VIT Engineering VIT Engineering Solved Paper-2015

  • question_answer
    If the matrix \[\text{A=}\left[ \begin{matrix}    \text{1} & \text{3} & \text{1}  \\    \text{-1} & \text{2} & \text{-3}  \\    \text{0} & \text{1} & \text{2}  \\ \end{matrix} \right]\text{,}\]  then adj (adj A) is equal to

    A)           \[\left[ \begin{matrix}    \text{12} & \text{36} & \text{12}  \\    \text{-12} & \text{24} & \text{-36}  \\    \text{0} & \text{12} & \text{24}  \\ \end{matrix} \right]\]

    B)           \[\left[ \begin{matrix}    \text{12} & \text{26} & \text{-12}  \\    \text{24} & 36 & \text{-36}  \\    \text{0} & \text{12} & \text{-24}  \\ \end{matrix} \right]\]

    C)             \[\left[ \begin{matrix}    \text{12} & \text{-12} & 36  \\    \text{24} & -24 & \text{-36}  \\    \text{0} & \text{12} & \text{24}  \\ \end{matrix} \right]\]

    D)  None of the above

    Correct Answer: A

    Solution :

    Given \[\begin{align}   & Ca{{\left( OH \right)}_{20}}+2C{{O}_{2}}\to Ca{{\left( HC{{O}_{3}} \right)}_{2}} \\  & \text{YExcessZ} \\ \end{align}\] \[\begin{align}   & Ca{{\left( HC{{O}_{3}} \right)}_{2}}\xrightarrow{Heat}CaC{{O}_{3}}+C{{O}_{2}}\uparrow +{{H}_{2}}O \\  & ZX \\ \end{align}\]      \[\begin{align}   & Zn{{\left( OH \right)}_{2}}+2\overset{-}{\mathop{OH}}\,\to ZnO_{2}^{2-}+2{{H}_{2}}O \\  & \text{AcidBaseSaltWater} \\ \end{align}\]             \[\begin{align}   & Zn{{\left( OH \right)}_{2}}+2{{H}^{+}}\to Z{{n}^{2+}}+2{{H}_{2}}O \\  & \text{BaseAcidSaltWater} \\ \end{align}\] \[{{\left[ \text{Cu}{{\left( \text{N}{{\text{H}}_{\text{3}}} \right)}_{\text{4}}} \right]}^{\text{2+}}}\text{}{{\left[ \text{Cu}{{\left( \text{en} \right)}_{\text{2}}} \right]}^{\text{2+}}}\text{}{{\left[ \text{Cu}\left( \text{trien} \right) \right]}^{\text{2+}}}\text{.}\]        \[{{\left[ \text{Fe}{{\left( {{\text{H}}_{\text{2}}}\text{O} \right)}_{\text{6}}} \right]}^{\text{3+}}}\text{}{{\left[ \text{Fe}{{\left( \text{N}{{\text{O}}_{\text{2}}} \right)}_{\text{6}}} \right]}^{\text{3-}}}\text{}{{\left[ \text{Fe}{{\left( \text{N}{{\text{H}}_{\text{3}}} \right)}_{\text{6}}} \right]}^{\text{3-}}}\]                      \[\because \]                      \[\text{N}{{\text{O}}_{\text{2}}}^{\text{-}}\]                        \[{{\text{E}}_{\text{1}}}\text{=}{{\text{E}}_{\text{2}}}\text{=}\frac{\text{1}}{\text{4 }\!\!\pi\!\!\text{ }{{\text{ }\!\!\varepsilon\!\!\text{ }}_{\text{0}}}}\text{.}\frac{\text{q}}{{{\text{r}}^{\text{2}}}}\]


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