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

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

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

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

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

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

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

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

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?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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