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# Height and Distance · Mathematics · JEE Main

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JEE Main 2023 (Online) 11th April Evening Shift
The angle of elevation of the top $$\mathrm{P}$$ of a tower from the feet of one person standing due South of the tower is $$45^{\circ}$$ and from the...
JEE Main 2023 (Online) 6th April Morning Shift
From the top $$\mathrm{A}$$ of a vertical wall $$\mathrm{AB}$$ of height $$30 \mathrm{~m}$$, the angles of depression of the top $$\mathrm{P}$$ and bo...
JEE Main 2022 (Online) 29th July Morning Shift
The angle of elevation of the top of a tower from a point A due north of it is $$\alpha$$ and from a point B at a distance of 9 units due west of A is...
JEE Main 2022 (Online) 28th July Evening Shift
A horizontal park is in the shape of a triangle $$\mathrm{OAB}$$ with $$\mathrm{AB}=16$$. A vertical lamp post $$\mathrm{OP}$$ is erected at the point...
JEE Main 2022 (Online) 27th July Evening Shift
The angle of elevation of the top P of a vertical tower PQ of height 10 from a point A on the horizontal ground is $$45^{\circ}$$. Let R be a point on...
JEE Main 2022 (Online) 27th July Morning Shift
Let a vertical tower $$A B$$ of height $$2 h$$ stands on a horizontal ground. Let from a point $$P%$$ on the ground a man can see upto height $$h$$ of...
JEE Main 2022 (Online) 25th July Morning Shift
A tower PQ stands on a horizontal ground with base $$Q$$ on the ground. The point $$R$$ divides the tower in two parts such that $$Q R=15 \mathrm{~m}... JEE Main 2022 (Online) 29th June Evening Shift From the base of a pole of height 20 meter, the angle of elevation of the top of a tower is 60$$^\circ$$. The pole subtends an angle 30$$^\circ$$at t... JEE Main 2022 (Online) 28th June Morning Shift Let AB and PQ be two vertical poles, 160 m apart from each other. Let C be the middle point of B and Q, which are feet of these two poles. Let$${\pi ...
JEE Main 2021 (Online) 31st August Morning Shift
A vertical pole fixed to the horizontal ground is divided in the ratio 3 : 7 by a mark on it with lower part shorter than the upper part. If the two p...
JEE Main 2021 (Online) 27th August Evening Shift
Two poles, AB of length a metres and CD of length a + b (b $$\ne$$ a) metres are erected at the same horizontal level with bases at B and D. If BD = x...
JEE Main 2021 (Online) 26th August Evening Shift
A 10 inches long pencil AB with mid point C and a small eraser P are placed on the horizontal top of a table such that PC = $$\sqrt 5$$ inches and $$... JEE Main 2021 (Online) 25th July Morning Shift A spherical gas balloon of radius 16 meter subtends an angle 60$$^\circ$$at the eye of the observer A while the angle of elevation of its center from... JEE Main 2021 (Online) 20th July Evening Shift Let in a right angled triangle, the smallest angle be$$\theta$$. If a triangle formed by taking the reciprocal of its sides is also a right angled tr... JEE Main 2021 (Online) 18th March Evening Shift A pole stands vertically inside a triangular park ABC. Let the angle of elevation of the top of the pole from each corner of the park be$${\pi \over...
JEE Main 2021 (Online) 25th February Morning Shift
A man is observing, from the top of a tower, a boat speeding towards the lower from a certain point A, with uniform speed. At that point, angle of dep...
JEE Main 2021 (Online) 24th February Evening Shift
The angle of elevation of a jet plane from a point A on the ground is 60$$^\circ$$. After a flight of 20 seconds at the speed of 432 km/hour, the angl...
JEE Main 2021 (Online) 24th February Morning Shift
Two vertical poles are 150 m apart and the height of one is three times that of the other. If from the middle point of the line joining their feet, an...
JEE Main 2020 (Online) 6th September Evening Slot
The angle of elevation of the summit of a mountain from a point on the ground is 45°. After climbing up one km towards the summit at an inclination of...
JEE Main 2020 (Online) 4th September Evening Slot
The angle of elevation of a cloud C from a point P, 200 m above a still lake is 30°. If the angle of depression of the image of C in the lake from the...
JEE Main 2019 (Online) 12th April Evening Slot
The angle of elevation of the top of a vertical tower standing on a horizontal plane is observed to be 45o from a point A on the plane. Let B be the p...
JEE Main 2019 (Online) 10th April Morning Slot
ABC is a triangular park with AB = AC = 100 metres. A vertical tower is situated at the mid-point of BC. If the angles of elevation of the top of the ...
JEE Main 2019 (Online) 9th April Evening Slot
Two poles standing on a horizontal ground are of heights 5m and 10 m respectively. The line joining their tops makes an angle of 15º with ground. Then...
JEE Main 2019 (Online) 8th April Evening Slot
Two vertical poles of heights, 20 m and 80 m stand a part on a horizontal plane. The height (in meters) of the point of intersection of the lines join...
JEE Main 2019 (Online) 12th January Evening Slot
If the angle of elevation of a cloud from a point P which is 25 m above a lake be 30o and the angle of depression of reflection of the cloud in the la...
JEE Main 2019 (Online) 10th January Morning Slot
Consider a triangular plot ABC with sides AB = 7m, BC = 5m and CA = 6m. A vertical lamp-post at the mid point D of AC subtends an angle 30o at B. The ...
JEE Main 2018 (Online) 16th April Morning Slot
A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road. If it takes 18 min. for the angl...
JEE Main 2018 (Offline)
PQR is a triangular park with PQ = PR = 200 m. A T.V. tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P, Q ...
JEE Main 2018 (Online) 15th April Evening Slot
A tower T1 of height 60 m is located exactly opposite to a tower T2 of height 80 m on a straight road. Fromthe top of T1, if the angle of depression o...
JEE Main 2018 (Online) 15th April Morning Slot
An aeroplane flying at a constant speed, parallel to the horizontal ground, $$\sqrt 3$$ kmabove it, is obsered at an elevation of $${60^o}$$ from a ...
JEE Main 2017 (Offline)
Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that AP = 2AB. If $$\angl... JEE Main 2016 (Online) 10th April Morning Slot The angle of elevation of the top of a vertical tower from a point A, due east of it is 45o. The angle of elevation of the top of the same tower from ... JEE Main 2016 (Offline) A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of ele... JEE Main 2015 (Offline) If the angles of elevation of the top of a tower from three collinear points$$A, B$$and$$C,$$on a line leading to the foot of the tower, are$${30...
JEE Main 2014 (Offline)
A bird is sitting on the top of a vertical pole $$20$$ m high and its elevation from a point $$O$$ on the ground is $${45^ \circ }$$. It files off hor...
JEE Main 2013 (Offline)
$$ABCD$$ is a trapezium such that $$AB$$ and $$CD$$ are parallel and $$BC \bot CD.$$ If $$\angle ADB = \theta ,\,BC = p$$ and $$CD = q,$$ then AB is e...
AIEEE 2008
$$AB$$ is a vertical pole with $$B$$ at the ground level and $$A$$ at the top. $$A$$ man finds that the angle of elevation of the point $$A$$ from a c...
AIEEE 2007
A tower stands at the centre of a circular park. $$A$$ and $$B$$ are two points on the boundary of the park such that $$AB(=a)$$ subtends an angle of ...
AIEEE 2004
A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is {60^ \circ }...

## Numerical

JEE Main 2020 (Online) 6th September Morning Slot
The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be 45o. After walkin...
JEE Main 2020 (Online) 6th September Morning Slot
Let AD and BC be two vertical poles at A and B respectively on a horizontal ground. If AD = 8 m, BC = 11 m and AB = 10 m; then the distance (in meters...
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