NEW
New Website Launch
Experience the best way to solve previous year questions with mock tests (very detailed analysis), bookmark your favourite questions, practice etc...
1

JEE Main 2015 (Offline)

MCQ (Single Correct Answer)
English
Hindi
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 :
A
$$1:\sqrt 3 $$
B
$$2:3$$
C
$$\sqrt 3 :1$$
D
$$\sqrt 3 :\sqrt 2 $$

Explanation


As $$PB$$ bisects $$\angle APC,$$ therefore $$AB$$ $$:$$ $$BC$$ $$=PA:PC$$

Also in $$\Delta APQ,\sin {30^ \circ } = {h \over {PA}} \Rightarrow PA = 2h$$

and in $$\Delta CPQ,$$ $$\sin {60^ \circ } = {h \over {PC}} \Rightarrow PC = {{2h} \over {\sqrt 3 }}$$

$$\therefore$$ $$AB:BC = 2h:{{2h} \over {\sqrt 3 }} = \sqrt 3 :1$$

तीन संरेख बिंदुओं $$\mathrm{A, B}$$ तथा $$\mathrm{C}$$, एक ऐसी रेखा पर स्थित हैं जो एक मीनार के पाद की दिशा में ले जाती है, से एक मीनार के शिखर के उन्नयन कोण क्रमशः $$30^{\circ}, 45^{\circ}$$ तथा $$60^{\circ}$$ हैं, तो $$\mathrm{AB}: \mathrm{BC}$$ का अनुपात है :

A
$$1:\sqrt 3 $$
B
$$2:3$$
C
$$\sqrt 3 :1$$
D
$$\sqrt 3 :\sqrt 2 $$
2

JEE Main 2014 (Offline)

MCQ (Single Correct Answer)
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 horizontally straight away from the point $$O$$. After one second, the elevation of the bird from $$O$$ is reduced to $${30^ \circ }$$. Then the speed (in m/s) of the bird is
A
$$20\sqrt 2 $$
B
$$20\left( {\sqrt 3 - 1} \right)$$
C
$$40\left( {\sqrt 2 - 1} \right)$$
D
$$40\left( {\sqrt 3 - \sqrt 2 } \right)$$

Explanation

Let the speed be $$y$$ $$m/sec$$.

Let $$AC$$ be the vertical pole of height $$20$$ $$m.$$

Let $$O$$ be the point on the ground such that $$\angle AOC = {45^ \circ }$$

Let $$OC = x$$



Time $$t=1$$ $$s$$

From $$\Delta AOC,\,\,\tan {45^ \circ } = {{20} \over x}\,\,\,\,\,\,\,.....\left( i \right)$$

and from $$\Delta BOD,\,\,\tan {30^ \circ } = {{20} \over {x + y}}...\left( {ii} \right)$$

From $$(i)$$ and $$(ii),$$ we have $$x=20$$

and $${1 \over {\sqrt 3 }} = {{20} \over {x + y}}$$

$$ \Rightarrow {1 \over {\sqrt 3 }} = {{20} \over {20 + y}}$$

$$ \Rightarrow 20 + y = 20\sqrt 3 $$

So, $$y = 20\left( {\sqrt 3 - 1} \right)\,\,i.e.,$$

speed $$ = 20\left( {\sqrt 3 - 1} \right)m/s$$
3

AIEEE 2010

MCQ (Single Correct Answer)
For a regular polygon, let $$r$$ and $$R$$ be the radii of the inscribed and the circumscribed circles. A $$false$$ statement among the following is
A
There is a regular polygon with $${r \over R} = {1 \over {\sqrt 2 }}$$
B
There is a regular polygon with $${r \over R} = {2 \over 3}$$
C
There is a regular polygon with $${r \over R} = {{\sqrt 3 } \over 2}$$
D
There is a regular polygon with $${r \over R} = {1 \over 2}$$

Explanation



If $$O$$ is center of polygon and

$$AB$$ is one of the side, then by figure

$$\cos {\pi \over n} = {r \over R}$$

$$ \Rightarrow {r \over R} = {1 \over 2},{1 \over {\sqrt 2 }},{{\sqrt 3 } \over 2}\,\,for$$

$$n = 3,4,6$$ respectively.
4

AIEEE 2008

MCQ (Single Correct Answer)
$$AB$$ 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 certain point $$C$$ on the ground is $${60^ \circ }$$. He moves away from the pole along the line $$BC$$ to a point $$D$$ such that $$CD=7$$ m. From $$D$$ the angle of elevation of the point $$A$$ is $${45^ \circ }$$. Then the height of the pole is
A
$${{7\sqrt 3 } \over 2} {1 \over {\sqrt {3 - 1} }}m$$
B
$${{7\sqrt 3 } \over 2}\left( {\sqrt {3 + 1} } \right)m$$
C
$${{7\sqrt 3 } \over 2}\left( {\sqrt {3 - 1} } \right)m$$
D
$${{7\sqrt 3 } \over 2} {1 \over {\sqrt {3 + 1} }}m$$

Explanation



In $$\Delta ABC$$

$${h \over x} = \tan {60^ \circ } = \sqrt 3 $$

$$ \Rightarrow x = {h \over {\sqrt 3 }}$$

In $$\Delta ABD{h \over {x + 7}}$$

$$ = \tan {45^ \circ } = 1$$

$$ \Rightarrow h = x + 7 \Rightarrow h - {h \over {\sqrt 3 }} = 7$$

$$ \Rightarrow h = {{7\sqrt 3 } \over {\sqrt 3 - 1}} \times {{\sqrt 3 + 1} \over {\sqrt 3 + 1}}$$

$$ \Rightarrow h = {{7\sqrt 3 } \over 2}\left( {\sqrt 3 + 1\,m} \right)$$

Questions Asked from Properties of Triangle

On those following papers in MCQ (Single Correct Answer)
Number in Brackets after Paper Indicates No. of Questions
JEE Main 2022 (Online) 29th July Morning Shift (1)
JEE Main 2022 (Online) 28th July Evening Shift (1)
JEE Main 2022 (Online) 27th July Evening Shift (1)
JEE Main 2022 (Online) 27th July Morning Shift (1)
JEE Main 2022 (Online) 25th July Morning Shift (1)
JEE Main 2022 (Online) 29th June Evening Shift (1)
JEE Main 2022 (Online) 28th June Morning Shift (1)
JEE Main 2022 (Online) 27th June Morning Shift (1)
JEE Main 2021 (Online) 31st August Morning Shift (1)
JEE Main 2021 (Online) 27th August Evening Shift (1)
JEE Main 2021 (Online) 27th August Morning Shift (1)
JEE Main 2021 (Online) 26th August Evening Shift (1)
JEE Main 2021 (Online) 25th July Morning Shift (1)
JEE Main 2021 (Online) 20th July Evening Shift (1)
JEE Main 2021 (Online) 20th July Morning Shift (1)
JEE Main 2021 (Online) 18th March Evening Shift (1)
JEE Main 2021 (Online) 26th February Evening Shift (1)
JEE Main 2021 (Online) 25th February Morning Shift (1)
JEE Main 2021 (Online) 24th February Evening Shift (1)
JEE Main 2021 (Online) 24th February Morning Shift (1)
JEE Main 2020 (Online) 6th September Evening Slot (1)
JEE Main 2020 (Online) 4th September Evening Slot (1)
JEE Main 2020 (Online) 4th September Morning Slot (1)
JEE Main 2019 (Online) 12th April Evening Slot (1)
JEE Main 2019 (Online) 10th April Evening Slot (1)
JEE Main 2019 (Online) 10th April Morning Slot (1)
JEE Main 2019 (Online) 9th April Evening Slot (1)
JEE Main 2019 (Online) 8th April Evening Slot (2)
JEE Main 2019 (Online) 12th January Evening Slot (1)
JEE Main 2019 (Online) 11th January Evening Slot (1)
JEE Main 2019 (Online) 11th January Morning Slot (1)
JEE Main 2019 (Online) 10th January Evening Slot (1)
JEE Main 2019 (Online) 10th January Morning Slot (1)
JEE Main 2018 (Online) 16th April Morning Slot (1)
JEE Main 2018 (Online) 15th April Evening Slot (1)
JEE Main 2018 (Online) 15th April Morning Slot (1)
JEE Main 2016 (Online) 10th April Morning Slot (1)
JEE Main 2016 (Offline) (1)
JEE Main 2015 (Offline) (1)
JEE Main 2014 (Offline) (1)
AIEEE 2010 (1)
AIEEE 2008 (1)
AIEEE 2007 (1)
AIEEE 2005 (2)
AIEEE 2004 (2)
AIEEE 2003 (3)
AIEEE 2002 (2)

Joint Entrance Examination

JEE Main JEE Advanced WB JEE

Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN

Medical

NEET

CBSE

Class 12