Question : A well of 3 m in diameter is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

Option 1: 4.25 m

Option 2: 2.25 m

Option 3: 1.125 m

Option 4: 1.75 m

Question : A ball is to be made with an inner radius of 2 units and an outside radius of 3 units. How much material is required to make the ball?

Option 1: $\frac{19}{3} \pi$

Option 2: $19 \pi$

Option 3: $\frac{76}{3} \pi$

Option 4: $\pi$

Question : An athlete runs 8 times around a circular field of radius 7 m in 3 minutes 40 seconds. His speed (in km/hr) is:
(Take $\pi=\frac{22}{7}$ )

Option 1: $\frac{72}{25}$

Option 2: $\frac{118}{25}$

Option 3: $\frac{144}{25}$

Option 4: $\frac{108}{25}$

Question : The radius of the incircle of an equilateral $\Delta$ ABC of side $2\sqrt{3}$ cm is $x$ cm. The value of $x$ is:

Option 1: $\frac{1}{3}$

Option 2: $\frac{1}{2}$

Option 3: $1$

Option 4: $\sqrt{3}$

Question : If $\tan A = n\tan B$ and $\sin A=m \sin B$, then the value of $\cos^{2}A$ is:

Option 1: $\frac{m^{2}-1}{n^{2}+1}$

Option 2: $\frac{m^{2}+1}{n^{2}-1}$

Option 3: $\frac{m^{2}+1}{n^{2}+1}$

Option 4: $\frac{m^{2}-1}{n^{2}-1}$