JIPMAT (QA) PYQs

Two ships are sailing in the sea on the two sides of a lighthouse. The angles of elevation of the top of the lighthouse as observed from two ships are 30° and 45°, respectively. If the lighthouse is 100 m high, the distance between two ships is approximately:

Given below are two statements:

Statement I: $\frac{\cot 30^{\circ}+1}{\cot 30^{\circ}-1}=2\left(\cos 30^{\circ}+1\right)$

Statement II : $2 \sin 45^{\circ} \cos 45^{\circ}-\tan 45^{\circ} \cot 45^{\circ}=0$

Given below are two statement:

Statement I: If $\sin (\theta)=\frac{5}{13}$, then the value of $\tan (\theta)=\frac{5}{12}$

Statement II: if $\cot (\theta)=\frac{12}{5}$, then the value of $\sin (\theta)=\frac{5}{12}$

In the light of the above statements, choose the correct answer form the question below: