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Mathematics - Determinants

Practise 199 JEE Main previous year questions on Determinants, compiled from papers spanning 2002 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 JEE Main tests.

Determinants has been asked in 24 of the 25 years of JEE Main papers analysed (2002–2026), with 199 questions in all. 40% of them were easy, 52% moderate and 8% tough. Most of its questions came from 2021, with 28 questions that year. In the last three years (2024–2026) it had 37 questions across 49 papers, about 0.8 per paper.

The chapter's 5 topics are not weighted equally: System of Linear Equations (137 questions, 69%), Expansion of Determinants (53 questions, 27%), and Differentiation and Integration of Determinants (6 questions, 3%) have been asked the most. System of Linear Equations has also led over the last five years, with 67 questions. System of Linear Equations has produced the most tough questions (8).

  1. 1If the system of linear equations: , , has infinitely many solutions, then the value of equals:08 Apr, 2026 (E)System of Linear Equations
  2. 2The sum of all possible values of , for which the system of equations : has a non-trivial solution, is equal to :06 Apr, 2026 (E)System of Linear Equations
  3. 3Consider the system of linear equations in : , , , where is a differentiable function. If this system has infinitely many solutions for all 05 Apr, 2026 (M)System of Linear Equations
  4. 4If is defined by , , and , then is equal to :05 Apr, 2026 (E)Expansion of Determinants
  5. 5If the system of equations: has infinitely many solutions, then the value of is:04 Apr, 2026 (E)System of Linear Equations
  6. 6Let be such that the system of linear equations has no solution. Then is equal to :02 Apr, 2026 (M)System of Linear Equations
  7. 7If the system of equations , , has infinitely many solutions, then the point lies on the line02 Apr, 2026 (E)System of Linear Equations
  8. 8Among the statements : I: If , then , and II : If , then ,23 Jan, 2026 (M)Expansion of Determinants
  9. 9The system of linear equations has23 Jan, 2026 (E)System of Linear Equations
  10. 10Let n be the number obtained on rolling a fair die. If the probability that the system has a unique solution is , then the sum of and all po22 Jan, 2026 (E)System of Linear Equations
  11. 11If the system of equations has no solution, then the value of is equal to :21 Jan, 2026 (E)System of Linear Equations
  12. 12Let the system of equations : have infinitely many solutions. Then the radius of the circle centred at and touching the line is07 Apr, 2025 (M)System of Linear Equations
  13. 13Let the system of equations , have infinitely many solutions. Then the number of the solutions of this system, If are integers and satisfy ,07 Apr, 2025 (E)System of Linear Equations
  14. 14If , then is equal to03 Apr, 2025 (M)Differentiation and Integration of Determinants
  15. 15If the system of linear equations has infinitely many solutions, then the value of is :02 Apr, 2025 (M)System of Linear Equations
  16. 16If the system of equation has infinitely many solutions, then is equal to :02 Apr, 2025 (E)System of Linear Equations
  17. 17Let M and m respectively be the maximum and the minimum values of \(f(x)= | {array}{ccc} 1+ ^2 x & ^2 x & 4 4 x \\ ^2 x & 1+ ^2 x & 4 4 x \\29 Jan, 2025 (M)Expansion of Determinants
  18. 18Let be the values of m , for which the equations and have infinitely many solutions. Then the value of is equal to :29 Jan, 2025 (E)System of Linear Equations
  19. 19If the system of equations has infinitely many solutions, then is equal to24 Jan, 2025 (M)System of Linear Equations
  20. 20If the system of equations has infinitely many solutions, then is equal to :24 Jan, 2025 (E)System of Linear Equations
  21. 21For some , let . Then is equal to :24 Jan, 2025 (E)Expansion of Determinants
  22. 22If the system of equations has infinitely many solutions, then is equal to23 Jan, 2025 (M)System of Linear Equations
  23. 23The system of equations has no solution if23 Jan, 2025 (E)System of Linear Equations
  24. 24If the system of linear equations : where , has infinitely many solutions, then is equal to :22 Jan, 2025 (E)System of Linear Equations
  25. 25Let . If the system of equations has infinitely many solutions, then is equal to :09 Apr, 2024 (M)System of Linear Equations
  26. 26Consider the matrices : and . Let the set of all , for which the system of equations has a negative solution (i.e., and ), be the interval .09 Apr, 2024 (E)System of Linear Equations
  27. 27If and , then is equal to:08 Apr, 2024 (E)Expansion of Determinants
  28. 28If the system of equations has infinitely many solutions, then is equal to :08 Apr, 2024 (E)System of Linear Equations
  29. 29For and a natural number , let . Then06 Apr, 2024 (M)Expansion of Determinants
  30. 30Let . If for some , then is equal to _______06 Apr, 2024 (M)System of Linear Equations
  31. 31If the system of equations has infinitely many solutions, then is equal to________06 Apr, 2024 (E)System of Linear Equations
  32. 32If the system of equations has infinitely many solutions, then is equal to :05 Apr, 2024 (M)System of Linear Equations
  33. 33The values of , for which the system of equations has infinitely many solutions, satisfy the equation:05 Apr, 2024 (E)System of Linear Equations
  34. 34If the system of equations has a non-trivial solution, then is equal to :04 Apr, 2024 (M)System of Linear Equations
  35. 35If the system of equations 2 x + 3 y − z = 5 x + α y + 3 z = − 4 3 x − y + β z = 7 has infinitely many solutions, then 13 α β is equal to01 Feb, 2024 (M)System of Linear Equations
  36. 36Let the system of equations x + 2 y + 3 z = 5 , 2 x + 3 y + z = 9 , 4 x + 3 y + λ z = μ have infinite number of solutions. Then λ + 2 μ is e01 Feb, 2024 (E)System of Linear Equations
  37. 37If f x = x 3 2 x 2 + 1 1 + 3 x 3 x 2 + 2 2 x x 3 + 6 x 3 − x 4 x 2 − 2 for all x ∈ ℝ , then 2 f 0 + f ' 0 is equal to31 Jan, 2024 (M)Differentiation and Integration of Determinants
  38. 38If the system of linear equations x - 2 y + z = - 4 2 x + α y + 3 z = 5 3 x - y + β z = 3 has infinitely many solutions, then 12 α + 13 β is31 Jan, 2024 (M)System of Linear Equations
  39. 39Let A be a 3 × 3 real matrix such that A 1 0 1 = 2 1 0 1 , A − 1 0 1 = 4 − 1 0 1 , A 0 1 0 = 2 0 1 0 . Then, the system A − 3 I x y z = 1 2 31 Jan, 2024 (E)System of Linear Equations
  40. 40If f x = 2 cos 4 x 2 sin 4 x 3 + sin 2 2 x 3 + 2 cos 4 x 2 sin 4 x sin 2 2 x 2 cos 4 x 3 + 2 sin 4 x sin 2 2 x then 1 5 f ' ( 0 ) is equal t30 Jan, 2024 (M)Differentiation and Integration of Determinants
  41. 41Consider the system of linear equation x + y + z = 4 μ , x + 2 y + 2 λ z = 10 μ , x + 3 y + 4 λ 2 z = μ 2 + 15 , where λ , μ ∈ R . Which one30 Jan, 2024 (M)System of Linear Equations
  42. 42Consider the system of linear equations x + y + z = 5 , x + 2 y + λ 2 z = 9 and x + 3 y + λ z = μ , where λ , μ ∈ R . Then, which of the fol30 Jan, 2024 (E)System of Linear Equations
  43. 43Let for any three distinct consecutive terms a , b , c of an A.P, the lines a x + b y + c = 0 be concurrent at the point P and Q ( α , β ) b29 Jan, 2024 (E)System of Linear Equations
  44. 44The values of α , for which 1 3 2 α + 3 2 1 1 3 α + 1 3 2 α + 3 3 α + 1 0 = 0 , lie in the interval27 Jan, 2024 (E)Expansion of Determinants
  45. 45Let the system of linear equations x + 2 y - 9 z = 7 - x + 3 y + 7 z = 9 - 2 x + y + 5 z = 8 - 3 x + y + 13 z = has a unique solution x = , 15 Apr, 2023 (M)System of Linear Equations
  46. 46For the system of linear equations 2 x + 4 y + 2 a z = b x + 2 y + 3 z = 4 2 x + 5 y + 2 z = 8 which of the following is NOT correct?13 Apr, 2023 (M)System of Linear Equations
  47. 47If the system of equations 2 x + y - z = 5 2 x - 5 y + z = x + 2 y - 5 z = 7 has infinitely many solutions, then ( + ) 2 + ( - ) 2 is equal 13 Apr, 2023 (E)System of Linear Equations
  48. 48Let D k = 1 2 k 2 k - 1 n n 2 + n + 2 n 2 n n 2 + n n 2 + n + 2 . If k = 1 n D k = 96 , then n is equal to _________.12 Apr, 2023 (M)Summation of Determinants
  49. 49If the system of linear equations 7 x + 11 y + z = 13 5 x + 4 y + 7 z = 175 x + 194 y + 57 z = 361 has infinitely many solutions, then + + 211 Apr, 2023 (E)System of Linear Equations
  50. 50If x + 1 x x x x + x x x x + 2 = 9 8 103 x + 81 , then , 3 are the roots of the equation11 Apr, 2023 (E)Expansion of Determinants

Frequently Asked Questions

1.How many questions are available for Determinants?

This chapter includes 199 questions compiled from JEE Main papers spanning 2002 to 2026.

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

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

3.Is Determinants an important chapter for JEE Main Mathematics?

Determinants has appeared in 24 of the 25 years of JEE Main papers covered here, with 199 questions across 162 papers - about one per paper it appears in.

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

Of the 199 questions analysed for this chapter, 40% are easy, 52% moderate and 8% tough. 2021 had the most, with 28 questions.

5.Which topics in Determinants should I focus on?

These topics have carried the most weightage in Determinants:

  • System of Linear Equations - 137 questions (69%)
  • Expansion of Determinants - 53 questions (27%)
  • Differentiation and Integration of Determinants - 6 questions (3%)
  • System of Linear Equations has produced the most tough questions (8).
6.Is Determinants's weightage in JEE Main going up or down?

Across all 162 papers analysed, Determinants has averaged about 1.2 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.8 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.