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Manipal MET2017MathematicsBinomial Theorem

The middle term of ( x - 1 x )^6 is

Options

  1. A-20
  2. B-1
  3. C1
  4. DNone of these

Correct answer

A. -20

Step-by-step solution

Middle term is ( n 2 +1 ) th term for n even. Middle term = ( 6 2 +1 )=4 th term aligned T₄ & = ^6 C₃( x )^3 (- 1 x )⁶⁻³ & = 6! 3!3! ( x )^3 (-1)^3 ( x )^3 & = -6 5 4 6 & =-20 aligned

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