List of top Questions asked in KEAM- 2025

Evaluate the derivative of the function: \[ f(x) = x |x|, \quad \text{find} \quad f'(-10) \]
Find the values of: \[ \cos 75^\circ, \cos 15^\circ, \cos 45^\circ \]
Evaluate the expression: \[ \frac{\sin \frac{\pi}{7} + \sin \frac{3\pi}{7}}{1 + \cos \frac{\pi}{7} + \cos \frac{2\pi}{7}} \]
Benzene when treated with Br\(_2\) in the presence of FeBr\(_3\), gives 1,4-dibromobenzene and 1,2-dibromobenzene. Which type of reaction is this?
If force is 500 N and instantaneous velocity is 20 m/s, what is the instantaneous power?
If \[ (a - 2)^2 + (b - 2)^2 + (c - 2)^2 = 0, \text{ then } a + b + c = \]
What is the dimension of \[ \frac{M B}{K T} \] where \( M \) represents magnetic moment, \( K \) represents the Boltzmann constant, \( B \) represents the magnetic field, and \( T \) represents temperature?
Solution set of \( -12x > 38 \text{ for } x \in \mathbb{N} \) \[ -12x > 38 \]
If \[ \frac{x}{4} + \frac{x}{3} < 13, \text{ then } x \in \]
Evaluate the following sum: \[ \sum_{n=1}^{2025} i^n (1+i) \]
Given the following information: \[ n(A \times B) = 160, \quad n(B \times C) = 80, \quad n(A \times C) = 240 \] Find \( n(A) \).
If \( -5<x \leq -1 \), then \( -21 \leq 5x + 4 \leq b \). Find \( b \).
The velocity is given as \( \mathbf{v} = 3\hat{i} + 3\hat{j} \). Find the acceleration \( \mathbf{a} \).
An unbiased die is tossed until a sum \( S \) is obtained. If \( X \) denotes the number of times tossed, find the ratio \( \frac{P(X = 2)}{P(X = 5)} \).
The disease is caused by a deficiency of riboflavin.
Relations between the speed of X-ray, gamma-ray, and UV rays when they travel in a vacuum.
Which of the following has the highest \( K_b \) value?
Which of the following statement is true?
Which among the following has the highest molar elevation constant?
How can we decrease the effective capacitance of a parallel plate capacitor?
A cylindrical vessel contains 16 kg at 1 atm. A certain amount of substance is taken out so that pressure becomes 0.7 atm. Find the amount taken out (in kg).
Tension of a rope when a man of mass \( m \) climbs up or down with an acceleration \( a<g \)?
Number of sigma and pi bonds in methyl but-1-ene is:
What is the order of the SN2 reaction for the compounds: \[ \text{2-methyl-2-bromo-butene}, \quad \text{2-bromo-butene}, \quad \text{1-bromo-butane} \]
The reaction shown is: \[ \text{Phenol} + \text{CHCl}_3 + \text{NaOH} \rightarrow \text{Salicylaldehyde} \] What is the name of the above reaction?