The radius of a field in the shape of a sector is $50 \, m$. The cost of fencing its boundary is ₹ $5400$ at the rate of ₹ $30 / m$. Find the cost of tilling at the rate of ₹ $15 / m^2$. (in ₹)

In $\odot(O, r)$,the length of minor $\widehat{ACB}$ is $\frac{1}{6}$ times the circumference of the circle. Then,the measure of the angle subtended at the centre by minor $\widehat{ACB}$ is ......... (in $^{\circ}$)

The formula to find the length of a major arc of a circle is ............

The radius of a wheel of a car is $21 \, cm$. If it makes $800$ rotations per minute,find the speed of the car in $km/h$.

In the figure,a circle is inscribed in a square of side $5 \, cm$ and another circle is circumscribing the square. Is it true to say that the area of the outer circle is two times the area of the inner circle? Give reasons for your answer.

In a circle with radius $30\,cm$,a minor arc subtends an angle of measure $60^{\circ}$ at the centre. Then,the area of the minor sector formed by that arc is $\ldots \ldots \ldots \ldots$ $cm^{2}$. $(\pi = 3.14)$