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} 2 & 5 \\ 1 & 3 \end{bmatrix} $, $ B = \begin{bmatrix} 4 & -2 \\ -1 & 3 \end{bmatrix} $ and $ I $ is the identity matrix of the same order and $ A^t $ is the transpose of matrix $ A $, find the value of $ A^t \cdot B + BI $.
   • A.$\begin{bmatrix} 11 & 13 \\ 13 & 4 \end{bmatrix}$
   • B.$\begin{bmatrix} 7 & 4 \\ 17 & 1 \end{bmatrix}$
   • C.$\begin{bmatrix} 11 & -13 \\ 13 & -4 \end{bmatrix}$
   • D.$\begin{bmatrix} 3 & 1 \\ 17 & 11 \end{bmatrix}$
2. 2.Find the values of $x$ and $y$ that satisfy the following matrix equation: $$ \left[ \begin{array}{cc} -3 & 2 \\ 0 & -5 \end{array} \right] \left[ \begin{array}{c} x \\ 2 \end{array} \right] = \left[ \begin{array}{c} -5 \\ y \end{array} \right]. $$ Which of the following pairs is correct?
   • A.x = 3, y = -10
   • B.x = -3, y = 10
   • C.x = 1, y = -5
   • D.x = 3, y = 10
3. 3.If $ Y = \begin{bmatrix} 1 & 2 \\ -1 & 5 \end{bmatrix} $, find a matrix $ X $ such that $ 2X + Y = \begin{bmatrix} 5 & 0 \\ -3 & 3 \end{bmatrix} $.
4. 4.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^2 $. Find the values of $ p $ and $ q $.
5. 5.If $A = \begin{bmatrix} 1 & -1 \\ 2 & 3 \end{bmatrix}$ and $C = \begin{bmatrix} 2 & 3 \\ 1 & -11 \end{bmatrix}$, which matrix $B$ satisfies $BA = C$?
   • A.$\begin{bmatrix} 0 & 1 \\ 5 & -2 \end{bmatrix}$
   • B.$\begin{bmatrix} 1 & 0 \\ -2 & 5 \end{bmatrix}$
   • C.$\begin{bmatrix} 2 & 3 \\ 1 & -11 \end{bmatrix}$
   • D.$\begin{bmatrix} -1 & 2 \\ 3 & 0 \end{bmatrix}$