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Black Book Advanced Problems in MathematicsMathematicsFunctions

If [x] denotes the integral part of x for real x , and S = [ 1 4 ] + [ 1 4 + 1 200 ] + [ 1 4 + 1 100 ] + [ 1 4 + 3 200 ] + [ 1 4 + 199 200 ] then

Options

  1. AS is a composite number
  2. BExponent of S in 100! is 12
  3. CNumber of factors of S is 10
  4. D^ 2S C_r is max when r = 51

Correct answer

A. S is a composite number

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