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JEE Main202431 Jan 2024Evening ShiftMathematicsBinomial TheoremActual

If for some m , n ; 6 C m + 2 6 C m + 1 + 6 C m + 2 > 8 C 3 and n − 1 P 3 : n P 4 = 1 : 8 , then n P m + 1 + n + 1 C m is equal to

Options

  1. A380
  2. B376
  3. C384
  4. D372

Correct answer

D. 372

Step-by-step solution

Given: 6 C m + 2 6 C m + 1 + 6 C m + 2 > 8 C 3 ⇒ 6 C m + 6 C m + 1 + 6 C m + 1 + 6 C m + 2 > 8 C 3 ⇒ 7 C m + 1 + 7 C m + 2 > 8 C 3 ⇒ 8 C m + 2 > 8 C 3 ⇒ m = 2 Also, n − 1 P 3 : n P 4 = 1 : 8 ⇒ n − 1 n − 2 n − 3 n n − 1 n − 2 n − 3 = 1 8 ⇒ n = 8 ⇒ n P m + 1 + n + 1 C m = 8 P 3 + 9 C 2 ⇒ n P m + 1 + n + 1 C m = 8 × 7 × 6 + 9 × 8 2 ⇒ n P m + 1 + n + 1 C m = 372

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