Selecting consecutive terms in GP

Q. $x$ is one of the three consecutive numbers in G.P. whose sum is 38 and their product is 1728. The value of $x$ can be ___.

1. 18
2. 12
3. 4
4. 16

Q. Three positive numbers from an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. then the common ratio of the G.P. is:

1. $2-\sqrt{3}$
2. $2+\sqrt{3}$
3. $\sqrt{2}+\sqrt{3}$
4. $3+\sqrt{2}$

Q. If three distinct real numbers a, b, c are in G.P and $a+b+c=ax$, then

1. $xϵ[\frac{3}{4},\infty ]$
2. $xϵR^{+}$
3. $xϵ(-1,\infty )$
4. none of these

Q. If the product of three consecutive terms of G.P. is 216 and the sum of product of pair-wise is 156, then the numbers will be
[MNR 1978]

1. 1, 3, 9

2. 2, 6, 18

3. 3, 9, 27
4. 2, 4, 8

Q. If the $2^{nd},5^{th}$ and $9^{th}$ terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is:

1. 1
2. $\frac{7}{4}$
3. $\frac{8}{5}$
4. $\frac{4}{3}$

Q. If x, $G_1,G_2,$ y be the consecutive terms of a G.P., then the value of $G_1{G}_2$ will be

1. $\frac{x}{y}$
2. $\frac{y}{x}$
3. $\sqrt{xy}$
4. xy