NDA2024MathematicsBasics of MathematicsActual
What is the remainder when 2¹²⁰ is divided by 7 ?
Options
- A1
- B3
- C5
- D6
Correct answer
A. 1
Step-by-step solution
aligned & 2¹²⁰= (2^3 )⁴⁰=8⁴⁰=(1+7)⁴⁰ & =1+ ⁴⁰ C ₁ 7+ ⁴⁰ C ₂ 7^2+ + ⁴⁰ C ₁₀ 7⁷⁰ & =1+7 [⁴⁰ C ₁+ ⁴⁰ C ₂ 7+ + ⁴⁰ C ₄₀ 7³⁹ ] & Remainder =1 . aligned