List of top Mathematics Questions

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

The locus of centre of a circle which passes through the origin and cuts off a length of $4$ unit from the line $x = 3$ is

The image of the point $(3, 2, 1)$ in the plane $2x-y+3z = 7$ is

$\frac{\cos \, x}{\cos \, x -2y} = \lambda \, \Rightarrow \, \tan \, x - y$ is equal to

The roots of $ (x- a) (x - a-1) + (x - a -1) (x - a - 2) + (x - a) (x - a - 2) = 0 , a \in R$ are always

Let $f(x) = x^2 + ax + b,$ 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

If $x, y, z$ are all positive and are the $p^{th}, q^{th}$ and $r^{th}$ terms of a geometric progression respectively, then the value of the determinant $\begin{vmatrix} \log x & p & 1 \\ \log y & q & 1 \\ \log z & r & 1 \end{vmatrix} = 0 $ equals

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

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

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