JIPMAT 2023 (QA) PYQs

If $\sin \theta+\cos \theta=\frac{\sqrt{7}}{2}$, then $(\sin \theta-\cos \theta)$ is equal to :

If $\frac{\sin\theta + \cos\theta}{\sin\theta - \cos\theta} = 3$, then value of $\sin^4\theta - \cos^4\theta$ is

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: