Question

Let $a,b,c$ be three positive prime numbers. The progression in which $\sqrt{a},\sqrt{b},\sqrt{c}$ can be three terms (not necessarily consecutive) is

• A. A.P
• B. G.P
• C. H.P
• D. none of these

Answer 1

The correct option is D none of these

Assume the prime number to be $2,3,5$ or $11,23,29$.
Clearly, $\sqrt{2},\sqrt{3},\sqrt{5}$ are not in AP, GP, HP.
or $\sqrt{11},\sqrt{23},\sqrt{29}$ are not in AP, GP, HP
Hence, option $\left(d\right)$ is correct.