Question : Ashok runs $2 \frac{2}{3}$ times as fast as Bharat. If Ashok gives Bharat a head start of 160 m, then how far must the winning post be so that Ashok and Bharat can reach it at the same time?

Option 1: 225 m

Option 2: 256 m

Option 3: 240 m

Option 4: 200 m

Question : The value of $(0.3)^{[\frac {(200-146)}{(3 \times 3 \times 3)}-3]}$ is:

Option 1: $\frac{10}{3}$

Option 2: $\frac{5}{3}$

Option 3: $\frac{7}{3}$

Option 4: $\frac{8}{3}$

Question : If $\frac{\cos \beta}{\sec \alpha}=15$ and $\frac{\sin \beta}{\sec \alpha}=16$, the value of $\sin ^2 \beta$ is:

Option 1: $\frac{256}{481}$

Option 2: $-\frac{256}{481}$

Option 3: $\frac{481}{256}$

Option 4: $-\frac{481}{256}$

Question : What is the value of $\frac{\frac{1}{3}+\frac{1}{3}\times\frac{1}{3}}{\frac{1}{3}\times\frac{1}{3}+\frac{1}{3}}$?

Option 1: 1

Option 2: 3

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

Option 4: $\frac{1}{2}$

Question : If $\cot A = \frac{15}{8}$, then what will be the value of $\tan 2 A ?$

Option 1: $\frac{200}{161}$

Option 2: $\frac{240}{161}$

Option 3: $\frac{240}{173}$

Option 4: $\frac{220}{171}$

Question : If $M =\left ( \frac{3}{7} \right ) ÷ \left ( \frac{6}{5} \right ) ×\left ( \frac{2}{3} \right ) + \left ( \frac{1}{5} \right ) ×\left ( \frac{3}{2} \right )$ and $N = \left ( \frac{2}{5} \right ) × \left ( \frac{5}{6} \right ) ÷ \left ( \frac{1}{3} \right ) + \left ( \frac{3}{5} \right ) × \left ( \frac{2}{3} \right ) ÷ \left ( \frac{3}{5} \right )$,
then what is the value of $\frac{M}{N}$?

Option 1: $\frac{207}{560}$

Option 2: $\frac{339}{1120}$

Option 3: $\frac{113}{350}$

Option 4: $\frac{69}{175}$