The failure data of an equipment follows an exponential distribution. If the mean time between failures is 3000 hours, the reliability of the equipment for 750 hours is ______.

In a 4.2 m wide and 3.0 m high gallery in a coal seam, twelve shot holes are blasted per round. The holes are charged with 2 explosive cartridges of 435 g each. If the powder factor of the blast is 2.2 tonne/kg and specific gravity of coal is 1.4, the pull per round of blast in m is

The stadia readings with horizontal sight on a vertical staff held at 50 m from a tacheometer are 1.285 m and 1.780 m. The focal length of the object glass is 25 cm, and the distance between the object glass and the vertical axis of the tacheometer is 15 cm. The stadia interval in mm is ______.

In a shortwall panel, coal is extracted from the face by a continuous miner having rate of production 30 tonne/h. Coal having specific gravity of 1.4 is transported by shuttle cars of capacity 0.9 m$^3$ each to a feeder breaker located at 60 m from the face. If the average speed of the LHD is 0.5 m/s, and total loading and unloading time of LHD is 40 s, the number of LHDs required to match the production of the continuous miner is

Vertical photographs of an area lying 500 m above the mean sea level are to be taken at a scale of 1:20000 from an aircraft. If the camera has a focal length of 210 mm, the flying height of the aircraft above the mean sea level in m is ______.

Match the following locations with support types in coal mines.

The value of $\int_{0}^{4} \sqrt{16 - x^2} \, dx$ is

A ______ investigation can sometimes yield new facts, but typically organized ones are more successful.

The word that best fills the blank in the above sentence is

Match the following for a drilling system.

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