List of top Questions asked in KEAM

Evaluate the integral: $ \int_0^{\frac{\pi}{2}} \frac{1}{1 + \sin x} \, dx $
Evaluate the derivative of $ y = \cos x \times \sin y, \quad \frac{dy}{dx} \text{ at } \left( \frac{\pi}{6}, \frac{\pi}{5} \right) $

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

Moment of inertia of a disc about the axis passing through the center and perpendicular to the plane is \(I_1\). What is the moment of inertia about its diameter?
Ethyl alcohol on reaction with $ H_2SO_4 $ at 413 K gives:
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 $
Find the range of $ f(x) = \sqrt{x^2 + 4x + 4} $.
IUPAC name of allyl amine?
Find $ \frac{dy}{dx} $ for the equation: $ y = \cos x \times \sin y $
How many bridging complexes are there in $ \text{[Mg(Co)}_{10}\text{]} $?
In which reaction is Benzyl chloride converted to Benzaldehyde?
Ethanol is made unfit for drinking by adding?
If the resistance of a wire is 5 $ \Omega $ and 6 $ \Omega $ at 30°C and 40°C respectively, find the temperature coefficient of resistance.
Entropy decreases in which of the following reactions? $ \text{(A) } \text{Br}_2 (l) \to \text{Br}_2 (g) $ $ \text{(B) } \text{Br}_2 (g) \to \text{Br}_2 (l) $ $ \text{(C) } \text{Br}_2 (l) \to \text{Br}_2 (g) \text{ and } \text{Br}_2 (g) \to \text{Br}_2 (l) $
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.
A pn junction diode without bias acts as:
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 $)
If $ V $ is the velocity of wave in a rope having tension $ T $, find the velocity when the tension becomes $ 8T $.
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:
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?
1 torr = ________
What is the working principle of a Bunsen Burner?
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 $n$.