IPMAT Indore 2019 (MCQ) PYQs

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

If the angles $A, B, C$ of a triangle are in arithmetic progression such that $\sin(2A + B) = 1/2$ then $\sin(B + 2C)$ is equal to

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