IIM-K (BMSAT) 2025 (QA) PYQs

The number of pairs $(x, y)$ satisfying the equation $\sin x + \sin y = \sin(x + y)$ and $|x| + |y| = 1$ is

Ayesha is standing atop a vertical tower $200 m$ high and observes a car moving away from the tower on a straight, horizontal road from the foot of the tower. At 11:00 AM, she observes the angle of depression of the car to be $45^{\circ}$. At 11:02 AM, she observes the angle of depression of the car to be $30^{\circ}$. The speed at which the car is moving is approximately

Given that $\cos x + \cos y = 1$, the range of $\sin x - \sin y$ is