List of top Mathematics Questions

if $\begin{bmatrix}x\\ y\\ z\end{bmatrix} = \frac{1}{40} \begin{bmatrix}5&10&-5\\ -5&-2&13\\ 10&-4&6\end{bmatrix}\begin{bmatrix}5\\ 0\\ 5\end{bmatrix}$, then the value of $x + y + z$ is

If $x = \sin\: t \: \cos \: 2t$ and $y = \cos\: t\: \sin\: 2t$, then at $ t = \frac{\pi}{4}$, the value of $ \frac{dy}{dx} $ is equal to :

If $x=\sin(2\,\tan^{-1}2)$ and $y=\sin\left(\frac{1}{2}\tan^{-1}\frac{4}{3}\right)$ ,than

If $(x+iy) (2-3i)=4+i$, then values of $x$, $y$ are

If $x \in \left(-\frac{\pi}{2}, \frac{\pi }{2}\right)$, then the value of $tan^{-1}\left(\frac{tan\,x}{4}\right)+tan^{-1}\left(\frac{3\,sin\,2x}{5 + 3\,cos\,2x}\right)$ is

If $\overrightarrow{x}\times\overrightarrow{b} \,=\,\overrightarrow{c}\times\overrightarrow{b} $ and $ \overrightarrow{x}\,\bot\, \overrightarrow{a},$ then $\overrightarrow{x}$ is equal to

If $x \frac{dy}{dx} =y \left(\log \,y - \log \,x\right)$ then the solution of the equation is

If {x} denotes the fractional part of x, then $\lim_{x \to\left[a\right]} \frac{e^{\left\{x\right\}} - \left\{x\right\}-1}{\left\{x\right\}^{2}} $, where [a] denotes the integral part of a, is equal to

If $x, 2y, 3z$ are in $A.P$., where the distinct numbers $x, y, z$ are in $G.P$. then the common ratio of the $G.P$. is

If $x = 99^{50} + 100^{50}$ and $y = \left(101\right)^{50}$ then

If $x = a \cos \theta, y = b \sin \theta$, then $\frac{d^3 y}{dx^3}$ is equal to

If x + 1, 4x + 1, and 8x + 1 are in geometric progression, then what is the non-trivial value of x ?

If $x = 1 + a + a^2 + .................... $to infinity and $y = 1 + b + b^2 + ................... $to infinity, where a, b are proper fractions, then $1 + ab + a^2b^2 + .....$ to infinity is equal :

If $x^2 + 6x - 27 > 0$ and $x^2 - 3x - 4 < 0 $ then

If $u = \sin (m \cos^{-1} x), v = \cos (m \sin^{-1} x)$, then $\frac{du}{dv} = $

If $U= \{2, 3, 4, 5, 6, 7, 8, 9, 10, 11\}$, $A = \{2, 4, 7\}$, $B = \{3, 5, 7, 9, 11\}$ and $C = \{7, 8, 9, 10, 11\}$, compute $(A \cap U) \cap (B \cup C)$.

If two numbers $p$ and $q $ are chosen randomly from the set $\{1, 2, 3, 4\}$ with replacement, then the probability that $ p^2 \ge 4q$ is equal to

If two squares are chosen at random on a chess board, the probability that they have a side in common is

If two coins are tossed 5 times, the chance that there will be 5 heads and 5 tails is

If two events are independent, then

If two circular arcs of the same length subtend angles of $60^{\circ}$ and $80^{\circ}$ at their respective centres, then the ratio of their radii is

If $\theta =\cot^{-1}7+\cot ^{-1}8+\cot^{-1}18$, then $\cot\,\theta $ is equal to

If $\theta$ and $\phi$ are acute angles, $\sin \, \theta = \frac{1}{2} , \cos \, \phi = \frac{1}{3},$ then the value of $\theta + \phi $ lies in

If $\theta$ and $\phi$ are the roots of the equation $8x^2 + 22x + 5 = 0$ , then

If the value of $1 + 2 + 3 + ..........+n $ is $55,$ then the value of $1^3 + 2^3 + 3^3 + ..........+ n^3$ is