If $a, b, c$ are in $A.P.$ and $b, c, d$ are in $H.P.$,then

The arithmetic mean and the geometric mean of two distinct $2$-digit numbers $x$ and $y$ are two integers,one of which can be obtained by reversing the digits of the other (in base $10$ representation). Then,$x+y$ equals

If $n$ arithmetic means $a_1, a_2, \dots, a_n$ are inserted between $50$ and $100$ and $n$ harmonic means $h_1, h_2, \dots, h_n$ are inserted between the same two numbers,then $a_2 h_{n-1}$ is equal to

If $a, b, c$ are in $A.P.$ as well as in $G.P.$,then

Let the first three terms $2, p$ and $q$,with $q \neq 2$,of a $G.P.$ be respectively the $7^{\text{th}}$,$8^{\text{th}}$ and $13^{\text{th}}$ terms of an $A.P.$ If the $5^{\text{th}}$ term of the $G.P.$ is the $n^{\text{th}}$ term of the $A.P.$,then $n$ is equal to

If the geometric mean between two numbers is $4$ and the arithmetic mean is $5$,then the harmonic mean is .......