Assertion (A) & Reason (B) MCQ

MCQ 11 Mark

Assertion : If $A$ and $B$ are square matrices of order 2 , then $A B=B A$ is not always true.
Reason : Matrix multiplication is associative.

A
Both assertion and reason are correct and reason is the correct explanation of assertion.
✓
Both assertion and reason are correct but reason is not the correct explanation of assertion.
C
Assertion is correct but reason is incorrect.
D
Assertion is incorrect but reason is correct.

Answer

Correct option: B.

Both assertion and reason are correct but reason is not the correct explanation of assertion.

(b) Both assertion and reason are correct but reason is not the correct explanation of assertion.

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MCQ 21 Mark

Assertion : If $\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right] X=\left[\begin{array}{l}2 \\ 1\end{array}\right]$, then the order of matrix $X$ is $1 \times 2$.
Reason : The product $A B$ of two matrices $A$ and $B$ is possible if number of columns in $A$ is equal to the number of rows in B. Also, the order of the product matrix $A B$ is number of rows in $A X$ number of columns in B.

A
Both assertion and reason are correct and reason is the correct explanation of assertion.
B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
C
Assertion is correct but reason is incorrect.
✓
Assertion is incorrect but reason is correct.

Answer

Correct option: D.

Assertion is incorrect but reason is correct.

(d) Assertion is incorrect and reason is correct.
Explanation:
$\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]_{2 \times 2}[ X ]_{p \times q}=\left[\begin{array}{l}2 \\ 1\end{array}\right]_{2 \times 1}$
$\therefore 2=p$
and $2 \times q=2 \times 1$
$\Rightarrow q=1, p=2$
So, the order of matrix $X$ is $2 \times 1$.

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MCQ 31 Mark

Assertion : $\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]$ is a row matrix and [1 2 3] is a column matrix.
Reason: Matrix having only one row is called row matrix and matrix having only one column is called column matrix.

A
Both assertion and reason are correct and reason is the correct explanation of assertion.
B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
C
Assertion is correct but reason is incorrect.
✓
Assertion is incorrect but reason is correct.

Answer

Correct option: D.

Assertion is incorrect but reason is correct.

(d) Assertion is incorrect and reason is correct.

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MCQ 41 Mark

Assertion : Let $A=\left[\begin{array}{ll}2 & 3 \\ 7 & 5\end{array}\right]$ and
$B =\left[\begin{array}{cc}m-n & 6 \\ 14 & m+n\end{array}\right]$ If $2 A= B$,
then $m=7$ and $n=3$.
Reason : Two equal matrices have the same order and their corresponding elements are also equal.

✓
Both assertion and reason are correct and reason is the correct explanation of assertion.
B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
C
Assertion is correct but reason is incorrect.
D
Assertion is incorrect but reason is correct.

Answer

Correct option: A.

Both assertion and reason are correct and reason is the correct explanation of assertion.

(a) Both assertion and reason are correct and reason is the correct explanation of assertion.
Explanation:
$\begin{array}{l}2 A= B \\ \Rightarrow 2\left[\begin{array}{ll}2 & 3 \\ 7 & 5\end{array}\right]=\left[\begin{array}{cc}m-n & 6 \\ 14 & m+n\end{array}\right] \\ \Rightarrow\left[\begin{array}{cc}4 & 6 \\ 14 & 10\end{array}\right]=\left[\begin{array}{cc}m-n & 6 \\ 14 & m+n\end{array}\right] \\ \Rightarrow m-n=4 \text { and } m+n=10\end{array}$
Solving the two equations for $m$ and $n$, we get
$m=7$ and $n=3$.

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Mathematics Assertion (A) & Reason (B) MCQ

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