JIPMAT 2024 (QA) PYQs

The minimum value of $(2 \sin^2\theta + 3 \cos^2\theta)$ is

Two poles of height 6 m and 11 m stand vertically upright on a plane ground. If the distance between their foot is 12 m, then the distance between their tops is

Given below are two statements:

Statement I: $\frac{\cot 30^{\circ}+1}{\cot 30^{\circ}-1}=2\left(\cos 30^{\circ}+1\right)$

Statement II : $2 \sin 45^{\circ} \cos 45^{\circ}-\tan 45^{\circ} \cot 45^{\circ}=0$