Assertion :The possible dimension of a matrix consisting $27$ elements is $4.$ Reason: The number of ways of expressing $27$ as a product of two positive integers is $4.$

Both Assertion & Reason are individually correct & Reason is correct explanation of Assertion,

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Both Assertion & Reason are individually true but Reason is Not the correct explanation of Assertion.

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Assertion is correct but Reason is incorrect.

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Assertion is incorrect but Reason is correct.

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Solution

The correct option is C Assertion is correct but Reason is incorrect.
$27 = 1 \times 27$ and $3 \times 9$

Thus the number of ways of expressing $27$ as a product of two numbers is only $2$
Thus the Reason is false.

Also the possible dimensions of a matrix having $27$ elements are $1 \times 27, 27 \times 1, 3 \times 9, 9 \times 3$

$∴$ Assertion (A) is true and reason (R) is false.

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Assertion :The possible dimension of a matrix consisting 27 elements is 4. Reason: The number of ways of expressing 27 as a product of two positive integers is 4.

Assertion :The possible dimension of a matrix consisting $27$ elements is $4.$ Reason: The number of ways of expressing $27$ as a product of two positive integers is $4.$