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AP EAMCET202018 Sep 2020Evening ShiftMathematicsBinomial TheoremActual

Find the coefficient of (x^5 ) in ( (1+x+x^2 )^8 ).

Options

  1. A405
  2. B508
  3. C404
  4. D504

Correct answer

D. 504

Step-by-step solution

Given, Expansion is ( (1+x+x^2 )^8 ) Coefficient of (x^5 ) in above Expansion is ( aligned & 8 ! n₁ ! n₂ ! n₃ ! (1)^ n₁ (x)^ n₂ (x^2 )^ n₃ & (n₁+n₂+n₃ )=8 & and n₂+2 n₃=5 aligned ) ( array c|c|c n₁ & n₂ & n₃ 5 & 3 & 0 5 & 1 & 2 4 & 3 & 1 array ) Coefficient of ( aligned f^5 & = 8 ! 5 ! 3 ! 0 ! + 8 ! 5 ! 1 ! 2 ! + 8 ! 4 ! 3 ! 1 ! & =56+168+280=504 aligned ) Hence, option (d) is correct.

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