List of top Mathematics Questions

The differential equation of the rectangular hyperbola, where axes are the asymptotes of the hyperbola, is?

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

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

A coin is tossed $7$ times. Each time a man calls head. Find the probability that he wins the toss on more occasions.

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 :

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

An arch of a bridge is semi-elliptical with major axis horizontal. If the length the base is $9$ meter and the highest part of the bridge is $3$ meter from the horizontal; the best approximation of the height of the arch. $2$ meter from the centre of the base is

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

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

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-

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

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

If $a, b, c$ are three non-coplanar vectors and $p, q, r$ are reciprocal vectors, then $(la + mb + nc). (lp + mq + nr)$ is equal to

How many $5$ digit telephone numbers can be constructed using the digits $0$ to $9$, if each number starts with $67$ and no digit appears more than once ?

If $21^{st}$ and $22^{nd}$ terms in the expansion of $(1 + x)^{44}$ are equal, then $x$ is equal to

The triangle formed by the tangent to the curve $f (x) = x2 + bx - b$ at the point $(1,1)$ and the coordinate axes lies in the first quadrant. If its area is $2$, then the value of b is

If there is an error of $k\%$ in measuring the edge of a cube, then the percent error in estimating its volume is

Let $f ' (x),$ be differentiable $\forall \, x.$ If $f (1) = -2$ and $f '(x) \geq 2 \forall x \in [1, 6],$ then

If the points $(1, 2, 3)$ and $(2, -1, 0)$ lie on the opposite sides of the plane $2x + 3y - 2z = k,$ then

If the system of equations $x + ky - z = 0, 3x - ky - z = 0$ and $x - 3y + z = 0$, has non-zero solution, then $k$ is equal to

The minimum value of $\frac{x}{\log \, x}$ is

If a plane meets the coordinate axes at $A,B$ and $C$ such that the centroid of the triangle is $(1, 2, 4)$, then the equation of the plane is

Two lines $ \frac{x-1}{2} = \frac{y+1}{3} = \frac{z -1}{4}$ and $ \frac{x-3}{1} = \frac{y-k}{2} = z $ intersect at a point, if $k$ is equal to