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MHT CET202123 Sep 2021Morning ShiftMathematicsBinomial TheoremActual

The difference between the maximum values of ^6 C _ r and ^n C _ r 16 , then n =

Options

  1. A3
  2. B5
  3. C2
  4. D4

Correct answer

D. 4

Step-by-step solution

The maximum value of ^6 C _ r occurs at r = 6 2 =3 ^6 C ₃= 6 ! 3 ! 3 ! = 6 5 4 6 =20 As per data given | ^6 C ₃- ^ n C ₃ |=16 ^ n C ₃=20+16 or ^ n C ₃=20-16 If ^n C₃=36 n ! (n-3) ! n ! =36 n(n-1)(n-2)=216 is not possible for n N aligned & If ^ n C ₃=4 n ! ( n -3) ! 3 ! =4 n ( n -1)( n -2)=24 & n =4 aligned

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