Correct Answer - Option 2 : 7
Concept :
Divide the power with 4 if the remainder comes then substitute it as the power of a number placed at the unit place of the number given in the bracket.
Rule of Cyclicity
2, 3, 7 and 8: These numbers follow a cycle of 4 different numbers.
21 = 2, 22 = 4, 23 = 8 and 24 = 16
After that it starts repeating.
So, cycle of 2 has 4 different unit places 2, 4, 8, 6.
31 = 3, 32 = 9, 33 = 27 and 34 = 81
After that it starts repeating.
So, cycle of 3 has 4 different numbers 3, 9, 7, 1.
71 = 7, 72 = 49, 73 = 343 and 74 = 2401
So, cycle of 7 has 4 different unit places 7, 9, 3, 1.
81 = 8, 82 = 64, 83 = 512 and 84 = 4096
So, cycle of 7 has 4 different unit places 8, 4, 2, 6.
Unit digit of 4
4odd = 4, 4even = 6
Unit digit of 9
9odd = 9, 9even = 1
Unit digit of 6 is 6
Unit digit of 5 is 5
Calculation:
x = 1 + 22 + 33 + 44 + _ _ _ _ _ + 1010
According to the concept,
⇒ 1 + 4 + 7 + 6 + 5 + 6 + 3 + 6 + 9 + 0
⇒ 47
Unit digit = 7
∴ The unit digit of x is 7.
