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Manipal MET2010MathematicsBinomial Theorem

The number of terms in the expansion of ( 5 + [4] 11 )¹²⁴ which are integers, is equal to

Options

  1. A0
  2. B30
  3. C31
  4. D32

Correct answer

D. 32

Step-by-step solution

The general term in the expansion of ( 5 +4 11 )¹²⁴ is gathered T_ r+1 = ¹²⁴ C_r( 5 )^ 124-r ( [4] 11 )^r = ¹²⁴ C_r 5^ (124-r) / 2 11^ r / 4 gathered For integer terms r=0,4,8,12, , 124 Number of terms which are integers =32

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