CAT 1999 — QA Question 3

Note: 342 = 7³ – 1. On further simplification we get,

$\mathrm{R}\left[\frac{{\left(7^3\right)}^{28}}{342}\right]$ = $\mathrm{R}\left[\frac{{\left(343\right)}^{28}}{342}\right]$ = $\mathrm{R}{\left[\frac{343}{342}\right]}^{28}$ = $\mathrm{R}{\left[\frac{1}{342}\right]}^{28}$ = 1

∴ Remainder = 1, 

Hence, option (b).