Discussion

Explanation:

Here, Unit’s digit of 6824¹⁷⁹³ will be an even number.

Also, Unit’s digit of 3125³¹⁷ will always by 5.

Hence, Unit’s digit of 5 × even number will always be 0.

⇒ Unit’s digit of (6824)¹⁷⁹³ × (3125)³¹⁷ × (6681)⁴⁹¹ = 0.

Alternately,

Unit’s digit of powers of 4 have a cyclicity of 2 terms i.e., unit’s digit follows the pattern of 4 and 6.

⇒ Unit’s digit of 4^{odd number} = 4, and

⇒ Unit’s digit of 4^{even number} = 6.

Unit digit in (6824)¹⁷⁹³ = Unit digit in (4)¹⁷⁹³ = 4

Also, 

Unit digit in (3125)³¹⁷ = Unit digit in (5)³¹⁷ = 5

Unit digit in (6681)⁴⁹¹ = Unit digit in (1)⁴⁹¹ = 1

Required digit = Unit digit in (4 × 5 × 1) = 0.

Hence, option (a).

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