List of top Questions asked in KEAM- 2025

In a Carnot engine, efficiency is dependent on ________?
Which among the following acts as a Lewis acid? \[ A) \text{AlCl}_3, \quad B) \text{NH}_3, \quad C) \text{OH}^-, \quad D) \text{H}_2\text{O} \]
Given that \( \vec{a} \parallel \vec{b} \), \( \vec{a} \cdot \vec{b} = \frac{49}{2} \), and \( |\vec{a}| = 7 \), find \( |\vec{b}| \).
Given that \( |\mathbf{a} + \mathbf{b}| = \frac{\sqrt{14}}{2} \), where \( \mathbf{a} \) and \( \mathbf{b} \) are unit vectors, find the value of \( |\mathbf{a} + \mathbf{b}|^2 - |\mathbf{a} - \mathbf{b}|^2 \).
Find the standard deviation of the numbers: -3, 0, 3, 8.
The product of the first five terms of a GP is 32. What is the 3rd term?
Evaluate the integral: \[ \int \frac{2x^2 + 4x + 3}{x^2 + x + 1} \, dx \]
Evaluate the integral: \[ \int_{\frac{\pi}{10}}^{\frac{2\pi}{5}} \frac{\cot^3 x}{1 + \cot^3 x} \, dx \]
A solid sphere, hollow sphere, and solid cylinder start sliding from an inclined plane without rolling. Then the ratio of time taken by them to reach the ground is?
Given: \[ \sum_{k=0}^{5} \binom{10}{2k} = \alpha \quad \text{and} \quad \sum_{k=0}^{4} \binom{10}{2k+1} = \beta \] \text{Find the value of} \( \alpha - \beta \).
What is the formula of lanthanoids with sulfur?
Find the equation of the circle touching the x-axis at \( (9, 0) \) and the line \( y = 14 \).
\( M^0 L T^{-1} \) is the dimension of ___________?
Given the system of equations: \[ Z + \bar{Z} = 4 \quad \text{and} \quad Z - \bar{Z} = 6 \] Find \( |Z| \).
Evaluate the integral: \[ \int \frac{\sin^1 x}{\sqrt{1 - x^2}} \, dx \]
Solve the system of equations: \[ \begin{bmatrix} 4 & 9 \\ 12 & -3 \\ 8 & -2 \end{bmatrix} \begin{bmatrix} 7 \\ 9 \end{bmatrix} = \begin{bmatrix} \alpha \\ \beta \end{bmatrix} \]
If \( Z = \frac{2 - i}{\alpha + i} \) and \( 4 \, \text{Re}(Z) = 3 \, \text{Im}( \overline{Z} ) \), find \( \alpha \).
Find the value of \( Z^2 \) if \( Z = \left( 1 + \frac{1}{i} \right) \).
Given the line equation \( Ax + By + C = 0 \), which passes through the point \( (-10, 7) \) and is perpendicular to the line \( 11x - 8y - 16 = 0 \), find \( C \).
Work done on splitting a spherical drop into 8 droplets?
If $ \mu_s $ and $ \mu_k $ are static and kinetic friction, then:
Which of the following are neutral?
Evaluate the expression $ \frac{3 \tan 15^\circ - \tan 3 \times 15^\circ}{1 - 3 \tan^2 15^\circ} $
Given that $ x = \frac{\sin^2 \theta}{\tan \theta - \sec \theta}, \quad y = \frac{\sec \theta + \tan \theta}{\sec^2 \theta}, \quad \text{find} \, \frac{y}{x} $
If $ n(A) = 7 $ and the number of relations from A to B is 128. Then find } $ n(B) $.