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AP EAMCET202023 Sep 2020Morning ShiftMathematicsBinomial TheoremActual

If [ x ] represents the greatest integer not greater than x , then 1 + 1 100000 100000 =

Options

  1. A1
  2. B3
  3. C2
  4. D4

Correct answer

C. 2

Step-by-step solution

Let A = [ ( 1 + 1 10000 ) 10000 ] = [ ( 1 + 0 . 0001 ) 1000 ] We know that, ( 1 + x ) n = C 0 n + C 1 n · x + C 2 n · x 2 + C n n · x n A = [ C 0 1000 + C 1 1000 · ( 0 . 0001 ) + C 2 1000 · ( 0 . 0001 ) 2 + . . . . . . + C 1000 1000 · ( 0 . 0001 ) n ] A = [ 1 + 10000 × 0 . 0001 + 10000 × 999 2 × 10 - 8 + . . . . . . . . ] A = [ 1 + 1 + 0 . 49 + . . . ] A = [ 2 . 049 + . . . ] A = 2 .

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