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Previous year question hub

Properties Of Triangle - Trigonometry - Mathematics Previous Year Questions

Practice Properties Of Triangle - Trigonometry - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

45Papers
39Years
77Questions
1Topics

Properties Of Triangle question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Properties Of Triangle. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 47 61%
Easy 16 20.8%
Hard 12 15.6%
Not classified 2 2.6%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

Multiple Choices 35 45.5%
Subjective 31 40.3%
Fill in the blanks 6 7.8%
Numerical Answer Type (NAT) 5 6.5%

Subject weightage

Top subjects by unique question coverage.

Mathematics
77 Qs

Most asked topics

Top topics across the included previous year papers.

Trigonometry
77 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Properties Of Triangle
77 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

JEE ADVANCED 2023 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2021 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2021 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2020 PAPER 1 OFFLINE
2 Qs
JEE ADVANCED 2019 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2016 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2015 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2014 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2013 PAPER 2 OFFLINE
1 Qs
IIT JEE 2012 PAPER 2 OFFLINE
1 Qs
IIT JEE 2010 PAPER 1 OFFLINE
2 Qs
IIT JEE 2010 PAPER 2 OFFLINE
1 Qs
IIT JEE 2009 PAPER 2 OFFLINE
1 Qs
IIT JEE 2006
2 Qs
IIT JEE 2005
1 Qs
IIT JEE 2005 SCREENING
1 Qs
IIT JEE 2004 SCREENING
1 Qs
IIT JEE 2003
1 Qs
IIT JEE 2003 SCREENING
1 Qs
IIT JEE 2002 SCREENING
1 Qs
IIT JEE 2001
1 Qs
IIT JEE 2001 SCREENING
1 Qs
IIT JEE 2000 SCREENING
3 Qs
IIT JEE 2000
1 Qs
IIT JEE 1999
1 Qs
IIT JEE 1998
4 Qs
IIT JEE 1996
1 Qs
IIT JEE 1995 SCREENING
1 Qs
IIT JEE 1994
6 Qs
IIT JEE 1993
2 Qs
IIT JEE 1992
1 Qs
IIT JEE 1991
3 Qs
IIT JEE 1990
2 Qs
IIT JEE 1989
1 Qs
IIT JEE 1988
2 Qs
IIT JEE 1987
2 Qs
IIT JEE 1986
2 Qs
IIT JEE 1985
4 Qs
IIT JEE 1984
2 Qs
IIT JEE 1983
2 Qs
IIT JEE 1982
1 Qs
IIT JEE 1981
1 Qs
IIT JEE 1980
6 Qs
IIT JEE 1979
3 Qs
IIT JEE 1978
1 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
JEE ADVANCED 2023 PAPER 2 ONLINE20231View paper
JEE ADVANCED 2021 PAPER 1 ONLINE20211View paper
JEE ADVANCED 2021 PAPER 2 ONLINE20211View paper
JEE ADVANCED 2020 PAPER 1 OFFLINE20202View paper
JEE ADVANCED 2019 PAPER 1 OFFLINE20191View paper
JEE ADVANCED 2016 PAPER 1 OFFLINE20161View paper
JEE ADVANCED 2015 PAPER 1 OFFLINE20151View paper
JEE ADVANCED 2014 PAPER 2 OFFLINE20141View paper
JEE ADVANCED 2013 PAPER 2 OFFLINE20131View paper
IIT JEE 2012 PAPER 2 OFFLINE20121View paper
IIT JEE 2010 PAPER 1 OFFLINE20102View paper
IIT JEE 2010 PAPER 2 OFFLINE20101View paper
IIT JEE 2009 PAPER 2 OFFLINE20091View paper
IIT JEE 200620062View paper
IIT JEE 200520051View paper
IIT JEE 2005 SCREENING20051View paper
IIT JEE 2004 SCREENING20041View paper
IIT JEE 200320031View paper
IIT JEE 2003 SCREENING20031View paper
IIT JEE 2002 SCREENING20021View paper
IIT JEE 200120011View paper
IIT JEE 2001 SCREENING20011View paper
IIT JEE 200020001View paper
IIT JEE 2000 SCREENING20003View paper
IIT JEE 199919991View paper
IIT JEE 199819984View paper
IIT JEE 199619961View paper
IIT JEE 1995 SCREENING19951View paper
IIT JEE 199419946View paper
IIT JEE 199319932View paper
IIT JEE 199219921View paper
IIT JEE 199119913View paper
IIT JEE 199019902View paper
IIT JEE 198919891View paper
IIT JEE 198819882View paper
IIT JEE 198719872View paper
IIT JEE 198619862View paper
IIT JEE 198519854View paper
IIT JEE 198419842View paper
IIT JEE 198319832View paper
IIT JEE 198219821View paper
IIT JEE 198119811View paper
IIT JEE 198019806View paper
IIT JEE 197919793View paper
IIT JEE 197819781View paper

All Properties Of Triangle previous year questions

Practice every matching question in batches of 20, with every available option.

1
1978 · Mathematics · Trigonometry · Properties Of Triangle
IIT JEE 1978
A triangle \(ABC\) has sides \(AB=AC=5\) cm and \(BC=6\) cm Triangle \(A'B'C'\) is the reflection of the triangle \(ABC\) in a line parallel to \(AB\) placed at a distance \(2\) cm from \(AB\), outside the triangle \(ABC\). Triangle \(A''B''C''\) is the reflection of the triangle \(A'B'C'\) in a line parallel to \(BC\) placed at a distance of \(2\) cm from \(B'C'\) outside the triangle \(A'B'C'\). Find the distance between \(A\) and \(A''\).
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2
1979 · Mathematics · Trigonometry · Properties Of Triangle
IIT JEE 1979
(a) If a circle is inscribed in a right angled triangle \(ABC\) with the right angle at \(B\), show that the diameter of the circle is equal to \(AB+BC-AC\).

(b) If a triangle is inscribed in a circle, then the product of any two sides of the triangle is equal to the product of the diameter and the perpendicular distance of the third side from the opposite vertex. Prove the above statement.

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3
1979 · Mathematics · Trigonometry · Properties Of Triangle
IIT JEE 1979
If the bisector of the angle \(P\) of a triangle \(PQR\) meets \(QR\) in \(S\), then
A
\(QS=SR\)
B
\(QS:SR\) \(= PR:PQ\)
C
\(QS:SR=PQ:PR\)
D
None of these
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4
1979 · Mathematics · Trigonometry · Properties Of Triangle
IIT JEE 1979
(a) A balloon is observed simultaneously from three points \(A, B\) and \(C\) on a straight road directly beneath it. The angular elevation at \(B\) is twice that at \(A\) and the angular elevation at \(C\) is thrice that at \(A\). If the distance between \(A\) and \(B\) is a and the distance between \(B\) and \(C\) is \(b\), find the height of the balloon in terms of \(a\) and \(b\).

(b) Find the area of the smaller part of a disc of radius \(10\) cm, cut off by a chord \(AB\) which subtends an angle of at the circumference.

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5
1980 · Mathematics · Trigonometry · Properties Of Triangle
IIT JEE 1980
\(ABC\) is a triangle. \(D\) is the middle point of \(BC\). If \(AD\) is perpendicular to \(AC\), then prove that \(\cos A\,\cos C = {{2\left( {{c^2} - {a^2}} \right)} \over {3ac}}\)
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6
1980 · Mathematics · Trigonometry · Properties Of Triangle
IIT JEE 1980
\(ABC\) is a triangle with \(AB=AC\). \(D\) is any point on the side \(BC\). \(E\) and \(F\) are points on the side \(AB\) and \(AC\), respectively, such that \(DE\) is parallel to \(AC\), and \(DF\) is parallel to \(AB\). Prove that \(DF + FA + AE + ED = AB + AC\)
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7
1980 · Mathematics · Trigonometry · Properties Of Triangle
IIT JEE 1980
\(ABC\) is a triangle with \(\angle B\) greater than \(\angle C.\,D\) and \(E\) are points on \(BC\) such that \(AD\) is perpendicular to \(BC\) and \(AE\) is the bisector of angle \(A\). Complete the relation \(\angle DAE = {1 \over 2}\left[ {\left( {} \right) - \angle C} \right]\)
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8
1980 · Mathematics · Trigonometry · Properties Of Triangle
IIT JEE 1980
\(ABC\) is a triangle, \(P\) is a point on \(AB\), and \(Q\) is point on \(AC\) such that \(\angle AQP = \angle ABC\). Complete the relation \({{area\,\,of\,\,\Delta APQ} \over {area\,\,of\,\,\Delta ABC}} = {{\left( {...} \right)} \over {A{C^2}}}\)
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9
1980 · Mathematics · Trigonometry · Properties Of Triangle
IIT JEE 1980
In a \(\Delta ABC,\,\angle A = {90^ \circ }\) and \(AD\) is an altitude. Complete the relation \({{BD} \over {BA}} = {{AB} \over {\left( {....} \right)}}\).
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10
1980 · Mathematics · Trigonometry · Properties Of Triangle
IIT JEE 1980
(i) \(PQ\) is a vertical tower. \(P\) is the foot and \(Q\) is the top of the tower. \(A, B, C\) are three points in the horizontal plane through \(P\). The angles of elevation of \(Q\) from \(A\), \(B\), \(C\) are equal, and each is equal to \(\theta\). The sides of the triangle \(ABC\) are \(a, b, c\); and the area of the triangle \(ABC\) is \(\Delta\). Show that the height of the tower is \({{abc\tan \theta } \over {4\Delta }}\).

(ii) \(AB\) is vertical pole. The end \(A\) is on the level ground. \(C\) is the middle point of \(AB\). \(P\) is a point on the level ground. The portion \(CB\) subtends an angle \(\beta\) at \(P\). If \(AP = n\,AB,\) then show that tan\(\beta\) \(= {n \over {2{n^2} + 1}}\)

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11
1981 · Mathematics · Trigonometry · Properties Of Triangle
IIT JEE 1981
Let the angles \(A, B, C\) of a triangle \(ABC\) be in A.P. and let \(b:c = \sqrt 3 :\sqrt 2\). Find the angle \(A\).
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12
1982 · Mathematics · Trigonometry · Properties Of Triangle
IIT JEE 1982
A vertical pole stands at a point \(Q\) on a horizontal ground. \(A\) and \(B\) are points on the ground, \(d\) meters apart. The pole subtends angles \(\alpha\) and \(\beta\) at \(A\) and \(B\) respectively. \(AB\) subtends an angle \(\gamma\) and \(Q\). Find the height of the pole.
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13
1983 · Mathematics · Trigonometry · Properties Of Triangle
IIT JEE 1983
The ex-radii \({r_1},{r_2},{r_3}\) of \(\Delta\)\(ABC\) are H.P. Show that its sides \(a, b, c\) are in A.P.
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14
1983 · Mathematics · Trigonometry · Properties Of Triangle
IIT JEE 1983
From the top of a light-house 60 metres high with its base at the sea-level, the angle of depression of a boat is \({15^ \circ }\). The distance of the boat from the foot of the light house is
A
\(\left( {{{\sqrt 3 - 1} \over {\sqrt 3 + 1}}} \right)60\) metres
B
\(\left( {{{\sqrt 3 + 1} \over {\sqrt 3 - 1}}} \right)60\) metres
C
\({\left( {{{\sqrt 3 + 1} \over {\sqrt 3 - 1}}} \right)^2}\) metres
D
none of these
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15
1984 · Mathematics · Trigonometry · Properties Of Triangle
IIT JEE 1984
For a triangle \(ABC\) it is given that \(\cos A + \cos B + \cos C = {3 \over 2}\). Prove that the triangle is equilateral.
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16
1984 · Mathematics · Trigonometry · Properties Of Triangle
IIT JEE 1984
With usual notation, if in a triangle \(ABC\);
\({{b + c} \over {11}} = {{c + a} \over {12}} = {{a + b} \over {13}}\) then prove that \({{\cos A} \over 7} = {{\cos B} \over {19}} = {{\cos C} \over {25}}\).
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17
1985 · Mathematics · Trigonometry · Properties Of Triangle
IIT JEE 1985
In a triangle \(ABC\), if cot \(A\), cot \(B\), cot \(C\) are in A.P., then \({a^2},{b^2},{c^2}\), are in ............... progression.
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18
1985 · Mathematics · Trigonometry · Properties Of Triangle
IIT JEE 1985
A ladder rests against a wall at an angle \(\alpha\) to the horizintal. Its foot is pulled away from the wall through a distance \(a\), so that it slides \(a\) distance \(b\) down the wall making an angle \(\beta\) with the horizontal. Show that \(a = b\tan {1 \over 2}\left( {\alpha + \beta } \right)\)
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19
1985 · Mathematics · Trigonometry · Properties Of Triangle
IIT JEE 1985
In a triangle \(ABC\), the median to the side \(BC\) is of length \({1 \over {\sqrt {11 - 6\sqrt 3 } }}\) and it divides the angle \(A\) into angles \({30^ \circ }\) and \({45^ \circ }\). Find the length of the side \(BC\).
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20
1985 · Mathematics · Trigonometry · Properties Of Triangle
IIT JEE 1985
The set of all real numbers \(a\) such that \({a^2} + 2a,2a + 3\) and \({a^2} + 3a + 8\) are the sides of a triangle is ...........
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Showing 20 of 77 questions