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Mathematics - Properties of Triangles

Practise 25 JEE Advanced previous year questions on Properties of Triangles, compiled from papers spanning 2006 to 2023. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty JEE Advanced tests.

Properties of Triangles has been asked in 16 of the 27 years of JEE Advanced papers analysed (2000–2026), with 25 questions in all. 24% of them were easy, 52% moderate and 24% tough. Most of its questions came from 2006, with 4 questions that year. In the last three years (2024–2026) it had 0 questions across 6 papers, about 0 per paper.

The chapter's 5 topics are not weighted equally: Cosine Rule and Projection Formula (9 questions, 36%), Napiers Analogy, Area of Triangle & Half angle Formulae (8 questions, 32%), and Circle Connected to Triangle (4 questions, 16%) have been asked the most. Over the last five years the most frequent topics have been Sine Rule and its application (1), Circle Connected to Triangle (1), and Circle and Polygon (1). Cosine Rule and Projection Formula has produced the most tough questions (3).

  1. 1Consider an obtuse angled triangle A B C in which the difference between the largest and the smallest angle is 2 and whose sides are in arit2023 (Paper 2)Sine Rule and its application
  2. 2Consider an obtuse angled triangle A B C in which the difference between the largest and the smallest angle is 2 and whose sides are in arit2023 (Paper 2)Circle Connected to Triangle
  3. 3Let A B C be the triangle with A B = 1 , A C = 3 and B A C = 2 . If a circle of radius r 0 touches the sides A B , A C and also touches inte2022 (Paper 1)Circle and Polygon
  4. 4In a triangle A B C , let A B = 23 , B C = 3 and C A = 4 . Then the value of cot A + cot C cot B is2021 (Paper 1)Cosine Rule and Projection Formula
  5. 5Consider a triangle P Q R having sides of lengths p , q and r opposite to the angles P , Q and R , respectively. Then which of the following2021 (Paper 2)Cosine Rule and Projection Formula
  6. 6Let x , y and z be positive real numbers. Suppose x , y and z are the lengths of the sides of a triangle opposite to its angles X , Y and Z 2020 (Paper 1)Napiers Analogy, Area of Triangle & Half angle Formulae
  7. 7In a non-right-angled triangle P Q R , let p , q , r denote the lengths of the sides opposite to the angles at P , Q , R respectively. The m2019 (Paper 1)Circle Connected to Triangle
  8. 8In a triangle P Q R , l e t P Q R = 30 o and the sides P Q a n d Q R have lengths 10 3 a n d 10 , respectively. Then, which of the following2018 (Paper 1)Cosine Rule and Projection Formula
  9. 9Paragraph: Let be the origin, and be three unit vectors in the directions of the sides , , respectively, of a triangle . Question: If the tr2017 (Paper 2)Napiers Analogy, Area of Triangle & Half angle Formulae
  10. 10In a X Y Z let x , y , z , be the lengths of sides opposite to the angles, X , Y , Z , respectively and 2 s = x + y + z . If s - x 4 = s - y2016 (Paper 1)Napiers Analogy, Area of Triangle & Half angle Formulae
  11. 11Column I Column II A In a triangle X Y Z let a , b and c be the lengths of the angles X , Y and Z , respectively. If 2 a 2 b 2 = c 2 and = s2015 (Paper 1)Cosine Rule and Projection Formula
  12. 12In a triangle the sum of two sides is x and the product of the same two sides is y. If x 2 - c 2 = y , (where c is the third side of the tri2014 (Paper 2)Circle Connected to Triangle
  13. 13In a P Q R , P is the largest angle and cos P = 1 3 . Further the incircle of the triangle touches the sides P Q , Q R and R P at N , L and 2013 (Paper 2)Cosine Rule and Projection Formula
  14. 14Let be a triangle of area with and where , and are the lengths of the sides of the triangle opposite to the angles at and respectively. Then2012 (Paper 2)Napiers Analogy, Area of Triangle & Half angle Formulae
  15. 15If the angles and of a triangle are in an arithmetic progression and if and denote the lengths of the sides opposite to and respectively, th2010 (Paper 1)Sine Rule and its application
  16. 16Let be a triangle such that and let and denote the lengths of the sides opposite to and respectively. The value(s) of for which and is (are)2010 (Paper 1)Cosine Rule and Projection Formula
  17. 17Consider a triangle and let and denote the lengths of the sides opposite to vertices and respectively. Suppose and the area of the triangle 2010 (Paper 2)Cosine Rule and Projection Formula
  18. 18In a with fixed base , the vertex moves such that . If and denote the lengths of the sides of the triangle opposite to the angles and respec2009 (Paper 1)Napiers Analogy, Area of Triangle & Half angle Formulae
  19. 19Let and be two non-congruent triangles with sides , and angle . The absolute value of the difference between the areas of these triangles is2009 (Paper 2)Napiers Analogy, Area of Triangle & Half angle Formulae
  20. 20Paragraph: Consider the circle and the parabola . They intersect at and in the first and the fourth quadrants, respectively. Tangents to the2007 (Paper 1)Circle Connected to Triangle
  21. 21Let and be the vertices of the . The point inside the is such that the are of equal area. The coordinates of are2007 (Paper 2)Napiers Analogy, Area of Triangle & Half angle Formulae
  22. 22Inradius of a circle which is inscribed in an isosceles triangle one of whose angle is , is , then area of triangle is2006Sine Rule and its application
  23. 23If and are the sides of a such that has real roots, then2006Cosine Rule and Projection Formula
  24. 24Internal bisector of of meets side at . A line drawn through perpendicular to intersects the side at and side at . If and represent sides of2006Napiers Analogy, Area of Triangle & Half angle Formulae
  25. 25Match the following.2006Cosine Rule and Projection Formula

Frequently Asked Questions

1.How many questions are available for Properties of Triangles?

This chapter includes 25 questions compiled from JEE Advanced papers spanning 2006 to 2023.

2.Are these questions only from JEE Advanced, or from other exams too?

These are JEE Advanced questions specifically for the Properties of Triangles chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Properties of Triangles an important chapter for JEE Advanced Mathematics?

Properties of Triangles has appeared in 16 of the 21 years of JEE Advanced papers covered here, with 25 questions across 20 papers - about one per paper it appears in.

4.What is the difficulty level of Properties of Triangles questions in JEE Advanced?

Of the 25 questions analysed for this chapter, 24% are easy, 52% moderate and 24% tough. 2006 had the most, with 4 questions.

5.Which topics in Properties of Triangles should I focus on?

These topics have carried the most weightage in Properties of Triangles:

  • Cosine Rule and Projection Formula - 9 questions (36%)
  • Napiers Analogy, Area of Triangle & Half angle Formulae - 8 questions (32%)
  • Circle Connected to Triangle - 4 questions (16%)
  • Cosine Rule and Projection Formula has produced the most tough questions (3).
6.Is Properties of Triangles's weightage in JEE Advanced going up or down?

Across all 20 papers analysed, Properties of Triangles has averaged about 1.3 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.