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

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

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

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

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

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

$\tan^{-1}(\frac{x}{y})-\tan^{-1}(\frac{x-y}{x+y})$ 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 $A=\begin{bmatrix} 3 & 0 \\ 0 & 3 \\ \end{bmatrix}$, then find "A", $(n \in \mathbb{N})$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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