List of top Mathematics Questions

Area of the greatest rectangle that can be inscribed in the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ is :

Let $P$ be the point $(1, 0)$ and $Q$ a point on the locus $y^2 = 8x$. The locus of mid point of $PQ$ is:

If $C$ is the mid point of $AB$ and $P$ is any point outside $AB$, then :

The value of $a$ for which the sum of the squares of the roots of the equation $x^2 - (a - 2) x - a - 1 = 0$ assume the least value is

Let $\alpha$ and $\beta$ be the distinct roots of $ax^2 + bx + c = 0$ , then $\displaystyle \lim_{x \to\alpha} \frac{1- \cos \left(ax^{2} + bx + c\right)}{\left(x-\alpha\right)^{2}} $ is equal to

$\displaystyle \lim_{n \to\infty} \left[\frac{1}{n^{2}} \sec^{2} \frac{1}{n^{2}} + \frac{2}{n^{2}} \sec^{2} \frac{4}{n^{2}}.......... + \frac{1}{n}\sec^{2} 1 \right] $ equals

If in a frequency distribution, the mean and median are $21 $ and $22$ respectively, then its mode is approximately

If $x$ is so small that $x^3$ and higher powers of $x$ may be neglected, then $\frac{\left(1+x\right)^{\frac{3}{2}} - \left(1+ \frac{1}{2}x\right)^{3}}{\left(1-x\right)^{\frac{1}{2}}} $ may be approximated as

A real valued function $f (x) $.Satisfies the functional equation $f(x- y) =f (x) f(y)-f(a-x) f(a+y)$ where a is a given constant and $f(0) = 1$. Then $f(2a - x)$ is equal to

$A$ and$ B$ are two like parallel forces. A couple of moment $H$ lies in the plane of $A$ and $B$ and is contained with them. The resultant of $A$ and $B$ after combining is displaced through a distance :

if $p=\begin {bmatrix} \sqrt 3 /2 & 1/2 \\ -1/2 & \sqrt 3/2 \end {bmatrix} , A=\begin {bmatrix} 1 & 1 \\ 0 & 1 \end {bmatrix}$ and $ Q=PAP^T,\ then$ $P^TQ^{2005}P $ is

If $\int_{sin x}^1 \, t^2 f(t) dt =1-sin x, \forall x \in (0,\pi/2), \, then \, f\bigg(\frac{1}{\sqrt 3}\bigg)$ is

A variable plane $ \frac{x}{a}+ \frac{y}{b}+ \frac{z}{c} =1$ at a unit distance from origin cuts the coordinate axes at A. Band C. Centroid (x, y, z) satisfies the equation $ \frac{1}{x^2}+ \frac{1}{y^2}+ \frac{1}{z^2} =K.$ The value of K is

The number of ordered pairs $(\alpha, \beta), $ where $\alpha, \beta \in(-\pi, \pi)$ satisfying cos $(\alpha-\beta)=1 and cos (\alpha+\beta)=\frac{1}{e}$ is

If $\overrightarrow{a}$ and $\overrightarrow{b_1}$ are two unit vectors such that $\overrightarrow{a}+2\overrightarrow{b}$ and $5\overrightarrow{a}-4\overrightarrow{b}$ b, are perpendicular to each other, then the angle between $\overrightarrow{a} and \overrightarrow{b}$ is

In a $\triangle$ ABC, among the following which one is true?

The shaded region, where $P = (-1,0), Q = (-1 + \sqrt 2,\sqrt 2 )R = (-1 + \sqrt 2,-\sqrt 2), S = (1,0)$ is represented by

The minimum value of $| a + b\omega + c \omega^2|$ , where $ a, b$ and $c$ are all not equal integers and $\omega \, (\ne 1)$ is a cube root of unity, is

Let $f (x) = ax^2 + bx + c, a \ne 0$ and $\Delta =b^2 -4ac.$ If $a+ \beta,$ $a^2+ \beta^2$ and $a^3+ \beta^3$ are in GP, then

The area of the equilateral triangle, in which three coins of radius 1 cm are placed, as shown in the figure, is