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AP EAMCET20224 Jul 2022Evening ShiftMathematicsBinomial TheoremActual

The least value of n so that C 3 n - 1 + C 4 n - 1 > C 3 n

Options

  1. A11
  2. B9
  3. C8
  4. D7

Correct answer

C. 8

Step-by-step solution

Given: C 3 n - 1 + C 4 n - 1 > C 3 n ⇒ C 4 - 1 n - 1 + C 4 n - 1 > C 3 n ⇒ C 4 n > C 3 n ∵ C r - 1 n + C r n = C r n + 1 ⇒ n ! 4 ! × n - 4 ! > n ! 3 ! × n - 3 ! ⇒ 3 ! × n - 3 ! > 4 ! × n - 4 ! ⇒ 3 ! × n - 3 × n - 4 ! > 4 × 3 ! × n - 4 ! ⇒ n - 3 > 4 ⇒ n > 7 So, least value of n is 8 .

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