Milk is an example of

The value of $a$ such that $f(x) = \sqrt{3} \sin x - \cos x - 2ax + b$ decreases for all real values of $x$ is given by:

$\int_0^1 \sin \left(2 \tan ^{-1} \sqrt{\frac{1+x}{1-x}}\right) d x$ is equal to :

$A$ fire hydrant delivers water of density $\rho$ at a volume rate $L$. The water travels vertically upward through the hydrant and then makes a $90^o$ turn to emerge horizontally at speed $V$. The pipe and nozzle have a uniform cross-section throughout. The force exerted by the water on the corner of the hydrant is

If the circle $x^2 + y^2 + 6x - 2y + k = 0$ bisects the circumference of the circle $x^2 + y^2 + 2x - 6y - 15 = 0$,then $k =$

Changes in $GnRH$ pulse frequency in females is controlled by circulating levels of