Class 12 Determinants Mock Test (CBSE)

Topics in Determinants

• Determinant of a square matrix
• Area of a triangle using determinants
• Minors and cofactors
• Adjoint of a matrix
• Inverse of a matrix
• Consistency of a system of linear equations
• Solving linear equations by matrix method

Determinants practice questions with answers

1. Q1Multiple choice·1 mark
   If $A$ is a square matrix of order $2$ such that $|3A| = k|A|$, then the value of $k$ is:

   1. (a)6
   2. (b)9
   3. (c)3
   4. (d)27
   Show answer and step marks

   1. Correct option: (b) $9$+1

   Answer: (b)
2. Q2Multiple choice·1 mark
   If a system of linear equations given by $AX = B$ has infinitely many solutions, then:

   1. (a)$|A| = 0$ and $(\text{adj } A)B = O$
   2. (b)$A = O$
   3. (c)$|A| \neq 0$
   4. (d)$|A| = 0$ and $(\text{adj } A)B \neq O$
   Show answer and step marks

   1. Correct option: (a) $|A| = 0$ and $(\text{adj } A)B = O$+1

   Answer: (a)

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