List of top Mathematics Questions

If the ratio of the roots of the equation $px^2 + qx + r = 0$ is $a : b$, then $\frac{ab}{\left(a+b\right)^{2}} = $

The number of real values of $ x $ which satisfy the equation $ |\frac{x}{x-1}| + |x| = \frac{x}{|x-1|} $ is

The circle passing through the point (-1,0) and touching the Y-axis at (0, 2) also passes through the point

Let $E$ and $F$ be two independent events. The probability that exactly one of them occurs is $\frac{11}{25}$ and the probability of none of them occurring is $\frac{2}{25}$ . If $P(T)$ denotes the probability of occurrence of the event $T$, then

Let the eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be reciprocal to that of the ellipse $x^2+4y^2=4.$ If the hyperbola passes through a focus of the ellipse, then

Let $\overrightarrow{a}=\overrightarrow{i}+\overrightarrow{j}+\hat{k}, \overrightarrow{b}=\hat{i}-\hat{j}+\hat{k} $ and $\overrightarrow{c}=\overrightarrow{i}-\overrightarrow{j}-\overrightarrow{k} $ be three vectors. A vector $\hat{v}$ in the plane of $\overrightarrow{a}$ and $ \overrightarrow{b},$ whose projection on $\overrightarrow{c} $ is $\frac{1}{\sqrt{3}},$ is given by

The vector(s) which is/are coplanar with vectors $\widehat{i} + \widehat{j}+2\widehat{k}$ and $\widehat{i} + 2\widehat{j}+\widehat{k},$ are perpendicular to the vector $\widehat{i} + \widehat{j}+\widehat{k}$ is / are

Let $f : R \rightarrow R$ be a function such that $f (x + y) = f (x) + f (y), \forall x, y \in R$. If $f (x )$ is differentiable at $x = 0$, then

Let P(6,3) be a point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1.$ If the norm al at the point P intersects the X -axis at (9, 0), then the eccentricity of the hyperbola is

If $ H_n = 1+\frac{1}{2} + ..... + \frac{1}{n}, $ then the value of $ S_n = 1+\frac{3}{2} + \frac{5}{3} + .....+\frac{2n-1}{n} is $

The eccentricity of the hyperbola with latus rectum $ 12 $ and semi-conjugate axis $ 2\sqrt{3} $ , is

If the normal at the point $ P(\theta) $ to the ellipse $ \frac{x^2}{14} + \frac {y^2}{5} = 1 $ intersects it again at the point $ Q(2\theta), $ then $ cos \theta $ equals to

If the parabolas $ y^2 = 4x $ and $ x^2 = 32y $ intersect at $ (16, 8) $ at an angle $ \theta $ , then $ \theta $ equals to

If $ asin^{-1}x - bcos^{-1} x = c $ , $ a sin^{-1}x + b cos^{-1} x $ is equal to

If algebraic sum of distances of a variable line from points $ (2,0) $ , $ (0,2) $ and $ (-2- 2) $ is zero, then the line passes through the fixed point

The length of the perpendicular distance of the point $ (-1,\,4,\,0) $ from the line $ \frac{x}{1}=\frac{y}{3}=\frac{z}{1} $ is equal to

The number of lines making equal angles with the coordinate axes in three dimensional geometry is equal to

The projection of a line segment $OP$ through origin $O$, on the coordinate axes are $8, 5, 6$. Then, the length of the line segment $OP$ is equal to

In the binomial expansion of $(1+x)^{15}$ the coefficients of $x^r$ and $x^{r+3}$ are equal Then $r$ is _______

The roots of the quadratic equation $x^{2}-2\sqrt{3}x-22 = 0 $ are :

Prem invested a certain sum of money in a simple interest bond whose value grew to Rs 300 at the end of 3 years and to Rs 400 at the end of another 5 years. What was the rate of interest in which he invested his sum ?

If 5 students utilize 18 pencils in 9 days, how long at the same rate will 66 pencils last for 15 students?

The value of $\begin{vmatrix}1&2&3\\ -4&3&6\\ 2&-7&9\end{vmatrix} $ is

If $a > b > 0, Sec^{-1} \left(\frac{a+b}{a-b} \right)= 2 \; Sin^{-1}x $ then $x = $ _____

If $a^x = b^{y} = c^{z} = d^{u}$ and $a, b,\, c,\, d$ are in $GP$, then $x,\, y,\, z,\, u$ are in