IIM-K (BMSAT) 2025 (QA) 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

The angle of elevation of the top of a pole from a point A on the ground is 30°. The angle of elevation changes to 45°, after moving 20 meters towards the base of the pole. Then the height of the pole, in meters, 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