List of top Mathematics Questions asked in KEAM

Solve the following differential equation and integrate: $ \frac{dy}{dx} + \frac{2x}{1 + x^2} \cdot y = x $

Evaluate the integral: $ \int \frac{\sec^2(\sqrt{2x+5})}{\sqrt{2x+5}} \, dx $

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 $ n(A) = 7 $ and the number of relations from A to B is 128. Then find } $ n(B) $.

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) $.

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

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 $.

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} $

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

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

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

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

Evaluate the integral: $ \int_0^{\frac{\pi}{2}} \frac{1}{1 + \sin x} \, dx $

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

Evaluate the derivative of $ y = \cos x \times \sin y, \quad \frac{dy}{dx} \text{ at } \left( \frac{\pi}{6}, \frac{\pi}{5} \right) $

Evaluate the integral: \[ \int_{-3}^{3} \left\lfloor x \right\rfloor \, dx \]

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