JEE Main & Advanced Sample Paper JEE Main Sample Paper-43

  • question_answer
    The value of the sum of the series\[3{{\cdot }^{n}}{{C}_{0}}-8{{\cdot }^{n}}{{C}_{1}}+13{{\cdot }^{n}}{{C}_{2}}-18{{\,}^{n}}{{C}_{3}}+...\]

    A)  0                                

    B)  \[{{3}^{n}}\]

    C)  \[{{5}^{n}}\]                      

    D)  None of these

    Correct Answer: A

    Solution :

     The general term of the series is \[-h=-u{{t}_{2}}+\frac{1}{2}gt_{2}^{2}\]          \[0=u({{t}_{2}}-{{t}_{1}})+\frac{1}{2}g(t_{1}^{2}-t_{2}^{2})\] \[u=\frac{1}{2}g({{t}_{1}}+{{t}_{2}})\]  Sum of the series is given by \[h=\frac{g{{t}_{1}}{{t}_{2}}}{2}\] \[\sqrt{2}\,mv\] \[\sqrt{2}\,mv'=(2m)\,v\] \[\Rightarrow \]

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