List of top Questions asked in JEE Main- 2026

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

If \( 3\sin t - 12\cos t - 3 = p \), then the sum of all integral values of 'p' such that the equation has at least one real root, is:

If \( \tan A \) and \( \tan B \) are roots of the equation \( x^2 - 2x - 5 = 0 \), then the value of \( 10\left(\sin^2\left(\frac{A+B}{2}\right)\right) \) is:

If the system of equations (in variables \(x, y, z\)): \(x - 2y + tz = 0\), \(3x + 5y + t^2 z = 0\), and \(6x + ty + f(t)z = 0\) has infinitely many solutions (where \(f(t)\) represents a real function), then:

If \( \vec{r} \times \vec{a} + \vec{a} \times \vec{b} = \vec{0} \), \( \vec{a} = \sqrt{7}\hat{i} + \hat{j} + \hat{k} \), \( \vec{b} = \hat{j} - 2\hat{k} \) and \( \vec{r} \cdot \vec{a} = 0 \), then the value of \( |3\vec{r}|^2 \) is:

On a postcard one of the two words either KANPUR or ANANTPUR is written. If only two consecutive letters AN are visible on the postcard, then the probability that the written word is ANANTPUR, is:

If \( \alpha = \frac{\pi}{4} + \sum_{p=1}^{11} \tan^{-1} \left( \frac{2^{p-1}}{1 + 2^{2p-1}} \right) \), then the value of \( \tan(\alpha) \) is:

If \( \alpha, \beta \) are the roots of the quadratic equation \( ax^2 + bx + c = 0 \) and \( |\alpha - \beta| = \sqrt{11} \), \( \alpha + \beta = 3i \), then the value of \( (\alpha^3 - \beta^3) \) is:

Consider an equilateral \( \Delta PQR \), where \( P(3, 5) \) and the side \( QR \) lies on the line \( x + y = 4 \). If the orthocentre of \( \Delta PQR \) is \( (\alpha, \beta) \), then \( 9(\alpha + \beta) \) is equal to:

If \( S_1: x^2 + y^2 - 6x - 8y + 21 = 0 \) and \( S_2: x^2 + y^2 + 6x + 8y + \lambda = 0 \), then the distance of the centre of \( S_2 \) to the farthest point on \( S_1 \) is:

A and B play a tennis match which will not result in a draw. The player who wins 5 rounds first will be the winner of the match. The number of ways such that A can win the match is:

The area enclosed between the region given by \( xy \le 27 \) and \( 1 \le y \le x^2 \) is:

Let \( S_n \) be the sum of the first \( n \) terms of an A.P. If \( S_n = 3n^2 + 5n \), then the sum of the squares of the first 10 terms of the given A.P. is:

The value of \( \lim_{x \to 0} \frac{x^2 \sin^2 x}{x^2 - \sin^2 x} \) is equal to:

In the expansion of \( (1 + \alpha x)^{26} \) and \( (1 - \alpha x)^{28} \), the coefficient of the middle term is the same, then the value of \( \alpha \) is:

An object is placed in air (\(n_1 = 1\)) at a distance \(4R\) from a spherical refracting surface that separates air from a medium of refractive index \(n_2 = 1.4\). The surface has a radius of curvature \(R\), with its centre lying in the second medium. Find the magnitude of magnification of the image formed.

\( \int_{-\pi/4}^{\pi/4} \frac{32 \cos^4 \theta}{1 + e^{\sin \theta}} \, d\theta \) is equal to:

A block of mass \(m\) is released from height \(h\) on a smooth plane. If the normal force on the top of the circular part is \(3mg\), find \(h\).

In an AC series circuit supply voltage \(V_{\text{rms}} = 100\) volts; \(R = 80\,\Omega\), \(X_L = 80\,\Omega\) and source frequency is \(f = 50\) Hz. Find the power factor.

The value of \( 1^3 - 2^3 + 3^3 - 4^3 + \dots + 15^3 \) is equal to:

Consider the reaction:

Find the number of moles of benzene formed if the efficiency of reaction is 60%.

Electric field at the centre of a semi-circular ring of radius \(10\,\text{cm}\) is \(100\,\text{V/m}\). Find the charge on the ring if the charge distribution is uniform.

If \( x_1, x_2, \dots, x_{25} \) be 25 observations such that \( \sum_{i=1}^{25} (x_i + 5)^2 = 2500 \) and \( \sum_{i=1}^{25} (x_i - 5)^2 = 1000 \). Then, the ratio of Mean and Standard deviation of the given observations is:

Match the following:

Sucrose hydrolyses in acidic medium to form glucose and fructose which follows first order kinetics. If the half-life of sucrose is 3 hrs, find the % of sucrose left after 6 hrs.