List of top Mathematics Questions

$1 + \sec^2 x \cdot \sin^2 x = $
In how many ways can the letters of the word “MULTIPLE” be arranged keeping the position of the vowels fixed?
The value of $\tan\left(\dfrac{7\pi}{8}\right)$ is
In a triangle $ABC$, $\left(\tan \dfrac{A}{2} \tan \dfrac{B}{2} \tan \dfrac{C}{2} \right)^2 \le$
If a set $A$ has $m$ elements and the set $B$ has $n$ elements, then the number of injections from $A$ to $B$ is
The sum of the real roots of the equation $|x - 2|^2 + |x - 2| - 2 = 0$ is
If $e^{i\theta = \cos\theta + i\sin\theta$ then}
$\sum_{n=0}^{\infty} \dfrac{\cos(n\theta)}{2^n} \div \sum_{n=0}^{\infty} \dfrac{\cos(n\theta)}{5^n} =$
Let $A = \begin{bmatrix} -2 & x & 1 \\ x & 1 & 1 \\ 2 & 3 & -1 \end{bmatrix}$. If the roots of the equation $\det A = 0$ are $l, m$ then $l^3 - m^3 =$
If $A = \begin{bmatrix} 2 & -3\\ -4 & 1 \end{bmatrix}$, then $(A^T)^2 + (12A)^T = $
If $A = \begin{bmatrix} 1 & 0 & 0 \\ a & -1 & 0 \\ b & c & 1 \end{bmatrix}$ is such that $A^2 = I$, then
Multiplicative inverse of the complex number $(\sin\theta, \cos\theta)$ is
$\left\{ x \in \mathbb{R} \,\middle|\, \frac{\sqrt{|x^2 - 2|x| - 8}}{\log(2 - x - x^2)} \text{ is a real number} \right\} =$
The domain of the real valued function $f(x) = \sin\left(\log\left(\frac{\sqrt{4 - x^2}}{1 - x}\right)\right)$ is
The differential equation of the family of circles passing through origin and having centers on x-axis is:
If \( \int_{0}^{\pi/2} \sin^m x \cos^4 x \, dx = \frac{7\pi}{2048} \), then \( m = \)
Evaluate \( \lim_{n \to \infty} \left( \frac{1^2}{n^3 + 1^3} + \frac{2^2}{n^3 + 2^3} + \cdots + \frac{n^2}{n^3 + n^3} \right) \)
The function \( f(x) = 2x^3 - 9ax^2 + 12a^2x + 1 \ (a>0) \) attains its maximum and minimum at \( p \) and \( q \) respectively and \( p^2 = q \). Then the value of \( a \) is:
The curves \( y = x^2 - 1 \) and \( y = 8x - x^2 - 9 \)
Evaluate the integral \( \int \frac{1 - k \cos^2 x}{\sin^k x \cos^2 x} dx \).
If \( f(x) = \frac{e^x - 1}{e^x + 1} \), then \( \lim_{x \to \infty} f(x) \) is:
Let \( ax + by + cz + d = 0 \) be the equation of a plane. Given that \( 4a + 4b + c = 0 \) and \( a + 2b + c = 0 \), then the value of \( d \) is:
Suppose \( d_1 \) and \( d_2 \) are respectively the lengths of intercepts of the circle \( x^2 + y^2 = 4 \) and \( x^2 + y^2 - 10x - 14y + 65 = 0 \) on the line \( 2x - 2y = 3 \). Then which of the following is true?
The triangle formed by \( x^2 - 4xy + y^2 = 0 \) and \( x + y + 4\sqrt{6} = 0 \) is:
If \( \left(x_1, \frac{1}{x_1}\right), \left(x_2, \frac{1}{x_2}\right), \left(x_3, \frac{1}{x_3}\right), \left(x_4, \frac{1}{x_4}\right) \) lie on the boundary of a circle of radius 4, then the value of \( x_1 x_2 x_3 x_4 \) is:
The equation of bisectors of the angle between the lines given by \( 3x^2 + 5xy + 4y^2 = 0 \) is: