If three distinct numbers a,b and c are in GP and the equation ax2+2bx+c=0 and dx2+2ex+f=0 have a common root, then which of the following statements is correct?
d,e,f are in A.P
\(\frac{d}{a},\frac{e}{b},\frac{f}{c}\) are in A.P
d,e,f are in G.P
\(\frac{d}{a},\frac{e}{b},\frac{f}{c}\) are in G.P
a,b, and c are three distinct numbers and from the equation –

What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)