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KCET2008MathematicsBinomial 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

Now, 3² 4( 5) (3² )² 16( 5) 1( 5) (3⁴ )²⁵ (1)²⁵( 5) 3¹⁰⁰ 1( 5) and 2² 4( 5) (2² )² 16( 5) 1( 5) (2⁴ )¹² 1¹²( 5) 1( 5) 2⁴⁸ 2² 4( 5) 3¹⁰⁰ 2⁵⁰=1 4( 5) Hence, remainder is 4 .

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