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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.

35Papers
15Years
39Questions
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 35 89.7%
Hard 3 7.7%
Easy 1 2.6%

Question type distribution

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

Multiple Choices 31 79.5%
Numerical Answer Type (NAT) 8 20.5%

Subject weightage

Top subjects by unique question coverage.

Mathematics
39 Qs

Most asked topics

Top topics across the included previous year papers.

Trigonometry
39 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Properties Of Triangle
39 Qs

Paper coverage

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

JEE MAIN 2025 ONLINE 22ND JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 23RD JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 29TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 4TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 6TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 9TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 10TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 12TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 15TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 1ST FEBRUARY MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 30TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 25TH JUNE MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 27TH JUNE MORNING SHIFT
1 Qs
JEE Main 2021 (Online) 24th February Evening Shift
1 Qs
JEE Main 2021 (Online) 26th February Evening Shift
1 Qs
JEE MAIN 2021 ONLINE 16TH MARCH EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 16TH MARCH MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 20TH JULY MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 25TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 27TH AUGUST MORNING SHIFT
1 Qs
JEE MAIN 2020 ONLINE 4TH SEPTEMBER MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 10TH APRIL EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 10TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 11TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 11TH JANUARY MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 12TH APRIL EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 8TH APRIL EVENING SLOT
1 Qs
JEE MAIN 2018 OFFLINE
1 Qs
AIEEE 2012
1 Qs
AIEEE 2010
1 Qs
IIT-JEE 2007
1 Qs
AIEEE 2005
2 Qs
AIEEE 2004
1 Qs
AIEEE 2003
3 Qs
AIEEE 2002
2 Qs

Included previous year papers

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

PaperYear / sessionQuestions in this viewOpen
JEE MAIN 2025 ONLINE 22ND JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 23RD JANUARY MORNING SHIFT20251View paper
JEE MAIN 2024 ONLINE 29TH JANUARY MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 4TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 6TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 9TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2023 ONLINE 10TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 12TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 15TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 1ST FEBRUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 30TH JANUARY MORNING SHIFT20231View paper
JEE MAIN 2022 ONLINE 25TH JUNE MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 27TH JUNE MORNING SHIFT20221View paper
JEE Main 2021 (Online) 24th February Evening Shift20211View paper
JEE Main 2021 (Online) 26th February Evening Shift20211View paper
JEE MAIN 2021 ONLINE 16TH MARCH EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 16TH MARCH MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 20TH JULY MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 25TH JULY EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 27TH AUGUST MORNING SHIFT20211View paper
JEE MAIN 2020 ONLINE 4TH SEPTEMBER MORNING SLOT20201View paper
JEE MAIN 2019 ONLINE 10TH APRIL EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 10TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 11TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 11TH JANUARY MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 12TH APRIL EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 8TH APRIL EVENING SLOT20191View paper
JEE MAIN 2018 OFFLINE20181View paper
AIEEE 201220121View paper
AIEEE 201020101View paper
IIT-JEE 200720071View paper
AIEEE 200520052View paper
AIEEE 200420041View paper
AIEEE 200320033View paper
AIEEE 200220022View paper

All Properties Of Triangle previous year questions

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

1
2002 · Mathematics · Trigonometry · Properties Of Triangle
AIEEE 2002
The sides of a triangle are \(3x + 4y,\) \(4x + 3y\) and \(5x + 5y\) where \(x\), \(y>0\) then the triangle is :
A
right angled
B
obtuse angled
C
equilateral
D
none of these
Open complete paper
2
2002 · Mathematics · Trigonometry · Properties Of Triangle
AIEEE 2002
In a triangle with sides \(a, b, c,\) \({r_1} > {r_2} > {r_3}\) (which are the ex-radii) then :
A
\(a>b>c\)
B
\(a < b < c\)
C
\(a > b\) and \(b < c\)
D
\(a < b\) and \(b > c\)
Open complete paper
3
2003 · Mathematics · Trigonometry · Properties Of Triangle
AIEEE 2003
If in a \(\Delta ABC\) \(a\,{\cos ^2}\left( {{C \over 2}} \right) + c\,{\cos ^2}\left( {{A \over 2}} \right) = {{3b} \over 2},\) then the sides \(a, b\) and \(c\) :
A
satisfy \(a+b=c\)
B
are in A.P
C
are in G.P
D
are in H.P
Open complete paper
4
2003 · Mathematics · Trigonometry · Properties Of Triangle
AIEEE 2003
The sum of the radii of inscribed and circumscribed circles for an \(n\) sided regular polygon of side \(a,\) is :
A
\({a \over 4}\cot \left( {{\pi \over {2n}}} \right)\)
B
\(a\cot \left( {{\pi \over {n}}} \right)\)
C
\({a \over 2}\cot \left( {{\pi \over {2n}}} \right)\)
D
\(a\cot \left( {{\pi \over {2n}}} \right)\)
Open complete paper
5
2003 · Mathematics · Trigonometry · Properties Of Triangle
AIEEE 2003
In a triangle \(ABC\), medians \(AD\) and \(BE\) are drawn. If \(AD=4\),
\(\angle DAB = {\pi \over 6}\) and \(\angle ABE = {\pi \over 3}\), then the area of the \(\angle \Delta ABC\) is :
A
\({{64} \over 3}\)
B
\({8 \over 3}\)
C
\({{16} \over 3}\)
D
\({{32} \over {3\sqrt 3 }}\)
Open complete paper
6
2004 · Mathematics · Trigonometry · Properties Of Triangle
AIEEE 2004
The sides of a triangle are \(\sin \alpha ,\,\cos \alpha\) and \(\sqrt {1 + \sin \alpha \cos \alpha }\) for some \(0 < \alpha < {\pi \over 2}\). Then the greatest angle of the triangle is :
A
\({150^ \circ }\)
B
\({90^ \circ }\)
C
\({120^ \circ }\)
D
\({60^ \circ }\)
Open complete paper
7
2005 · Mathematics · Trigonometry · Properties Of Triangle
AIEEE 2005
If in a \(\Delta ABC\), the altitudes from the vertices \(A, B, C\) on opposite sides are in H.P, then \(\sin A,\sin B,\sin C\) are in :
A
G. P.
B
A. P.
C
A.P-G.P.
D
H. P
Open complete paper
8
2005 · Mathematics · Trigonometry · Properties Of Triangle
AIEEE 2005
In a triangle \(ABC\), let \(\angle C = {\pi \over 2}\). If \(r\) is the inradius and \(R\) is the circumradius of the triangle \(ABC\), then \(2(r+R)\) equals :
A
\(b+c\)
B
\(a+b\)
C
\(a+b+c\)
D
\(c+a\)
Open complete paper
9
2010 · Mathematics · Trigonometry · Properties Of Triangle
AIEEE 2010
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 \({r \over R} = {1 \over 2}\)
Open complete paper
10
2012 · Mathematics · Trigonometry · Properties Of Triangle
AIEEE 2012
In a \(\Delta PQR,{\mkern 1mu} {\mkern 1mu} {\mkern 1mu}\) If \(3{\mkern 1mu} \sin {\mkern 1mu} P + 4{\mkern 1mu} \cos {\mkern 1mu} Q = 6\) and \(4\sin Q + 3\cos P = 1,\) then the angle R is equal to :
A
\({{5\pi } \over 6}\)
B
\({{\pi } \over 6}\)
C
\({{\pi } \over 4}\)
D
\({{3\pi } \over 4}\)
Open complete paper
11
2018 · Mathematics · Trigonometry · Properties Of Triangle
JEE MAIN 2018 OFFLINE
Let the orthocentre and centroid of a triangle be A(-3, 5) and B(3, 3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter, is :
A
\({{3\sqrt 5 } \over 2}\)
B
\(\sqrt {10}\)
C
\(2\sqrt {10}\)
D
\(3\sqrt {{5 \over 2}}\)
Open complete paper
12
2019 · Mathematics · Trigonometry · Properties Of Triangle
JEE MAIN 2019 ONLINE 10TH APRIL EVENING SLOT
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) of this triangle is :
A
2\(\sqrt 3\)
B
4\(\sqrt 3\)
C
\({4 \over {\sqrt 3 }}\)
D
\({2 \over {\sqrt 3 }}\)
Open complete paper
13
2019 · Mathematics · Trigonometry · Properties Of Triangle
JEE MAIN 2019 ONLINE 10TH JANUARY EVENING SLOT
With the usual notation, in \(\Delta\)ABC, if \(\angle A + \angle B\) = 120o, a = \(\sqrt 3\) \(+\) 1, b = \(\sqrt 3\) \(-\) 1 then the ratio \(\angle A:\angle B,\) is :
A
9 : 7
B
7 : 1
C
5 : 3
D
3 : 1
Open complete paper
14
2019 · Mathematics · Trigonometry · Properties Of Triangle
JEE MAIN 2019 ONLINE 11TH JANUARY EVENING SLOT
Given \({{b + c} \over {11}} = {{c + a} \over {12}} = {{a + b} \over {13}}\) for a \(\Delta\)ABC with usual notation.

If   \({{\cos A} \over \alpha } = {{\cos B} \over \beta } = {{\cos C} \over \gamma },\) then the ordered triad (\(\alpha\), \(\beta\), \(\gamma\)) has a value :
A
(19, 7, 25)
B
(7, 19, 25)
C
(5, 12, 13)
D
(3, 4, 5)
Open complete paper
15
2019 · Mathematics · Trigonometry · Properties Of Triangle
JEE MAIN 2019 ONLINE 11TH JANUARY MORNING SLOT
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 – c2 = y, where c is the length of the third side of the triangle, then the circumradius of the triangle is :
A
\({y \over {\sqrt 3 }}\)
B
\({c \over 3}\)
C
\({c \over {\sqrt 3 }}\)
D
\({3 \over 2}\)y
Open complete paper
16
2019 · Mathematics · Trigonometry · Properties Of Triangle
JEE MAIN 2019 ONLINE 12TH APRIL EVENING SLOT
A triangle has a vertex at (1, 2) and the mid points of the two sides through it are (–1, 1) and (2, 3). Then the centroid of this triangle is :
A
\(\left( {{1 \over 3},2} \right)\)
B
\(\left( {{1 \over 3},{5 \over 3}} \right)\)
C
\(\left( {1,{7 \over 3}} \right)\)
D
\(\left( {{1 \over 3},1} \right)\)
Open complete paper
17
2019 · Mathematics · Trigonometry · Properties Of Triangle
JEE MAIN 2019 ONLINE 8TH APRIL EVENING SLOT
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 lengths of the sides of this triangle is :
A
5 : 9 : 13
B
5 : 6 : 7
C
4 : 5 : 6
D
3 : 4 : 5
Open complete paper
18
2020 · Mathematics · Trigonometry · Properties Of Triangle
JEE MAIN 2020 ONLINE 4TH SEPTEMBER MORNING SLOT
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\(\left( {\Delta ABC} \right) = 5\sqrt 5\) s units, then the abscissa of the vertex C is :
A
\(1 + 2\sqrt 5\)
B
\(2\sqrt 5 - 1\)
C
\(1 + \sqrt 5\)
D
\(2 + \sqrt 5\)
Open complete paper
19
2021 · Mathematics · Trigonometry · Properties Of Triangle
JEE MAIN 2021 ONLINE 16TH MARCH EVENING SHIFT
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 cm2 and R and r are respectively the radii of circumcircle and incircle of \(\Delta\)ABC, then the value of 2R + r (in cm) is equal to ___________.
Enter a numerical response
Open complete paper
20
2021 · Mathematics · Trigonometry · Properties Of Triangle
JEE MAIN 2021 ONLINE 16TH MARCH MORNING SHIFT
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 which touches C1 and the lines AD and AB are tangent to it, is also drawn. Let a tangent line from the point C to the circle C2 meet the side AB at E. If the length of EB is \(\alpha\) + \({\sqrt 3 }\) \(\beta\), where \(\alpha\), \(\beta\) are integers, then \(\alpha\) + \(\beta\) is equal to ____________.
Enter a numerical response
Open complete paper

Showing 20 of 39 questions