List of top Mathematics Questions

The two curves $x^3 - 3xy^2 + 2 = 0$ and $3x^2y - y^3 = 2$

Two dice are thrown simultaneously, the probability of obtaining a total score of $5$ is

Two cards are drawn at random from a pack of $52$ cards. The probability of these two being "Aces" is

The general solution of $\cot\, \theta + \tan\, \theta = 2$ is

The simplified form of $i^{n} + i^{n +1} + i^{n +2} + i^{n +3}$ is

The sum of $1^{st}$ $n$ terms of the series $\frac{1^{2}}{1}+\frac{1^{2}+2^{2}}{1+2}+\frac{1^{2}+2^{2}+3^{2}}{1+2+3} + ...$

The slope of the tangent to the curve $ { x = t^2 + 3t -8 , y = 2t^2 - 2t - 5}$ at the point $(2, -1)$ is

If $x y z$ are not equal and $\neq$ 0, $\neq$ 1 the value of $\begin{vmatrix} \log x& \log y& \log z\\ \log 2x& \log 2y& \log 2z\\ \log 3x& \log 3y& \log 3z\end{vmatrix}$ is equal to

The solution for the differential equation ${ \frac{dy}{y} +\frac{ dx}{x} = 0 }$ is

The maximum value of $\left( \frac{1}{x} \right)^x$ is

The length of latus rectum o f the parabola $4y^2 + 3x + 3y + 1 = 0$ is

If $A= \frac {1} { \pi}\begin{bmatrix} \sin^{-1} (\pi x) & \tan^{-1} (\frac {x}{\pi}) \\[0.3em] \sin^{-1}\frac {x}{\pi}& \cot^{-1}(\pi x) \end{bmatrix}$ , $B= \frac {1} { \pi}\begin{bmatrix} -\cos^{-1} (\pi x) & \tan^{-1} (\frac {x}{\pi}) \\[0.3em] \sin^{-1}(\frac {x}{\pi})& -\tan^{-1}(\pi x) \end{bmatrix}$ then $A - B$ is equal to

The value of $\int \frac{e^{6 \log x} -e^{5 \log x}}{e^{4 \log x} - e^{3 \log x}} dx$ is equal to

The value of the $\sin \; 1^{\circ} + \sin \; 2^{\circ} +......+ \sin 359^{\circ}$ is equal to

If $\vec{a}$ and $\vec{b}$ are unit vectors then what is the angle between $\vec{a}$ and $\vec{b}$ for $\sqrt{3} \, \vec{a} - \vec{b}$ to be unit vector ?

The value of $\tan \frac{\pi}{8}$ is equal to

If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISNA is

If $[x]$ denotes the greatest integer less than or equal to $x$, then the value of the integral $\int\limits^{{2}}_{{0}}x^2 [x] dx$

If the matrix $A=\begin{pmatrix}2&0&0\\ 0&2&0\\ 2&0&2\end{pmatrix},$ then $A^{n}=\begin{pmatrix}a&0&0\\ 0&a&0\\ b&0&a\end{pmatrix}, n\,\in\,N$ where

For non-zero vectors $\vec{a} $ and $\vec{b} $ if $\left|\vec{a}+\vec{b}\right|

The letters of the word COCHIN are permuted and all permutation are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is

The value of $\sin^{-1}\left ( \cos\, \frac { 53 \pi}{5}\right)$ is

The derivative of $y = x^{\sin\,x}$ is

The only integral root of the equation $ \begin{vmatrix}2-y&2&3\\ 2&5-y&6\\ 3&4&10-y\end{vmatrix} =0 $ is

Value of $\left[\left(\log_{b}\,a\right)\left(\log_{c}\,b\right)\left(\log_{a}\,c\right)\right]$ is