Q44 / 90 · KVPY 2015 (SB/SX) · Mathematics

Let $\left(1+x+x^{2}\right)^{2014}=a_{0}+a_{1} x+a_{2} x^{2}+a_{3} x^{3}+\ldots . .+a_{s+28} x^{4028}$ and let $$ \begin{array}{l} A=a_{0}-a_{3}+a_{6}-\ldots \ldots+a_{4026} \\ B=a_{1}-a_{4}+a_{7}-\ldots \ldots .-a_{4027} \\ C=a_{2}-a_{5}+a_{8}-\ldots \ldots .+a_{4028} \end{array} $$ Then

  • A
    $|A|=|B|>|C|$
  • B
    $|A|=|B| < |C|$
  • Correct answer
    C
    $|A|=|C|>|B|$
  • D
    $|A|=|C| < |B|$

Hence, the correct answer is option: 'C'.

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