List of top Questions asked in JEE Main- 2026

Find the number of real solutions of \[ x|x-3|+|x-1|+3=0 \]

If \( O \) is the vertex of the parabola \( x^2 = 4y \), \( Q \) is a point on the parabola. If \( C \) is the locus of the point which divides \( OQ \) in the ratio \( 2:3 \), then the equation of the chord of \( C \) which is bisected at the point \( (1,2) \) is:

Find the sum of all real solutions of
$|x + 1|^2 - 4|x + 1| + 3 = 0$

Let $\vec{a}=2\hat{i}-5\hat{j}+5\hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+3\hat{k}$. If $\vec{c}$ is a vector such that $2(\vec{a}\times\vec{c})+3(\vec{b}\times\vec{c})=\vec{0}$ and $(\vec{a}-\vec{b})\cdot\vec{c}=-97$, then $|\vec{c}\times\hat{k}|^2$ is equal to

Let \[ f(x) = [x]^2 - [x+3] - 3,\quad x \in \mathbb{R}, \] where \([\,\cdot\,]\) denotes the greatest integer function. Then

Let \( \frac{x^2}{2} + \frac{y^2}{1} = 1 \) and \( y = x + 1 \) intersect each other at points A & B, then \( \angle AOB \) (where O is the centre of the ellipse) is:

If \[ \int e^x \left( \frac{x^2 - 2}{\sqrt{1 + x(1 - x)^{3/2}}} \right) \, dx = f(x) + c \quad \text{and} \quad f(0) = 1 \] find \( f\left( \frac{1}{2} \right) \):

If \( z = \dfrac{\sqrt{3}}{2} + \dfrac{i}{2} \), \( i = \sqrt{-1} \), then \[ \left(z^{201} - i\right)^8 \] is equal to

If \[ \int_0^6 \left( x^3 + \lfloor x^{1/3} \rfloor \right) \, dx = \alpha \] and \[ \int_0^{\frac{\pi}{2}} \frac{\sin^2 x}{\sin^6 x + \cos^6 x} \, dx = \beta, \] then the value of \( ab^2 \) is equal to:

If \( P(10, 2\sqrt{15}) \) lies on the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) and the length of the latus rectum is 8, then the square of the area of \( \Delta PS_1S_2 \) is [where \( S_1 \) and \( S_2 \) are the foci of the hyperbola].

Let \( \vec{a} = \hat{i} - 2\hat{j} + 3\hat{k} \), \( \vec{b} = 2\hat{i} + \hat{j} - \hat{k} \), \( \vec{c} = \lambda \hat{i} + \hat{j} + \hat{k} \) and \( \vec{v} = \vec{a} \times \vec{b} \). If \( \vec{v} \cdot \vec{c} = 11 \) and the length of the projection of \( \vec{b} \) on \( \vec{c} \) is \( p \), then find the value of \( 9p^2 \).

Let \(L\) be the distance of point \(P(-1,2,5)\) from the line \[ \frac{x-1}{2}=\frac{y-3}{2}=\frac{z+1}{1} \] measured {parallel to a line having direction ratios \(4,\,3,\,-5\). Then \(L^2\) is equal to: }

If \((9+7\alpha-7\beta)^{20} + (9\alpha+7\beta-7)^{20} + (9\beta+7-7\alpha)^{20} + (14+7\alpha+7\beta)^{20}\) is \(m^{10}\) then the value of m is : (where \(\alpha = \frac{-1+i\sqrt{3}}{2}\) \& \(\beta = \frac{-1-i\sqrt{3}}{2}\))

The area bounded by \[ 2 - 4x \leq y \leq x^2 + 4 \quad \text{and} \quad x = \frac{1}{2}, \, x \geq 0, \, y \geq 0 \] (in square units) is:

Match the List-I and List-II:

Consider the following data: \[ \text{Na(s)} + \frac{1}{2} \text{Cl}_2 \text{(g)} \rightarrow \text{NaCl(s)} \quad \Delta H^\circ = -411 \, \text{kJ/mole} \] \[ \text{Na(s)} \rightarrow \text{Na(g)} \quad \Delta H^\circ = 107 \, \text{kJ/mole} \] \[ \text{Cl}_2 \text{(g)} \rightarrow 2\text{Cl}(g) \quad \Delta H^\circ = 242 \, \text{kJ/mole} \] \[ \text{Cl(g)} + e^- \rightarrow \text{Cl}^-(g) \quad \Delta H^\circ = -355 \, \text{kJ/mole} \] \[ \text{Na(g)} \rightarrow \text{Na}^+(g) + e^- \quad \Delta H^\circ = 502 \, \text{kJ/mole} \] Find the lattice energy of NaCl(s).

For a given reaction $A \rightarrow nB$, a graph is given between concentration and time. Find value of n for above reaction, based on the information given in graph for $10 \text{ min}$.

If for Li$^{2+}$ ion, electron is in transition between energy levels such that sum of principal quantum numbers is 4 and difference is 2, then find the wavelength (in cm) emitted for transition between these energy levels.
[Given: $R = 1.1 \times 10^5\ \text{cm}^{-1}$]

Sum of molar mass of gas $(x) & (y)$ is :