IPMAT Indore 2021 (MCQ) PYQs

If (\sin \alpha+\sin \beta=\frac{\sqrt{2}}{\sqrt{3}}) and (\cos \alpha+\cos \beta=\frac{1}{\sqrt{3}}), then the value of (\left(20 \cos \left(\frac{\alpha-\beta}{2}\right)\right)^{2}) is _________.

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