List of top Mathematics Questions

If $\frac{^{n+2}C_6}{^{n-2}P_2} = 11$, then $n$ satisfies the equation :

If the four letter words (need not be meaningful ) are to be formed using the letters from the word $"MEDITERRANEAN"$ such that the first letter is $R$ and the fourth letter is $E$, then the total number of all such words is :

Direction cosines of the line $\frac{x+2}{2} = \frac{2y-5}{3}, z = -1$ is

The sum $\displaystyle\sum^{10}_{r=1}(r^2 + 1) \times (r!)$ is equal to :

If the sum of the first ten terms of the series $\left(1 \frac{3}{5}\right)^{2} + \left(2 \frac{2}{5}\right)^{2} + \left(3 \frac{1}{5}\right)^{2} + 4^{2} + \left(4 \frac{4}{5}\right)^{2} + .... , $ is $\frac{16}{5} m , $ then $m$ is equal to :

If $\omega$ is an imaginary cube root of unity, then the value of $\left(2-\omega\right)\left(2-\omega^{2}\right)+2\left(3-\omega\right)\left(3-\omega^{2}\right)+.....+\left(n-1\right)\left(n-\omega\right)\left(n-\omega^{2}\right)$

If $ X=\left\{-2, -1, 0, 1,2,3, 4, 5, 6, 7, 8\right\} $ and $ A=\left\{x : \left|x-2\right|\le3, x \, is\,an\, integer\right\}, $ then $ X-A= $

The integral $\displaystyle\int \frac{dx}{(1+ \sqrt{x}) \sqrt{x - x^2}}$ is equal to (where $C$ is a constant of integration)

The system of linear equations $x + \lambda y - z = 0$ $\lambda x -y - z = 0$ $x + y - \lambda z = 0$ has a non-trivial solution for :

Let $ A(a, 0) $ , $ B(0, b) $ and $ C (1, 1) $ be three points. If $ \frac{1}{a}+\frac{1}{b}=1 $ , then the three points are

If Matrix $A = \begin{bmatrix}1&2\\ 4&3\end{bmatrix}$ such that $Ax = I$, then $X = $_______

If $p :$ Every square is a rectangle $q :$ Every rhombus is a kite then truth values of $p ? q$ and $p ? q$ are __________ and ___________ respectively.

If $ y=tan^{-1}\left(\frac{2x}{1+3x^{2}}\right)+tan^{-1}\left(\frac{5+x}{1-5x}\right) $ , then $ \frac{dy}{dx}= $

$\int \left(\frac{\left(x^{2}+2\right)a^{\left(x +tan^{-1}x\right)}}{x^{2}+1}\right)dx = $

The coefficient of $ x^{2} $ in the expansion of $ (1 + x + x^{2} + x^{3})^{10} $ is

The value of $ \displaystyle\lim_{x\to\infty} \left(\frac{x+5}{x+2}\right)^{x} $ is equal to

The mean of $ 100 $ items was $ 60 $ . Later it was found that two items were misread as $ 69 $ and $ 96 $ instead of $ 66 $ and $ 99 $ respectively. The correct mean of the $ 100 $ items is

A normal to the curve $ 2x^{2 }- y^{2} = 14 $ at the point $ (x_{1}, y_{1}) $ is parallel to the straight line $ x + 3y = 4 $ . Then the point $ (x_{1}, y_{1}) $ is

The value of integral \(\int{e^x}(\frac{cosx+sinx}{cos^2x})dx\)

When $ y = vx $ , $ y $ and $ x $ are variables, the differential equation $ \frac{dy}{dx}=\frac{2xy}{x^{2}-y^{2}} $ reduces to

Let the function $ f(x) $ be continuous in the interval $ [a, b] $ and differentiable in $ (a, b) $ . Then there is at least one point $ c $ in $ (a, b) $ at which the tangent to the curve $ y = f (x) $ is parallel to

$\int\left(\frac{4e^{2}-25}{2e^{x}-5}\right)dx = Ax+B \,\,log |2e^{x}-5|+c$ then

Let $ P\left(x\right)=^{10}C_{x} \left(\frac{1}{2}\right)^{10} , x=0, 1, 2, \ldots,10 $ be the probability mass function of a binomial distribution $ X $ . Then the mean of $ X $ is