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.

Question

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. (A) Assertion is correct, reason is correct; reason is a correct explanation for assertion (B) Assertion is correct, reason is correct; reason is not a correct explanation for assertion (C) Assertion is correct, reason is incorrect (D) Assertion is incorrect, reason is correct

Tardigrade Admin · Accepted Answer

32=25 Number of ways of expressing 32 as product of two positive integers =(5+1/2)=3 Possible dimensions of a matrix are 1 × 32,32 × 1,2 × 16,16 × 2,4 × 8,8 × 4 =6 ⇒ Assertion is true and Reason is false

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 $6$ .

Assertion is correct, reason is correct; reason is a correct explanation for assertion

Assertion is correct, reason is correct; reason is not a correct explanation for assertion

Assertion is correct, reason is incorrect

Assertion is incorrect, reason is correct

$32 = 2^{5}$
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

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.