List of top Questions asked in JEE Main- 2026

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 \( \alpha, \beta \) 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:

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:

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 \( 1^3 - 2^3 + 3^3 - 4^3 + \dots + 15^3 \) 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:

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.

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:

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.

\( \int_{-\pi/4}^{\pi/4} \frac{32 \cos^4 \theta}{1 + e^{\sin \theta}} \, d\theta \) 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 \(h\).

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.

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

Consider the reaction:

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

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.

Select the correct statements : (a) Glucose has 2 anomeric forms.
(b) Both forms have difference in configuration at \(C_1\) carbon.
(c) \(\alpha\)-form has more melting point than \(\beta\)-form.
(d) Specific rotation of \(\alpha\)-form is \(+19^\circ\) and \(\beta\)-form has \(+112^\circ\).
(e) \(\alpha\)-form crystallises at \(307^\circ\) and \(\beta\)-form crystallises at \(371^\circ\).

Find dimensions of \( \dfrac{A}{B} \) if \[ \left( P + \frac{A^2}{B} \right) + \frac{1}{2}\rho V^2 = \text{constant}, \] where \( P \rightarrow \) pressure, \( \rho \rightarrow \) density, \( V \rightarrow \) speed.

If $Z$ be a complex number such that $|Z + 2| = |Z - 2|$ and $\text{arg} \left( \frac{Z - 3}{Z + 1} \right) = \frac{\pi}{4}$, then the value of $|Z|^2$ is

Let mean and median of 9 observations 8, 13, a, 17, 21, 51, 103, b, 67 are 40 and 21 respectively where a > b. If mean deviation about median is 26 then 2a is :-

If $f(x)$ is a non-constant polynomial satisfying $f(x) = f'(x)f''(x)$ and $f(0) = 0$. Then the value of $\int_0^2 f(x) dx + f'(2) + f''(2)$ is :

A particle is moving along the \(x\)-axis where the speed varies as \[ v^2 = 100 - x^2 \] Determine the time period.

Let in a $\triangle ABC$, given that $A \equiv (1, 2)$, mid-point of $AB$ is $(-5, -1)$ and centroid is $(3, 4)$ then circumcentre is $(\alpha, \beta)$, then the value of $21(\alpha + \beta)$ is :