List of top Mathematics Questions

If the determinant of the matrix \( \begin{bmatrix} |x| & 1 & 2 \\ 4 & 1 & x \\ 1 & -1 & 3 \end{bmatrix} \) equals -10, then the values of \( x \) are:
Find the area bounded by the curves \( y = 2x \) and \( y = x^2 \):
The degree of the differential equation \( (y^m)^2 + (\sin y')^4 + y = 0 \) is:
Evaluate \( \int_{-\pi/2}^{\pi/2} \sin^9 x \cos^2 x \, dx \):
The integral \( \int \frac{dx}{1 + e^x} \) is:
The lines \( \frac{x + 3}{-2} = \frac{y}{1} = \frac{z - 4}{3} \) and \( \frac{x - 1}{\mu} = \frac{y - 1}{\mu + 1} = \frac{z}{\mu + 2} \) are perpendicular to each other. Then the value of \( \mu \) is:
Evaluate \( \cos \left( \cot^{-1} \left( \frac{7}{24} \right) \right) \):
Find the area of the smaller segment cut-off from the circle \( x^2 + y^2 = 25 \) by \( x = 3 \):
If \( f(x) = \left\{ \begin{array}{ll} mx + 1, & \text{when } x \leq \frac{\pi}{2} \\ \sin x + n, & \text{when } x > \frac{\pi}{2} \end{array} \right. \) is continuous at \( x = \frac{\pi}{2} \), then the values of \( m \) and \( n \) are:
Evaluate \( \lim_{x \to 0} \frac{\sin 2x + \sin 5x}{\sin 4x + \sin 6x} \):
If \( g(x) = -\sqrt{25 - x^2} \), then \( g'(1) \) is:
Evaluate \( \int x \cos x \, dx \):
Evaluate \( \int \frac{dx}{x^2 (x^4 + 1)^{3/4}} \):
The function \( f(x) = 2x^3 + 9x^2 + 12x - 1 \) is decreasing in the interval:
The length of the minor axis of the ellipse with foci \( (\pm 2, 0) \) and eccentricity \( \frac{1}{3} \) is:
If A and B are two sets, such that A has 20 elements, \( A \cup B \) has 32 elements, and \( A \cap B \) has 10 elements, the number of elements in the set B is:
Let \( X \) and \( Y \) be subsets of \( \mathbb{R} \). If \( f : X \rightarrow Y \) given by \( f(x) = -8(x + 5)^2 \) is one-to-one, then the codomain \( Y \) is:
Let \( \vec{a} = \hat{i} - \hat{j} \), \( \vec{b} = \hat{j} - \hat{k} \), and \( \vec{c} = \hat{k} - \hat{i} \), then the value of \( \vec{b} \cdot (\vec{a} + \vec{c}) \) is:
If \( z_1 \) and \( z_2 \) are two complex numbers with \( |z_1| = 1 \), then \( \left| \frac{z_1 - z_2}{1 - z_1 \overline{z_2}} \right| \) is equal to:
The maximum value of \( y = 12 - |x - 12| \) in the range \( -11 \leq x \leq 11 \) is:
If \( \vec{a} \) and \( \vec{b} \) are non-collinear unit vectors and \( |\vec{a} + \vec{b}|^2 = 3 \), then \( (3\vec{a} + 2\vec{b}) \cdot (3\vec{a} - \vec{b}) \) is equal to:
The integral \( \int_{-2}^4 x^2 |x| \, dx \) is equal to:
The value of \( \cos 26^\circ + \cos 54^\circ + \cos 126^\circ + \cos 206^\circ + \cos 240^\circ \) is:
If \( 2 \sin \left( \frac{\pi}{3} - 2x \right) - 1 = 0 \), \( 0<x<\frac{\pi}{2} \), then the value of \( x \) is:
If \( x_1, i=2, 3, \ldots, n \) are \( n \) observations such that \( \sum_{i=1}^{n} x_i^2 = 550 \), mean \( \bar{x} = 5 \) and variance is zero, then the number of observations is equal to: