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 :

  • A
    1 and 2 only
  • B
    2 and 3 only
  • C
    1 and 3 only
  • Correct answer
    D
    1,2 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'.

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