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Find the values of $x$,if: $(i)$ $\left|\begin{array}{ll}2 & 4 \\ 5 & 1\end{array}\right|=\left|\begin{array}{cc}2 x & 4 \\ 6 & x\end{array}\right|$ (ii) $\left|\begin{array}{ll}2 & 3 \\ 4 & 5\end{array}\right|=\left|\begin{array}{ll}x & 3 \\ 2 x & 5\end{array}\right|$

The area (in square unit) of the region enclosed by the curves $y=x^2$ and $y=x^3$ is

For the reaction $C_{(s)} + CO_{2_{(g)}} \rightleftharpoons 2CO_{(g)}$,the partial pressures of $CO_2$ and $CO$ are $2.0 \ atm$ and $4.0 \ atm$ respectively at equilibrium. The $K_p$ for the reaction is

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