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AP EAMCET201922 Apr 2019Morning ShiftMathematicsBinomial TheoremActual

Consider the following statements I : The number of non-trivial even divisors of the number (2^ ₁ 3^ ₂ 4^ ₃ 5^ ₄ 6^ ₅ ), is ( ( ₁+1 ) ( ₂+1 ) ( ₃+1 ) ( ₄+1 ) ( ₅+1 )-2 ) II : The number of non-trivial odd divisors of the number (2^ ₁ 3^ ₂ 4^ ₃ 5^ ₄ 6^ ₅ ), is ( ₂+ ₄+ ₅+ ₂ ₄+ ₄ ₅ ). Then

Options

  1. AI is false and II is false
  2. BI is true and II is true
  3. CI is false and II is true
  4. DI is true and II is false

Correct answer

C. I is false and II is true

Step-by-step solution

Given number (=2^ ₁ 3^ ₂ 4^ ₃ 5^ ₄ 6^ ₅ ) (=2^ ₁+2 ₃+ ₅ 3^ ₂ + ₅ 5^ ₄ ) Number of non-trivial even divisors (= ( ₁+2 ₃+ ₅ ) ( ₂+ ₅+1 ) ( ₄+1 )-1 ) And, number of non-trivial odd divisors ( aligned & = ( ₂+ ₅+1 ) ( ₄+1 )-1 & = ₂+ ₄+ ₅+ ₂ ₄+ ₄ ₅+1-1 aligned ) ( ) Statement ( I ) is false and ( II ) is true.

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