List of top Mathematics Questions

If the points $ (2a,\,a),\,(a,\,2a) $ and $ (a,\,\,a) $ form a triangle of area $ 32\text{ }sq $ units, then the centroid of the triangle is
Let \(f:R\to R\) be a function such that the third derivative of \(f(x)\) vanishes for all \(x\). If \(f(0)=1,\,f'(2)=4\) and \(f''(1)=2,\) then \(f(x)\) equals to
In the binomial expansion of $ {{(a-b)}^{n}},\,\,n\,\,\ge \,5, $ the sum of $5^{th}$ and $6^{th}$ term is zero. Then, $ \frac{a}{b} $ is equal to
If $ f(x)={{\log }_{e}}\,(1+x)-{{\log }_{e}}(1-x), $ then the value of $ \int_{-1/2}^{1/2}{f(x)\,\,\,dx} $ equals to
The angle between the two lines $ \frac{2-x}{1}=\frac{y}{2}=\frac{z+3}{1} $ and $ \frac{x-4}{4}=\frac{y-1}{1}=\frac{z-5}{2} $ is
If $p :$ The earth is round, $q : 3 + 4 = 7 $ then $\left(\sim p\right)\vee\left(\sim q\right)$ is
If $\frac{\sin x}{\cos x} \times \frac{\sec x}{\operatorname{cosec} x} \times \frac{\tan x}{\cot x}=9, $ where $x \in\left(0, \frac{\pi}{2}\right)$, then the value of $x$ is equal to
Let $A$ and $B$ be two mutually exclusive events such that $ P(A\cap {{B}^{c}})=0.25 $ and $ P({{A}^{c}}\cap B)=0.5 $ . Then, $ P\{(A\cup {{B}^{c}})\} $ is equal to
$\int\frac{1+log\,x}{\left(1+x\,log\,x\right)^{2}}dx$ is equal to
If one of the slopes of the pair of lines $ax^2 + 2hxy + by^2 = 0$ is $n$ times the other then
The last digit of number $7^{886}$ is
The perimeter of a sector is a constant. If its area is to be maximum, then the sectorial angle is
$p \rightarrow \sim q$ can also be written as
If the product of $n$ positive real numbers is one, then their sum is
$\frac {\sin 70^\circ\, +\cos 40^\circ} {\cos 70^\circ + \sin 40^\circ}$=
If $(4)^{\log_9 3} + (9)^{\log_2 4} = (10)^{\log_x 83}$, then X is equal to
If $\omega$ is a cube root of unity, then the value of determinant $\begin{vmatrix}1+\omega&\omega^{2}&\omega \\ \omega^{2} + \omega &-\omega &\omega^{2} \\ 1+\omega^{2} &\omega &\omega^{2} \end{vmatrix}$
$ y =\tan^{-1} \left( \frac{1}{1+x+x^{2}} \right) + \tan ^{-1} \left( \frac{1}{x^{2}+3x+3} \right) + \tan ^{-1} \left( \frac{1}{x^{2}+5x+7} \right) + ......+ $ upto $n$ terms, then $ \frac{dy}{dx} $ at $x = 0$ and $n = 1$ is equal to
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}}} = $