List of top Mathematics Questions

DIRECTION for the question: In the following question, some groups of letters are given. All of which, except one, share a common similarity while one is different. Choose the odd one out. (a) DAH (b) IFM (c) ROV (d) QNT (e) SPW

If \( P(A \cap B) = \frac{2}{25} \) and \( P(A \cup B) = \frac{8}{25} \), then find the value of \( P(A) \).

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

Evaluate the following sum: \[ \sum_{n=1}^{2025} i^n (1+i) \]

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

Find the minimum of the function \[ f(x) = |x+2| \]

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

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

Evaluate the limit: \[ \lim_{x \to 2} \frac{(x^3 - 8) \sin(x - 2)}{x^2 - 4x + 4} \]

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

If \[ (a - 2)^2 + (b - 2)^2 + (c - 2)^2 = 0, \text{ then } a + b + c = \]

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

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

If \[ \frac{x}{4} + \frac{x}{3} < 13, \text{ then } x \in \]

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 \[ 4x^2 + 24x + 9y^2 - 18y + 9 = 0 \]

Integrating factor of \[ \frac{dy}{dx} - 2y = 2x - 3 \]

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

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

Evaluate the following integral: \[ \int e^x \left[\frac{1}{1+x(1+x)^2}\right] dx \]