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JEE Main & Advanced JEE Main Paper (Held on 12-4-2019 Morning)

  • question_answer
    If\[\alpha \]and \[\beta \]are the roots of the equation \[375{{x}^{2}}25x2=0,\]then[JEE Main Held on 12-4-2019 Morning] \[\underset{n\to \infty }{\mathop{\lim }}\,\sum\limits_{r=1}^{n}{{{\alpha }^{r}}}+\underset{n\to \infty }{\mathop{\lim }}\,\sum\limits_{r=1}^{n}{{{\beta }^{r}}}\]is equal to:

    A) \[\frac{21}{346}\]                              

    B) \[\frac{29}{358}\]

    C) \[\frac{1}{12}\]          

    D) \[\frac{7}{116}\]

    Correct Answer: C

    Solution :

    \[375{{x}^{2}}-25x-2=0\]           \[\alpha +\beta =\frac{25}{375},\alpha \beta =\frac{-2}{375}\] \[\Rightarrow \](\[\alpha +{{\alpha }^{2}}+...\]upto infinite terms) \[+(\beta +{{\beta }^{2}}+...\]upto infinite terms) \[=\frac{\alpha }{1-\alpha }+\frac{\beta }{1-\beta }=\frac{1}{12}\]                      


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