In this question we just have to look at the units digit to find out the remainder.

3^(8n+3) will always result in an odd integer for any value of n

therefore units place of the integer will either 3 or 7

3^(8n+3) +2 = either 5 or 9

Therefore we can eliminate all the options but 0 and 4.

The units place of 3^(8n+3) will always be 7

Hence the answer is 4.

Whats the OA?

My answer is 4. using Mod Arithemetic,,

3^(8n+3) + 2 % 5

(3^ 8n.27)+ 2%5

using remainder theorem

3^8n%5 ~ 1
27%5~ 2

2%5~ 2



1*2 + 2 ~ 4

hence the answer.

whts the OA?

Ya my take on the is also 4
...

the power is the multiple of 8 and to which 3 is added

so it is in the range 11,19,27,......

3 power of any of the number 11,19,27 will always give me the unit digit has 7

for the fact series of number 3 raised to somethign follows 3,9,7,1,3,9,7,1.....

so so the unit digits we constantly get here is ! the number 9

so the remainder is 4

vishu

Could you tell me what are the types of exercices in which the "method of the unit" cannot be used to determine the remainder?

IMO E. OA pls.

yes ...ans is 'e' i.e, 4

yes ...ans is 'e' i.e, 4

yes ...ans is 'e' i.e, 4