JEE Main 2026 (Online) 28th January Evening Shift

The reactions which produce alcohol as the product are :
A. $\mathrm{CH}_4 + \mathrm{O}_2 \xrightarrow{\mathrm{Mo}_2\mathrm{O}_3,\ \Delta} $
B. $2\mathrm{CH}_3\mathrm{CH}_3 + 3\mathrm{O}_2 \xrightarrow{(\mathrm{CH}_3\mathrm{COO})_2\mathrm{M...

The correct order of acidic strength of the major products formed in the given reactions, is :A. $\mathrm{PhNH}_2 \xrightarrow[\substack{\text { (2) } \mathrm{CuCN}^2 \\ \text { (3) } \mathrm{H}_3 \mathrm{O}^{+} / \Delta}]{\text { (1) } \ma...

Which of the following reaction is NOT correctly represented?

Identify the correct statements :The presence of –NO2 group in benzene ringA. activates the ring towards electrophilic substitutions.B. deactivates the ring towards electrophilic substitutions.C. activates the ring towards nucleophilic subs...

The cyclic cations having the same number of hyperconjugation are :Choose the correct answer from the options given below :

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

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




List – I

List – II







A.  XeO3

B.  XeF2

C.  XeO2F2

D.  XeOF4





I.  BrF5

II.  NH3

III.  [I3]−

IV.  ...

Observe the following equilibrium in a 1 L flask. A(g) ⇌ B(g) At T(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 T(K) to establish the equilibrium agai...

A → B (first reaction)C → 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 hour. The activatio...

A student performed analysis of aliphatic organic compound ‘X’ which on analysis gave C = 61.01%, H = 15.25%, N = 23.74%.This compound, on treatment with HNO2/H2O produced another compound ‘Y’ which did not contain any nitrogen atom. Howeve...

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-propyla...

The correct increasing order of spin-only magnetic moment values of the complex ions
[MnBr4]2− (A), [Cu(H2O)6]2+ (B), [Ni(CN)4]2− (C) and [Ni(H2O)6]2+ (D) is :

The number of isoelectronic species among $Sc^{3+}, Cr^{2+}, Mn^{3+}, Co^{3+}$ and $Fe^{3+}$ is ‘n’. If ‘n’ moles of AgCl is formed during the reaction of complex with formula $CoCl_3(en)_2NH_3$ with excess of $AgNO_3$ solution, then the nu...

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 ...

A volume of x mL of 5 M NaHCO3 solution was mixed with 10 mL of 2 M H2CO3 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 mV, then the value of x...

For strong electrolyte $\Lambda_m$ increases slowly with dilution and can be represented by the equation\(\Lambda_m = \Lambda_m^\circ - A c^{1/2}\)Molar conductivity values of the solutions of strong electrolyte AB at 18°C are given below :...

Consider the following reactions$\mathrm{Na_2B_4O_7} \xrightarrow{\Delta} 2X + Y\(\mathrm{CuSO_4} + Y \xrightarrow{\text{Non-Luminous flame}} Z + SO_3\)2Z + 2X + \text{Carbon} \xrightarrow{\text{Luminous flame}} 2Q + \mathrm{Na_2B_4O_7} + C...

Given below are two statements :Statement I : The increasing order of boiling point of hydrogen halides is HCl < HBr < HI < HF.Statement II : The increasing order of melting point of hydrogen halides is HCl < HBr < HF < HI.In the light of t...

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

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...

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 incr...

For the given reaction;CaCO3 + 2HCl → CaCl2 + H2O + CO2If 90 g CaCO3 is added to 300 mL of HCl which contains 38.55% HCl by mass and has density 1.13 g mL−1, then which of the following option is correct?Given molar mass of H, Cl, Ca and O ...

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

Two positively charged particles $m_1$ and $m_2$ have been accelerated across the same potential difference of 200 keV as shown below.[Given mass of $m_1 = 1$ amu and $m_2 = 4$ amu]The deBroglie wavelength of $m_1$ will be $x$ times of $m_2...

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

Let Q(a, b, c) be the image of the point 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

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 $P_1$ and $P_2$ is six times the area of the bounded region enclosed between the line $y = \alpha x$, $\alpha > 0$ and $P_1$,...

Given below are 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 ...

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

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

Let$A = \{ z \in \mathbb{C} : |z - 2| \leq 4 \}$ and$B = \{ z \in \mathbb{C} : |z - 2| + |z + 2| = 5 \}$.Then the max $\{|z_1 - z_2| : z_1 \in A \text{ and } z_2 \in B \}$ is :

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

Let $f$ be a differentiable function satisfying $f(x) = 1 - 2x + \int\limits_0^x e^{(x-t)} f(t)\,dt$, $x \in \mathbb{R}$ and let $g(x) = \int\limits_0^x (f(t) + 2)^{15} (t - 4)^6 (t + 12)^{17}\,dt$, $x \in \mathbb{R}$. If $p$ and $q$ are re...

Let $y = y(x)$ 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 t...

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 :

Given below are two statements :
Statement I : The function $f: \mathbb{R} \to \mathbb{R}$ defined by $f(x) = \frac{x}{1 + |x|}$ is one-one.
Statement II : The function $f: \mathbb{R} \to \mathbb{R}$ defined by $f(x) = \frac{x^2 + 4x - 30}{...

The sum of all the elements in the range of $f(x) = \text{Sgn}(\sin x) + \text{Sgn}(\cos x) + \text{Sgn}(\tan x) + \text{Sgn}(\cot x)$, $x \neq \frac{n\pi}{2}, n \in \mathbb{Z}$, where
$\text{Sgn}(t) = \begin{cases} 1, & \text{if } t > 0 \...

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

Let \(f(x)=\int \frac{d x}{x^{2 / 3}+2 x^{1 / 2}},\) be such that $f(0) = -26 + 24 \log_e(2)$. If $f(1) = a + b \log_e(3)$, where $a, b \in \mathbb{Z}$, then $a + b$ is equal to :

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 :

Let $f(x) = \lim\limits_{\theta \to 0} \left( \frac{\cos \pi x - x^\left( \frac{2}{\theta} \right) \sin(x-1)}{1 + x^\left( \frac{2}{\theta} \right) (x-1)} \right),\ x \in \mathbb{R}$. Consider the following two statements :(I) $f(x)$ is dis...

Let $A = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix}$ and $B$ be two matrices such that $A^{100} = 100B + I$. Then the sum of all the elements of $B^{100}$ is _______

Let A be the focus of the parabola $y^2 = 8x$. Let the line $y = mx + c$ 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 $(BC)^2$ is equal to :

Three persons enter in a lift at the ground floor. The lift will go up to 10th 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, i...

The probability distribution of a random variable X is given below :table {width: 100%;border-collapse: collapse;margin: 20px 0;}th {background-color: blue;color: white;border: 1px solid lightgrey;padding: 10px;}td {border: 1px solid lightg...

Let the arithmetic mean of $\frac{1}{a}$ and $\frac{1}{b}$ be $\frac{5}{16}$, $a > 2$. If $\alpha$ is such that $a$, $4$, $\alpha$, $b$ are in A.P., then the equation $\alpha x^2 - a x + 2(\alpha - 2b) = 0$ has :

$ \frac{6}{3^{26}} + \frac{10 \cdot 1}{3^{25}} + \frac{10 \cdot 2}{3^{24}} + \frac{10 \cdot 2^2}{3^{23}} + \ldots + \frac{10 \cdot 2^{24}}{3} $ is equal to :

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

Let P be a point in the plane of the vectors $\overrightarrow{AB}=3\hat{i} + \hat{j} - \hat{k}$ and $\overrightarrow{AC}=\hat{i} - \hat{j} + 3\hat{k}$ such that P is equidistant from the lines AB and AC. If $|\overrightarrow{AP}| = \frac{\s...

If the distance of the point $P(43, \alpha, \beta)$, $\beta < 0$, from the line $\vec{r} = 4\hat{i} - \hat{k} + \mu (2\hat{i} + 3\hat{k}), \mu \in \mathbb{R}$ along a line with direction ratios $3, -1, 0$ is $13\sqrt{10}$, then $\alpha^2 + ...