List of top Questions asked in KEAM

If $ | \vec{a} | = 3 $, $ | \vec{b} | = 2 $, then find $ (3\vec{a} - 2\vec{b}) \cdot (3\vec{a} + 2\vec{b}) $.

Evaluate the integral: $ \int \frac{\sec^2(\sqrt{2x+5})}{\sqrt{2x+5}} \, dx $

The value of $ i^3 + i^4 + i^5 $+ .. + $i^{93}$ is:

If $ |\vec{a}| = 5 $, $ |\vec{b}| = 8 $, $ |\vec{a} - \vec{b}| = 7 $, find the angle between  $ \vec{a} $ and $ \vec{b} $.

Find the value of $ \cot^{-1}(1) + \cot^{-1}(2) + \cot^{-1}(3) $
Product of uncertainty in position (\(\Delta x\)) and uncertainty in velocity (\(\Delta v\)) has unit:
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.
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.
The orbital velocity of a satellite is $ V_0 $, at a height $ h = R $ (where $ R $ is the radius of the Earth) from the surface of the Earth. What is the relationship between $ V_0 $ and the escape velocity $ V_e $?
What is the force to be applied on a body of mass 200g to change its velocity by 25 m/s in 5 seconds?
A body hanged by a rope in a lift which is moving upward with a constant acceleration of $ 0.2 \, \text{m/s}^2 $. The tension in the rope is 80 N. Find the mass of the body.
A musician hits a drum 90 times in a minute. The time period of hit is:
If an inductor coil of self-inductance 2H stores 25J of magnetic energy, then the current passing through it is:
If $ F = 6\pi \eta x $, find the dimension of $ x $.
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 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?
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 $.