List of top Questions asked in JEE Main- 2026

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

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 _________.

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

The value of the integral $\int_{\pi/6}^{\pi/3} \left( \frac{4 - \csc^2 x}{\cos^4 x} \right) dx$ is:

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

The value of the integral $\int_0^\infty \frac{\log_e (x)}{x^2 + 4} dx$ is:

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

The square of the distance of the point of intersection of the lines $\vec{r} = (\hat{i} + \hat{j} - \hat{k}) + \lambda(a\hat{i} - \hat{j})$, $a \neq 0$ and $\vec{r} = (4\hat{i} - \hat{k}) + \mu(2\hat{i} + a\hat{k})$ from the origin is:

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 $\vec{r} \times \vec{a} + \vec{a} \times \vec{b} = \vec{0}$ and $\vec{r} \cdot \vec{a} = 0$, then $|3\vec{r}|^2$ is equal to:

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

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:

Let P be a moving point on the circle $x^2 + y^2-6x-8y + 21 = 0$. Then, the maximum distance of P from the vertex of the parabola $x^2 + 6x + y + 13 = 0$ is equal to:

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 P(3, $\alpha$) lies on E and O is the origin, then the area of $\Delta$POS is equal to:

The mean deviation about the mean for the data

56 is equal to:

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

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

The sum $\sum_{n=1}^{10} \frac{528}{n(n+1)(n+2)}$ is equal to:

Let A be a 3 x 3 matrix such that
$A^T \begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix} = \begin{pmatrix} 5 \\ 2 \\ 2 \end{pmatrix}$, $A \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} = \begin{pmatrix} 3 \\ 1 \\ 1 \end{pmatrix}$, $A \begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix} = \begin{pmatrix} 3 \\ 4 \\ 4 \end{pmatrix}$ and $A \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} = \begin{pmatrix} 1 \\ 3 \\ 1 \end{pmatrix}$
If det(A) = 1, then det(adj($A^2$ + A)) is equal to:

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:

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

The correct statements among the following are:
A. Mo(VI) and W(VI) are less stable than Cr(VI).
B. Ce⁴⁺ and Tb⁴⁺ are oxidant while Eu²⁺ and Yb²⁺ are reductant.
C. Cm and Am have seven unpaired electrons.
D. Actinoid contraction is greater from element to element than lanthanoid contraction.
Choose the correct answer:

Statement I: The covalency of oxygen is generally two but it can exceed up to four. The oxidation state of oxygen in SO₂ is -2 and in OF₂ it is +2.
Statement II: The anomalous behaviour of oxygen when compared to the other elements of group 16 is due to its small size and high electronegativity.
In the light of the above statements, choose the correct answer:

A monoatomic anion (A⁻) has 45 neutrons and 36 electrons. Atomic mass, group in the periodic table and physical state at room temperature of the element (A) respectively are

Consider the first order reaction R → P. The fraction of molecules decomposed in the given first order reaction can be expressed as