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 $\pi = 3.14$).

If ${c^2} > {a^2}(1 + {m^2})$,then the line $y = mx + c$ will intersect the circle ${x^2} + {y^2} = {a^2}$ at:

If two distinct chords,drawn from the point $(p, q)$ on the circle ${x^2} + {y^2} = px + qy$ (where $pq \neq 0$),are bisected by the $x$-axis,then:

Given two circles $x^2+y^2+8x-6y-24=0$ and $x^2+y^2-4x+10y+20=0$. Then they are

The number of common tangents of the circles $x^2+y^2-4=0$ and $x^2+y^2-6x-8y-24=0$ is

Two circles in the first quadrant of radii $r_1$ and $r_2$ touch the coordinate axes. Each of them cuts off an intercept of $2$ units with the line $x+y=2$. Then $r_1^2+r_2^2-r_1 r_2$ is equal to $...........$