IPMAT Indore 2019 (SA) PYQs

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 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

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