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Mathematics - Determinants

Practise 130 NDA previous year questions on Determinants, 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.

Determinants has been asked in 17 of the 21 years of NDA papers analysed (2006–2026), with 130 questions in all. 23% of them were easy, 74% moderate and 3% tough. Most of its questions came from 2023, with 14 questions that year. In the last three years (2024–2026) it had 18 questions across 5 papers, about 3.6 per paper.

The chapter's 4 topics are not weighted equally: Expansion of Determinants (105 questions, 81%), System of Linear Equations (19 questions, 15%), and Differentiation and Integration of Determinants (3 questions, 2%) have been asked the most. Expansion of Determinants has also led over the last five years, with 34 questions. Expansion of Determinants has produced the most tough questions (3).

  1. 1Let where is any constant, then what is at equal to ?2026 (Phase 1)Differentiation and Integration of Determinants
  2. 2If , then what is the value of ?2026 (Phase 1)Expansion of Determinants
  3. 3If is a square matrix such that , then , where is the transpose of , is equal to2026 (Phase 1)Multiplication of Determinants
  4. 4If , then what is the value of ?2026 (Phase 1)Expansion of Determinants
  5. 5Let and . If is positive, then which one of the following is correct ?2026 (Phase 1)Expansion of Determinants
  6. 6If and , , , , are the cofactors of the elements , , , , respectively, then what is equal to?2025 (Phase 1)Expansion of Determinants
  7. 7Consider the following statements in respect of the determinant : I. is positive if . II. is negative if k = 0$. How many of the statements 2025 (Phase 1)Expansion of Determinants
  8. 8If where , then what is equal to?2025 (Phase 1)Expansion of Determinants
  9. 9If , then what is the value of ?2025 (Phase 1)Expansion of Determinants
  10. 10Consider the following in respect of a non-singular matrix : I. II. III. How many of the above are correct?2025 (Phase 1)Multiplication of Determinants
  11. 11The system of equations ,2025 (Phase 2)System of Linear Equations
  12. 12In obtaining the solution of the system of equations , and by Cramer's rule, the value of is obtained by dividing by , where . What is the v2025 (Phase 2)System of Linear Equations
  13. 13The value of the determinant is equal to2025 (Phase 2)Expansion of Determinants
  14. 14If , , are the sides of a triangle and is the perimeter of the triangle, then what is equal to?2025 (Phase 2)Expansion of Determinants
  15. 15Consider the following statements: Statement-I: If is an matrix, then , where is a scalar. Statement-II: If is a matrix obtained from by mul2025 (Phase 2)Expansion of Determinants
  16. 16For what value of is determinant for every ?2024 (Phase 1)Expansion of Determinants
  17. 17If then what is modulus of Z equal to?2024 (Phase 2)Expansion of Determinants
  18. 18If then what is the value of ?2024 (Phase 2)Expansion of Determinants
  19. 19The system of linear equations and has2023 (Phase 1)System of Linear Equations
  20. 20Let be a system of 3 liner equations with 3 -unknowns. Let and be its two distinct solutions. If the combination is a solution of ; where , 2023 (Phase 1)System of Linear Equations
  21. 21What is the sum of the roots of the equation2023 (Phase 1)Expansion of Determinants
  22. 22If are in AP , then what is equal to?2023 (Phase 1)Expansion of Determinants
  23. 23Paragraph: Question: If for every , then which one of the following is correct?2023 (Phase 1)Expansion of Determinants
  24. 24[QUESTION] Paragraph: Question: If , then is a root of which one of the following equation?2023 (Phase 1)Expansion of Determinants
  25. 25Paragraph: Question: What is equal to?2023 (Phase 1)Expansion of Determinants
  26. 26Paragraph: Question: What is equal to?2023 (Phase 1)Expansion of Determinants
  27. 27Paragraph: Question: What is equal to?2023 (Phase 1)Expansion of Determinants
  28. 28Let A be a skew-symmetric matrix of order 3 . What is the value of Where I is the identity matrix of order 3 ?2023 (Phase 2)Expansion of Determinants
  29. 29If , then what is the value of ?2023 (Phase 2)Expansion of Determinants
  30. 30If all elements of a third order determinant are equal to 1 or –1, then the value of the determinant is:2023 (Phase 2)Expansion of Determinants
  31. 31The value of the determinant of a matrix of order 3 is 3 . If C is the matrix of cofactors of the matrix A , then what is the value of deter2023 (Phase 2)Expansion of Determinants
  32. 32If , then what is equal to?2023 (Phase 2)Expansion of Determinants
  33. 33If and where , then is2022 (Phase 1)Expansion of Determinants
  34. 34If and , then what is the value of ?2022 (Phase 1)Expansion of Determinants
  35. 35Under which of the following conditions does the determinant vanish? 1. 2. 3. Select the correct answer using the code given below :2022 (Phase 1)Expansion of Determinants
  36. 36For what value of is the matrix singular?2022 (Phase 1)Expansion of Determinants
  37. 37Consider the determinant If and the minors of , are respectively then what is the value of ?2022 (Phase 2)Expansion of Determinants
  38. 38Paragraph: Let be the determinant of a matrix , where and be the cofactors of respectively. Question: What is the value of2022 (Phase 2)Expansion of Determinants
  39. 39Paragraph: Let be the determinant of a matrix , where and be the cofactors of respectively. Question: What is the value of ?2022 (Phase 2)Expansion of Determinants
  40. 40Paragraph: Let be the determinant of a matrix , where and be the cofactors of respectively. Question: What is the value of ?2022 (Phase 2)Expansion of Determinants
  41. 41Paragraph: Let and where is symmetric matrix and is skew-symmetric matrix. Question: What is the minimum value of determinant of ?2022 (Phase 2)Expansion of Determinants
  42. 42If is the value of the determinant then what is the value of the following determinant? or or 12021 (Phase 1)Expansion of Determinants
  43. 43If and , then what is the value of the following determinant?2021 (Phase 1)Expansion of Determinants
  44. 44If are in GP, then what is the value of the following determinant?2021 (Phase 1)Expansion of Determinants
  45. 45Let where and are any four different prime numbers less than 20 . What is the maximum value of the determinant?2021 (Phase 1)Expansion of Determinants
  46. 46If the determinant then what is equal to?2021 (Phase 1)Expansion of Determinants
  47. 47then what is equal to?2021 (Phase 1)Expansion of Determinants
  48. 48The element in the row and the column of a determinant of third order is equal to . What is the value of the determinant?2021 (Phase 1)Expansion of Determinants
  49. 49With the numbers , all the possible determinants with these four different elements are constructed. What is the sum of the values of all su2021 (Phase 1)Expansion of Determinants
  50. 50What is the value of the following determinant?2021 (Phase 2)Expansion of Determinants

Frequently Asked Questions

1.How many questions are available for Determinants?

This chapter includes 130 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 Determinants chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Determinants an important chapter for NDA Mathematics?

Determinants has appeared in 17 of the 17 years of NDA papers covered here, with 130 questions across 32 papers - about 4 per paper it appears in.

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

Of the 130 questions analysed for this chapter, 23% are easy, 74% moderate and 3% tough. 2023 had the most, with 14 questions.

5.Which topics in Determinants should I focus on?

These topics have carried the most weightage in Determinants:

  • Expansion of Determinants - 105 questions (81%)
  • System of Linear Equations - 19 questions (15%)
  • Differentiation and Integration of Determinants - 3 questions (2%)
  • Expansion of Determinants has produced the most tough questions (3).
6.Is Determinants's weightage in NDA going up or down?

Across all 32 papers analysed, Determinants has averaged about 4.1 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 3.6 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.