Class 12 Maths MCQ – Matrices

This set of Class 12 Maths Chapter 3 Multiple Choice Questions & Answers (MCQs) focuses on “Matrices”. These MCQs are created based on the latest CBSE syllabus and the NCERT curriculum, offering valuable assistance for exam preparation.

1. If the order of the matrix is m×n, then how many elements will there be in the matrix?
a) mn
b) m2 n2
c) mn2
d) 2mn

Explanation: The number of elements for a matrix with the order m×n is equal to mn, where m is the number of rows and n is the number of columns in the matrix.

2. Which of the following is a matrix of the order 2×2 where the equation of the elements is given by aij=i+j.
a) A=$$\begin{bmatrix}1&1\\1&1\end{bmatrix}$$
b) A=$$\begin{bmatrix}4&5\\4&1\end{bmatrix}$$
c) A=$$\begin{bmatrix}2&3\\3&4\end{bmatrix}$$
d) A=$$\begin{bmatrix}1&2\\1&2\end{bmatrix}$$

Explanation: a11=1+1=2, a12=1+2=3, a21=2+1=3, a22=2+2=4
∴ A=$$\begin{bmatrix}a_{11}&a_{12}\\a_{21}&a_{22} \end{bmatrix}=\begin{bmatrix}2&3\\3&4\end{bmatrix}$$.

3. What is the order of the matrix A=$$\begin{bmatrix}3&5\\7&9\end{bmatrix}$$?
a) 2×3
b) 2×2
c) 3×3
d) 4×4

Explanation: The number of rows (m) and the number of columns (n) in the given matrix A=$$\begin{bmatrix}3&5\\7&9\end{bmatrix}$$ is 2. Therefore, the order of the matrix is 2×2(m×n).

4. The order of the matrix A=$$\begin{bmatrix}1&5&9\\4&8&6\end{bmatrix}$$ is 2×3.
a) True
b) False

Explanation: The given statement is true. In the matrix A=$$\begin{bmatrix}1&5&9\\4&8&6\end{bmatrix}$$ the number of rows(m) is 2 and the number of columns(n) is 3. Therefore, the order of the matrix is 2×3.

5. In a matrix with 9 elements, then the possible ordered pairs are (3, 3), (1, 9), (9, 1).
a) True
b) False

Explanation: The given statement is true. The possible orders in which the matrix can be formed are 3×3,9×1,1×9. Therefore, the ordered pairs are (3,3),(1,9),(9,1).
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6. Which of the following is not a possible ordered pair for a matrix with 6 elements.
a) (2,3)
b) (3,2)
c) (1,6)
d) (3,1)

Explanation: The possible orders in which the matrix with 6 elements can be formed are 2×3, 3×2, 1×6, 6×1. Therefore, the possible orders pairs are (2,3), (3,2), (1,6), (6,1). Thus, (3,1) is not possible.

7. Which of the following matrix is of the order 4×3.
a) A=$$\begin{bmatrix}3&4\\3&5\\4&5\end{bmatrix}$$
b) A=$$\begin{bmatrix}1&2&3\\5&7&9\end{bmatrix}$$
c) A=$$\begin{bmatrix}4&5&6 \\5&2&6\\6&4&7\\7&7&1\end{bmatrix}$$
d) A=$$\begin{bmatrix}1\\4\\6\end{bmatrix}$$

Explanation: The matrix A=$$\begin{bmatrix}4&5&6\\5&2&6\\6&4&7\\7&7&1\end{bmatrix}$$ is a 4×3 matrix as it has 4 rows and 3 columns.

8. Consider the matrix A=$$\begin{bmatrix}2&4&5\\1&6&4\\2&8&9\end{bmatrix}$$. Find the element a32.
a) 5
b) 6
c) 4
d) 8

Explanation: a32 is the element represented in the form aij i is the row number and j is the column number. Therefore, the element a32 is the element in the third row (i=3)and second column (j=2) which is 8.

9. What is the order of the matrix A=$$\begin{bmatrix}2&3\\1&9\\5&2\end{bmatrix}$$?
a) 2×3
b) 3×2
c) 2×2
d) 3×3

Explanation: The given matrix A=$$\begin{bmatrix}2&3\\1&9\\5&2\end{bmatrix}$$ has 3 rows and 2 columns. Therefore, the order of the matrix is 3×2.

10. Given a matrix A=$$\begin{bmatrix}2&3&9\\3&9&6\\1&6&7\end{bmatrix}$$, which of the elements aij follows the condition i=j.
a) 9, 9, 1
b) 2, 9, 7
c) 2, 3, 9
d) 2, 3, 1

Explanation: The elements following the condition i=j will have the same row number and column number. The elements are a11, a22, a33 which in the matrix A are 2, 3, 9 respectively.

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