Question

Assertion :The number of ways of writing $10800$ as the product of two positive integers is $30$. Reason: The $10800$ is divisible by exactly three prime numbers.

• A. Both (A) & (R) are individually true & (R) is correct explanation of (A),
• B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).
• C. (A)is true but (R) is false,
• D. (A)is false but (R) is true.

Answer 1

The correct option is B Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).

$10800=2^4\ast 3^3\ast 5^2$
Thus, the number has 3 prime factors.
Hence, number of factors = $(4+1)\ast (3+1)\ast (2+1)=60$
Thus, the number of ways in which the number can be written as the product of two factors = $\frac{60}{2}=30$.
Hence, both statements are true, but the 2nd is not a correct explanation for the 1st.
Hence, (b) is correct.