n = 1, 8n+3=11 so units digit of 3^(11) = 7 and 3^(11) + 2 ends with 9

n = 2, 8n+3=19 so units digit of 3^(19) = 7 and 3^(19) + 2 ends with 9

so answer is E (correct??)

yes E is right.....

In this problem just increase the power as much as you can
for example we can write the above example as

(3.3^(2(4n+1)) + 2)/5
=>( 3.9^(4n+1) + 2)/5

for first part as 9%5 = 4 and 4 ^4n+1is always a number with units digit as 4 hence remainder is 4 as 4n+1 is Odd

3* 4 = 12 & 12%5 = 2

Hence adding Both 2+2 = 4

Hence the remainder is 4