2. Solved Papers
  3. JAMIA MILLIA ISLAMIA

JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2014

  • question_answer
    If the sum of roots of equation \[{{x}_{1}}=-3\,\,\,and\,\,\,{{y}_{1}}=4\] is equal to sum of squares of their reciprocals, then \[\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{x+1}{x+2} \right)}^{2x+1}}=\underset{x\to \infty }{\mathop{\lim }}\,{{\left( 1-\frac{1}{x+2} \right)}^{2x+1}}\]and \[=\underset{x\to \infty }{\mathop{\lim }}\,{{\left[ {{\left( 1-\frac{1}{x+2} \right)}^{x+2}} \right]}^{\frac{2x+1}{x+2}}}\]are in

    A) GP                                         

    B) HP

    C) AP                                         

    D) None of these

    Correct Answer: C

    Solution :

                    Let roots of equation \[{{Q}_{1}}{{R}_{2}}\ne {{Q}_{2}}{{R}_{1}}\]are\[{{Q}_{1}}{{R}_{2}}={{Q}_{2}}{{R}_{1}}\] and\[s=\frac{{{t}^{2}}}{4}\] Then, \[T\propto V\]and \[T\propto {{V}^{2}}\] According to the question, \[T\propto \frac{1}{{{V}^{2}}}\] \[T\propto \frac{1}{V}\]                \[\text{6}\times \text{1}{{0}^{-\text{7}}}\text{A}-{{\text{m}}^{\text{2}}}\] \[\text{5 g}/\text{c}{{\text{m}}^{\text{3}}}\]     \[\text{8}\text{.3}\times \text{1}{{0}^{\text{6}}}\] \[\text{1}.\text{2}\times \text{1}{{0}^{-\text{7}}}\]        \[\text{3}\times \text{1}{{0}^{-\text{6}}}\] \[CaC{{l}_{2}}\] \[\text{MgS}{{\text{O}}_{\text{4}}}\] \[\text{MgS}{{\text{O}}_{\text{4}}}\]    \[CaC{{l}_{2}}\] Hence, \[A\to B,B\to C\] and \[C\to A\] are in AP.


You need to login to perform this action.
You will be redirected in 3 sec spinner