List of top Questions asked in KEAM

Given $ Z_1 = \frac{1}{2} + \frac{\sqrt{3}}{2}i, \quad Z_2 = -\frac{1}{2} - \frac{\sqrt{3}}{2}i, \quad \text{and} \quad w = Z_1 + Z_2, \quad \text{find} \, w. $
The ratio of angular velocity of two satellites at a distance $ r $ and $ 2r $ from the centre of the earth is:

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

If a box has 8 red balls, 12 white balls, 17 black balls. If two balls are taken one by one without replacement, then the probability of taking one red ball and one black ball is
Which complex has dsp$^2$ hybridisation?
Evaluate the following limit: $ \lim_{x \to 0} \frac{1 + \cos(4x)}{\tan(x)} $
Find the area of the triangle formed by the lines: $ y = -4, \quad y = x, \quad y = -4 $
What is incorrect for Bond order?
Find the limit: $ \lim_{x \to 11} \frac{x - 11}{\sqrt{49 + x^2} - 13} $

Which of the following statement is correct? 
- i) Positive temperature coefficient 
- ii) Charge carrier in semiconductor are ions and electrons

Solve for $ \alpha $ if: $ \cos^{-1}(2 \sin \alpha) = \frac{47}{12} $
Find object distance of concave mirror of $ R = 24 \, \text{cm} $ which gives magnification of 3.
If ABCD is a rectangle, $ AB = 5i + 4j - 3k $ and $ AD = 3i + 2j - k $, then find $ BD $.
Find the value of $ \sin 60^\circ - \sin 80^\circ + \sin 100^\circ - \sin 120^\circ $
Which has a higher boiling point ?
Formula of chromium ore?
The transition of an atom from $ n = \infty $ to $ n = 3 $ represents:
Bromomethane on reaction with Na and dry ether gives:
Write the product of the reaction: $ \text{CH}_3 \text{CH}_2 \text{CH}_2 \text{O} \text{Na} + \text{C}_6 \text{H}_5 \text{Br} \to ? $
Ethyl alcohol on reaction with $ H_2SO_4 $ at 413 K gives:
If $ \mu_s $ and $ \mu_k $ are static and kinetic friction, then:
Find the value of $ \cot^{-1}(1) + \cot^{-1}(2) + \cot^{-1}(3) $
What is the hydration enthalpy of sucrose?
Given $ y = \sec(\tan^{-1}(x)) $, find $ \frac{dy}{dx} $ at $ x = \sqrt{3} $.
Find the log $ K $ value, if $ \Delta G = -11.4 $ and $ 2.303 \cdot RT = 5.7 \times 10^1 $.