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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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?

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

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

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

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

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

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

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

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

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

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?

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

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

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

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