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MHT CET202619 April 2026Evening ShiftMathematicsBinomial TheoremActual

If ^ n C₄, ^ n C₅ and ^ n C₆ are in arithmetic progression (A.P.), then the value of n is...

Options

  1. A5 or 11
  2. B7 or 14
  3. C8 or 15
  4. D6 or 13

Correct answer

B. 7 or 14

Step-by-step solution

Given that ^ n C₄, ^ n C₅, ^ n C₆ are in A.P. 2 ^ n C₅ = ^ n C₄ + ^ n C₆ 2 n! 5!(n-5)! = n! 4!(n-4)! + n! 6!(n-6)! Multiplying the entire equation by 6!(n-4)! n! : 2 6 (n-4) = 6 5 + (n-4)(n-5) 12n - 48 = 30 + n^2 - 9n + 20 n^2 - 21n + 98 = 0 (n-7)(n-14) = 0 n = 7 or n = 14 Answer: 7 or 14

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