IPMAT Indore 2020 (MCQ) PYQs

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

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 _________.

If $cos \alpha$ + $cos \beta$ = 1 then the maximum value of $sin \alpha - sin \beta$ is