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

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

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

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

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

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

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

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

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

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

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

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?

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

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

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?

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

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

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

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

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

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

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

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

$\tan(\sin^{-1}{x})$ 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 $A=\begin{bmatrix} \alpha & 2 \\ 2 & \alpha \\ \end{bmatrix}$ and $|A^3|=125$ then the value of $\alpha$ is

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

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

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

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