If  ${\log _5}2,\,{\log _5}({2^x} - 3)$ and  ${\log _5}(\frac{{17}}{2} + {2^{x - 1}})$ are in $A.P.$ then the value of $x$ is :-

Let $3,7,11,15, \ldots, 403$ and $2,5,8,11, \ldots, 404$ be two arithmetic progressions. Then the sum, of the common terms in them, is equal to.....................

If $b + c,$ $c + a,$ $a + b$ are in $H.P.$, then $\frac{a}{{b + c}},\frac{b}{{c + a}},\frac{c}{{a + b}}$ are in

The sum of the numbers between $100$ and $1000$, which is divisible by $9$ will be

If the ${p^{th}}$ term of an $A.P.$ be $q$ and ${q^{th}}$ term be $p$, then its ${r^{th}}$ term will be

If $a,b,c$ are in $A.P.$, then $\frac{1}{{\sqrt a + \sqrt b }},\,\frac{1}{{\sqrt a + \sqrt c }},$ $\frac{1}{{\sqrt b + \sqrt c }}$ are in