List of top Mathematics Questions

If $y = \sin^{2} \left(\tan^{-1} \sqrt{\frac{1-x^{2}}{1+x^{2}}}\right), $ then $\frac{dy}{dx}$ =
If $\alpha, \beta , \gamma$ are the roots of the equation $x^3 - 3x^2 + 2x - 1 = 0$ then the value of $[(1 - \alpha) (1 -\beta )(1 - \gamma)]$ is
The value of $\tan 10^{\circ}\, \tan 20^{\circ} \, \tan 30^{\circ} \, \tan 40^{\circ} \, \tan 50^{\circ}\, \tan 60^{\circ} \tan 70^{\circ} \, \tan 80^{\circ} =$
Equation of chord of the circle $x^2 + y^2 + 4x - 6y - 9 = 0 $ bisected at (0, 1) is
The multiplicative inverse of $ \frac{3 + 4i}{4 - 5 i}$ is
If $\frac{2}{9!} + \frac{2}{3! \,7!}+\frac{1}{5! \,5!} =\frac{2^{a}}{b!}$ where $a,b \in \, N$ then theordered pair $(a, b)$ is
$\displaystyle\lim_{x\to0} \left(\frac{1+5x^{2}}{1+3x^{2}}\right)^{\frac{1}{x^{2}}} = $
Identify the false statement
In the group $G = \{1, 5, 7, 11\}$ under $\otimes_{12}$ the value of $7 \otimes_{12} 11^{-1}$ is equal to
Which of the following is a subgroup of the group $G = \{1, 2, 3, 4, 5, 6\}$ under $\otimes_7$ ?
The parametric equation of a parabola is $x = t^2 + 1, y = 2t + 1$. The cartesian equation of its directrix is
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 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 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
There are $100$ students in a class. In an examination, $50$ of them failed in Mathematics, $45$ failed in Physics, $40$ failed in Biology and $32$ failed in exactly two of the three subjects. Only one student passed in all the subjects. Then the number of students failing in all the three subjects.
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
If $\log _{e}\left(x^{2}-16\right) \leq \log _{e}(4 x-11)$, then
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
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