Jump to a section

Mathematics - Determinants

Practise 45 WBJEE 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 WBJEE tests.

Determinants has been asked in 17 of the 18 years of WBJEE papers analysed (2009–2026), with 45 questions in all. 31% of them were easy, 53% moderate and 16% tough. Most of its questions came from 2015, with 6 questions that year. In the last three years (2024–2026) it had 6 questions across 3 papers, about 2 per paper.

The chapter's 6 topics are not weighted equally: Expansion of Determinants (30 questions, 67%), System of Linear Equations (8 questions, 18%), and Miscellaneous (3 questions, 7%) have been asked the most. Expansion of Determinants has also led over the last five years, with 8 questions. Expansion of Determinants has produced the most tough questions (3).

  1. 1Let . If , then the value of is2026Expansion of Determinants
  2. 2Let . If , then equals to2025Expansion of Determinants
  3. 3If are positive real numbers each distinct from unity, then the value of the determinant is2025Expansion of Determinants
  4. 4Let . Suppose and are respectively maximum and minimum values of . Then is equal to2025Expansion of Determinants
  5. 5Let , then2024Miscellaneous
  6. 6If and and , then2024Expansion of Determinants
  7. 7Let \(A\) and \(B\) are orthogonal matrices and \( {det} A+ {det} B=0\). Then2023Miscellaneous
  8. 8Let \(A= ( {array}{ccc}2 & 0 & 3 \\ 4 & 7 & 11 \\ 5 & 4 & 8 {array} )\). Then2023Expansion of Determinants
  9. 9If the matrix \(M_r\) is given by \(M_r= ( {array}{cc}r & r-1 \\ r-1 & r {array} )\) for \(r=1,2,3, \) then \( {det} ( {M}_1 )+ {det} ( {M}_2023Expansion of Determinants
  10. 10Let \( , \) be the roots of the equation \(a x^2+b x+c=0, a, b, c\) real and \(s_n= ^n+ ^n\) and \( | {array}{ccc}3 & 1+s_1 & 1+s_2 \\ 1+s_12023Expansion of Determinants
  11. 11If , then coefficient of in is2022Differentiation and Integration of Determinants
  12. 12Under which of the following condition(s) does(do) the system of equations possesses (possess) unique solution?2022System of Linear Equations
  13. 13Let . Then2022Differentiation and Integration of Determinants
  14. 14Let Let be the roots of , where denotes the identity matrix. If , then the set of possible values of is2021Expansion of Determinants
  15. 15If be the term of a G.P. then is equal to2021Expansion of Determinants
  16. 16The determinant is2021Expansion of Determinants
  17. 17is true for2021Expansion of Determinants
  18. 18Let and , then2020Expansion of Determinants
  19. 19If , then2020Expansion of Determinants
  20. 20The system of equations has infinitely many solutions in . Then,2019System of Linear Equations
  21. 21If . Then is {array}{l} {array} denotes the det of the identity matrix of order 3 )2018Expansion of Determinants
  22. 22If , then the value of is equal to2018Expansion of Determinants
  23. 23If , then the value of is independent of2018Summation of Determinants
  24. 24If the following three linear equations have a non-trivial solution, then2018System of Linear Equations
  25. 25If the polynomial then the constant term of is and are positive integers2018Expansion of Determinants
  26. 26The linear system of equations has2017System of Linear Equations
  27. 27Let . Then all solutions of the equation det is2017Multiplication of Determinants
  28. 28The value of det , where , lies2017Expansion of Determinants
  29. 29Let be such that If then the value of is2017Expansion of Determinants
  30. 30If and are greater than 1 , then the value of is2016Expansion of Determinants
  31. 31The value of such that the system of equations , has no solution, is2015System of Linear Equations
  32. 32Then, is equal to2015Expansion of Determinants
  33. 33The least positive value of , so that the lines and are concurrent, is2015System of Linear Equations
  34. 34The number of distinct real roots of in the interval is2015Expansion of Determinants
  35. 35If is defined as Then, the range of is2015Expansion of Determinants
  36. 36If is an imaginary cube root of unity, then the value of the determinant is2015Expansion of Determinants
  37. 37Let denote the identity matrix and be a matrix obtained by rearranging the columns of . Then,2014Miscellaneous
  38. 38The value of determinant is2013Expansion of Determinants
  39. 39If and are angles of , then the value of is equal to2012Expansion of Determinants
  40. 40The number of real values of for which the system of equations has infinite number of solutions is2012System of Linear Equations
  41. 41The system of linear equations has2012System of Linear Equations
  42. 42If \(z= ( {array}{ccc}1 & 1+2 i & -5 i \\ 1-2 i & -3 & 5+3 i \\ 5 i & 5-3 i & 7 {array} )\) then \((i= {-1})\)2011Expansion of Determinants
  43. 43If one of the cube roots of 1 be \( \), then \( | {array}{ccc}1 & 1+ ^2 & ^2 \\ 1-i & -1 & ^2-1 \\ -i & -1+ & -1 {array} |=\)2011Expansion of Determinants
  44. 44\( | {array}{lll}a-b & b-c & c-a \\ b-c & c-a & a-b \\ c-a & a-b & b-c {array} |=\)2011Expansion of Determinants
  45. 45is an imaginary cube root of unity and then one of the values of is2010Expansion of Determinants

Frequently Asked Questions

1.How many questions are available for Determinants?

This chapter includes 45 questions compiled from WBJEE papers spanning 2010 to 2026.

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

These are WBJEE 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 WBJEE Mathematics?

Determinants has appeared in 17 of the 18 years of WBJEE papers covered here, with 45 questions across 17 papers - about 3 per paper it appears in.

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

Of the 45 questions analysed for this chapter, 31% are easy, 53% moderate and 16% tough. 2015 had the most, with 6 questions.

5.Which topics in Determinants should I focus on?

These topics have carried the most weightage in Determinants:

  • Expansion of Determinants - 30 questions (67%)
  • System of Linear Equations - 8 questions (18%)
  • Miscellaneous - 3 questions (7%)
  • Expansion of Determinants has produced the most tough questions (3).
6.Is Determinants's weightage in WBJEE going up or down?

Across all 17 papers analysed, Determinants has averaged about 2.6 questions per paper. In the last three years (2024–2026), that average has fallen, at about 2.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.