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AP EAMCET202017 Sep 2020Evening ShiftMathematicsBinomial TheoremActual

If the (m ) th term is the middle term in expansion of ( (x^2- 1 2 x )²⁰ ). Find coefficient of (T_ m+3 ).

Options

  1. A( ²⁰ C ₁₃ 2⁻¹³ )
  2. B(- ²⁰ C ₁₃ 2¹³ )
  3. C(- ²⁰ C ₁₃ 2⁻¹³ )
  4. D( ²⁰ C ₁₃ 2¹³ )

Correct answer

A. ( ²⁰ C ₁₃ 2⁻¹³ )

Step-by-step solution

Expansion of ( (x^2- 1 2 x )²⁰ ) contains ' 21 ' terms. So middle term is, ( 20 2 +1=11 ) term ( m=11 ) Now, ( aligned T_ m+3 & =T_ 11+3 =T_ 13+1 & = 20 13 (x^2 )²⁰⁻¹³ (- 1 2 x )¹³ & = 20 13 x^7(-1)¹³ 2¹³, x¹³ aligned ) So coefficient is, ( ²⁰ C ₁₃ 2⁻¹³ ^ )

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