List of top Mathematics Questions

The sum of n terms of the following series; $1^3 + 3^3 + 5^3 + 7^3 + ....$ is

The number of values of $k$ for which the equation $x^2 - 3x + k = 0$ has two distinct roots lying in the interval $(0, 1)$ are

The points of the ellipse $16x^2 + 9y^2 = 400$ at which the ordinate decreases at the same rate at which the abscissa increases is/are given by

In $\Delta ABC \left(a-b\right)^{2} cos^{2} \frac{C}{2} + \left(a+b\right)^{2} sin^{2} \frac{C}{2} = $

The number of points at which the function $f \left(x\right)=max \left\{a-x, a+x, b\right\}, -\infty, 0 < a < b$ cannot be differentiable

$\displaystyle\lim_{x \to 0} \frac{xe^x - \sin \, x}{x}$ is equal to

If $\frac{1}{^{5}C_{r}}+\frac{1}{^{6}C_{r}} =\frac{1}{^{4}C_{r}}$, then the value of $r$ equals to

The simplified form of $\tan^{-1}$ $\left(\frac{x}{y}\right)$ $- \tan^{-1}$ $\left(\frac{x-y}{x+y}\right)$ is equal to

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