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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2000

  • question_answer
    If\[\omega \]is an imaginary cube root of 1, then\[{{(1+\omega +{{\omega }^{2}})}^{6}}+{{(1-\omega +{{\omega }^{2}})}^{5}}\]is equal to:

    A)  16                         

    B)                         8                            

    C)         9                                            

    D)         27

    E)         32

    Correct Answer: E

    Solution :

    \[{{(1+\omega -{{\omega }^{2}})}^{5}}+{{(1-\omega +{{\omega }^{2}})}^{5}}\] \[={{(-{{\omega }^{2}}-{{\omega }^{2}})}^{5}}+{{(-\omega -\omega )}^{5}}\] \[=-32{{({{\omega }^{2}})}^{5}}+(-32){{\omega }^{5}}\] \[=-32(\omega +{{\omega }^{2}})=32\]


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