List of top Mathematics Questions

If one end of a diameter of the ellipse $ 4x^2 + y^2 = 16$ is $(\sqrt{3},2)$, then the other end is

The line $ y = 2x + c$ touches the ellipse $\frac{x^2}{16}+\frac{y^2}{4}=1$ if c is equal to

The locus of the centre of the circle \(x^2 + y^2 + 4x \,\cos \,\theta - 2y\, sin \theta - 10 = 0\) is

If the normal at one end of a latus-rectum of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ passes through one extremity of the minor axis, then the eccentricity of the ellipse is given by the equation

Consider an infinite geometric series with first term a and common ratio r. If its sum is 4 and the second term is 3/4 then

The sum of distances of any point on the ellipse $3x^2+4y^2=24$ from its foci is

If $\alpha$ and $\beta$ are $(\alpha < \beta)$ the roots of the equation $x^2+bx+c=0,$ where $c < 0 < b$,the

If $ x^2 + y^2 = 1$, then

A straight line through the origin O meets the parallel lines $4x + 2y = 9 $ and $2x + y + 6 = 0$ at points P and Q respectively. Then, the point O divides the segment PQ in the ratio

Let f : R $\to$ R be any function. Define g : R $\to$ R by g(x) = |f(x)| for all x. Then g is

For the equation $3x^2+px+3=0,p>0,$ if one of the root is square of the other, then p is equal to

If $\overrightarrow{a}, \overrightarrow{b}$ and $\overrightarrow{c}$ are unit coplanar vectors, then the scalar triple product $[2\overrightarrow{a}-\overrightarrow{b}2\overrightarrow{b}-\overrightarrow{c}2\overrightarrow{c}-\overrightarrow{a}]$ is

In a $\triangle ABC, $ 2 ac sin $ \bigg [ \frac{1}{2} (A - B + C ) \bigg ] $ is equal to

For x $ \in $ R, $ lim_{ x \to \infty} \bigg( \frac{x - 3}{ x + 2}\bigg)^x $ is equal to

The incentre of the triangle with vertices $(1, \sqrt{3}), (0,0)$ and $ (2,0) is $

Let $f(x) = \begin{cases} |x|, & \quad \text{for}\, 0 < | x | \le 2 \\ 1, & \quad \text{for} \, x = 0 \end{cases}$ then at x = 0, f has

For all $x\,\in\,(0,1)$

If $a, b, c, d$ are positive real numbers such that $a + b +c + d = 2,$ then $M =(a + b) (c+d) $ satisfies the relation.

For $2 \le \, r \, \le \, n,\binom{n}{r}+2 \binom{n}{r-1}+\binom{n+2}{r}$ is equal to

if $\ f ( x )$ $=\bigg \{ \begin {array} \ e^{\cos x}\sin \ x \\ 2 \\ \end {array} \begin {array} \ for |x|\le 2 \\ \text{otherwise} \\ \end {array}$ then $\int^{3}_{-2} f ( x ) \ dx$ is equal to

The value of the integral $ \int^{e^2}_{e^{-1}} \bigg | \frac{ \log_e \, x }{ x } \bigg | \, dx $ is

The eccentricity of the conic $3x^2 + 4y^2 = 24$ is

If $ i = \sqrt -1$ then $ 4 + 5 \bigg(-\frac{1}{2}+\frac{i\sqrt 3}{2}\bigg)^{334}+3\bigg(-\frac{1}{2}+\frac{i\sqrt 3}{2}\bigg)^{365}$ is equal to

In a $\triangle PQR, \angle R = \frac{\pi}{2} , \, if \, tan \, \bigg( \frac{ P}{2}\bigg) $ and \, tan $ \bigg( \frac{ Q}{2}\bigg)$ are the roots of the equation $ ax^2 + bx + c = 0 \, (a \ne 0 )$, then

The function f (x) = $ [ x]^2 - [ x]^2 $ (where, [x] is the greatest integer less than or equal to x), is discontinuous at