List of top Mathematics Questions

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 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 $?$

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

If the value of $C_0 + 2 \cdot C_1 + 3 \cdot C_2 + \dots+ (n+1) \cdot C_n=576$ ,then n is equal to

The set of zeros of $ f(x) = 0 $ is a non-empty set, when $ f(x) = 0 $ , when $ f(x) $ is equal to

Let $ L $ denote the set of all straight lines in a plane. Let a relation $ R $ be defined on $L$ by $ L_1 $ $R L_2 $ if and only if the straight line $ L_1 $ is perpendicular to the straight line $ L_2 $ . Then, $ R $ is

The minimum area of the triangle formed by the variable line $3 \, \cos\,\theta \cdot x + 4 \,\sin \,\theta \cdot y = 12$ and the co-ordinate axes is

Let $w = \frac{\sqrt 3 + i }{2}$ and $P = \{W^n:n=1,2,3,....\}$ Further $H_1 = \bigg \{z \in C: Re \, z >\frac{1}{2}\bigg \}$ and $H_2=\bigg[ z\in C: Re \,z