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JEE Main & Advanced Sample Paper JEE Main Sample Paper-13

  • question_answer
    Let \[{{a}_{1}},\,\,{{a}_{2}},\,\,{{a}_{3}},...\] and \[{{b}_{1}},\,\,{{b}_{2}},\,{{b}_{3}},\,...\] be two distinct infinite GP?s. The sum of each one is 1. If \[{{a}_{2}}={{b}_{2}}\] and \[{{a}_{3}}=\frac{1}{8},\] then\[{{b}_{3}}\] is equal to

    A)  \[\frac{\sqrt{5}-1}{4}\]                

    B)  \[\frac{\sqrt{5}-2}{4}\]

    C)  \[\frac{\sqrt{5}-2}{8}\]                

    D)  \[\frac{\sqrt{5}-1}{8}\]

    Correct Answer: C

    Solution :

     Take the two infinite GP is \[{{H}_{2}}\] and \[2HCO{{O}^{\odot -}}\xrightarrow{\,}\,2HCO{{O}^{\bullet }}+2{{e}^{-}}\] Their sums are 1 each \[2HCO{{O}^{\bullet }}\xrightarrow{\,}\,{{H}_{2}}+2C{{O}_{2}}\]               \[2{{H}_{2}}O+2{{e}^{-}}\xrightarrow{\,}\,{{H}_{2}}+2O{{H}^{\odot -}}\]    \[\therefore \] \[{{H}_{2}}\]       \[C{{O}_{2}}\] \[{{H}_{2}}\]       \[CuS{{O}_{4}}(aq)\] \[Cu\]   \[SO_{4}^{2-}\] \[{{H}_{2}}O\] \[2{{H}_{2}}O\xrightarrow{\,}\,{{O}_{2}}+4{{H}^{\oplus }}+4{{e}^{-}}\] Now,     \[{{H}^{+}}\] \[{{K}_{sp}}\]


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