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Properties of Triangle
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A horizontal park is in the shape of a triangle $$\mathrm{OAB}$$ with $$\mathrm{AB}=16$$. A vertical lamp post $$\mathrm...
JEE Main 2022 (Online) 28th July Evening Shift
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The angle of elevation of the top P of a vertical tower PQ of height 10 from a point A on the horizontal ground is $$45^...
JEE Main 2022 (Online) 27th July Evening Shift
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Let a vertical tower $$A B$$ of height $$2 h$$ stands on a horizontal ground. Let from a point $$P%$$ on the ground a ma...
JEE Main 2022 (Online) 27th July Morning Shift
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A tower PQ stands on a horizontal ground with base $$Q$$ on the ground. The point $$R$$ divides the tower in two parts s...
JEE Main 2022 (Online) 25th July Morning Shift
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The lengths of the sides of a triangle are 10 + x2, 10 + x2 and 20 $$-$$ 2x2. If for x = k, the area of the triangle is ...
JEE Main 2022 (Online) 27th June Morning Shift
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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 o...
JEE Main 2022 (Online) 28th June Morning Shift
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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 subte...
JEE Main 2022 (Online) 29th June Evening Shift
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A vertical pole fixed to the horizontal ground is divided in the ratio 3 : 7 by a mark on it with lower part shorter tha...
JEE Main 2021 (Online) 31st August Morning Shift
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Two poles, AB of length a metres and CD of length a + b (b $$\ne$$ a) metres are erected at the same horizontal level wi...
JEE Main 2021 (Online) 27th August Evening Shift
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Let $${{\sin A} \over {\sin B}} = {{\sin (A - C)} \over {\sin (C - B)}}$$, where A, B, C are angles of triangle ABC. If ...
JEE Main 2021 (Online) 27th August Morning Shift
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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 P...
JEE Main 2021 (Online) 26th August Evening Shift
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A spherical gas balloon of radius 16 meter subtends an angle 60$$^\circ$$ at the eye of the observer A while the angle o...
JEE Main 2021 (Online) 25th July Morning Shift
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Let in a right angled triangle, the smallest angle be $$\theta$$. If a triangle formed by taking the reciprocal of its s...
JEE Main 2021 (Online) 20th July Evening Shift
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If in a triangle ABC, AB = 5 units, $$\angle B = {\cos ^{ - 1}}\left( {{3 \over 5}} \right)$$ and radius of circumcircle...
JEE Main 2021 (Online) 20th July Morning Shift
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A pole stands vertically inside a triangular park ABC. Let the angle of elevation of the top of the pole from each corne...
JEE Main 2021 (Online) 18th March Evening Shift
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The triangle of maximum area that can be inscribed in a given circle of radius 'r' is :
JEE Main 2021 (Online) 26th February Evening Shift
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A man is observing, from the top of a tower, a boat speeding towards the lower from a certain point A, with uniform spee...
JEE Main 2021 (Online) 25th February Morning Slot
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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 ...
JEE Main 2021 (Online) 24th February Evening Slot
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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 t...
JEE Main 2021 (Online) 24th February Morning Slot
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The angle of elevation of the summit of a mountain from a point on the ground is 45°. After climbing up one km towards t...
JEE Main 2020 (Online) 6th September Evening Slot
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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 i...
JEE Main 2020 (Online) 4th September Evening Slot
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A triangle ABC lying in the first quadrant has two vertices as A(1, 2) and B(3, 1). If $$\angle BAC = {90^o}$$ and area$...
JEE Main 2020 (Online) 4th September Morning Slot
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The angle of elevation of the top of a vertical tower standing on a horizontal plane is observed to be 45o from a point ...
JEE Main 2019 (Online) 12th April Evening Slot
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The angles A, B and C of a triangle ABC are in A.P. and a : b = 1 : $$\sqrt 3 $$. If c = 4 cm, then the area (in sq. cm)...
JEE Main 2019 (Online) 10th April Evening Slot
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ABC is a triangular park with AB = AC = 100 metres. A vertical tower is situated at the mid-point of BC. If the angles o...
JEE Main 2019 (Online) 10th April Morning Slot
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Two poles standing on a horizontal ground are of heights 5m and 10 m respectively. The line joining their tops makes an ...
JEE Main 2019 (Online) 9th April Evening Slot
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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 ...
JEE Main 2019 (Online) 8th April Evening Slot
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If the lengths of the sides of a triangle are in A.P. and the greatest angle is double the smallest, then a ratio of len...
JEE Main 2019 (Online) 8th April Evening Slot
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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 ref...
JEE Main 2019 (Online) 12th January Evening Slot
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Given $${{b + c} \over {11}} = {{c + a} \over {12}} = {{a + b} \over {13}}$$ for a $$\Delta $$ABC with usual notation. ...
JEE Main 2019 (Online) 11th January Evening Slot
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In a triangle, the sum of lengths of two sides is x and the product of the lengths of the same two sides is y. If x2 – c...
JEE Main 2019 (Online) 11th January Morning Slot
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With the usual notation, in $$\Delta $$ABC, if $$\angle A + \angle B$$ = 120o, a = $$\sqrt 3 $$ $$+$$ 1, b = $$\sqrt 3...
JEE Main 2019 (Online) 10th January Evening Slot
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Consider a triangular plot ABC with sides AB = 7m, BC = 5m and CA = 6m. A vertical lamp-post at the mid point D of AC su...
JEE Main 2019 (Online) 10th January Morning Slot
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A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road. If...
JEE Main 2018 (Online) 16th April Morning Slot
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A tower T1 of height 60 m is located exactly opposite to a tower T2 of height 80 m on a straight road. Fromthe top of T1...
JEE Main 2018 (Online) 15th April Evening Slot
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An aeroplane flying at a constant speed, parallel to the horizontal ground, $$\sqrt 3 $$ kmabove it, is obsered at an el...
JEE Main 2018 (Online) 15th April Morning Slot
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The angle of elevation of the top of a vertical tower from a point A, due east of it is 45o. The angle of elevation of t...
JEE Main 2016 (Online) 10th April Morning Slot
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If the angles of elevation of the top of a tower from three collinear points $$A, B$$ and $$C,$$ on a line leading to th...
JEE Main 2015 (Offline)
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A bird is sitting on the top of a vertical pole $$20$$ m high and its elevation from a point $$O$$ on the ground is $${4...
JEE Main 2014 (Offline)
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For a regular polygon, let $$r$$ and $$R$$ be the radii of the inscribed and the circumscribed circles. A $$false$$ stat...
AIEEE 2010
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$$AB$$ is a vertical pole with $$B$$ at the ground level and $$A$$ at the top. $$A$$ man finds that the angle of elevati...
AIEEE 2008
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A tower stands at the centre of a circular park. $$A$$ and $$B$$ are two points on the boundary of the park such that $$...
AIEEE 2007
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In a triangle $$ABC$$, let $$\angle C = {\pi \over 2}$$. If $$r$$ is the inradius and $$R$$ is the circumradius of the ...
AIEEE 2005
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If in a $$\Delta ABC$$, the altitudes from the vertices $$A, B, C$$ on opposite sides are in H.P, then $$\sin A,\sin B,\...
AIEEE 2005
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The sides of a triangle are $$\sin \alpha ,\,\cos \alpha $$ and $$\sqrt {1 + \sin \alpha \cos \alpha } $$ for some $$0 &...
AIEEE 2004
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A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank ...
AIEEE 2004
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If in a $$\Delta ABC$$ $$a{\cos ^2}\left( {{C \over 2}} \right) + {\cos ^2}\left( {{A \over 2}} \right) = {{3b} \over 2}...
AIEEE 2003
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In a triangle $$ABC$$, medians $$AD$$ and $$BE$$ are drawn. If $$AD=4$$, $$\angle DAB = {\pi \over 6}$$ and $$\angle A...
AIEEE 2003
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The sum of the radii of inscribed and circumscribed circles for an $$n$$ sided regular polygon of side $$a, $$ is
AIEEE 2003
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In a triangle with sides $$a, b, c,$$ $${r_1} > {r_2} > {r_3}$$ (which are the ex-radii) then
AIEEE 2002
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The sides of a triangle are $$3x + 4y,$$ $$4x + 3y$$ and $$5x + 5y$$ where $$x$$, $$y>0$$ then the triangle is
AIEEE 2002
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If a rectangle is inscribed in an equilateral triangle of side length $$2\sqrt 2 $$ as shown in the figure, then the squ...
JEE Main 2021 (Online) 25th July Evening Shift
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In $$\Delta$$ABC, the lengths of sides AC and AB are 12 cm and 5 cm, respectively. If the area of $$\Delta$$ABC is 30 cm...
JEE Main 2021 (Online) 16th March Evening Shift
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Let ABCD be a square of side of unit length. Let a circle C1 centered at A with unit radius is drawn. Another circle C2 ...
JEE Main 2021 (Online) 16th March Morning Shift
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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...
JEE Main 2020 (Online) 6th September Morning Slot
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