XAT 2020 — QA & DI Question 8

$R\left[\frac{{19}^{20}}{7}\right]$ = $R\left[\frac{5^{20}}{7}\right]$ = $R\left[\frac{{25}^{10}}{7}\right]$ = $R\left[\frac{4^{10}}{7}\right]$ = $R\left[\frac{{16}^5}{7}\right]$ = $R\left[\frac{2^5}{7}\right]$ = $R\left[\frac{32}{7}\right]$ = 4

$R\left[\frac{{20}^{19}}{7}\right]$ = $R\left[\frac{{(-1)}^{19}}{7}\right]$ = -1

$R\left[\frac{{19}^{20}-{20}^{19}}{7}\right]$ = 4 - (-1) = 5

Hence, option (a).