In sulphur estimation, $2.0 \times 10^{-3} \mathrm{~mol}$ of an organic compound $(\mathrm{X})$ (molar mass $76 \mathrm{~g} \mathrm{~mol}^{-1}$ ) gave 0.4813 g of barium sulphate (molar mass $233 \mathrm{~g} \mathrm{~mol}^{-1}$ ). The percentage of sulphur in the compound $(\mathrm{X})$ is $\_\_\_\_$ $\times 10^{-1} \%$ (Nearest integer)

For the function $f:[1, \infty) \rightarrow[1, \infty)$ defined by $f(x)=(x-1)^4+1$, among the two statements:

(I) The set $\mathrm{S}=\left\{x \in[1, \infty): f(x)=f^{-1}(x)\right\}$ contains exactly two elements, and

(II) The set $\mathrm{S}=\left\{x \in[1, \infty): f(x)=f^{-1}(x+1)\right\}$ is an empty set,

Let $\mathrm{S}=\left\{z \in \mathrm{C}: z^2+4 z+16=0\right\}$. Then $\sum\limits_{z \in \mathrm{~S}}|z+\sqrt{3} \mathrm{i}|^2$ is equal to :

If the system of equations :

$$ \begin{aligned} & x+y+z=5 \\ & x+2 y+3 z=9 \\ & x+3 y+\lambda z=\mu \end{aligned} $$

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