List of top Mathematics Questions

The slope of the line touching both the parabolas $y^2 = 4x$ and $x^2 = - 32y$ is :

Three positive numbers form an increasing $G.P.$ If the middle term in this $G.P.$ is doubled, then new numbers are in $A.P.$ Then, the common ratio of the $G.P.$ is

If $ 1 + x^4 + x^5 = \sum\limits^{5}_{i =0} a_i$ $(1 + x)^i$ , for all $x$ in $R$, then $a_2$ is:

Let the population of rabbits surviving at a time $t$ be governed by the differential equation $\frac {dp(t)}{dt}=\frac {1}{2} p(t)-200.$ If $p(0)=100,$ then $p(t)$ is equal to

If $X = \{4^n- 3 n - 1: n \in N \}$ and $Y = \{9 (n - 1): n \in N \}$ ,where $N$ is the set of natural numbers, then $ X \cup Y$ is equal to

The area (in sq units) of the region described by $A=\left\{(x, y): x^{2}+y^{2} \leq 1\right.$ and $\left.y^{2} \leq 1-x\right\}$ is:

The coefficient of $x^{50}$ in the binomial expansion of $(1 + x)^{1000} + x (1 + x)^{999} + x^2(1 + x)^{998} + .... + x^{1000}$ is:

Equation of the line of the shortest distance between the lines $\frac{x}{1} = \frac{y}{-1} = \frac{z}{1}$ and $\frac{x-1}{0} = \frac{y+1}{-2} = \frac{z}{1}$ is :

Let $f\left(n\right) = \left[\frac{1}{3} + \frac{3n}{100}\right]{n},$ where $\left[n\right]$ denotes the greatest integer less than or equal to n. Then $\sum\limits^{56}_{n = 1} \Delta_{r} f\left(n\right)$ is equal to :

If a line intercepted between the coordinate axes is trisected at a point $A(4, 3)$, which is nearer to $x$-axis, then its equation is :

The number of terms in an $A.P$. is even; the sum of the odd terms in it is $24$ and that the even terms is $30$. If the last term exceeds the first term by $10 \frac{1}{2},$ then the number of terms in the $A.P$. is :

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 $(T_0 -T_2 + T_4 - .......)^2 + (T_1 - T_3 + T_5 - .....)^2 =$

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 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-

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

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