Determinants

Class 12 · Mathematics

68 questions24 easy30 medium14 hard

Sample Questions

Q1.The value of |[[1+a,1,1],[1,1+b,1],[1,1,1+c]]| is:

  • Aabc(1/a + 1/b + 1/c + 1)
  • Babc + bc + ca + ab
  • Cabc
  • Da + b + c

Q2.A·adj(A) equals:

  • A|A|·A
  • BI
  • C|A|·I
  • Dadj(A)·|A|

Q3.The cofactor Aij of an element aij is related to its minor Mij by:

  • AAij = Mij
  • BAij = (–1)^(i+j) Mij
  • CAij = i·j·Mij
  • DAij = (i+j)·Mij

Q4.The value of |[[a+b, c, c],[a, b+c, a],[b, b, c+a]]| is:

  • A4abc
  • Babc
  • Ca+b+c
  • D0

Q5.The value of the determinant |[[a,b,c],[b,c,a],[c,a,b]]| when a + b + c = 0 is:

  • Aa³ + b³ + c³
  • B0
  • Ca² + b² + c²
  • D3abc

Q6.This is a sample question to preview what you'll get in the full practice test...

  • A. Option one
  • B. Option two
  • C. Option three
  • D. Option four
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Concepts Covered

Adjoint of a matrixApplications of determinantsArea of triangle using determinantsCofactors and minorsConsistency of linear equationsCramer's ruleDeterminant of order 1, 2, 3Inverse of a matrix using adjointProperties of determinantsSingular and non-singular matrices

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