If 2^100≡ r±od 5 , then r is equal to :

The correct answer is Option (4) → 1

A small power of 2 leaves remainder 1 on division by 5:

    \(2^4=16\equiv 1\pmod 5\)

Since 100 = 4 × 25:

    \(2^{100}=\left(2^4\right)^{25}\equiv 1^{25}=1\pmod 5\)

So r = 1.