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Mathematics - Properties of Triangles

Practise 64 NDA previous year questions on Properties of Triangles, compiled from papers spanning 2010 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty NDA tests.

Properties of Triangles has been asked in 17 of the 21 years of NDA papers analysed (2006–2026), with 64 questions in all. 13% of them were easy, 83% moderate and 5% tough. Most of its questions came from 2011, with 10 questions that year. In the last three years (2024–2026) it had 13 questions across 5 papers, about 2.6 per paper.

The chapter's 5 topics are not weighted equally: Sine Rule and its application (37 questions, 58%), Cosine Rule and Projection Formula (19 questions, 30%), and Napiers Analogy, Area of Triangle & Half angle Formulae (6 questions, 9%) have been asked the most. Sine Rule and its application has also led over the last five years, with 15 questions. Sine Rule and its application has produced the most tough questions (3).

  1. 1The angles , and of a triangle are in the ratio . If the longest side of the triangle is units, then what is the perimeter of the triangle ?2026 (Phase 1)Sine Rule and its application
  2. 2In a triangle , if , and are the lengths of the sides opposite to the angles , and respectively, then what is equal to ?2026 (Phase 1)Sine Rule and its application
  3. 3Consider the following for the three (03) items that follow: The sides of a triangle are cm, cm and cm. Consider the following statements: I2025 (Phase 1)Cosine Rule and Projection Formula
  4. 4Consider the following for the three (03) items that follow: The sides of a triangle are cm, cm and cm. What is equal to?2025 (Phase 1)Cosine Rule and Projection Formula
  5. 5Consider the following for the three (03) items that follow: The sides of a triangle are cm, cm and cm. What is the area of the triangle?2025 (Phase 1)Napiers Analogy, Area of Triangle & Half angle Formulae
  6. 6Consider the following for the two (02) items that follow: In a triangle , two sides and are in the ratio and their opposite corresponding a2025 (Phase 1)Sine Rule and its application
  7. 7Consider the following for the two (02) items that follow: In a triangle , two sides and are in the ratio and their opposite corresponding a2025 (Phase 1)Sine Rule and its application
  8. 8If are the sides of triangle ABC , then what is equal to?2024 (Phase 1)Sine Rule and its application
  9. 9If in a triangle , then what is the value of the determinant ; where are sides of the triangle?2024 (Phase 1)Sine Rule and its application
  10. 10In a triangle and . What is the value of2024 (Phase 1)Cosine Rule and Projection Formula
  11. 11Consider the following statements: 1. In a triangle , if 0 , then the triangle is an acute angled triangle. 2. In a triangle , if 0 , the tr2024 (Phase 1)Sine Rule and its application
  12. 12In a triangle What is the area of the triangle if ?2024 (Phase 2)Sine Rule and its application
  13. 13In a triangle and . What is equal to?2024 (Phase 2)Sine Rule and its application
  14. 14Paragraph: The perimeter of a triangle ABC is 6 times the AM of sine of angle of the triangle. Further and . Question: What is the perimeter2023 (Phase 1)Cosine Rule and Projection Formula
  15. 15Paragraph: The perimeter of a triangle is 6 times the of sine of angle of the triangle. Further and . Consider the following statements: 1. 2023 (Phase 1)Sine Rule and its application
  16. 16Paragraph: In the triangle Question: What is the nature of the triangle?2023 (Phase 1)Cosine Rule and Projection Formula
  17. 17Paragraph: In the triangle Question: If , what is the area of the triangle?2023 (Phase 1)Cosine Rule and Projection Formula
  18. 18Paragraph: In a triangle is the largest angle and . Further the in-circle of the triangle touches the sides and at and respectively such tha2023 (Phase 1)Sine Rule and its application
  19. 19Paragraph: In a triangle \(P Q R, P\) is the largest angle and \( P= {1}{3}\). Further the in-circle of the triangle touches the sides \(P Q2023 (Phase 1)Circle Connected to Triangle
  20. 20The angles A, B and C of a triangle ABC are in the ratio 3 : 5 : 4. What is the value of equal to?2023 (Phase 2)Sine Rule and its application
  21. 21The angles A, B and C of a triangle ABC are in the ratio 3 : 5 : 4. What is the ratio of2023 (Phase 2)Sine Rule and its application
  22. 22Let be the lengths of sides respectively of a triangle . If is the perimeter and is the area of the triangle, then what is equal to?2022 (Phase 1)Napiers Analogy, Area of Triangle & Half angle Formulae
  23. 23What is the diameter of a circle inscribed in a regular polygon of 12 sides, each of length 1 cm ?2022 (Phase 2)Circle and Polygon
  24. 24Paragraph: is a triangular plot with and . A lamp post is situated at the middle point of the side . The lamp post subtends an angle at the 2022 (Phase 2)Sine Rule and its application
  25. 25Paragraph: is a triangular plot with and . A lamp post is situated at the middle point of the side . The lamp post subtends an angle at the 2022 (Phase 2)Sine Rule and its application
  26. 26Paragraph: is a triangular plot with and . A lamp post is situated at the middle point of the side . The lamp post subtends an angle at the 2022 (Phase 2)Cosine Rule and Projection Formula
  27. 27In a triangle . What is equal to?2022 (Phase 2)Cosine Rule and Projection Formula
  28. 28The sides of a triangle are and . What is the sum of the acute angles of the triangle?2021 (Phase 1)Cosine Rule and Projection Formula
  29. 29What is the area of the triangle with sides and angle ?2021 (Phase 1)Napiers Analogy, Area of Triangle & Half angle Formulae
  30. 30Paragraph: Read the following information and answer: is a trapezium such that and are parallel and is perpendicular to them. Let and and . 2020Sine Rule and its application
  31. 31Consider the following statements : 1. If is a right-angled triangle, right-angled at and if , then . 2. If and if the triangle is not right2020Sine Rule and its application
  32. 32Consider the following statements : 1. If in a triangle and , then it must be an obtuse-angled triangle. 2. There exists no triangle with an2020Sine Rule and its application
  33. 33If the angles of a triangle are in the ratio , then the corresponding sides are in the ratio2019 (Phase 1)Sine Rule and its application
  34. 34If the angles of a triangles ABC are in AP and , then what is the measure of angle A ?2019 (Phase 2)Sine Rule and its application
  35. 35In a triangle if and , then what is angle B equal to?2018 (Phase 1)Sine Rule and its application
  36. 36If and are the angles of a triangle (not an equilateral triangle) such that and are in GP, then what is equal to?2018 (Phase 1)Sine Rule and its application
  37. 37ABC is a triangle inscribed in a circle with centre O . Let , where . Let . Which one of the following is correct?2018 (Phase 1)Sine Rule and its application
  38. 38Consider the following for triangle ABC : 1. 2. 3. 4. Which of the above are correct?2017 (Phase 1)Sine Rule and its application
  39. 39In a triangle . The value of is2017 (Phase 2)Napiers Analogy, Area of Triangle & Half angle Formulae
  40. 40In triangle ABC , if then the triangle is2017 (Phase 2)Sine Rule and its application
  41. 41Consider a tiangle ABC in which What is the value of2016 (Phase 1)Napiers Analogy, Area of Triangle & Half angle Formulae
  42. 42Consider the following statements: 1. If ABC is an equilateral triangle, then . 2. If ABC is a triangle in which , then 3. If is any triangl2016 (Phase 1)Sine Rule and its application
  43. 43In a triangle and angle . Then the other two angles are2015 (Phase 1)Cosine Rule and Projection Formula
  44. 44If are the sides of a triangle , then where , is2015 (Phase 2)Sine Rule and its application
  45. 45Consider a triangle ABC satisfying The sides of the triangle are in2015 (Phase 2)Sine Rule and its application
  46. 46Consider a triangle ABC satisfying are in2015 (Phase 2)Sine Rule and its application
  47. 47Consider the following statements: 1. There exists no triangle ABC for which . 2. If the angles of a triangle are in the ratio , then its si2014 (Phase 1)Sine Rule and its application
  48. 48In a triangle , then what is C equal to?2014 (Phase 2)Sine Rule and its application
  49. 49In any triangle and . Then what is equal to?2013 (Phase 1)Cosine Rule and Projection Formula
  50. 50If the angles of a triangle are and and the included side is , then what is the area of the triangle?2013 (Phase 2)Napiers Analogy, Area of Triangle & Half angle Formulae

Frequently Asked Questions

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

This chapter includes 64 questions compiled from NDA papers spanning 2010 to 2026.

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

These are NDA 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 NDA Mathematics?

Properties of Triangles has appeared in 17 of the 17 years of NDA papers covered here, with 64 questions across 28 papers - about 2 per paper it appears in.

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

Of the 64 questions analysed for this chapter, 13% are easy, 83% moderate and 5% tough. 2011 had the most, with 10 questions.

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

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

  • Sine Rule and its application - 37 questions (58%)
  • Cosine Rule and Projection Formula - 19 questions (30%)
  • Napiers Analogy, Area of Triangle & Half angle Formulae - 6 questions (9%)
  • Sine Rule and its application has produced the most tough questions (3).
6.Is Properties of Triangles's weightage in NDA going up or down?

Across all 28 papers analysed, Properties of Triangles has averaged about 2.3 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 2.6 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.