Number System Question 7 - CAT 2024

Step-by-Step Explanation

According to Fermat's Little Theorem, since 11 is a prime number:

3¹¹⁻¹ = 3¹⁰ ≡ 1 (mod 11)

Divide the exponent 333 into blocks of 10:

333 = 10 × 33 + 3

3³³³ = ( 3¹⁰ )³³ × 3³ ≡ (1)³³ × 27 (mod 11)

3³³³ ≡ 27 (mod 11)

Find the final remainder of 27 divided by 11:

27 = 11 × 2 + 5 ⇒ Remainder = 5

Correct Option: A