Correct Answer - Option 2 :
\(\rm 20\over 3\)
CONCEPT :
Three numbers x, y, and z are in H.P if and only if [2y = x + z]
So, \(\rm {1\over x}\ , {1\over y} \ and \ {1\over z}\) are in A.P. if and only if: 2y = x + z.
CALCULATION:
Given: Three numbers 5, p and 10 are in Harmonic progression
⇒ \(\rm {1\over 5}\ , {1\over p} \ and \ {1\over 10}\) are in A.P
Now, According to the concept used
⇒ 2 ⋅\(\rm {1\over p}\) = \(\rm {1\over 5} + \rm {1\over 10}\)
⇒ 2 ⋅\(\rm {1\over p}\) = \(\rm \frac {2\ + \ 1}{10}\)
⇒ p = \(\rm 20\over 3\)
∴ The value of p is 20/3.