The minute hand of a watch is $1.5 \, \text{cm}$ long. How far does its tip move in $40$ minutes (in $, \text{cm}$)? (Use $\pi = 3.14$).

Let a circle $C$ pass through the points $(4, 2)$ and $(0, 2)$,and its centre lie on the line $3x + 2y + 2 = 0$. Then the length of the chord of the circle $C$ whose midpoint is $(1, 2)$ is:

$A$ rectangle $R$ with end points of one of its sides as $(1, 2)$ and $(3, 6)$ is inscribed in a circle. If the equation of a diameter of the circle is $2x - y + 4 = 0$,then the area of $R$ is

$A$ line meets the coordinate axes at $A(a, 0)$ and $B(0, b)$. If the perpendicular distances from $A$ and $B$ to the tangent drawn at the origin to the circumcircle of $\triangle OAB$ are $m$ and $n$ respectively,then the diameter of that circle is

For the line $3x + 2y = 12$ and the circle $x^2 + y^2 - 4x - 6y + 3 = 0$,which of the following statements is true?

$A$ line is drawn through a fixed point $P(\alpha, \beta)$ to cut the circle $x^{2}+y^{2}=r^{2}$ at $A$ and $B$. Then $PA \cdot PB$ is equal to