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Mathematics - Determinants

Practise 51 KCET previous year questions on Determinants, compiled from papers spanning 2007 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 KCET tests.

Determinants has been asked in 19 of the 20 years of KCET papers analysed (2007–2026), with 51 questions in all. 39% of them were easy, 39% moderate and 22% tough. Most of its questions came from 2017, with 6 questions that year. In the last three years (2024–2026) it had 8 questions across 3 papers, about 2.7 per paper.

The chapter's 6 topics are not weighted equally: Expansion of Determinants (38 questions, 75%), Differentiation and Integration of Determinants (4 questions, 8%), and Summation of Determinants (3 questions, 6%) have been asked the most. Expansion of Determinants has also led over the last five years, with 9 questions. Expansion of Determinants has produced the most tough questions (10).

  1. 1Which of the following is correct?2026Miscellaneous
  2. 2If A and B are invertible square matrices of order n, then which of the following is not correct?2026Multiplication of Determinants
  3. 3The system of equations and has2026System of Linear Equations
  4. 4If and , then the value of k is2025Expansion of Determinants
  5. 5If is a square matrix of order , then the value of is2025Expansion of Determinants
  6. 6If then is2024Expansion of Determinants
  7. 7If and , then is2024Differentiation and Integration of Determinants
  8. 8Let . Then, is2024Expansion of Determinants
  9. 9The value of is2023Expansion of Determinants
  10. 10If is singular matrix, then the value of is equal to2023Expansion of Determinants
  11. 11If and , then2023Expansion of Determinants
  12. 12If there are two values of ' ' which makes determinant Then, the sum of these number is2022Expansion of Determinants
  13. 13If the vertices of a triangle are and , then the area of the triangle is2022Expansion of Determinants
  14. 14If , then2022Summation of Determinants
  15. 15If , then is equal to2020Expansion of Determinants
  16. 16If and are square matrices of same order and is a skew symmetric matrix, then is2020Expansion of Determinants
  17. 17If \( A= [ {array}{ll}1 & 3 \\ 4 & 2 {array} ], B= [ {array}{cc}2 & -1 \\ 1 & 2 {array} ] \) then \( |A B B^{ } |= \)2019Expansion of Determinants
  18. 18If the value of a third order determinant is \( 16 \), then the value of the determinant formed by replacing each of its elements by its co 2019Expansion of Determinants
  19. 19The constant term in the expansion of \( | {array}{ccc}3 x+1 & 2 x-1 & x+2 \\ 5 x-1 & 3 x+2 & x+1 \\ 7 x-2 & 3 x+1 & 4 x-1 {array} | \) is2019Expansion of Determinants
  20. 20If \( x, y, z R \), then the value of determinant \[ | {array}{lll} (5^{x}+5^{-x} )^{2} & (5^{x}-5^{-x} )^{2} & 1 \\ (6^{x}+6^{-x} )^{2} & (2018Expansion of Determinants
  21. 21The value of determinant \( | {array}{ccc}a-b & b+c & a \\ b-a & c+a & b \\ c-a & a+b & c {array} | \) is2018Expansion of Determinants
  22. 22If \( (x_{1}, y_{1} ), (x_{2}, y_{2} ) \) and \( (x_{3}, y_{3} ) \) are the vertices of a triangle whose area is ' \( k \) ' square units, t2018Expansion of Determinants
  23. 23Let \( A \) be a square matrix of order \( 3 3 \), then \( |5 A|= \)2018Expansion of Determinants
  24. 24The value of \( ^{2} 45^{ }- ^{2} 15^{ } \) is2017Expansion of Determinants
  25. 25The value of \( _{ 0} {1- 4 }{1- 6 } \) is2017Expansion of Determinants
  26. 26The contrapositive statement of the statement "If \( x \) is prime number, then \( x \) is odd" is2017Summation of Determinants
  27. 27If \( f(x)=8 x^{2}, g(x)=x^{ {1}{3}} \) then \( f o g(x) \) is2017Differentiation and Integration of Determinants
  28. 28If a matrix \( {A} \) is both symmetric and skewsymmetric, then2017Miscellaneous
  29. 29If \( 2 [ {array}{ll}1 & 3 \\ 0 & x {array} ]+ [ {array}{ll}y & 0 \\ 1 & 2 {array} ]= [ {array}{ll}5 & 6 \\ 1 & 8 {array} ] \) then the valu2017Summation of Determinants
  30. 30If \( x y z \) are all different and not equal to zero and \( | {array}{cccc}1+x & 1 & 1 \\ 1 & 1+y & 1 \\ 1 & 1 & 1+z {array} |=0 \) then t2016Expansion of Determinants
  31. 31If \( A \) is any square matrix of order \( 3 3 \) then \( |3 A| \) is equal to2016Expansion of Determinants
  32. 32If \( x y z \) are not equal and \( 0, 1 \) the value of \( | {array}{ccc} x & y & z \\ 2 x & 2 y & 2 z \\ 3 x & 3 y & 3 z {array} | \) is e2016Expansion of Determinants
  33. 33If \( Z= {( {3}+i)^{3}(3 i+4)^{2}}{(8+6 i)^{2}} \), then \( |Z| \) is equal to2015Multiplication of Determinants
  34. 34If \( \) and \( \) are the roots of \( x^{2}-a x+b^{2}=0 \), then \( ^{2}+ ^{2} \) is equal to2015Differentiation and Integration of Determinants
  35. 35Equation of line passing through the point \( (2,3,1) \) and parallel to the line of intersection of the plane \( x-2 y-z+5=0 \) and \( x+y+2015Expansion of Determinants
  36. 36A box contains \( 6 \) red marbles numbers from \( 1 \) through \( 6 \) and \( 4 \) white marbles \( 12 \) through \( 15 . \) Find the proba2015Expansion of Determinants
  37. 37The two curves \( x^{3}-3 x y^{2}+2=0 \) and \( 3 x^{2} y-y^{3}=2 \)2015System of Linear Equations
  38. 38Equation of the plane perpendicular to the line \( {x}{1}= {y}{2}= {z}{3} \) and passing through the point \( (2, \), \( 3,4) \) is2014Expansion of Determinants
  39. 39The line \( {x-2}{3}= {y-3}{4}= {z-4}{5} \) is parallel to the plane2014Expansion of Determinants
  40. 40Lines \( {x-2}{1}+ {y-3}{1}= {z-4}{-K} \) and \( {x-1}{K}= {y-4}{2}= {z-5}{1} \) are co-planar if2014Expansion of Determinants
  41. 41If and , then is equal to2013Expansion of Determinants
  42. 42If and , then is equal to2013Differentiation and Integration of Determinants
  43. 43If , then e is equal to2012Expansion of Determinants
  44. 44is equal to2011Expansion of Determinants
  45. 45The constant term of the polynomial is2010Expansion of Determinants
  46. 46Let be the mid point of the line joining to a point on the curve . Then, locus of is symmetrical about2010Expansion of Determinants
  47. 47If and , then is equal to2009Expansion of Determinants
  48. 48If , then are2009Expansion of Determinants
  49. 49The value of is equal to2009Expansion of Determinants
  50. 50If and , then2008Expansion of Determinants

Frequently Asked Questions

1.How many questions are available for Determinants?

This chapter includes 51 questions compiled from KCET papers spanning 2007 to 2026.

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

These are KCET 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 KCET Mathematics?

Determinants has appeared in 19 of the 20 years of KCET papers covered here, with 51 questions across 19 papers - about 3 per paper it appears in.

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

Of the 51 questions analysed for this chapter, 39% are easy, 39% moderate and 22% tough. 2017 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 - 38 questions (75%)
  • Differentiation and Integration of Determinants - 4 questions (8%)
  • Summation of Determinants - 3 questions (6%)
  • Expansion of Determinants has produced the most tough questions (10).
6.Is Determinants's weightage in KCET going up or down?

Across all 19 papers analysed, Determinants has averaged about 2.7 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 2.7 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.