List of top Mathematics Questions

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:

A box contains 24 identical balls of which one ball is black and the remaining balls are green. Three balls are taken simultaneously and randomly. The number of ways of getting only green balls, is