Relation between AM,GM,HM for 2 numbers

Q. If x, y, z are distinct positive integers then value of expression (x + y) (y + z) (z + x) is

1. is equal to 8xyz
2. is greater than 8xyz
3. is smaller than 8xyz
4. is equal to 4xyz

Q.

For three distinct positive numbers $p,q\mathrm{and}r$, if $p+q+r=a$, then:

1. $\frac{1}{p}+\frac{1}{q}+\frac{1}{r}>\frac{18}{a}$

2. $\frac{1}{p}+\frac{1}{q}+\frac{1}{r}>\frac{9}{a}$

3. $\frac{1}{p}+\frac{1}{q}+\frac{1}{r}<\frac{3}{a}$

4. $\frac{1}{p}+\frac{1}{q}+\frac{1}{r}<\frac{6}{a}$

Q.

If the harmonic mean between two positive numbers is to their geometric mean as 12:13. The numbers are in the ratio

1. 12:13

2. $\frac{1}{12}:\frac{1}{13}$

3. 4:9

4. $\frac{1}{4}:\frac{1}{9}$