ICSE Class 10 Matrices — Mock Test (2027)
Free online mock test for Matrices (ICSE Class 10 Mathematics) — 20 competency-based questions based on the latest CISCE 2027 syllabus, with instant marking. Try the samples below, then take the full test free.
What to expect: This mock test covers key concepts from the Matrices chapter — including application-based and competency-focused questions aligned with how ICSE actually sets the paper.
Tip: Attempt without notes first to identify gaps, then review explanations for any wrong answers. Retake after a few days for best retention.
Sample questions
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1.If $A = \begin{bmatrix} 1 & 4 \\ 0 & -1 \end{bmatrix}$ and $B = \begin{bmatrix} 4 & 10 \\ 0 & -1 \end{bmatrix}$, which of the following correctly shows the relationship between AB and BA?
- A.$AB = BA = \begin{bmatrix} 4 & 6 \\ 0 & 1 \end{bmatrix}$
- B.$AB = \begin{bmatrix} 4 & 6 \\ 0 & 1 \end{bmatrix}$, $BA = \begin{bmatrix} 4 & 14 \\ 0 & 1 \end{bmatrix}$
- C.$AB = \begin{bmatrix} 1 & 4 \\ 0 & -1 \end{bmatrix}$, $BA = \begin{bmatrix} 4 & 10 \\ 0 & -1 \end{bmatrix}$
- D.$AB = BA = \begin{bmatrix} 5 & 14 \\ 0 & 0 \end{bmatrix}$
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2.Given, $A = \begin{bmatrix} p & 0 \\ 0 & 2 \end{bmatrix}$, $B = \begin{bmatrix} 0 & -q \\ 1 & 0 \end{bmatrix}$, $C = \begin{bmatrix} 2 & -2 \\ 2 & 2 \end{bmatrix}$ and $BA = C^p$, then find the values of $p$ and $q$.
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3.If $A = \left[ \begin{array}{rr} 7 & 3 \\ 5 & 2 \end{array} \right]$ and $B = \left[ \begin{array}{rr} 2 & 5 \\ 4 & 5 \end{array} \right]$, then the matrix $C$ such that $2A + 3C = 8B$, is
- A.$\left[ \begin{array}{cc} \frac{7}{3} & \frac{21}{3} \\ \frac{4}{3} & \frac{21}{3} \end{array} \right]$
- B.$\left[ \begin{array}{cc} 2 & 12 \\ 22 & 24 \end{array} \right]$
- C.$\left[ \begin{array}{cc} 7 & 17 \\ 11 & 16 \end{array} \right]$
- D.$\left[ \begin{array}{cc} \frac{7}{3} & \frac{34}{3} \\ \frac{22}{3} & \frac{36}{3} \end{array} \right]$
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4.Given $ A = \begin{bmatrix} 6 & 2 \\ 5 & -4 \end{bmatrix} $ and $ B = \begin{bmatrix} 1 & 2 \\ -5 & 1 \end{bmatrix} $, find the matrix $ X $ such that $ 2A + 3B - 5X = 0 $. Which of the following represents the matrix $ X $?
- A.$ X = \begin{bmatrix} 3 & 2 \\ -1 & -1 \end{bmatrix} $
- B.$ X = \begin{bmatrix} 15 & 10 \\ -5 & -5 \end{bmatrix} $
- C.$ X = \begin{bmatrix} 3 & 1 \\ -2 & -1 \end{bmatrix} $
- D.$ X = \begin{bmatrix} 2 & 2 \\ 1 & -2 \end{bmatrix} $
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5.State with reason, whether the following are true or false. $A$, $B$ and $C$ are matrices of order $2 \times 2$. (i) $A \cdot B = B \cdot A$ (ii) $(A + B)^2 = A^2 + 2AB + B^2$ (iii) $A \cdot (B \cdot C) = (A \cdot B) \cdot C$ (iv) $A \cdot (B + C) = A \cdot B + A \cdot C$
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