Sum of Infinite Terms

Q. If a ball is dropped from a height of $40\text{m}$ and bounce back upto $60\%$ of the orginal height, then total distance travelled (in $\text{m}$) by the ball before coming to rest is

Q. If $x=a+\frac{a}{r}+\frac{a}{r^2}+....\infty ,y=b-\frac{b}{r}+\frac{b}{r^2}-....\infty ,andz=c+\frac{c}{r^2}+\frac{c}{r^4}+....\infty ,\left(r\right|>1,c\ne 0then\frac{xy}{z}=$
.

1. $\frac{ab}{c}$
2. $\frac{ac}{b}$
3. abc
4. $\frac{c}{ab}$

Q. If $\alpha ,\beta$ are the roots of the equation $x^2-4x+\lambda =0$ and $\gamma ,\delta$ are the roots of the equation $x^2-64x+\mu =0$ and $\alpha ,\beta ,\gamma ,\delta$ forms an increasing G.P., then the value of $\frac{\mu }{\lambda }$ is

Q. An infinite GP can have a finite sum if the common ratio is more than 1.

1. False
2. True

Q. If $x=a+\frac{a}{r}+\frac{a}{r^2}+\cdots \infty ,$ $y=b-\frac{b}{r}+\frac{b}{r^2}-\cdots \infty$ and $z=c+\frac{c}{r^2}+\frac{c}{r^4}+\cdots \infty$ for $|r|>1,$ then the value of $\frac{xy}{z}$ is

1. $\frac{ab}{c}$
2. $\frac{a{b}^2}{c}$
3. $\frac{ac}{b}$
4. $\frac{a^{2}b}{c}$