List of top Mathematics Questions asked in KEAM

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
Evaluate the integral: $ \int e^{-x} \cdot e^{3x} \, dx $
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} $
If $ \cos^{-1}(x) - \sin^{-1}(x) = \frac{\pi}{6} $, then find } $ x $.
Evaluate the integral: $ \int \frac{1}{x(x^4 + 1)} \, dx $

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) $
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.

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 $
In a linear programming problem (L.P.P.), the corner points of the feasible region are $ (5, 0), (10, 0) $ and $ (4, 1) $. Find the maximum value of $ Z = 2x + 3y $.
Evaluate the following integral: $ \int e^{2\theta} \left( 2 \cos^2 \theta - \sin 2\theta \right) \, d\theta $
Evaluate the following limit: $ \lim_{\theta \to 0} \frac{\theta \sin 2\theta}{1 - \cos 2\theta} $