List of top Mathematics Questions

If the one end of a diameter of the circle $x^2 + y^2 + 3x + y - 6 = 0$ is at $(-4,-2)$, then the other end of the diameter is at

The value of $\sin\left(2\sin^{-1}\frac{3}{5}\right)$ is equal to

The vertex of a parabola is at $(2,-5)$ and the focus is at $(5,-5)$. The equation of the parabola is

Given that $i^2 = -1$. Then $i^{13} + i^{14} + i^{15} + \ldots + i^{2026}$ is equal to:

The number of terms in the sequence $2, 6, 18, \ldots, 1458$ is:

A straight line makes $y$-intercept of 5. If the angle made by the line with $y$-axis is $60^\circ$ and the line intersects $x$-axis in the negative direction, then the equation of the line is

Let $P = \left(\frac{15}{2}(\csc \theta + \sin \theta), \; 8(\csc \theta - \sin \theta)\right)$, where $\theta$ is a variable parameter. Then the locus of $P$ is

The value of $\sin^{-1}\left(\sin \dfrac{5\pi}{9} \cos \dfrac{\pi}{9} + \sin \dfrac{\pi}{9} \cos \dfrac{5\pi}{9}\right)$ is equal to:

The domain of the function $f(x) = 2\sin^{-1}(2x-1) - \dfrac{\pi}{4}$ is:

If $\tan \alpha = \dfrac{5}{6}$ and $\tan \beta = \dfrac{1}{11}$, where $0<\alpha,\beta<\dfrac{\pi}{2}$ then $\alpha + \beta =$:

The value of $\sin6^\circ \cos36^\circ \sin66^\circ + \cos12^\circ \sin42^\circ \sin18^\circ$ is equal to:

Let $f(x) = \dfrac{2x+3}{x-2}, \, x \in \mathbb{R}, \, x \neq 2$ and $h(x) = f(f(x))$. Then $h(h(10))$ is equal to:

The first and last term of a G.P. are 7 and 448 respectively. If the sum is 889, then the common ratio is

The inverse of the function $f(x) = x^2 + 4x + 4, \, x \leq -2$ is $f^{-1}(x) =$

The value of $\dfrac{(1+i)^n}{(1-i)^{n-4}}$, where $i=\sqrt{-1}$ and $n$ is an integer, is:

Let $x$ and $y$ be real numbers. If $(3+i)x + y + (1-i)y + 3i - 4 = (2x+1)i + (x-y+2)i$, where $i=\sqrt{-1}$, then the pair $(x,y)$ is equal to:

Let $z_1 = \dfrac{5+7i}{7-5i}, \, z_2 = \dfrac{3+2i}{3-2i}$ and $z_3 = \dfrac{1+11i}{11-i}$. Then $z_1\overline{z_1} + z_2\overline{z_2} + z_3\overline{z_3}$ is equal to:

Let $t_1, t_2, t_3, \ldots, t_{2n}$ be in G.P. with common ratio $r$. Then:

If $\dfrac{4^{n+1} + 16^{n+1}}{4^n + 16^n}$ is the Geometric Mean between $4$ and $16$, then the value of $n$ is:

If $4\sin^2 x - 2(1+\sqrt{3})\sin x + \sqrt{3} = 0$ and $15^\circ<x<150^\circ$, then the values of $x$ are:

Let $x$ be a real number such that $\dfrac{x-3}{x-2} \geq 1$. Then the solution set of the inequality is:

There are two main entrances to a building with five floors. Each entrance leads to three lifts and each lift can stop at all the five floors. A person enters the building and reaches a floor. The number of possible ways that the person can reach the floor, is

If $\sin \theta \cos \theta>0$, then $\theta$ lies

The sum of all 3-digit numbers that can be formed using $1,2,3,4$ without repetitions is

If ${}^9P_5 = (504)({}^6P_r)$, then the value of $r$ is equal to: