What is the unit digit of  (17¹² + 38⁷⁹) × 1853¹⁹⁴⁷ ?

Correct option is A

Solution:
To find the unit digit of a product like
(17¹² + 38⁷⁹) × 1853¹⁹⁴⁷,
we analyze the unit digit of each number individually.

Step 1: Unit digit of 17¹²
The unit digit of powers of 7 cycles in:
7, 9, 3, 1 (cycle length = 4)

12 mod 4 = 0 => choose 4th term in cycle → 1

So, unit digit of 17¹² = 1

Step 2: Unit digit of 38⁷⁹
The unit digit of powers of 8 cycles in:
8, 4, 2, 6 (cycle length = 4)

79 mod 4 = 3 => choose 3rd term → 2

So, unit digit of 38⁷⁹ = 2

Step 3: Add the unit digits:
17¹² + 38⁷⁹ => 1 + 2 = 3

Step 4: Unit digit of 1853¹⁹⁴⁷
The unit digit of 3 cycles in:
3, 9, 7, 1 (cycle length = 4)

1947 mod 4 = 3 => choose 3rd term → 7

So, unit digit of 1853¹⁹⁴⁷ = 7

Step 5: Final multiplication
(17¹² + 38⁷⁹) × 1853¹⁹⁴⁷ => 3 × 7 = 21

So, unit digit = 1

Final Answer: (a) 1