }{2}\right)$, then ${\sin }^2\beta +3{\cos }^2\beta$ is equal to:

Let $\frac{x^2}{f(a^2+7a+3)}+\frac{y^2}{f(3a+15)}=1$ represent an ellipse with major axis along the y-axis, where f is a strictly decreasing positive function on R. If the set of all possible values of a is R-$[\alpha ,\beta ]$, then ${\alpha }^2+{\beta }^2$ is equal to:

Consider two radiations of wavelengths:

1. λ₁ = 2000 Å

2. λ₂= 6000 Å

The ratio of the energies of these two radiations (E₁/E₂) is ________. (Nearest integer)

The sum of squares of all real solution of the equation

${\log }_{(x+1)}(2x^2+5x+3)=4-{\log }_{(2x+3)}(x^2+2x+1)$

is equal to _______.

The total number of aromatic compounds/species from the following is

K₁ and K₂ be the maximum kinetic energies of photoelectrons emitted from a surface of a given material for the light of wavelength λ₁ and λ₂, respectively. If λ₁ = 2 λ₂ then the work function of material is given by :

If the system of linear equations:

x + y + z = 6,

x + 2y + 5z = 10,

2x + 3y + $\lambda z=\mu$

, has infinitely many solutions, then the value of $\lambda +\mu$ equals.

Find the correct statements related to group 15 hydrides.

A. Reducing nature increases from NH₃ to BiH₃

B. Tendency to donate lone pair of electrons decreases from NH₃ to BiH₃

C. The stability of hydrides decreases from NH₃ to BiH₃

D. HEH bond angle decreases from NH₃ to SbH₃ (E = Elements of group 15)

Choose the correct answer from the options given below

Let $\vec{a}=4\hat{i}-\hat{j}+3\hat{k}$, $\vec{b}=10\hat{i}+2\hat{j}-\hat{k}$ and a vector $\vec{c}$ be such that $2(\vec{a}\times \vec{b})+3(\vec{b}\times \vec{c})=\vec{0}$.

If $\vec{a}\cdot \vec{c}=15$, then $\vec{c}\cdot (\hat{i}+\hat{j}-3\hat{k})$ is equal to:

Let

$A=\left[\begin{array}{ccc}\alpha & amp;1& amp;2\\ 2& amp;3& amp;0\\ 0& amp;4& amp;5\end{array}\right]$ and

$B=\left[\begin{array}{ccc}1& amp;0& amp;0\\ 0& amp;-5\alpha & amp;0\\ 0& amp;4\alpha & amp;-2\alpha \end{array}\right]+\mathrm{adj}(A).If\det (B)=66,$

then $\det (\mathrm{adj}(A))$ equals:

Given at 298 K :

$E_{{\mathrm{Fe}}^{2+}/\mathrm{Fe}}^{\circ }=X\text{Volt}$

$E_{{\mathrm{Fe}}^{3+}/\mathrm{Fe}}^{\circ }=Y\text{Volt}$

The $E_{{\mathrm{Fe}}^{3+}/{\mathrm{Fe}}^{2+}}^{\circ }$ in Volt at 298 K is given by :

Let y = y(x) be the solution of the differential equation

$x\sqrt{1-x^2}dy$ +$\left(y\sqrt{1-x^2}-x{\cos }^{-1}x\right)dx=0$, where $x\in (0,1)$,

${\lim }_{x\to 1^{-}}y(x)=1$, . Then $y\left(\frac{1}{2}\right)$ is equal to:

Two masses of 3.4 kg and 2.5 kg are accelerated from an initial speed of 5 m/s and 12 m/s, respectively. The distances traversed by the masses in the 5^th second are 104 m and 129 m, respectively. The ratio of their momenta after 10 s is $\frac{x}{8}$. The value of x is __________.

Let $f(x)=\{\begin{array}{llc}\frac{1}{3},& amp;x\le \frac{\pi }{2}& \\ \frac{b(1-\sin x)}{(\pi -2x{)}^2},& amp;x& gt;\frac{\pi }{2}\end{array}$

If f is continuous at $x=\frac{\pi }{2}$, then the value of ${\int }_0^{3b-6}|x^2+2x-3|dx$ is:

Some distance star is to be observed by some telescope of diameter of objective lens a, at an angular resolution of 3.0 × 10^-7 radian. If the wavelength of light from the star reaching the telescope is 500 nm, the minimum diameter of the objective lens of the telescope is __________ cm. (Nearest integer)

Given below are two statements for catalytic properties of transition metals :

Statement I : First row transition metals which act as catalyst utilise their 3d electrons only for formation of bonds between reactant molecules and atoms on the surface of catalyst.

Statement II : There is increase in the concentration of reactants on the surface of catalyst which strengthens the bonds in reacting molecules.

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

Let O be the vertex of the parabola y²=4x and its chords OP and OQ are perpendicular to each other. If the locus of the midpoint of the line segment PQ is a conic C, then the length of its latus rectum is:

Given below are two statements :

Given : Molar mass of C, H, O, Cl are 12, 1, 16 and 35.5 g mol⁻¹, respectively.

Statement I : In 30%(w/w) solution of methanol in CCl₄ (at T K), the mole fraction of CCl₄ is equal to 0.33.

Statement II : Mixture of methanol and CCl₄ shows positive deviation deviation from Raoult’s law.

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

A current carrying circular loop of radius 2 cm with unit normal $\hat{n}=\frac{\hat{k}+\hat{i}}{\sqrt{2}}$ is placed in a magnetic field, $\vec{B}=B_0\left(3\hat{i}+2\hat{k}\right)$. If $B_0=4\times 10^{-3}\text{T}$ and current I = 100√2 A, the torque experienced by the loop is __________ Wb.A. (π = 3.14)

If

then 9α is equal to_____.

The output Y for the given inputs A and B to the circuit is :

Given below are two statements :

Statement I : Vapours of the liquid with higher boiling point condense before vapours of the liquid with lower boiling points in fractional distillation.

Statement II : The vapours rising up in the fractionating column become richer in high boiling component of the mixture. In the light of the above statements,

choose the correct answer from the option given below :

Which statements are True?

A. In Hoffmann bromamide degradation, 4 moles of NaOH and 2 moles of Br₂ are consumed per mole of an amide.

B. Hoffmann bromamide reaction is not given by alkyl amides.

C. Primary amines can be synthesized by Hoffmann bromamide degradation.

D. Secondary amide on reaction with Br₂ and NaOH will give secondary amine.

E. The by-products of Hoffmann degradation are Na₂CO₃, NaBr and H₂O.

Choose the correct answer from the options given below :

Given below are two statements : R = 8.314 J K^-1 mol^-1 and 1 cal = 4.2 J

Statement I : When Ea = 12.6 kcal/mol, the room temperature rate constant is doubled by a 10°C increase in temperature (298 K to 308 K)

Statement II : For a first order reaction A → B,

Here [A]₀ is the initial concentration of A and t_1/2 is half-life of reaction.

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

Let $\alpha =3{\sin }^{-1}\left(\frac{6}{11}\right)$ and $\beta =3{\cos }^{-1}\left(\frac{4}{9}\right)$, where inverse trigonometric functions take only the principal values. Given below are two statements:

Statement I : cos(α + β) > 0

Statement II : cos(α) < 0

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

Given below are two statements :

Statement I : The number of pairs among [Ti⁴⁺, V²⁺], [V²⁺, Mn²⁺], [Mn²⁺, Fe³⁺] and [V²⁺, Cr²⁺] in which both ions are coloured is 3.

Statement II : The number of pairs among [La³⁺, Yb²⁺], [Lu³⁺, Ce⁴⁺] and [Ac³⁺, Lr³⁺] ions in which both are diamagnetic is 3.

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

Bromine trifluoride autoionizes to form $\mathrm{Br}{\mathrm{F}}_2^{+}\text{ and }\mathrm{Br}{\mathrm{F}}_4^{-}$ and BrF₄⁻. The shapes of the cation and anion are respectively ______, and ______.

For the function $f(x)=e^{\sin |x|}-|x|,x\in \mathbb{R}$, consider the following statements:

Statement I : f is differentiable for all x ∈ R.

Statement II : f is increasing in $\left(-\pi ,-\frac{\pi }{2}\right)$.

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

Consider the relation R on the set {-2,-1,0,1,2} defined by (a,b) ∈ R if and only if 1+ab>0.

Then among the statements:

I. The number of elements in R is 17

II. R is an equivalence relation

The stored charge in the capacitor in steady state of the following circuit is __________ μC.

A 5 mg particle carrying a charge of $5\pi \times 10^{-6}C$ is moving with velocity of $(3\hat{i}+2\hat{k})\times 10^{-2}$ m/s in a region having magnetic field $\vec{B}=0.1\hat{k}{\text{Wb/m}}^2$. It moves a distance of α meter along $\hat{k}$ when it completes 5 revolutions. The value of α is __________.

Number of paramagnetic complexes among the following is ________.

Light ray incident along a vector $\overrightarrow{AO}(\overrightarrow{AO}=2\hat{i}-3\hat{j})$ emerges out along vector $\overrightarrow{OB}(\overrightarrow{OB}=C\hat{i}-4\hat{j})$ as shown in the figure below. The value of C is __________.

Given below are two statements :

Statement-I : Due to increase in van der Waals forces, the order of boiling points is CH₃CH₂CH₂I > CH₃CH₂I > CH₃I.

Statement-II : As p-dichlorobenzene is more symmetric, its melting point is higher than o-dichlorobenzene, however its boiling point is lower than o-dichlorobenzene. In the light of the above statements, choose the correct answer from the options given below :

Solid carbon, CaO and CaCO₃ are mixed and allowed to attain equilibrium at T K.

$\mathrm{CaC}{\mathrm{O}}_3(s)\rightleftharpoons \mathrm{CaO}(s)+\mathrm{C}{\mathrm{O}}_2(g),K_{p1}=0.08\mathrm{atm}$

$\mathrm{C}(s)+\mathrm{C}{\mathrm{O}}_2(g)\rightleftharpoons 2\mathrm{CO}(g),K_{p2}=2\mathrm{atm}$

The partial pressure of CO is ______ × 10^-1 atm.

If

$26\left(\frac{2^3}{3}\left(\genfrac{}{}{0ex}{}{13}{2}\right)+\frac{2^5}{5}\left(\genfrac{}{}{0ex}{}{12}{4}\right)+\frac{2^7}{7}\left(\genfrac{}{}{0ex}{}{12}{6}\right)+\cdots +\frac{2^{13}}{13}\left(\genfrac{}{}{0ex}{}{12}{12}\right)\right)=3^{13}-\alpha ,$

then \alpha is equal to:

Consider the equation

Where H = magnetic field; E = electric field; ε = permittivity, x = distance, t = time. The values of p, q, r and s respectively are :

Consider the following reactions in which all the reactants and products are present in gaseous state

$2xy\rightleftharpoons x_2+y_2,K_1=2.5\times 10^5$

$xy+\frac{1}{2}{z}_2\rightleftharpoons xyz,K_2=5\times 10^{-3}$

The value of K₃ for the equilibrium

$\frac{1}{2}{x}_2+\frac{1}{2}{y}_2+\frac{1}{2}{z}_2\rightleftharpoons xyz\text{ is:}$

n-Butane on monochlorination under photochemical conditions gives an optically active compound “P”. “P” on further chlorination gives dichloro compounds.

The number of dichloro compounds obtained (ignore stereoisomers) is :

Let $f:(1,\infty )\to \mathbb{R}$ be defined by

$f(x)=\frac{x-1}{x+1}.If{f}^{i+1}(x)=f\left(f^i(x)\right),$

$i=1,2,\dots ,25$, where $f^0(x)=x,andg(x)+f^{26}(x)=0$, for $x\in (1,\infty )$, then the area of the region bounded by the curves y=g(x), 2y=2x-3, y=0, x=4 is:

Consider the circle C : x² + y² – 6x – 8y – 11 = 0. Let a variable chord AB of the circle C subtend a right angle at the origin. If the locus of the foot of the perpendicular drawn from the origin on the chord AB is the circle x² + y² – αx – βy – γ = 0, then α + β + 2γ is equal to_____.

A 30 cm long solenoid has 10 turns per cm and area of 5 cm². The current through the solenoid coil varies from 2 A to 4 A is 3.14 s. The e.m.f. induced in the coil is α × 10^-5 V. The value α is __________.

The value of the integral ${\int }_0^2\frac{\sqrt{x(x^2+x+1)}}{\sqrt{x+1}\sqrt{x^4+x^2+1}}dx$ is equal to:

A candidate has to go to the examination centre to appear in an examination. The candidate uses only one means of transportation for the entire distance out of bus, scooter and car. The probabilities of the candidate going by bus, scooter and car are respectively $\frac{2}{5}$,$\frac{1}{5}$and $\frac{2}{5}$. The probabilities that the candidate reaches late at the examination centre are $\frac{1}{5}$, $\frac{1}{3}$and $\frac{1}{4}$ if the candidate uses bus, scooter and car respectively. Given that the candidate reached late at the examination centre, the probability that the candidate travelled by bus is: