IPMAT Indore 2019 (MCQ) PYQs

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

The value of $\cos^2\left(\frac{\pi}{8}\right) + \cos^2\left(\frac{3\pi}{8}\right) + \cos^2\left(\frac{5\pi}{8}\right) + \cos^2\left(\frac{7\pi}{8}\right)$ is

The set of all real value of $p$ for which the equation $3 \sin^2x + 12 \cos x - 3 = p$ has at least one solution is