List of top Questions asked in JEE Advanced- 2025

Let $ \alpha $ and $ \beta $ be the real numbers such that $$ \lim_{x \to 0} \frac{1}{x^3} \left( \frac{\alpha}{2} \int_{0}^{x} \frac{1}{1 - t^2} \, dt + \beta x \cos x \right) = 2. $$ Then the value of $ \alpha + \beta $ is __________.

Evaluate the definite integral: \[ I = \int_{\frac{1}{2}}^{2} \frac{\tan^{-1} x \, dx}{2x^2 - 3x + 2} \]

Let \[ f(x) = \begin{cases} \frac{7}{2}, & x = 0 \\ \frac{6x + \sin x}{2x + \sin x}, & x \neq 0 \end{cases} \] Then, which of the following statements are correct?

A mass \(2m\) collides elastically with a stationary mass \(m\). After collision, the angle \(\theta\) is formed between their velocities. Find the maximum possible value of \(\theta\).

Let a complex number \(z\) satisfy the equation \[ |z - z_1| = 2 |z - z_2|,\quad \text{where } z_1 = 1 + 2i,\ z_2 = 3i \] Then choose the correct options:

If \[ \alpha = \frac{1}{\sin 60^\circ \sin 61^\circ} + \frac{1}{\sin 62^\circ \sin 63^\circ} + \dots + \frac{1}{\sin 118^\circ \sin 119^\circ} \] Then find the value of \(\dfrac{\csc^2 1^\circ}{\alpha^2}\)

Let \[ \left(1 + \frac{2}{5}x\right)^{23} = \sum_{i=0}^{23} a_i x^i \] If the maximum value of \(a_i\) occurs at \(i = r\), find the value of \(r\).

Find the dimensional formula of the quantity \(\alpha\), given: \[ \alpha = \frac{S^2 \cdot \sigma}{k}, \quad S = \frac{\text{EMF}}{\text{time}},\quad \sigma = \text{electric conductivity},\quad k = \text{thermal conductivity} \]

Evaluate the limit: \[ \lim_{x \to 0} \frac{\frac{\alpha}{2} \int_0^x \frac{dt}{1 - t^2} + \beta x \cos x}{x^3} = \gamma \]

Given the differential equation: \[ x^2 \frac{dy}{dx} + xy = x^2 + y^2, \quad \text{with } y(1) = 0 \] Find the value of \(\frac{y^2(e)}{y(e^2)}\).