Properties of Geometric Progression

Q. State true or false:

1. True
2. False

Q. The value of $x$ for which the numbers $2x+1,5x+1$ and $11x+1$ are in G.P. is ___ ($x$ is a natural number).

1. -1
2. 1
3. 2
4. 3

Q. $\mathrm{If}A=2^{65}\mathrm{and}B=2^{64}+2^{63}+2^{62}+....+2^0,\mathrm{Which}\mathrm{of}\mathrm{thew}\mathrm{following}\mathrm{is}\mathrm{true}?$

1. $B\mathrm{is}{2}^{64}\mathrm{more}\mathrm{than}A$
2. $B\mathrm{is}\mathrm{larger}\mathrm{than}A\mathrm{by}1$
3. $A\mathrm{is}\mathrm{larger}\mathrm{than}B\mathrm{by}1$
4. $A\mathrm{and}B\mathrm{are}\mathrm{equal}$

Q.

If $a,b,c$ are in A.P. and $a,c-b,b-a$ are in G.P., where$a\ne b\ne c$, then $a:b:c$ is ___.

1. 1:2:4

2. 3:2:1

3. 1:2:3

4. 1:3:5

Q. If $x,y$ and $z$ are three consecutive terms of a G.P such that $xyz=8,$ then $y$ equals ____.

1. 8
2. 7
3. 2
4. 32

Q. Solve $x^2-11x+10=0$

Q.

If $a,b,c$ are in G.P., then ___.

1. $a(b^2+a^2)$ = $c(b^2+c^2)$

2. $a^2(b+c)$ = $c^2(a+b)$

3. $b^2=\frac{a}{c}$

4. $a(b^2+c^2)$ = $c(a^2+b^2)$

Q.

If the roots of the cubic equation $a{x}^3+b{x}^2+cx+d=0$ are in G.P., then ___.

1. $c^{3}a=b^{3}d$

2. $c{a}^3=b{d}^3$

3. $a^{3}b=c^{3}d$

4. $a{b}^3=c{d}^3$

Q. If x, 2y, 3z are in A.P., where the distinct numbers x, y, z are in G.P. then the common ratio of the G.P. is

1. 3
2. $\frac{1}{3}$
3. 2
4. $\frac{1}{2}$

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 form an increasing GP. If the middle term of the GP is doubled, then new numbers are in AP. Then, the common ratio of the GP is ___.

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

Q. In a G.P , the product of the two terms equidistant from its beginning and from its end is always a constant.

1. True
2. False

Q. In a G.P , the product of the two terms equidistant from its beginning and from its end is always a constant.

1. False
2. True