Match List I with List II LIST ILIST II A. 3^3 ≡ b ±od9 I.4 B. 2^5 ≡…

The correct answer is Option (2) → A - II, B - III, C - I, D - IV

Here b is the remainder when the power is divided by the modulus.

(A) \(3^3 \equiv b \pmod{9}\)

This matches (II) 0.

    \(3^3 = 27 = 9 \times 3 + 0\)

(B) \(2^5 \equiv b \pmod{15}\)

This matches (III) 2.

    \(2^5 = 32 = 15 \times 2 + 2\)

(C) \(4^3 \equiv b \pmod{10}\)

This matches (I) 4.

    \(4^3 = 64 = 10 \times 6 + 4\)

(D) \(5^3 \equiv b \pmod{12}\)

This matches (IV) 5.

    \(5^3 = 125 = 12 \times 10 + 5\)

So the matching is A - II, B - III, C - I, D - IV.