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.If $A = \begin{bmatrix} 3 & 5 \\ 4 & -2 \end{bmatrix}$ and $B = \begin{bmatrix} 2 \\ 4 \end{bmatrix}$, is the product AB possible? Give a reason. If yes, which of the following represents AB?
   • A.No, because the number of columns in A does not match the number of rows in B.
   • B.Yes, because the number of columns in A equals the number of rows in B, and AB is $\begin{bmatrix} 26 \\ 0 \end{bmatrix}$.
   • C.Yes, because the number of rows in A equals the number of columns in B, and AB is $\begin{bmatrix} 26 \\ 0 \end{bmatrix}$.
   • D.No, because matrix multiplication is never possible when one matrix is a column matrix.
2. 2.If $A = \begin{bmatrix} 3 & 0 \\ 5 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} -4 & 2 \\ 1 & 0 \end{bmatrix}$, what is the result of $A^2 - 2AB + B^2$?
   • A.$$\begin{bmatrix} 51 & -20 \\ 54 & -17 \end{bmatrix}$$
   • B.$$\begin{bmatrix} 49 & -18 \\ 50 & -15 \end{bmatrix}$$
   • C.$$\begin{bmatrix} 53 & -22 \\ 56 & -19 \end{bmatrix}$$
   • D.$$\begin{bmatrix} 50 & -21 \\ 55 & -16 \end{bmatrix}$$
3. 3.Given $ A = \begin{bmatrix} 1 & 1 \\ 8 & 3 \end{bmatrix} $, evaluate $ (A^2 - 4A) $.
4. 4.If $A = \begin{bmatrix} 2 & -1 \\ -1 & 3 \end{bmatrix}$, evaluate $A^2 - 3A + 2I$, where $I$ is a unit matrix of order 2. Which of the following matrices is the correct result?
   • A.$\begin{bmatrix} 1 & -2 \\ -2 & 3 \end{bmatrix}$
   • B.$\begin{bmatrix} 4 & -5 \\ -5 & 10 \end{bmatrix}$
   • C.$\begin{bmatrix} 0 & -1 \\ -1 & 2 \end{bmatrix}$
   • D.$\begin{bmatrix} 3 & -4 \\ -4 & 7 \end{bmatrix}$
5. 5.Find the values of $x$ and $y$, if $$ \left[ \begin{array}{cc} 1 & 2 \\ 3 & 3 \end{array} \right] \left[ \begin{array}{cc} x & 0 \\ 0 & y \end{array} \right] = \left[ \begin{array}{cc} x & 0 \\ 9 & 0 \end{array} \right] $$