Height and Distance - JEE Main Previous Year Question with Solutions

Q. $\mathrm{ABCD}$ is a trapezium such that $\mathrm{AB}$ and $\mathrm{CD}$ are parallel and $\mathrm{BC} \perp \mathrm{CD} .$ If $\angle \mathrm{ADB}=\theta, \mathrm{BC}=$ $\mathrm{p}$ and $\mathrm{CD}=\mathrm{q},$ then $\mathrm{AB}$ is equal to (1) $\frac{\left(p^{2}+q^{2}\right) \sin \theta}{p \cos \theta+q \sin \theta}$ (2) $\frac{p^{2}+q^{2} \cos \theta}{p \cos \theta+q \sin \theta}$ (3) $\frac{p^{2}+q^{2}}{p^{2} \cos \theta+q^{2} \sin \theta}$ (4) $\frac{\left(p^{2}+q^{2}\right) \sin \theta}{(p \cos \theta+q \sin \theta)^{2}}$ [JEE-MAINS-2013]

Q. If the angles of elevation of the top of a tower from three collinear points A, B and C, on a line leading to the foot of the tower, are $30^{\circ}, 45^{\circ}$ and $60^{\circ}$ respectively, then the ratio, AB : BC, is: (1) $1: \sqrt{3}$ (2) 2 : 3 (3) $\sqrt{3}: 1$ (4) $\sqrt{3}: \sqrt{2}$ [JEE(Main)-2015]

Q. A man is walking towards a vertical pillar in a straight path, at a uniform speed. Then the time taken (in minutes) by him, form B to reach the pillar, is : (1) 5         (2) 6          (3) 10           (4) 20 [JEE(Main)-2016]

Q. Let a vertical tower AB have its end A on the level ground. Let C be the mid-point tanis equal to :- (1) $\frac{4}{9}$ (2) $\frac{6}{7}$ (3) $\frac{1}{4}$ (4) $\frac{2}{9}$ [JEE(Main)-2017]

Q. PQR is a triangular park with $\mathrm{PQ}=200 \mathrm{m}$. A T.V. tower stands at the mid-point of $\mathrm{QR} .$ If the angles of elevation of the top of the tower at $\mathrm{P}, \mathrm{Q}$ and $\mathrm{R}$ are respectively $45^{\circ},$ $\left.30^{\circ} \text { and } 30^{\circ}, \text { then the height of the tower (in } \mathrm{m}\right)$ is- (1) 50 (2) $100 \sqrt{3}$ (3) $50 \sqrt{2}$ (4) 100 [JEE(Main)-2018]