List of top Questions asked in KEAM

Two satellites are revolving at a distance of 2.5R and 7.5R from the center of the Earth. Find the ratio of time period of the satellites.

Find the incorrect statement: 
A) Isobaric - constant pressure 
B) Isochoric - constant volume 
C) Isothermal - constant temperature 
D) Adiabatic - involves heat exchange

Which of the following cannot form hydrogen bonding?
A) Phenol  
B) Diethyl ether 
C) Aniline 

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 $z$.
Which of the following is an interstitial compound?
Which is a Lewis acid?
Phenol is treated with conc. $ H_2SO_4 $, and then with conc. $ HNO_3 $. The compound A and B are formed.
Find the area between the line $ y = x - 1 $, $ y = 0 $, $ -2 \leq y \leq 2 $.
Evaluate the integral: $ \int e^{x + \frac{1}{x}} \frac{x^2 - 1}{x^2} \, dx $
Find the value of: $ \sin 75^\circ \times \sin 15^\circ \times \sin 45^\circ $
If $ \tan^{-1}(x) = \tan^{-1}\left( 3 - \frac{\pi}{4} \right) $, find $ x $.
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) $
If $ f(x) = \log 3 - \sin x $, $ y = f(f(x)) $, find $ y(0) $.

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

Find the magnetic field inside a solenoid having number of turns 7000, length 1m, and current 1 A.
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} $.
Find $ \frac{dy}{dx} $ for the equation: $ y = \cos x \times \sin y $
IUPAC name of allyl amine?
In which reaction is Benzyl chloride converted to Benzaldehyde?
Ethanol is made unfit for drinking by adding?