List of top Mathematics Questions

Evaluate the integral: \[ \int e^x \sec(x) \left( \tan(x) + 1 \right) \, dx \]
Given the set $ S = \{ a, b, c, d, e, f \} $, find the total number of subsets with an odd number of elements.
The cubic polynomial \( 2x^3 - 3x^2 - 36x + 28 \) is increasing in the range of \( x \). Find the interval where the function is increasing.
Evaluate the integral: $ \int \frac{1}{x(x^4 + 1)} \, dx $
Solve the differential equation: $ (1 + y) \, dx = (1 + x) \, dy $
If $ \sum_{k=0}^{n+1} C_k^n = 512 $, find $ \sum_{k=0}^{n} C_k^n $.
Maximize \( z = 3x + 4y \) subject to \( x + y \leq 4 \), \( x \geq 0 \), \( y \geq 0 \). What is the maximum value of \( z \)?
If \( P(A \cap B) = \frac{2}{25} \) and \( P(A \cup B) = \frac{8}{25} \), then find the value of \( P(A) \).
Equation of line through (0, 0, 1) and (1, 1, 0)
Equation of line through (0, 0, 1) and (1, 1, 0)
Evaluate the following integral: \[ \int e^x \left[\frac{1}{1+x(1+x)^2}\right] dx \]
Find the limit: \[ \lim_{x \to 0} \frac{\sin[x]}{[x]}, \text{ where } [x] \text{ represents greatest integer function} \]
Given that \( \mathbf{a} \times (2\hat{i} + 3\hat{j} + 4\hat{k}) = (2\hat{i} + 3\hat{j} + 4\hat{k}) \times \mathbf{b} \), \( |\mathbf{a} + \mathbf{b}| = \sqrt{29} \), \( \mathbf{a} \cdot \mathbf{b} = ? \)
Given that \( \mathbf{a} \times (2\hat{i} + 3\hat{j} + 4\hat{k}) = (2\hat{i} + 3\hat{j} + 4\hat{k}) \times \mathbf{b} \), \( |\mathbf{a} + \mathbf{b}| = \sqrt{29} \), \( \mathbf{a} \cdot \mathbf{b} = ? \)

Find the mean deviation of the following data: 

Evaluate: \[ \sec \left( \cos^{-1} \left( \frac{2024}{2025} \right) \right) \]
Evaluate the following statement: \[ f(x) = \sin(|x|) - |x| \text{ is not differentiable at } x = \underline{\hspace{2cm}} \]
Evaluate the integral: \[ \int \frac{\sin(2x)}{\sin(x)} \, dx \]
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 minimum of the function \[ f(x) = |x+2| \]
Evaluate the following sum: \[ \sum_{n=1}^{2025} i^n (1+i) \]
If \[ \frac{x}{4} + \frac{x}{3} < 13, \text{ then } x \in \]
Axis of parabola is \( x = 0 \). If the vertex is at a distance of 3 from the origin above the x-axis, find the vertex.
Find the integral: \[ \int \left( \sin^{-1} \sqrt{x} + \cos^{-1} \sqrt{x} \right) \, dx \]