Question

15²²/3¹¹ + 14³³/7¹¹ + 20⁹⁹/2⁷⁷, Find the unit place.

1. 4
2. 6
3. 9
4. 3

Answer 1

Correct Answer - Option 4 : 3

Concept used:
In this type of questions, we must divide the power of given number by 4. If remainders are 1, 2, 3 and 0 (that means completely divisible) then power of that number will be 1, 2, 3 and 4 respectively.
Now,

Calculation:
15²²/3¹¹ + 14³³/7¹¹ + 20⁹⁹/2⁷⁷, Find the unit place
⇒ (3 × 5)²²/3¹¹ + (7 × 2)³³/7¹¹ + (2 × 10)⁹⁹/2⁷⁷
⇒ (3²² × 5²²)/3¹¹ + (7³³ × 2³³)/7¹¹ + (2⁹⁹ × 10⁹⁹)/2⁷⁷
⇒ (3¹¹ × 5²²) + (7²² × 2³³) + (2²² × 10⁹⁹)
Powers 11/4 = 3 remainder, 22/4 = 2 remainder, 33/4 = 1 remainder and 99/4 = 3 remainder
⇒ 3³ × 5² + 7² × 2¹ + 2² × 10³
Unit digits:
⇒ 7 × 5 + 9 × 2 + 0
⇒ 5 + 8 
⇒ 3 
∴ The unit digit is 3.