List of top Mathematics Questions

The value of integral $\int\limits_{-1}^{1} \frac{\left|x+2\right|}{x+2} dx$ is

The length of the diameter of the circle which cuts three circles $x^2 + y^2 - x - y - 14 = 0;$ $x^2 + y^2 + 3x - 5y - 10 = 0 ;$ $x^2 + y^2 - 2x + 3y - 27 = 0$ orthogonally, is

The angle between the lines joining the foci of an ellipse to one particular extremity of the minor axis is $90^{\circ}$ The eccentricity of the ellipse is

The equation $\sqrt{3}\, \sin \,x+\cos\,x = 4$ has

If If $n =(2020)$, then $\frac {1}{\log_2n}+\frac {1}{\log_3n}+\frac {1}{\log_4n}+............+\frac {1}{\log_{2020} n}$

The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse $x^2 + 9y^2 = 9$ meets its auxiliary circle a t the point M. Then, the area (insqunits) of the triangle with vertices at A, M and the origin O is

If $\alpha, \beta, \gamma$ are the roots of $x^{3}+4 x+1=0$, then the equation whose roots are $\frac{\alpha^{2}}{\beta+\gamma}, \frac{\beta^{2}}{\gamma+\alpha},\,\frac{\gamma^{2}}{\alpha+\beta}$ is

The number of subsets of $\{1, 2, 3 ,............,9\}$ containing at least one odd number is

For $|x|<1$, the constant term in the expansion of $\frac{1}{(x-1)^{2}(x-2)}$ is

$p$ points are chosen on each of the three coplanar lines. The maximum number of triangles formed with vertices at these points is

Match the following.

Let $f(x)=x^{2}+a x +b,$ where $a, b \in R .$ If $f(x)=0$ has all its roots imaginary, then the roots of $f(x)+f'(x)+f''(x)=0$ are

A binary sequence is an array of $0's$ and $1's$. The number of $n$ -digit binary sequences which contain even number of $0's$ is

The number of subsets of $\{1,2,3, \ldots, 9\}$ containing at least one odd number is

$ \int e^{x} \frac{\left(x-1\right)}{x^{2}} dx $ is equal to

$ \int_{0}^{x}{\log \,(\cot \,x\,+\,\tan t)\,dt} $ =

The value of $ \displaystyle\lim_{n\to\infty} \left[\frac{n}{n^{2}+1^{2}}+\frac{n}{n^{2}+2^{2}}+\ldots+\frac{1}{n^{2}+2n}\right] $ is

The modulus of $\frac{1-i}{3+i}+\frac{4i}{5}$ is

$ \int\left[sin \left(log\,x\right)+cos\left(log\,x\right)\right]dx $ is equal to

If $ {{\tan }^{-1}}\,2 $ and $ {{\tan }^{-1}}\,3 $ are two angles of a triangle, then the third angle is

The sum of the series $ \left( 1+\frac{{{({{\log }_{e}}\,n)}^{2}}}{2!}+\frac{{{({{\log }_{e}}n)}^{4}}}{4!}+... \right) $ is

The image of the point $ (6,3,9) $ in the straight line $ x-2=\frac{1-y}{2}=\frac{z}{2} $ is

The term independent of $x$ in the expansion of $ {{\left( \sqrt{\frac{x}{3}}+\frac{3}{2{{x}^{2}}} \right)}^{10}} $ is

The number of ways in which $5$ boys and $5$ girls can be seated for a photograph so that no two girls sit next to each other is

If $ {{x}_{1}},{{x}_{2}},......{{x}_{18}} $ are observations such, that $ \sum\limits_{j=1}^{18}{({{x}_{j}}-8)=9} $ and $ \sum\limits_{j=1}^{18}{{{({{x}_{j}}-8)}^{2}}=45,} $ then the standard deviation of these observations is