In a sublevel stope, 20 m high excavation is made with ring drilling in a 6 m wide orebody. In an effective shift time of 6 hrs, three rings are blasted resulting in 9 m extraction length. LHDs of 5.0 m$^3$ bucket capacity and cycle time of 5 minutes are used for ore transportation. The number of LHDs required for this operation is ______.

A coal seam lying at a depth of 200 m is developed by bord and pillar method. Pillars are 30 m centre to centre with a gallery width of 4 m. Unit weight of the overlying strata is 28 kN/m$^3$. If the pillar strength is 9.32 MPa, the factor of safety of pillar is ______.

Following information about a longwall retreating panel is given.

Panel length = 1800 m Face length = 150 m Depth of web = 0.6 m Shearer travels at a speed of 1.5 m/min along the face. Each cutting cycle requires a non-operational time of 2 h 20 min. The panel is fully extractable. The number of working days required to extract the panel is ______.

In a direct rope haulage operating along a 1500 m long incline, 180 tonne of coal is hauled in 7 hours. The average rope speed is 7.5 km/h. The set changing time for the tubs is 2 minutes each at the top and bottom of the incline. If the tub capacity is 1.0 tonne, the number of tubs in the set is ______.

An SDL of 1.0 tonne capacity operates with a cycle time of 6 minutes. The dimension of the face is 4 m x 3 m. Five blasts are conducted per shift with an average pull of 1.2 m. If the density of blasted coal is 0.8 tonne/m$^3$, the time required by the SDL in the shift to lift all the prepared coal in hours is ______.

In underground face blasting, the pull is found to be 10% less than the drillhole length. The headings of 3.6 m width are supported by prop density of 1.44/m$^2$. The hole length is 1.5 m, and 6 rounds of blasting are done in the panel per shift. The number of props to be erected in a shift is ______.

The immediate roof of a mine is supported by bolts of length 1.5 m, arranged in 1.2 m x 1.2 m grid pattern. If the unit weight of roof rock is 2.25 tonne/m$^3$ and load carrying capacity of each bolt is 7.5 tonne, the factor of safety of the support system is ______.

In a level terrain, a vertical orebody of 20 m uniform width is worked by surface mining method. The density of the ore is 2.5 tonne/m$^3$. The ultimate pit has a depth of 60 m, width of 20 m at pit bottom, and a pit slope of 45°. The overall stripping ratio for this condition in m$^3$/tonne is ______.

A 20 m long steel tape used for survey is found to be short by 10 cm. If the area measured with the steel tape is 5000 m$^2$, the actual area in m$^2$ is ______.

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