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JEE Main202125 Jul 2021Evening ShiftMathematicsBinomial TheoremActual

If P r n = P r + 1 n and C r n = C r - 1 n , then the value of r is equal to:

Options

  1. A1
  2. B4
  3. C2
  4. D3

Correct answer

C. 2

Step-by-step solution

We have, P r n = P r + 1 n ⇒ n ! n - r ! = n ! n - r - 1 ! ⇒ n - r = 1           … 1 and C r n = C r - 1 n ⇒ n ! r ! n - r ! = n ! r - 1 ! n - r + 1 ! ⇒ 1 r n - r ! = 1 n - r + 1 n - r ! ⇒ n - r + 1 = r ⇒ n + 1 = 2 r             … 2 From equation 1   &   2 , we get 2 r - 1 - r = 1 ⇒ r = 2 .

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