Solid carbon, CaO and $\mathrm{CaCO}_3$ are mixed and allowed to attain equilibrium at T K .

$$ \begin{array}{ll} \mathrm{CaCO}_3(\mathrm{~s}) \rightleftharpoons \mathrm{CaO}(\mathrm{~s})+\mathrm{CO}_2(\mathrm{~g}) & \mathrm{Kp}_1=0.08 \mathrm{~atm} \\ \mathrm{C}(\mathrm{~s})+\mathrm{CO}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{CO}(\mathrm{~g}) & \mathrm{Kp}_2=2 \mathrm{~atm} \end{array} $$

The partial pressure of CO is __ $\times 10^{-1} \mathrm{~atm}$

Consider the relation $R$ on the set $\{-2,-1,0,1,2\}$ defined by $(a, b) \in R$ if and only if $1+a b>0$. Then, among the statements :

I. The number of elements in R is 17

II. R is an equivalence relation

The number of values of $z \in \mathbb{C}$, satisfying the equations $|z-(4+8 i)|=\sqrt{10}$ and $|z-(3+5 i)|+|z-(5+11 i)|=4 \sqrt{5}$, is $:$

If the system of linear equations :

$$ \begin{aligned} & x+y+z=6 \\ & x+2 y+5 z=10 \\ & 2 x+3 y+\lambda z=\mu \end{aligned} $$

has infinitely many solutions, then the value of $\lambda+\mu$ equals: