If the sum and product of four positive consecutive terms of a G.P., are 126 and 1296 , respectively, then the sum of common ratios of all such GPs is

For the system of linear equations

$$x+y+z=6$$

$$\alpha x+\beta y+7 z=3$$

$$x+2 y+3 z=14$$

which of the following is NOT true ?

Let $$\mathrm{R}$$ be a relation on $$\mathrm{N} \times \mathbb{N}$$ defined by $$(a, b) ~\mathrm{R}~(c, d)$$ if and only if $$a d(b-c)=b c(a-d)$$. Then $$\mathrm{R}$$ is