List of top Questions asked in JEE Main- 2026

A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field $\vec{E}_1 = E_0 \hat{x}$. If another electric field $\vec{E}_2 = 2E_0 (\hat{y} + \hat{z})$ is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)?

A river of width 200 m is flowing from west to east with a speed of 18 km/h. A boat, moving with speed of 36 km/h in still water, is made to travel one-round trip (bank to bank of the river). Minimum time taken by the boat for this journey and also the displacement along the river bank are _________ and _________} respectively.

\( \text{SF}_4 \) is isostructural with:

Two blocks of masses 2 kg and 1 kg respectively are tied to the ends of a string which passes over a light frictionless pulley as shown in the figure below. The masses are held at rest at the same horizontal level and then released. The distance traversed by the centre of mass in 2 s is _______ m.

A point light source emits E.M. waves in free space. A detector, placed at a distance of $L$ m, measures the intensity as $I_0$. The detector is now shifted to another location on the same spherical surface ensuring the angle between original location and new location as $45^{\circ}$. The measured intensity at new location will be ————.

The energy released when $\frac{7}{17.13} \text{ kg}$ of ${}^7_3\text{Li}$ is converted into ${}^4_2\text{He}$ by proton bombardment is $\alpha \times 10^{32} \text{ eV}$. The value of $\alpha$ is ____. (Nearest integer)
(Mass of ${}^7_3\text{Li} = 7.0183 \text{ u}$, mass of ${}^4_2\text{He} = 4.004 \text{ u}$, mass of proton $= 1.008 \text{ u}$ and $1 \text{ u} = 931 \text{ MeV}/c^2$ and Avogadro number $= 6.0 \times 10^{23}$)

If \( 26 \left( \dfrac{2^3 \cdot \binom{12}{2}}{3} + \dfrac{2^5 \cdot \binom{12}{4}}{5} + \dots + \dfrac{2^{13} \cdot \binom{12}{12}}{13} \right) = 3^{13 - \alpha} \), then find the value of \( \alpha \).

Two blocks ($P$ and $Q$) with respectively masses $2\text{ kg}$ and $1.5\text{ kg}$ are joined by a massless thread. These blocks are mounted on a frictionless pully which is fixed on the edge of a cube $(S)$, as shown in the figure below. Block $P$ is positioned on the top surface which has no friction and block $Q$ is in contact with side-surface, having coefficient friction $\mu$. The cube $(S)$ moves towards the right with acceleration of $\frac{g}{2}$, where $g$ is gravitational acceleration. During this movement the block $P$ and $Q$ remain stationary. The value of $\mu$ is ______. (take $g = 10\text{ m/s}^2$)

If \(\int_0^{\pi/4} \left[ \cot(x - \frac{\pi}{3}) - \cot(x + \frac{\pi}{3}) + 1 \right] dx = \alpha \log(\sqrt{3} - 1)\) then \(9\alpha\) is

The mean & variance of \(x_1, x_2, x_3, x_4\) is 1 and 13 respectively and the mean and variance of \(y_1, y_2, \dots, y_6\) be 2 and 1 respectively, the variance of \(x_1, x_2, \dots, x_4, y_1, y_2, \dots, y_6\) will be

The number of values of \(z \in \mathbb{C}\) satisfying \(|z-4-8i| = \sqrt{10}\) and \(|z-3-5i| + |z-5-11i| = 4\sqrt{5}\) is

Locus of the mid-point of chord of circle \(x^2 + y^2 - 6x - 8y - 11 = 0\), subtending a right angle at the center is

Let \( \frac{x^2}{f(a^2 + 2a + 7)} + \frac{y^2}{f(3a + 14)} = 1 \) represent an ellipse. The major axis of the given ellipse is the y-axis and \( f \) is a decreasing function. If the range of \( a \) is \( R - [\alpha, \beta] \), then \( \alpha + \beta \) is:

A person has 3 different bags & 4 different books. The number of ways in which he can put these books in the bags so that no bag is empty, is

If \( \alpha = 3 + 4 + 8 + 9 + 13 + \dots \) up to 40 terms and \( (\tan \beta)^{\frac{\alpha}{1020}} \) is the root of the equation \( x^2 - x - 2 = 0 \), then the value of \( \sin^2 \beta + 3\cos^2 \beta \) is:

The line passing through point of intersection of \(3x + 4y = 1\) and \(4x + 3y = 1\) intersects axes at P and Q, then locus of midpoint of PQ is

Let \(\vec{a} = 4\hat{i} - \hat{j} + 3\hat{k}\), \(\vec{b} = 10\hat{i} + 2\hat{j} - \hat{k}\) and a vector \(\vec{c}\) be such that \(2(\vec{a} \times \vec{b}) + 3(\vec{b} \times \vec{c}) = 0\). If \(\vec{a} \cdot \vec{c} = 15\), then the value of \(\vec{c} \cdot (\hat{i} + \hat{j} - 3\hat{k})\) is

A person goes to college either by bus, scooter or car. The probability that he goes by bus is \(\frac{2}{5}\), by scooter is \(\frac{1}{5}\) and by car is \(\frac{3}{5}\). The probability that he entered late in college if he goes by bus is \(\frac{1}{7}\), by scooter is \(\frac{3}{7}\) and by car is \(\frac{1}{7}\). If it is given that he entered late in college, then the probability that he goes to college by car is

Statement 1: \( f(x) = e^{|\sin x| - |x|} \) is differentiable for all \( x \in \mathbb{R} \).
Statement 2: \( f(x) \) is increasing in \( x \in \left( -\pi, -\frac{\pi}{2} \right) \).

If \((x\sqrt{1-x^2}) \, dy - (y\sqrt{1-x^2} - x^2 \cos^{-1} x) \, dx = 0\) and \(\lim_{x \to 1^-} y(x) = 1\), then \(y\left(\frac{1}{2}\right)\) is

If \(\alpha = 3\sin^{-1}\left(\frac{6}{11}\right)\) and \(\beta = 3\cos^{-1}\left(\frac{4}{9}\right)\), consider statements:
Statement 1: \(\cos(\alpha + \beta) > 0\)
Statement 2: \(\cos\alpha < 0\)
Then which of the following is true?

Which of the following statement is correct about Hoffmann’s bromamide degradation reaction?
(a) Alkyl amide do not react.
(b) Secondary amide do not form secondary amide.
(c) Ratio of NaOH and Br₂ is 4 : 2.
(d) Na₂CO₃, NaBr and H₂O also formed along with amine.

Product is:

Find total number of aromatic compounds from the given organic molecules.