List of top Mathematics Questions asked in KEAM

If $ f(x) = \frac{\sqrt{x^4}}{\sqrt{x^2}} $, find $ f'(27) $.

Find the value of $ \cot^{-1}(1) + \cot^{-1}(2) + \cot^{-1}(3) $

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} $

Evaluate the expression $ \frac{3 \tan 15^\circ - \tan 3 \times 15^\circ}{1 - 3 \tan^2 15^\circ} $

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. $

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 limit: $ \lim_{\theta \to 0} \frac{\theta \sin 2\theta}{1 - \cos 2\theta} $

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 expression: $ \frac{\cos 75^\circ - \cos 15^\circ}{\cos 75^\circ + \cos 15^\circ} $

Find the value of: $ \sin 75^\circ \times \sin 15^\circ \times \sin 45^\circ $

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 $

Evaluate the integral: $ \int \frac{1}{x(x^4 + 1)} \, dx $

Evaluate the following expression: $ \frac{\cos 75^\circ - \cos 15^\circ}{\cos 75^\circ + \cos 15^\circ} $

Evaluate the integral: $ \int e^{x + \frac{1}{x}} \frac{x^2 - 1}{x^2} \, dx $

Evaluate the following integral: $ \int e^{2\theta} \left( 2 \cos^2 \theta - \sin 2\theta \right) \, d\theta $

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 $ \tan^{-1}(x) = \tan^{-1}\left( 3 - \frac{\pi}{4} \right) $, find $ x $.

Find the range of $ f(x) = \sqrt{x^2 + 4x + 4} $.

If $ f(x) = \log 3 - \sin x $, $ y = f(f(x)) $, find $ y(0) $.

Length of latus rectum of ellipse \[ \frac{x^2}{9} + \frac{y^2}{16} = 1 \]

Evaluate the integral: \[ \int \frac{\log(1+x)}{1+x} \, dx \]