List of top Questions asked in KEAM

The dimensional formula of product of moment of inertia and square of angular velocity is:
Find the limit: $ \lim_{x \to 0^+} 2 \left\lfloor x \right\rfloor - \frac{x}{|x|} $
If $ f(x) = \frac{1}{x^2} $, $ u = f(x) $, and $ f'(x) $, then find $ \frac{du}{dx} $.
Evaluate the following limit: $ \lim_{x \to 0} \frac{1 + \cos(4x)}{\tan(x)} $
Solve for $ \alpha $ if: $ \cos^{-1}(2 \sin \alpha) = \frac{47}{12} $

If $ X = A \times B $, $ A = \begin{bmatrix} 1 & 2 \\-1 & 1 \end{bmatrix} $, $ B = \begin{bmatrix} 3 & 6 \\5 & 7 \end{bmatrix} $, find $ x_1 + x_2 $.

Which of the following are neutral?
Given $ y = \sec(\tan^{-1}(x)) $, find $ \frac{dy}{dx} $ at $ x = \sqrt{3} $.
The ratio of the velocity of light in a vacuum to that in a medium is?
Evaluate the expression $ \frac{3 \tan 15^\circ - \tan 3 \times 15^\circ}{1 - 3 \tan^2 15^\circ} $
Find the area of the triangle formed by the lines: $ y = -4, \quad y = x, \quad y = -4 $
Which complex has dsp$^2$ hybridisation?
Find the domain of the function: $ f(x) = \sqrt{7 - 11x} $
Find the term independent of $ x $ in $ \left( 2x - \frac{5}{x^2} \right)^6 $
If $ f(x) = \frac{\sqrt{x^4}}{\sqrt{x^2}} $, find $ f'(27) $.
4 masses are placed at 4 corners of square ABCD. If one mass is removed from the corner B, then the centre of mass lies in the line joining
What is incorrect for Bond order?
If ABCD is a rectangle, $ AB = 5i + 4j - 3k $ and $ AD = 3i + 2j - k $, then find $ BD $.

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

If Young's modulus and densities are in the ratio 3:2 and 3:1 respectively, the ratio of velocity of sound is:
Equation of parabola having focii (-3, 1) and (3, 1)
Which has a higher boiling point ?
Formula of chromium ore?
Find the value of $ \sin 60^\circ - \sin 80^\circ + \sin 100^\circ - \sin 120^\circ $
Bromomethane on reaction with Na and dry ether gives: