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.

Sample questions

1. 1.Given $A = \begin{bmatrix} 1 & 0 \\ -1 & 7 \end{bmatrix}$ and $I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$, what value of $k$ satisfies $A^2 = 8A + kI$?
   • A.k = -7
   • B.k = 7
   • C.k = -1
   • D.k = 1
2. 2.Given, $A = \begin{bmatrix} 2 & 0 \\ -1 & 7 \end{bmatrix}$ and $I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ and $A^2 = 9A + mI$. Find $m$.
3. 3.Given matrices $A = \begin{bmatrix} 2 -1 \\ 2 0 \end{bmatrix}$, $B = \begin{bmatrix} -3 2 \\ 4 0 \end{bmatrix}$, and $C = \begin{bmatrix} 1 0 \\ 0 2 \end{bmatrix}$, find the matrix $X$ such that $A + X = 2B + C$.
   • A.$X = \begin{bmatrix} -7 5 \\ 6 2 \end{bmatrix}$
   • B.$X = \begin{bmatrix} -5 3 \\ 4 1 \end{bmatrix}$
   • C.$X = \begin{bmatrix} -6 4 \\ 5 3 \end{bmatrix}$
   • D.$X = \begin{bmatrix} -8 6 \\ 7 1 \end{bmatrix}$
4. 4.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.$\left[ \begin{array}{cc} \frac{7}{3} & \frac{34}{3} \\ \frac{22}{3} & \frac{36}{3} \end{array} \right]$
5. 5.If $A = \begin{bmatrix} 1 & -1 \\ 2 & -1 \end{bmatrix}$, $B = \begin{bmatrix} a & 1 \\ b & -1 \end{bmatrix}$ and $(A + B)^2 = A^2 + B^2$, find $a$ and $b$.