List of top Mathematics Questions asked in KEAM

Find $ \frac{dy}{dx} $ for the equation: $ y = \cos x \times \sin y $

Solve the differential equation: $ (1 + y) \, dx = (1 + x) \, dy $

Evaluate the integral: \[ \int e^x \sec(x) \left( \tan(x) + 1 \right) \, dx \]

If $ \sum_{k=0}^{n+1} C_k^n = 512 $, find $ \sum_{k=0}^{n} C_k^n $.

Find the limit: \[ \lim_{x \to 0} \frac{\sin(\pi \sin^2 x)}{x^2} \]

Find the values of: \[ \cos 75^\circ, \cos 15^\circ, \cos 45^\circ \]

Find the integral: \[ \int \left( \sin^{-1} \sqrt{x} + \cos^{-1} \sqrt{x} \right) \, dx \]

Evaluate the derivative of the function: \[ f(x) = x |x|, \quad \text{find} \quad f'(-10) \]

Evaluate the integral: \[ \int \frac{\cos \theta}{2 - \sin^2 \theta} \, d\theta \]

Evaluate the following statement: \[ f(x) = \sin(|x|) - |x| \text{ is not differentiable at } x = \underline{\hspace{2cm}} \]

Find the center of the ellipse given by the equation \[ 4x^2 + 24x + 9y^2 - 18y + 9 = 0 \]

Given the following probabilities: \[ P(A) = 0.7, P(B) = 0.5, P(A \cup B) = 0.9, \quad \text{find} \quad P(A/B) \]

Solution set of \( -12x > 38 \text{ for } x \in \mathbb{N} \) \[ -12x > 38 \]

Evaluate the expression: \[ \frac{\sin \frac{\pi}{7} + \sin \frac{3\pi}{7}}{1 + \cos \frac{\pi}{7} + \cos \frac{2\pi}{7}} \]

Evaluate the following integral: \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \left( x^4 + x^3 + x \right) \cos x \, dx \]

Find the limit: \[ \lim_{x \to 0} \frac{\sin[x]}{[x]}, \text{ where } [x] \text{ represents greatest integer function} \]

Evaluate the integral: \[ \int \frac{\sin(2x)}{\sin(x)} \, dx \]