$A$ calcite crystal is placed over a dot on a piece of paper and rotated. On seeing through the calcite,one will see:

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

Select the correct option on the basis of the following sentences regarding a gland's function:
$(I)$ Hormones increase alertness.
$(II)$ Hormones increase the heart beat.
$(III)$ Stimulate the breakdown of glycogen.
$(IV)$ Stimulate the breakdown of lipids and proteins.

$A$ body is projected vertically upwards at time $t=0$ and it is seen at a height $H$ at time $t_1$ and $t_2$ seconds during its flight. The maximum height attained is ($g$ is acceleration due to gravity).

If the parametric equations of the circle passing through the points $(3,4), (3,2)$ and $(1,4)$ are $x=a+r \cos \theta$ and $y=b+r \sin \theta$,then find the value of $b^a r^a$.

Exhausted permutit does not contain $.......$ ion.