An aircraft executes a horizontal loop with a speed of $150 \, m/s$ with its wings banked at an angle of $12^\circ$. The radius of the loop is .......... $km$. $(g = 10 \, m/s^2)$

The cumulative number of ill patients $N( t )$ during an epidemic in a country is given by the following equation $N(t)=\frac{N_0 \exp (t / \tau)}{1+N_0(\exp (t / \tau)-1) / N_s}$ where $N _0$ is the initial population of ill patients, $\tau$ a positive constant and $N _5\left( > > N _0\right)$ is a large number. Then, which of the following statements is true ?