List of top Questions asked in JEE Main- 2026

A magnetic field vector in an electromagnetic wave is represented by
$\vec{B} = B_0 \sin \left( 2\pi \nu t - \frac{2\pi x}{\lambda} \right) \hat{j}$. Its associated electric field vector is _______.

The temperature of a metal strip having coefficient of linear expansion $\alpha$ is increased from $T_1$ to $T_2$ resulting in increase of its length by $\Delta L_1$. The temperature is further increased from $T_2$ to $T_3$ such that the increase in its length is $\Delta L_2$.
Given $T_3 + T_1 = 2T_2$ and $T_2 - T_1 = \Delta T$, the value of $\Delta L_2$ is ________.

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: If the average kinetic energy of $H_2$ and $O_2$ molecules, kept in two different sized containers are same, then their temperatures will be same.
Reason R: The r.m.s. speed of $H_2$ and $O_2$ molecules are same at same temperature.
Choose the correct answer from the options given below

A uniform disc of radius $R$ and mass $M$ is free to oscillate about the axis A as shown in the figure. For small oscillations the time period is _______.
(g is acceleration due to gravity)

If $x$ and $y$ coordinates of a projectile as a function of time $(t)$ are given as $24t$ and $43.6t - 4.9t^2$, respectively, then the angle (in degrees) made by the projectile with horizontal when $t = 2$ s is _______.

A water spray gun is attached to a hose of cross sectional area $30 \text{ cm}^2$. The gun comprises of 10 perforations each of cross sectional area of $15 \text{ mm}^2$. If the water flows in the hose with the speed of 50 cm/s, calculate the speed at which the water flows out from each perforation. (Neglect any edge effects)

A metal string A is suspended from a rigid support and its free end is attached to a block of mass M. Second block having mass 2M is suspended at the bottom of the first block using a string B. The area of cross sections of strings A and B are same. The ratio of lengths of strings of A to B is 2 and the ratio of their Young's moduli ($Y_A / Y_B$) is 0.5. The ratio of elongations in A to B is _______.

The height in terms of radius of the earth ($R$), at which the acceleration due to gravity becomes $g/9$, where $g$ is acceleration due to gravity on earth's surface, is

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

At $t = 0$, a body of mass 100 g starts moving under the influence of a force $(5\hat{i} + 10\hat{j})$ N. After 2 s its position is $(2x\hat{i} + 5y\hat{j})$ m. The ratio $x : y$ is______.

Let $f(x) = \begin{cases} e^{x-1}, & x<0 \\ x^2 - 5x + 6, & x \ge 0 \end{cases}$ and $g(x) = f(|x|) + |f(x)|$. If the number of points where $g$ is not continuous and is not differentiable are $\alpha$ and $\beta$ respectively, then $\alpha + \beta$ is equal to _______.

Let $f$ be a twice differentiable function such that $f(x) = \int_0^x \tan(t-x) dt - \int_0^x f(t) \tan t dt, x \in (-\frac{\pi}{2}, \frac{\pi}{2})$. Then $f''(\frac{\pi}{6}) + 12 f'(-\frac{\pi}{6}) + f(\frac{\pi}{6})$ is equal to ________.

Let A, B and C be the vertices of a variable right angled triangle inscribed in the parabola $y^2 = 16x$. Let the vertex B containing the right angle be $(4, 8)$ and the locus of the centroid of $\Delta ABC$ be a conic $C_0$. Then three times the length of latus rectum of $C_0$ is _______.

Let A, B be points on the two half-lines $x - \sqrt{3}|y| = \alpha, \alpha>0$ at a distance of $\alpha$ from their point of intersection P. The line segment AB meets the angle bisector of the given half-lines at the point Q. If $PQ = \frac{9}{2}$ and R is the radius of the circumcircle of $\Delta PAB$, then $\frac{\alpha^2}{R}$ is equal to ________

From a month of 31 days, 3 different dates are selected at random. If the probability that these dates are in an increasing A.P. is equal to $a/b$, where $a, b \in \mathbb{N}$ and $\gcd(a, b) = 1$, then $a + b$ is equal to _______

Let for some \(\alpha \in \mathbb{R}\), \(f: \mathbb{R} \rightarrow \mathbb{R}\) be a function satisfying \(f(x + y) = f(x) + 2y^2 + y + \alpha xy\) for all \(x, y \in \mathbb{R}\). If \(f(0) = -1\) and \(f(1) = 2\), then the value of \(\sum_{n=1}^{5} (\alpha + f(n))\) is:

Let \(A = \{ (a, b, c) : a, b, c \text{ are non-negative integers and } a + b + 2c = 22 \}\). Then \(n(A)\) is equal to:

The integral \(\int_{0}^{1} \cot^{-1}(1 + x + x^2) dx\) is equal to:

The area of the region bounded by the curves \(x + 3y^2 = 0\) and \(x + 4y^2 = 1\) is equal to:

Let \(\hat{u}\) and \(\hat{v}\) be unit vectors inclined at an acute angle such that \(|\hat{u} \times \hat{v}| = \frac{\sqrt{3}}{2}\). If \(\vec{A} = \lambda \hat{u} + \hat{v} + (\hat{u} \times \hat{v})\), then \(\lambda\) is equal to:

The shortest distance between the lines
\(\vec{r} = (\frac{1}{3}\hat{i} + \frac{8}{3}\hat{j} - \frac{1}{3}\hat{k}) + \lambda(2\hat{i} - 5\hat{j} + 6\hat{k})\)
and \(\vec{r} = (-\frac{2}{3}\hat{i} - \frac{1}{3}\hat{k}) + \mu(\hat{j} - \hat{k}), \lambda, \mu \in \mathbb{R}\), is:

Let \(H: \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) be a hyperbola such that the distance between its foci is 6 and the distance between its directrices is \(\frac{8}{3}\). If the line \(x = \alpha\) intersects the hyperbola H at the points A and B such that the area of the triangle AOB is \(4\sqrt{15}\), where O is the origin, then \(a^2\) equals:

If \((2\alpha + 1, \alpha^2 - 3\alpha, \frac{\alpha - 1}{2})\) is the image of \((\alpha, 2\alpha, 1)\) in the line \(\frac{x - 2}{3} = \frac{y - 1}{2} = \frac{z}{1}\), then the possible value(s) of \(\alpha\) is (are):

In the expansion of \(\left( 9x - \frac{1}{3\sqrt{x}} \right)^{18}, x>0\), if the term independent of \(x\) is \((221)k\), then \(k\) is equal to:

\(\max_{0 \leq x \leq \pi} \left( 16 \sin\left(\frac{x}{2}\right) \cos^3\left(\frac{x}{2}\right) \right)\) is equal to: