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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 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

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

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

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

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

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

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

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

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

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

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

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

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