List of top Questions asked in KEAM- 2025

Given the following probabilities: \[ P(A) = 0.7, P(B) = 0.5, P(A \cup B) = 0.9, \quad \text{find} \quad P(A/B) \]
Find the probability of getting at most 2 heads when 4 coins are tossed.
Evaluate the following integral: \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \left( x^4 + x^3 + x \right) \cos x \, dx \]
Evaluate the following integral: \[ \int e^x \left[\frac{1}{1+x(1+x)^2}\right] dx \]
Find the values of: \[ \cos 75^\circ, \cos 15^\circ, \cos 45^\circ \]
Evaluate the derivative of the function: \[ f(x) = x |x|, \quad \text{find} \quad f'(-10) \]
Evaluate the following statement: \[ f(x) = \sin(|x|) - |x| \text{ is not differentiable at } x = \underline{\hspace{2cm}} \]
Coefficient of friction is the ratio of?
Friedel Craft's reaction is an example of:
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?
Given the following concentrations and rates, which one corresponds to the rate law for the reaction? \[ [A] = 0.10 \quad [D] = 0.2 \quad \text{Rate} = 0.2 \] \[ [A] = 0.2 \quad [D] = 0.2 \quad \text{Rate} = 0.4 \] \[ [A] = 0.10 \quad [D] = 0.1 \quad \text{Rate} = 0.05 \]
What is the ratio of de Broglie wavelength of the particles if their kinetic energy are 0.002 eV and 2 eV respectively?
What is the ratio of de Broglie wavelength of the particles if their kinetic energy are 0.002 eV and 2 eV respectively?
The position of body varies as \[ S = 9t^2 - 6t. \text{ What is the time at which the body becomes at rest?} \]
A first-order reaction is 75 percent completed in 6000s. What is the half-life?
Molecule with 2\( \sigma \) and 2\( \pi \) bonds:
According to Huygen's principle, secondary wavelets move:
A block is tied to a string of length 98 cm and is rotated in a horizontal circle. Find the angular velocity if the centripetal acceleration \( a = g \).
Find the \( \Delta G \) during the reaction: \[ \text{H}_2\text{O}(l) \rightleftharpoons \text{H}_2\text{O}(g) \quad \Delta S = +1 \, \text{kJ/mol} \, \text{at} \, 100^\circ C \]
A guitar string is vibrating in the third harmonic. The number of nodes and antinodes present are:
Water flows through a pipe with velocity \( V_1 = 3 \, \text{m/s} \) where the area of the pipe is \( A_1 \). What is the velocity \( V_2 \), where the diameter of the pipe is half of that at area \( A_1 \)?
Evaluate the following sum: \[ \sum_{n=1}^{2025} i^n (1+i) \]
The most basic oxide
If \( n \) cells of emf \( E \) and internal resistance \( r \) are connected in parallel, what is the equivalent emf and internal resistance of the combination?
Galvanometer can be converted into a voltmeter by connecting...