List of top Mathematics Questions

The area of the circle passing through the points $(5, \pm2)$, $(1,2)$ is
A circle has its centre in the first quadrant and passes through $(2, 3)$. If this circle makes intercepts of length 3 and 4 respectively on $x = 2$ and $y = 3$, its equation is
Suppose $\triangle ABC$ is an isosceles triangle with $\angle C = 90^\circ$, $A = (2, 3)$ and $B = (4, 5)$. Then the centroid of the triangle is
A manager decides to distribute Rs. 20000 between two employees X and Y. He knows X deserves more than Y, but does not know how much more. So, he decides to arbitrarily break Rs. 20000 into two parts and gives X the bigger part. Then, the chance that X gets twice as much as Y or more is
In a box, there are 8 red, 7 blue, and 6 green balls. One ball is picked randomly. The probability that it is neither red nor green is
Five-digit numbers are formed using digits 1,2,3,4,5 without repetition. Then the probability that the randomly chosen number is divisible by 4 is
If the mean of the data $p,6,6,7,8,11,15,16$ is 3 times $p$, then the mean deviation of the data from its mean is
If $4 + 6(e^{2x} + 1)\tanh x = 11\cosh x + 11\sinh x$, then $x =$
If $a = 2$, $b = 3$, $c = 4$ in a triangle $ABC$, then $\cos C =$
In a triangle $ABC$, $(b + c)\cos A + (c + a)\cos B + (a + b)\cos C =$
In a triangle $ABC$, $\left(\tan \dfrac{A}{2} \tan \dfrac{B}{2} \tan \dfrac{C}{2} \right)^2 \le$
The value of $\tan\left(\dfrac{7\pi}{8}\right)$ is
If $\dfrac{13x + 43}{2x^2 + 17x + 30} = \dfrac{A}{2x + 5} + \dfrac{B}{x + 6}$, then $A^2 + B^2 = $
$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 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}
$\sum_{n=0}^{\infty} \dfrac{\cos(n\theta)}{2^n} \div \sum_{n=0}^{\infty} \dfrac{\cos(n\theta)}{5^n} =$
If a set $A$ has $m$ elements and the set $B$ has $n$ elements, then the number of injections from $A$ to $B$ is
Multiplicative inverse of the complex number $(\sin\theta, \cos\theta)$ is
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
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 $l^3 - m^3 =$
The domain of the real valued function $f(x) = \sin\left(\log\left(\frac{\sqrt{4 - x^2}}{1 - x}\right)\right)$ 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 differential equation of the family of circles passing through origin and having centers on x-axis is: