Question

The last two digits of the numbers 3⁴⁰⁰ are 01.

Options

• True

• False

Answer 1

This statement is True.

Explanation:

Given that 3⁴⁰⁰ = (9)²⁰⁰ = (10 – 1)²⁰⁰

∴ (10 – 1)²⁰⁰ = ²⁰⁰C₀(10)²⁰⁰ – ²⁰⁰C₁(10)¹⁹⁹ + ... – ²⁰⁰C₁₉₉(10)¹ + ²⁰⁰C₂₀₀(1)²⁰⁰

= 10²⁰⁰ – 200 × 10¹⁹⁹ + … – 10 × 200 + 1

So, it is clear that last two digits are 01.