List of top Questions asked in KEAM- 2025

Evaluate the integral: $ \int \frac{1}{x(x^4 + 1)} \, dx $
Evaluate the integral: $ \int \frac{1}{x(x^4 + 1)} \, dx $
Evaluate the following integral: $ \int \frac{\sec x}{(\sec x + \tan x)^2} \, dx $
Evaluate the following integral: $ \int e^{2\theta} \left( 2 \cos^2 \theta - \sin 2\theta \right) \, d\theta $
Evaluate the integral: $ \int e^{x + \frac{1}{x}} \frac{x^2 - 1}{x^2} \, dx $
Evaluate the integral: $ \int_0^{\frac{\pi}{2}} \frac{1}{1 + \sin x} \, dx $

In a GP 9, 3, $ \frac{1}{3} $, $ \frac{1}{9} $, … find the 25th term.

Given the reaction: $ \text{Cr}_2\text{O}_7^{2-} + x e^- + y H^+ \to 2 \text{Cr}^{3+} + z H_2O $ Find the values of $x$, $y$, and $z$.
The effective capacitance when $n$ identical capacitors are connected in parallel is 10μF, and when connected in series is 0.4μF. Find the value of $n$.
The effective capacitance when $n$ identical capacitors are connected in parallel is 10μF, and when connected in series is 0.4μF. Find the value of $n$.
A pn junction diode without bias acts as:
Phenol is treated with conc. $ H_2SO_4 $, and then with conc. $ HNO_3 $. The compound A and B are formed.
IUPAC name of allyl amine?
The displacement of a body varies with time $ t $ as $ S = \frac{1}{2} t^2 - 6t $. Find the time at which the velocity becomes zero.
The displacement of a body varies with time $ t $ as $ S = \frac{1}{2} t^2 - 6t $. Find the time at which the velocity becomes zero.
What is the ratio of distances travelled by a body in the first two intervals of 5 seconds? (Given the initial velocity $ u = 1 \, \text{m/s} $ and the body moves with a constant acceleration of $ 5 \, \text{m/s}^2 $)
Bernoulli's principle is applicable to:
If $ P_0 $ is the atmospheric pressure and $ P $ is the pressure at a depth $ h $, find the Guage pressure.
Work done to move a charge of 5C from P to Q is 10J. If the potential at P is 0.5V, then the potential at Q is:
Two particles of the same mass have charges in the ratio 3 : 1. What is the ratio of their time periods when they enter a constant magnetic field with the same velocity?
The initial amount of radioactive element in a sample is $ 6 \times 10^3 $. After 48 years, the number of radioactive elements becomes $ 0.75 \times 10^3 $. Find the half-life.
How many bridging complexes are there in $ \text{[Mg(Co)}_{10}\text{]} $?
If the mean free path of a gas molecule at 27°C is $ 10 \times 10^{-7} \, \text{m} $, then the mean free path at 87°C is:
When an electron is accelerated through a 480V, the wavelength is $ \lambda $. Find the wavelength in terms of $ \lambda $ if it is accelerated through 120V.
Which of the following is an interstitial compound?