IPMAT Indore 2019 (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 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