R D Sharma Solutions for Chapter: Geometric Progressions, Exercise 8: MULTIPLE CHOICE QUESTIONS (MCQs)

If $\left(4^3\right)\left(4^6\right)\left(4^9\right)\left(4^{12}\right)\dots \left(4^{3x}\right)=(0.0625{)}^{-54},$ the value of $x$ is

Given that $x>0,$ the sum $\sum _{n=1}^{\infty }{\left(\frac{x}{x+1}\right)}^{n-1}$ equals

In a G.P. of even number of terms, the sum of all terms is five times the sum of the odd terms. The common ratio of the G.P. is

Let $x$ be the A.M. and $y, z$ be two G.M.s between two positive numbers. Then, $\frac{y^3+z^3}{xyz}$ is equal to

The product $\left(32\right), \left(32{)}^{1/6}, \right(32{)}^{1/36}\dots$ to $\infty$ is equal to

The two geometric means between the numbers $1$ and $64$ are

In a G.P. if the $(m+n{)}^{th}$ term is $p$ and $(m-n{)}^{th}$ term is $q$, then its $m^{th}$ term is

Let $S$ be the sum, $P$ be the product and $R$ be the sum of the reciprocals of $3$ terms of a G.P. then $P^2{R}^3:S^3$ is equal to