$\frac{\sin \theta}{1 - \cot \theta} + \frac{\cos \theta}{1 - \tan \theta} = $

The air density at Mount Everest is less than that at sea level. Mountaineers find that for one trip lasting a few hours,the extra oxygen needed corresponds to $30,000 \ cc$ at sea level (pressure $1 \ atm$,temperature $27^{\circ}C$). Assuming that the temperature around Mount Everest is $-73^{\circ}C$ and that the oxygen cylinder has a capacity of $5.2 \ L$,the pressure at which $O_2$ must be filled in the cylinder is ..... $atm$.

$\cos 36^{\circ} - \cos 72^{\circ}$ is equal to

Given that $a, b \in \{0, 1, 2, \ldots, 9\}$ with $a+b \neq 0$ and that $\left(a+\frac{b}{10}\right)^x = \left(\frac{a}{10}+\frac{b}{100}\right)^y = 1000$. Then,$\frac{1}{x}-\frac{1}{y}$ is equal to

Which of the following is a reducing sugar?

$ABCD$ is a square with side $16$ units and $A$ is the origin. If the equation of the circle circumscribing the square $ABCD$ is $x^2+y^2=4k(x+y)$,then $k=$