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Mathematics - Determinants

Practise 22 JEE Advanced previous year questions on Determinants, compiled from papers spanning 2007 to 2024. 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.

Determinants has been asked in 14 of the 27 years of JEE Advanced papers analysed (2000–2026), with 22 questions in all. 27% of them were easy, 59% moderate and 14% tough. Most of its questions came from 2009, with 3 questions that year. In the last three years (2024–2026) it had 1 question across 6 papers, about 0.2 per paper.

The chapter's 3 topics are not weighted equally: System of Linear Equations (14 questions, 64%), Expansion of Determinants (6 questions, 27%), and Miscellaneous (2 questions, 9%) have been asked the most. System of Linear Equations has also led over the last five years, with 2 questions. System of Linear Equations has produced the most tough questions (2).

  1. 1Let and , where denotes the determinant of . Then the number of elements in is2024 (Paper 1)Expansion of Determinants
  2. 2Let , and be real numbers. Consider the following system of linear equations x + 2 y + z = 7 x + z = 11 2 x - 3 y + z = Match each entry in 2023 (Paper 1)System of Linear Equations
  3. 3Let p , q , r be non-zero real numbers that are, respectively, the 10 th , 100 th and 1000 th terms of a harmonic progression. Consider the 2022 (Paper 1)System of Linear Equations
  4. 4Let and be real numbers such that the system of linear equations is consistent. Let represent the determinant of the matrix Let be the plane2021 (Paper 1)System of Linear Equations
  5. 5Let and be real numbers such that the system of linear equations is consistent. Let represent the determinant of the matrix Let be the plane2021 (Paper 1)System of Linear Equations
  6. 6Let x R and let P = 1 1 1 0 2 2 0 0 3 , Q = 2 x x 0 4 0 x x 6 and R = P Q P - 1 . Then which of the following options is/are correct?2019 (Paper 2)Expansion of Determinants
  7. 7Let S be the of all column matrices b 1 b 2 b 3 such that b 1 , b 2 , b 3 and the system of equations (in real variables) - x + 2 y + 5 z = 2018 (Paper 2)System of Linear Equations
  8. 8Let P be a matrix of order 3 3 such that all the entries in P are from the set - 1 , 0, 1 . Then, the maximum possible value of the determin2018 (Paper 2)Miscellaneous
  9. 9Which of the following is (are) NOT the square of a 3 3 matrix with real entries?2017 (Paper 1)Expansion of Determinants
  10. 10For a real number , if the system 1 2 1 2 1 x y z = 1 - 1 1 of linear equations, has infinitely many solutions, then 1 + + 2 =2017 (Paper 1)System of Linear Equations
  11. 11The total number of distinct x R for which x x 2 1 + x 3 2 x 4 x 2 1 + 8 x 3 3 x 9 x 2 1 + 27 x 3 = 10 is2016 (Paper 1)Expansion of Determinants
  12. 12Let a , , u R . Consider the system of linear equations a x + 2 y = 3 x - 2 y = Which of the following statement(s) is (are) correct ?2016 (Paper 2)System of Linear Equations
  13. 13Which of the following values of satisfy the equation 1 + 2 1 + 2 2 1 + 3 2 2 + 2 2 + 2 2 2 + 3 2 3 + 2 3 + 2 2 3 + 3 2 = - 648 ?2015 (Paper 1)Expansion of Determinants
  14. 14Let be a matrix and let , where for . If the determinant of is 2 , then the determinant of the matrix is2012 (Paper 1)Expansion of Determinants
  15. 15Let be a positive real number and let If , then is equal to [Note : adj denotes the adjoint of a square matrix and denotes the largest integ2010 (Paper 2)Miscellaneous
  16. 16Paragraph: Let be the set of all symmetric matrices all of whose entries are either 0 or 1 . Five of these entries are 1 and four of them ar2009 (Paper 1)System of Linear Equations
  17. 17Paragraph: Let be the set of all symmetric matrices all of whose entries are either 0 or 1 . Five of these entries are 1 and four of them ar2009 (Paper 1)System of Linear Equations
  18. 18Let be points with integer coordinates satisfying the system of homogeneous equations . Then, the number of such points for which is2009 (Paper 2)System of Linear Equations
  19. 19Consider three planes and Let and be the lines of intersection of the planes and and and , respectively. Statement 1 Atleast two of the line2008 (Paper 1)System of Linear Equations
  20. 20Consider the system of equations and Statement 1 The system of equations has no solution for . Statement 2 The determinant , for .2008 (Paper 1)System of Linear Equations
  21. 21Consider the lines given by Match the Statements/Expressions in Column I with the Statements/Expressions in Column II.2008 (Paper 2)System of Linear Equations
  22. 22Consider the following linear equations Match the conditions/expressions in Column I with statements in Column II.2007 (Paper 1)System of Linear Equations

Frequently Asked Questions

1.How many questions are available for Determinants?

This chapter includes 22 questions compiled from JEE Advanced papers spanning 2007 to 2024.

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

These are JEE Advanced 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 JEE Advanced Mathematics?

Determinants has appeared in 14 of the 21 years of JEE Advanced papers covered here, with 22 questions across 17 papers - about one per paper it appears in.

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

Of the 22 questions analysed for this chapter, 27% are easy, 59% moderate and 14% tough. 2009 had the most, with 3 questions.

5.Which topics in Determinants should I focus on?

These topics have carried the most weightage in Determinants:

  • System of Linear Equations - 14 questions (64%)
  • Expansion of Determinants - 6 questions (27%)
  • Miscellaneous - 2 questions (9%)
  • System of Linear Equations has produced the most tough questions (2).
6.Is Determinants's weightage in JEE Advanced going up or down?

Across all 17 papers analysed, Determinants has averaged about 1.3 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.2 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.