List of top Mathematics Questions

Five persons entered the lift cabin on the ground floor of an eight floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of all $5$ persons leaving at different floors is

Let $T_n$ be the number of all possible triangles formed by joining vertices of an $n$-sided regular polygon. If $T_{n+1} - T_n = 10$, then the value of $n$ is

The area of the region enclosed between parabola $y^2 = x$ and the line $y = mx$ is $\frac{1}{48}. $

If the distance between the foci of an ellipse is equal to the length of the latus rectum, then its eccentricity is

Let $f(?) = (1+sin^2?)(2-sin^2?)$. Then for all values of $?$

There are two coins, one unbiased with probability $\frac{1}{2}$ of getting heads and the other one is biased with probability $\frac{3}{4}$ of getting heads. A coin is selected at random and tossed. It shows heads up. Then the probability that the unbiased coin was selected is

The limit of $ \sum\limits^{1000}_{ n-1} (-1)^n \, x^n $ as $x?8$

The value of the determinant $\begin{vmatrix}1+a^{2}-b^{2}&2ab&-2b\\ 2ab&1-a^{2}+b^{2}&2a\\ 2b&-2a&1-a^{2}-b^{2}\end{vmatrix}$ is equal to

The value of the integral is equal to $\int\limits^{\frac{\pi}{3}}_{\frac{\pi}{6}} \frac{\left(sin\,x - xcos\, x\right)}{x\left(x+sin\,x\right)}dx$ is

If $f(x) = e^x (x - 2)^2$ then

The value of the integral $ \int\limits^2_{1}e^{x} \left(log_{e} \,x + \frac{x+1}{x}\right)dx$ is

The value of $I = \int \limits^ \frac{\pi}{4}_{0}\left(tan^{n+1} x\right)dx + \frac{1}{2} \int \limits^ \frac{\pi}{2}_{0} tan^{n-1} \left(x / 2\right)dx$ is equal to

Suppose $z = x + iy$ where $x$ and $y$ are real numbers and $i = \sqrt{-1}$. The points $(x, y)$ for which $\frac{z - 1}{z - i} $ is real, lie on

For the curve $x^2+4xy+8y^2=64$ the tangents are parallel to the x-axis only at the points

If $\alpha, \beta$ are the roots of the quadratic equation $x^2+ax+b=0, (b\ne 0)$; then the quadratic equation whose roots are $\alpha -\frac{1}{\beta}, \beta - \frac{1}{\alpha}$ is

The range of the function $f(x)= \sin [x],-\frac {\pi}{4} < x < \frac {\pi}{4}$ where $[x]$ denotes the greatest integer $\leq x$, is ________

If $a$ is a vector perpendicular to both $b$ and $c$, then

The angle between the lines $\sin^2 \alpha \cdot y^2 - 2xy \cdot \cos^2 \alpha + (\cos^2 \alpha - 1)x^2 = 0$, is

The equation of the tangent to the parabola $y^2 = 4x$ inclined at an angle of $\frac{\pi}{4}$ to the $+ve$ direction of $x$-axis is

If $\frac {(x+1)^2}{x^3+x}=\frac {A}{x}+\frac {Bx+C}{x^2+1}$, then $\sin^{-1} \,A + \tan ^{-1} \,B + sec ^{-1} \,C$ is equal to