Height and Distance – JEE Main Previous Year Question with Solutions

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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]

Sol. (1)

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]

Sol. (3)

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]

Sol. (1)

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]

Sol. (4)

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]

Sol. (4)