JIPMAT (QA) PYQs

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

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:

The minimum value of $(2 \sin^2\theta + 3 \cos^2\theta)$ is