In a small metal mine a battery powered locomotive hauls a train of mine tubs such that:

The weight of the train of mine tubs, tonne : 3.0

The coefficient of friction between the wheels and the rails : 0.06

The coefficient of adhesion between the loco wheels and the rails : 0.2

Time required from the start to reach a speed of 1.8 m/s through constant acceleration, min : 3.0

Upward gradient to be negotiated : 1 in 20

The minimum weight of the locomotive in tonnes to meet these design requirements, is______. (round off to one decimal place)

In a surface mine bench, overburden is removed by the shovel-dumper combination. For the dumper:

Time required at the loading station : 3.0 min

Time required at the unloading station : 1.0 min

Distance between loading and unloading stations : 4.5 km

Average speed during loaded travel : 12.0 km/hr

Average speed during empty travel : 18.0 km/hr

Minimum number of dumpers required to avoid idle time of the shovel, is ______. (in integer)

In a bord and pillar development panel, headings of 4.4 m × 2.5 m are advanced using solid blasting. The average pull per round of blast is 1.2 m. On an average 12 faces are blasted per day. Density of coal is 1500 kg/m³. The mine operates in three shifts. If the average daily employment is 330 persons, labour productivity (OMS) of the panel in tonne, is ______. (round off to two decimal places)

The point ‘A’ as shown in the Coward flammability diagram represents the gas composition of a sealed-off area of a coal mine. The volume of the sealed-off area is 10000 m³. Inert gas is proposed to be injected into the sealed-off area so that the gas composition comes below the LEL (lower explosibility limit). The minimum volume of the inert gas required (at the same pressure as that of the sealed-off area), in m³ is ______. (round off to one decimal place)

A mine has a reserve of 150 million tonne (Mt) and is designed for a maximum production capacity of 5 Mt per year. In the first year the production is 2 Mt and it increases by 20% each year. The reserve in Mt that remains at the end of 15 years, is ______. (round off to two decimal places)

An art gallery engages a security guard to ensure that the items displayed are protected. The diagram below represents the plan of the gallery where the boundary walls are opaque. The location the security guard posted is identified such that all the inner space (shaded region in the plan) of the gallery is within the line of sight of the security guard. If the security guard does not move around the posted location and has a 360° view, which one of the following correctly represents the set of ALL possible locations among the locations P, Q, R and S, where the security guard can be posted to watch over the entire inner space of the gallery.

Consider the following square with the four corners and the center marked as P, Q, R, S and T respectively.

Let X, Y and Z represent the following operations: X: rotation of the square by 180 degree with respect to the S-Q axis. Y: rotation of the square by 180 degree with respect to the P-R axis. Z: rotation of the square by 90 degree clockwise with respect to the axis perpendicular, going into the screen and passing through the point T.

Consider the following three distinct sequences of operation (which are applied in the left to right order).

(1) XYZZ (2) XY (3) ZZZZ

Which one of the following statements is correct as per the information provided above?

A safety device consists of two independent critical components $X_1$ and $X_2$ . The failure of any one or both of these components can cause an accident. The failure probabilities of components $X_1$ and $X_2$ are 0.2 and 0.1, respectively. The probability of occurrence of an accident is _____. (round off to two decimal places)

In a uniaxial compressive strength test, a rock sample of diameter 50 mm fails at an angle of 60° as shown in the figure. If the peak load at failure is 120 kN, the normal and shear stresses on failure plane respectively, in MPa are ______ and ______.

A coal mining company examines the option of buying two types of dumpers with the following details.

In order to minimize the operating cost, the optimum fleet of dumpers of Type-1 and Type-2, respectively are