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JEE Main20254 Apr 2025Morning ShiftMathematicsBinomial TheoremActual

For an integer n 2 , if the arithmetic mean of all coefficients in the binomial expansion of (x+y)^ 2 n-3 is 16 , then the distance of the point P (2 n-1, n^2-4 n ) from the line x+y=8 is:

Options

  1. A2
  2. B2 2
  3. C5 2
  4. D3 2

Correct answer

D. 3 2

Step-by-step solution

No. of terms in (x+y)^ (2 n-3) [ array c (2 n-3+1) (2 n-2) array ]. sum of all coefficients =2^ 2 n-3 (Put x = y =1 ) Arithmetic mean of all coefficients aligned & = ( 2^ 2 n-3 2 n-2 )=16 & 2^ 2 n-3 =2^5(n-1) n=5 & P (2 n-1, n^2-4 n )=(9,5) aligned aligned & x+y=8 & P M= | 9+5-8 2 |= 6 2 = 3 2 2 =3 2 aligned

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