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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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?

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

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

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

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

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

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