The ratio of angular speeds of the minute hand and the hour hand of a watch is

The point $P$ is equidistant from $A(1, 3)$,$B(-3, 5)$,and $C(5, -1)$. Then $PA$ is equal to:

$x = \log \left( \frac{1}{y} + \sqrt{1 + \frac{1}{y^2}} \right) \Rightarrow y$ is equal to

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 $k$ is equal to :

$19 \ g$ of a mixture containing $NaHCO_3$ and $Na_2CO_3$ on complete heating liberated $1.12 \ L$ of $CO_2$ at $STP$. The weight of the remaining solid was $15.9 \ g$. What is the weight (in $g$) of $Na_2CO_3$ in the mixture before heating?

$\sinh ^{-1} 2 + \sinh ^{-1} 3 = x \Rightarrow \cosh x$ is equal to