If the system of equation $2x + 3y =\, -1; 3x + y = 2; \lambda x + 2y = \mu $ is consistent, then

  • A

    $\lambda  - \mu  = 2$

  • B

    $\lambda  + \mu  = -1$

  • C

    $\lambda  + \mu  = 3$

  • D

    $\lambda  - \mu + 8= 0$

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If ${A_i} = \left[ {\begin{array}{*{20}{c}}{{a^i}}&{{b^i}}\\{{b^i}}&{{a^i}}\end{array}} \right]$and if $|a|\, < 1,\,|b|\, < 1$, then $\sum\limits_{i = 1}^\infty {\det ({A_i})} $is equal to

$\left| {\,\begin{array}{*{20}{c}}1&a&{{a^2} - bc}\\1&b&{{b^2} - ac}\\1&c&{{c^2} - ab}\end{array}\,} \right| = $

  • [IIT 1988]

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