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  4. Assertion: The possible dimensions of a matrix containing 32 elements is 6. Reason: The No. of ways of expressing 32 as a product of two positive integers is 6.

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Q. Assertion : The possible dimensions of a matrix containing $32$ elements is $6$.
Reason : The No. of ways of expressing $32$ as a product of two positive integers is $6$.

Matrices

Solution:

$32=2^{5}$
Number of ways of expressing $32$ as product of two positive integers
$=\frac{5+1}{2}=3$
Possible dimensions of a matrix are
$\{1 \times 32,32 \times 1,2 \times 16,16 \times 2,4 \times 8,8 \times 4\}=6$
$\Rightarrow $ Assertion is true and Reason is false