Which of the following geometric progressions has the common ratio as √2?

Correct option is (B) \(\sqrt3 ,\sqrt6 ,\sqrt{12} ,......\)

In a G.P. common ratio is \(r=\frac{a_2}{a_1}\)

(A) \(\sqrt2 ,\sqrt6 ,\sqrt{18} ,......\)

\(r=\frac{a_2}{a_1}=\frac{\sqrt6}{\sqrt2}\)

\(=\frac{\sqrt3.\sqrt2}{\sqrt2}=\sqrt3\)

(B) \(\sqrt3 ,\sqrt6 ,\sqrt{12} ,......\)

\(r=\frac{\sqrt6}{\sqrt3}\)

\(=\frac{\sqrt3.\sqrt2}{\sqrt3}=\sqrt2\)

(C) \(\sqrt5 ,\sqrt{15} ,\sqrt{45} ,......\)

\(r=\frac{a_2}{a_1}=\frac{\sqrt{15}}{\sqrt5}\)

\(=\frac{\sqrt3.\sqrt5}{\sqrt5}=\sqrt3\)

(D) \(\sqrt7 ,\sqrt{21} ,\sqrt{63} ,......\)

\(r=\frac{a_2}{a_1}=\frac{\sqrt{21}}{\sqrt7}\)

\(=\frac{\sqrt7.\sqrt3}{\sqrt7}=\sqrt3\)

Correct option is B) √3, √6, \(\sqrt{12}\),...........