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KVPY Sample Paper KVPY Stream-SX Model Paper-11

  • question_answer
    The coefficient of r in the expansion of \[{{\left( \frac{1-{{t}^{6}}}{1-t} \right)}^{3}}\]is:

    A) 12

    B) 15

    C) 10

    D) 14

    Correct Answer: B

    Solution :

    \[{{(1-{{t}^{6}})}^{3}}\,{{(1-t)}^{-\,3}}\]
    \[(1-{{t}^{18}}-3{{t}^{6}}+3{{t}^{12}})\,{{(1-t)}^{-\,3}}\]
    \[\Rightarrow \] Coefficient of \[{{t}^{4}}\]in \[{{(1-r)}^{-\,3}}\]
    \[{}^{3+4-1}{{C}_{4}}={}^{6}{{C}_{2}}=15.\]


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