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AP EAMCET202021 Sep 2020Evening ShiftMathematicsBinomial TheoremActual

What is the coefficient of ( y^3 x^8 ) in ((x+y)⁻⁵ ), when ( | y x | < 1 ) ?

Options

  1. A-35
  2. B-30
  3. C-25
  4. D10

Correct answer

A. -35

Step-by-step solution

Since ((x+y)⁻⁵= 1 (x+y)^5 = 1 x^5 (1+ y x )⁻⁵, | y x | < 1 ) ( ) Coefficient of ( y^3 x^8 in (x+y)⁻⁵ ) ( aligned & = coefficient of y^3 x^8 in 1 x^5 (1+ y x )⁻⁵ & = coefficient of y^3 x^3 in (1+ y x )⁻⁵ & = -5(-5-1)(-5-2) 3 ! =-35 aligned ) Hence, option (a) is correct.

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