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

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

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

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

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 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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?

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

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

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

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

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

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

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

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

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