List of top Mathematics Questions

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

$ \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 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 term independent of $x$ in the expansion of $ {{\left( \sqrt{\frac{x}{3}}+\frac{3}{2{{x}^{2}}} \right)}^{10}} $ 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 point on the x-axis equidistant from the points $ (4,3,1) $ and $ (-2,\,-6,\,-2) $ is

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

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

The number of diagonals of a polygon of $20$ sides is

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

If the third term of a $G.P.$ is $3$, then the product of its first $5$ terms is

If $X$ and $Y$ are $ 2\times 2 $ matrices such that $ 2X+3Y=O $ and $ X+2Y=I, $ where $ O $ and $ I $ denote the $ 2\times 2 $ zero matrix and the $ 2\times 2 $ identity matrix, then $X$ is equal to

The value of $\begin{vmatrix} \log_5\,729 & \log_3\,5 \\[0.3em] \log_5\,27 & \log_9\,25 \end{vmatrix}.\begin{vmatrix} \log_3\,5 & \log_{27}\,5 \\[0.3em] \log_5\,9 & \log_5\,9 \end{vmatrix}=$

If $ f\,(x)=\underset{y\to x}{\mathop{lim}}\,\,\frac{{{\sin }^{2}}y-{{\sin }^{2}}x}{{{y}^{2}}-{{x}^{2}}}, $ then $ \int{4x\,\,f(x)\,\,dx} $ =

$x \in R : \frac{2x -1}{x^3 + 4x^2 + 3x} \in R$ Equals

If the sum to $2n$ terms of the $ A.P. \text{ }2,\text{ }5,\text{ }8,11,... $ is equal to the sum to $n$ terms of the $\text{ }57,\text{ }59,\text{ }61,\text{ }63,\text{ }...\text{ }, $ then $n$ =

In a boolean algebra $B$ with respect to $' +' $ and $'.',$ $ x' $ denotes the negation of $ x\in B $ . Then