List of top Mathematics Questions

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

The number of solutions of the equation $ \sin \,x\,\,\cos \,\,3x=\sin \,3x\,\,\cos \,5x $ in $ \left[ 0,\frac{\pi }{2} \right] $ is

$ \frac{^{8}{{C}_{0}}}{6}{{-}^{8}}{{C}_{1}}{{+}^{8}}{{C}_{2}}\cdot 6{{-}^{8}}{{C}_{3}}{{.6}^{2}}+....{{+}^{8}}{{C}_{8}}{{\cdot 6}^{7}} $ is equal to

The value of $ {{\cos }^{-1}}\,\left( \sin \,\frac{7\pi }{6} \right) $ is equal to

In $ \Delta \,\,ABC $ if $ si{{n}^{2}}A+si{{n}^{2}}B+si{{n}^{2}}C=2, $ then the triangle is

The point on the x-axis equidistant from the points $ (4,3,1) $ and $ (-2,\,-6,\,-2) $ is

If $ (3+i)\,(z+\bar{z})-(2+i)(z-\bar{z})+14i\,=0, $ then $ z\bar{z} $ is equal to

Find the function $ f(x_1, x_2, x_3) $ satisfying $ f(x_1, x_2, x_3) = 1 $ at $ x_1 = 1, x_2 = x_3 = 0 $ .

Joint equation of pair of lines through $ (3, - 2) $ and parallel to $ x^2 - 4xy + 3y^2 = 0 $ is