List of top Mathematics Questions asked in KEAM

Find the term independent of $ x $ in $ \left( 2x - \frac{5}{x^2} \right)^6 $
Evaluate the integral $ I = \int \frac{\sin 4x}{\sin 2x} \, dx $
If ABCD is a rectangle, $ AB = 5i + 4j - 3k $ and $ AD = 3i + 2j - k $, then find $ BD $.
Evaluate the integral: $ \int \frac{\sec^2(\sqrt{2x+5})}{\sqrt{2x+5}} \, dx $
Evaluate the integral: $ \int e^{-x} \cdot e^{3x} \, dx $
Evaluate the integral: $ \int_0^\pi \frac{\tan x}{\cos x} \, dx = \int_0^\pi \frac{\sin x}{\cos^2 x} \, 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} $.

Evaluate the integral: $ \int_{-1}^1 |x - 3| \, dx $
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. $
If $ a, a r, a r^2 $ are in a geometric progression (G.P.), then find the value of: $ \left| a \quad a r \right| \quad \left| a r^2 \quad a r^3 \right| = \left| a r^3 \quad a r^6 \right| $
If $ a_n = 2^{n-1} $, where $ n = 1, 2, 3, ... $, then find $ \sum_{n=1}^{20} a_n $.
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
Given $ y = \sec(\tan^{-1}(x)) $, find $ \frac{dy}{dx} $ at $ x = \sqrt{3} $.
If $ \tan\left( \alpha - \frac{\pi}{12} \right) = \frac{1}{\sqrt{3}} $, find $ \alpha $.
Solve the following differential equation and integrate: $ \frac{dy}{dx} + \frac{2x}{1 + x^2} \cdot y = x $
If $ n(A) = 7 $ and the number of relations from A to B is 128. Then find } $ n(B) $.
Equation of parabola having focii (-3, 1) and (3, 1)
Given the set $ S = \{ a, b, c, d, e, f \} $, find the total number of subsets with an odd number of elements.
If $ f(x) = \frac{1}{x^2} $, $ u = f(x) $, and $ f'(x) $, then find $ \frac{du}{dx} $.
Find the value of $ \sin 60^\circ - \sin 80^\circ + \sin 100^\circ - \sin 120^\circ $
Find the domain of the function: $ f(x) = \sqrt{7 - 11x} $
Given that $ x = \frac{\sin^2 \theta}{\tan \theta - \sec \theta}, \quad y = \frac{\sec \theta + \tan \theta}{\sec^2 \theta}, \quad \text{find} \, \frac{y}{x} $
Solve for $ \alpha $ if: $ \cos^{-1}(2 \sin \alpha) = \frac{47}{12} $
If $ f(x) = \frac{\sqrt{x^4}}{\sqrt{x^2}} $, find $ f'(27) $.