$A$ circular wire of radius $7\,cm$ is cut and bent again into an arc of a circle of radius $12\,cm$. The angle subtended by the arc at the centre is ......$^o$

If a circle with radius $2.5$ units passes through the points $(2, 3)$ and $(5, 7)$,then its centre is

The area of the circle whose centre is at $(1, 2)$ and which passes through the point $(4, 6)$ is

If $z_1$ is a point on $z\bar{z} = 1$ and $z_2$ is another point on $(4 - 3i)z + (4 + 3i)\bar{z} - 15 = 0$,then $|z_1 - z_2|_{min}$ is (where $i = \sqrt{-1}$)

The line $2x - 3y = 1$ divides the circular region $x^2 + y^2 \leq 6$ into two parts. If $S = \left\{ \left(2, \frac{3}{4}\right), \left(\frac{5}{2}, \frac{3}{4}\right), \left(\frac{1}{4}, -\frac{1}{4}\right), \left(\frac{1}{8}, \frac{1}{4}\right) \right\}$,then the number of points in the set $S$ that lie inside the smaller part is:

If the point $(\lambda, 1+\lambda)$ lies inside the circle $x^2+y^2=1$,then