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

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?

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

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

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

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

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

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

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

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

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

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

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

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

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

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?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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