Q181 / 270 · NDA 2019 (Phase 2) · Mathematics
Let $a, b, c$ be in AP and $k \neq 0$ be a real number. Which of the following are correct?
1. $k a, k b, k c$ are in AP 2. $k-a, k-b, k-c$ are in AP
3. $\frac{a}{k}, \frac{b}{k}, \frac{c}{k}$ are in AP
Select the correct answer using the code given below :
- A1 and 2 only
- B2 and 3 only
- C1 and 3 only
- Correct answerD1,2 and 3
Solution
$A P$ remains an $A P$ if it is multiplied, divided and subtracted by a constant number.
$\therefore$ All three statements are correct.
Hence, the correct answer is option: 'D'.