If $\alpha, \beta$ are the roots of $x^2 - px + q = 0$ and $\alpha', \beta'$ are the roots of $x^2 - p'x + q' = 0$,then find the value of $(\alpha - \alpha')^2 + (\beta - \alpha')^2 + (\alpha - \beta')^2 + (\beta - \beta')^2$.
- A$2(p^2 - 2q + p'^2 - 2q' - pp')$
- B$2(p^2 - 2q + p'^2 - 2q' - qq')$
- C$2(p^2 - 2q - p'^2 - 2q' - pp')$
- D$2(p^2 - 2q - p'^2 - 2q' - qq')$
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Calculate the heat of combustion (in $kJ$) of methane from the following data:
$(I)$ $C_{(graphite)} + 2H_{2(g)} \rightarrow CH_{4(g)} \quad \Delta H = -74.8 \ kJ$
$(II)$ $C_{(graphite)} + O_{2(g)} \rightarrow CO_{2(g)} \quad \Delta H = -393.5 \ kJ$
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$(III)$ $H_{2(g)} + 1/2 O_{2(g)} \rightarrow H_2O_{(l)} \quad \Delta H = -286.2 \ kJ$
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