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?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$A=\{-1, 0, 1, 2\}, B=\{0, 1, 4\}$ and $f: A \to B\,$ defined by $f(x)=x^2$, then $f$ 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 $2x+3y \geq 12 \,$, $x+y \leq 5 , x\geq 0 \, and \, y \geq 0$

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

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

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

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

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

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