If the first term of an infinite geometric series is $x$ and its sum is $5$,then which of the following is true?

If $y = x + x^2 + x^3 + \dots \infty$,then $x = $

If $\frac{1}{2 \cdot 3^{10}}+\frac{1}{2^{2} \cdot 3^{9}}+\ldots+\frac{1}{2^{10} \cdot 3}=\frac{K}{2^{10} \cdot 3^{10}}$,then the remainder when $K$ is divided by $6$ is

The sum of an infinite geometric progression is $\frac{4}{3}$ and the first term is $\frac{3}{4}$. The common ratio is

The third term of a geometric progression is equal to the square of the first term. If its second term is $8$,then its sixth term will be:

If the sum of infinite terms of a $G.P.$ is $3$ and the sum of the squares of its terms is $3$,then its first term and common ratio are: