List of top Mathematics Questions

All the words that can be formed using alphabets $A, H, L, U$ and $R$ are written as in a dictionary (no alphabet is repeated). Rank of the word RAHUL is

A ray of light coming from the point $(1, 2)$ is reflected at a point $A$ on the $x$-axis and then passes through the point $(5, 3)$. The co-ordinates of the point $A$ is

The equation $x^2 - 2 \sqrt{3} xy + 3y^2 - 3x + 3 \sqrt{3} y - 4 = 0 $ represents

The line joining $(5,0)$ to $((10 \cos \theta, 10 \sin \theta)$ is divided internally in the ratio $2: 3$ at $P$. If $q$ varies, then the locus of $P$ is

The number of integral values of $\lambda$ for which $x^2 + y^2 + \lambda x + (1 - \lambda )y + 5 = 0 $ is the equation of a circle whose radius cannot exceed $5$, is

$ABC$ is a triangle in a plane with vertices $A(2, 3, 5), B(-1, 3, 2)$ and $C(\lambda , 5, \mu)$. If the median through $A$ is equally inclined to the coordinate axes, then the value of $(\lambda^3 + \mu^3 + 5)$ is :

The differential coefficient of $\log_{10} x$ with respect to $\log_{x} 10$ is

A wire of length $2$ units is cut into two parts which are bent respectively to form a square of side $= x$ units and a circle of radius $= r$ units. If the sum of the areas of the square and the circle so formed is minimum, then :

Let $p = \displaystyle\lim_{x \to 0^+ } ( 1 + \tan^2 \sqrt{x} )^{\frac{1}{2x}}$ then $log \,p$ is equal to

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 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