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COMEDK2019MathematicsBinomial Theorem

The remainder when 3¹⁰⁰ 2⁵⁰ is divided by 5 is

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

D. 4

Step-by-step solution

We have, aligned 3² &=4( 5) (3² )² &=16( 5)=1( 5) (3⁴ )²⁵ &=(1)²⁶( 5) 3¹⁰⁰ &=1( 5) Again 2² &=4( 5) (2² )² &=16( 5)=1( 5) (2⁴ )¹² &=(1)¹²( 5)=1( 5) 2¹⁸ 2² &=4( 5) 3¹⁰⁰ 2⁵⁰ &=1 4( 5)=4( 5) aligned

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