Let d(n) denote the number of positive divisors of a positive integer n. Which of the following are correct?<br>1. d(5)=d(11)<br>2. d(5) \cdot d(11)=d(55)<br>3. d(5)+d(11)=d(16)<br>Select the correct answer using the code given below:
- A. 1 and 3 only
- B. 1 and 2 only ✓
- C. 2 and 3 only
- D. 1, 2 and 3
Correct Answer: B. 1 and 2 only
Explanation
Prime numbers 5 and 11 have 2 divisors each, so d(5)=2 and d(11)=2. d(55) = d(5) \times d(11) = 4, making stmt 2 correct. For 16 (2^4), d(16) = 5, but d(5)+d(11) = 2+2=4 \neq 5. Stmt 3 is wrong.
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