The point of Concurrency of the right bisectors of the sides of a triangle is called

If $\tan {15^o}=2-\sqrt{3}\,$ then the value of $\cot^2{75^o}\,$ is

An escalator in a department store makes an angle of $45^o$ with the ground. How long is the escalator if it carries people a vertical distance of $24$ feet?

Which of the following is a point in the feasible region determined by the linear inequalities $2x+3y \leq 6\, and\, 3x-2y \leq16 \, ?$

Divide $\frac{5+2i}{4-3i}$

If the angle of depression of an object from a $75$m high tower is $30^o$, then the distance of the object from the tower is

The maximum value of the function $f=5x+3y$ subjected to the constraints $x \geq 3 \, and\, y \geq 3 \,$ is ________

With usual notations $rr_{1}r_{2}r_{3}=$

If $A=\begin{bmatrix} \alpha & 2 \\ 2 & \alpha \\ \end{bmatrix}$ and $|A^3|=125$ then the value of $\alpha$ is

A point is in Quadrant -III and on the unit circle. If its x-coordinate is $-\frac{4}{5}$ what is the y-coordinate of the point?

$\cos {50^o 50'}\cos {9^o 10'}-\sin {50^o 50'}\sin {9^o 10'}=$

If $\begin{vmatrix} 7a-5b & 3c \\ -1 & 2 \\ \end{vmatrix}=0$, then which one of the following is correct?

If $ |A| = 47$, then find $|A^t|$

If $f(x)=x^3-\frac{1}{x^3} $, then $f(x)+f(\frac{1}{x})=$

$\sin {\theta} \cos(90^o-\theta)+\cos {\theta} \sin(90^o-\theta)=$

$(\frac{2i}{1+i})^2$

If $det(A)=5$, then find $det(15A)$ where A is of order $2 \times 2$

$A=\{-1, 0, 1, 2\}, B=\{0, 1, 4\}$ and $f: A \to B\,$ defined by $f(x)=x^2$, then $f$ is

If $\tan(\alpha + \beta) = \frac{1}{2}\,$ and $\tan {\alpha} = \frac{1}{3} \,$, then $\tan {\beta}=$

$\tan^{-1}\sqrt{3}-\sec^{-1}(-2)\,$ is equal to

$\tan^{-1}(\frac{x}{y})-\tan^{-1}(\frac{x-y}{x+y})$ is equal to

$1+i^2+i^4+i^6+...+i^{2n}$

What is the domain of $f(x)=\sqrt\frac{2-x}{x+2}$ ?

If $z=x+iy$ and $|\frac{z-5i}{z+5i}|=1$ then $z$ lies on

If $\sin^{-1}{x}=y\,$ then

The domain of $y=\frac{x}{\sqrt{x^2-3x+2}}\,$ is

If $f(x)=x^2-3x+4$, then find the values of $x$ satisfying the equation $f(x)=f(2x+1)$

Maximize $5x+7y$, subject to the constraints $2x+3y \geq 12 \,$, $x+y \leq 5 , x\geq 0 \, and \, y \geq 0$

Solve $\sin{4x} \cos{x} + \cos{4x} \sin{x} =-$ for all radian solutions.

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

$\tan(\sin^{-1}{x})$ is equal to

If $A=\begin{bmatrix} 3 & 0 \\ 0 & 3 \\ \end{bmatrix}$, then find "A", $(n \in \mathbb{N})$

Find the profit function $p$ if it yields the value $11$ and $7$ at $(3, 7)$ and $(1, 7)$ respectively

The solution of the system of inequalities $x\geq\,0, x-5 \leq 0$ and $x \geq y$ is a polygonal region with the vertices as

If in an isosceles triangle, 'a' is the length of the base and 'b' the length of one of the equal sides, then its area is