The series-parallel configuration of a system, consisting of 6 independent components A, B, C, D, E, and F with their individual reliability, is shown in the figure:

The reliability of the system is ______.

500 coal miners were randomly selected from an underground coal mine. It was found that 50 workers experienced an injury in the year 2014. The distribution of injury based on younger age group ($age \leq 40$ years) and older age group ($age > 40$ years) generated the following cross classification table.

The odds of injury for the younger age group compared to the older age group is ______.

A bord and pillar panel is being planned at a depth of 300 m. The dimension of square pillar is 35 m centre-to-centre. The average unit weight of the overburden rock is $25 kN/m^3$. If the strength of the pillar is 14.0 MPa, the gallery width in m for a safety factor of 1.3 is ______.

Let $\sigma_1$ and $\sigma_3$ are major and minor principal stresses respectively. The equation $\sigma_1 = f(\sigma_3)$ denotes the failure envelop of a rock as shown in the figure. Match the zones (P, Q, R and S) with the legend code.

Legend

If the rank of the following matrix is less than 3, the values of $x$ are

In a mine, 200 and 250 persons are deployed in the Panels A and B (shown in figure) respectively in the largest shift. The panels produce 400 and 500 tonne/day respectively. The resistances of panels A and B are 0.3 $\text{Ns}^2\text{m}^{-8}$ and 0.4 $\text{Ns}^2\text{m}^{-8}$ respectively and the combined resistance of shaft and trunk airways is 0.5 $\text{Ns}^2\text{m}^{-8}$. The operating static pressure of the fan in Pa to provide the minimum air quantities in the panels as per CMR 1957 is ______.

A stream flowing at 15 $\text{m}^3/\text{s}$ has a tributary feeding into it with a flow rate of 7 $\text{m}^3/\text{s}$. The concentrations of chloride at the upstream of the junction and that of the tributary are 30 mg/L, and 50 mg/L respectively. Treating chloride as conservative substance and assuming complete mixing of two streams, the concentration of chloride in mg/L at the downstream is ______.

A sample of mine water has 100 mg/L of $Ca^{2+}$ and 10 mg/L of $Mg^{2+}$. The equivalent weights of $Ca^{2+}$ and $Mg^{2+}$ are 20 mg/meq and 12.2 mg/meq respectively. The hardness of mine water in unit of mg/L as CaCO$_3$ is ______.

A 1.1 m wide belt conveyor carries materials of bulk density 1.35 t/h$^3$ at a speed of 1.75 m/s. The average cross-sectional area of material is equal to $w^2 / 11$, where $w$ is the width of the belt in m. The carrying capacity of the conveyor in t/h is ______.

Out of the support categories given for an underground coal mine, identify the ‘active support’.