List of top Mathematics Questions

The probability that atleast one of the events $A$ and $B$ occurs is $ 0.5 $ . If $A$ and $B$ occur simultaneously with probability $ 0.2, $ then $ P({{A}^{c}})+P({{B}^{c}}) $ is equal to

Let $ f(x)=\frac{k}{1+{{x}^{2}}},\,-\infty < x < \infty $ be the probability density of a random variable. Then, $k$ equals to

The sum of $n$ terms of the series $ \frac{3}{{{1}^{2}}{{.2}^{2}}}+\frac{5}{{{2}^{2}}{{.3}^{2}}}+\frac{7}{{{3}^{2}}{{.4}^{2}}}+..... $ is equal to

The line $x=2 y$ intersects the ellipse $\frac{x^{2}}{4}+y^{2}=1$ at the points $P$ and $Q$. The equation of the circle with $P Q$ as diameter is

If $\sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2}$, then the value of $x^{9}+y^{9}+z^{9}-\frac{1}{x^{9} y^{9} z^{9}}$ is equal to

The number of integer values of $m$, for which the $x$-coordinate of the point of intersection of the lines $3x + 4y = 9$ and $y = mx + 1$ is also an integer, is

Let $A$ and $B$ be two events with $P\left(A^{c}\right)=0.3, P\left(B\right)=0.4$ and $P\left(A\cap B^{c}\right)=0.5$ Then $P\left(B|A \cup B^{c} \right) $ is equal to

Rolle's theorem is applicable in the interval $[-2, 2]$ for the function

If $\log _{e}\left(x^{2}-16\right) \leq \log _{e}(4 x-11)$, then

The incentre of an equilateral triangle is $(1,1)$ and the equation of one side is $3 x+4 y+3=0$ Then, the equation of the circumcircle of the triangle is

The coefficient of $x^{10}$ in the expansion of $1+\left(1+x\right)+\ldots+\left(1+x\right)^{20}$ is

An urn contains $8$ red and $5$ white balls. Three balls are drawn at random. Then the probability that balls of both colours are drawn is

The value of $\displaystyle \lim_{n \to \infty}\frac{\left(n!\right)^{\frac{1}{n}}}{n}$ is

The eccentric angle in the first quadrant of a point on the ellipse $\frac{x^{2}}{10}+\frac{y^{2}}{8}=1$ at a distance $3$ units from the centre of the ellipse is

Let $p, q$ and $r$ be the side4s opposite to the angles $P, Q$ and $R$, respectively in a $\Delta P Q R$. Then, $2 p r \sin \left(\frac{P-Q+R}{2}\right)$ equals

The least and the greatest distances of the point $(10, 7)$ from the circle $x^2 + y^2 - 4x - 2y - 20 = 0$ are

The area of the region bounded by the curves $y=x^{3}, y=\frac{1}{x}, x=2$ is

The solution of $25\frac{d^{2}y}{dx^{2}}-10 \frac{dy}{dx}+y=0, \, y\left(0\right) =1, \, y\left(1\right)=2e^{\frac{1}{5}} $ is

The value of the integral $\int\limits_{0}^{\pi / 2} \frac{1}{1+(\tan x)^{101}} d x$ is equal to

If the straight line $3x + 4y = k$ touches the circle $x^2 + y^2 = 16x$, then the value of $k$ is

The equations of the two tangents from $(-5, - 4)$ to the circle $x^2 + y^2 + 4x + 6y + 8 = 0$ are

The number of solutions of the equation $z^2+\bar{z}=0$, where $z \in C$ are

The characteristic equation of a matrix $A$ is $\lambda^3 - 5\lambda^2 - 3\lambda + 2 = 0$ then $| adj (A) |$ is equal to

The maximum value of $xe^{ -x}$ is