In a slake durability test, mass of the drum with samples before the test and mass of the drum with oven-dried samples after the test are 1.52 kg and 1.48 kg respectively. If the mass of the drum is 1.05 kg, slake durability index in percentage (rounded off to two decimal places) is ______.

A set of tubs is pulled by a 15 tonne diesel locomotive at a gradient of 1 in 100 with an acceleration of 0.05 m/s$^2$. The coefficient of adhesion between the wheel and the track is 0.2 and the frictional resistance coefficient is 0.01. The maximum mass, in tonne, the locomotive can pull (rounded off to one decimal place) is ______.

The characteristic curves of two mine fans installed in series in a fan drift are $P = 2000 - 6Q - 0.2Q^2$ and $P = 3000 - 8Q - 0.2Q^2$ where P is pressure in Pa and Q is quantity in m$^3$/s. If the mine quantity is 70 m$^3$/s, the mine resistance, in Ns$^2$m$^8$, (rounded off to two decimal places) is ______.

Three equipment A, B, and C located side by side and operating simultaneously produce a sound power level of 77.5 dB. The sound power levels of A and B are 68 dB and 70 dB respectively. The sound power level of C (rounded off to one decimal place) in dB, is ______.

If $x = 3^{1/3} + 3^{-1/3}$, the value of $3x^3 - 9x - 10$ is ______.

A pump delivers 3000 liter of water in 2.0 minutes through a pipe of length 1000 m laid on a gradient of 1 in 10. The combined efficiency of pump and motor is 70%. If friction and shock losses are negligible, the input power to the motor in kW (rounded off to one decimal place) is ______.

A sand water slurry of specific gravity 1.45 contains sand of grain density 2.6 g/cc. The weight percent of sand in the slurry (rounded off to two decimal places) is ______.

A shovel operates 300 days in a year, 2 shifts in a day, and 4 hours in a shift to achieve the target production of 30 Million tonne per annum.

• Bucket capacity of shovel: $15\ \text{m}^3$
• Shovel cycle time: $44\ \text{s}$
• Bucket fill factor: $0.85$
• Bulk density of the muck: $3.00\ \text{tonne/m}^3$

The minimum number of shovels required to achieve the production is ______.

The main surface fan of a mine as shown in the figure, has characteristic curve approximated by $P = 1700 - 10Q$, where P is pressure in Pa and Q is quantity in m$^3$/s. A booster fan is installed in section A such that there is no air flow in section B. The operating pressure of the main surface fan, in Pa, (rounded off to two decimal places) is ______.

Two points A and B are located 150 m apart in the East-West orientation on the bank of a river as shown in the figure. Considering a station C on the north bank the bearings of AC and BC are observed to be 42° and 335° respectively. The width of the river, in m, (rounded off to two decimal places) is ______.