List of top Mathematics Questions

Through the vertex $O$ of a parabola $y^2 = 4x$, chords $OP$ and $OQ$ are drawn at right angles to one another. The locus of the middle point of $PQ$ is

If $\begin{bmatrix}\alpha&\beta\\ \gamma&-\alpha\end{bmatrix}$ is square root of identity matrix of order $2$ then

The angle of intersection of the two circles $x^2 + y^2 - 2x - 2y = 0$ and $x^2 + y^2 = 4$, is

$i^{57} + \frac{1}{i^{25}}$, when simplified has the value

The number of all three elements subsets of the set $\{a_1, a_2, a_3 . . . a_n\}$ which contain $a_3$ is

The complex number $z = z + iy$ which satisfies the equation $\left| \frac{z-3i}{z+3i}\right| = 1 $, lies on

The product of n positive numbers is unity, then their sum is :

The coefficient of $x^4$ in the expansion of $(1 + x + x^2 + x^3)^{11}$, is

If $T_0, T_1, T_2.....T_n$ represent the terms in the expansion of $ (x + a)^n$, then $(T_0 -T_2 + T_4 - .......)^2 + (T_1 - T_3 + T_5 - .....)^2 =$

If the $(2p)^{th}$ term of a H.P. is $q$ and the $(2q)^{th}$ term is $p$, then the $2(p + q)^{th}$ term is-

Consider $\frac{x}{2} + \frac{y}{4} \ge1 $ and $\frac{x}{3} + \frac{y}{2} \le 1 , x ,y \ge0 $. Then number of possible solutions are :

If M. D. is $12$, the value of S.D. will be

If $A = \begin{bmatrix}1&1\\ 1&1\end{bmatrix}$ then $A^{100}$ :

If $P_1$ and $P_2$ be the length of perpendiculars from the origin upon the straight lines $x \sec \theta + y cosec \theta = a$ and $x \cos \theta - y \sin \theta = a \cos 2 \theta$ respectively, then the value of $4P_1{^2} + P_2{^2}$.

Let $f : R \to R$ be a function defined by $f(x) = \frac{x -m}{x-n}$ , where $m \neq n$, then

In how many ways can a committee of $5$ made out $6$ men and $4$ women containing atleast one woman?

Let $a \in R$ and let $f: R \rightarrow R$ be given by $f(x)=x^{5}-5 x+a$, then

If $\frac{1}{a} , \frac{1}{b} , \frac{1}{c} $ are in A. P., then $\left(\frac{1}{a} + \frac{1}{b} - \frac{1}{c}\right) \left(\frac{1}{b} + \frac{1}{c} - \frac{1}{a}\right) $ is equal to

The inverse of the matrix $A =\begin{bmatrix} {2}&{0} &{0}\\ {0}&{3}& {0} \\ {0}&{0}&{4}\\ \end{bmatrix}$ is

If $A$ is a matrix of order $3$, such that $A (adj A) = 10\, I$, then $|adj A| $ =

If $x^{2}+\alpha y^{2}+2 \beta y=a^{2} \quad$ represents a pair of perpendicular lines, then $\beta$ equals to

Which of the following is not a correct statement ?

Let C be the circle with centre at (1, 1) and radius = 1. If T is the circle centred at (0, y) passing through origin and touching the circle $C$ externally, then the radius of$ T $is equal to

Let $L_1$ be the length of the common chord of the curves $x^2+y^2 = 9$ and $y^2 = 8x,$ and $L_2$ be the length of the latus rectum of $y^2 = 8x,$ then :