A rectangular mine airway of 2.0 m width and 2.5 m height has a bend with deflection of $\frac{\pi}{4}$ radian. If the radius of curvature of the bend is 4.0 m, the shock factor of the bend is (round off to three decimals)

In an underground coal mine, two fatalities and three serious bodily injuries occurred during the year 2022. The average daily employment is 1100 and annual working days is 300. The severity index as per DGMS guideline for the mine is

For a geared engine winding system, the man winding cage is placed at its normal position at pit top of the shaft. As per CMR 2017, the minimum space, in m, between the center of the hole of the detaching hook attached to the rope shackle and detaching belt plate is

The value of integral, $I = \int_{0}^{\frac{\pi}{4}} \cos x \sin^3 x dx$ is

The value of $\lim_{x \to 0} \left( \frac{n \sin 5x}{\sin 3x} \right)$ is

In a M/M/1 system, the inter-arrival time of dumpers to a shovel follows exponential distribution with a mean arrival rate of 9 dumpers per hour. The service time of the shovel follows exponential distribution with a mean service rate of 12 dumpers per hour. The probability that exactly one dumper is available to the shovel is

If the major ($\sigma_1$) and minor ($\sigma_3$) principal stresses for a rock element have a relationship as $\sigma_3 = -\frac{1}{2}\sigma_1$, the maximum shear stress is expressed by

The ore that is NOT used for commercial extraction of metal is

The function of District Mineral Foundation established by state governments in India, is to

The percentage Fe and corresponding net value for an iron ore mine is given below

Assuming net value versus grade curve to be a straight line, and mining cost of waste is INR 1000 /m³; the correct representation of stripping ratio, SR (m³/tonne) versus Fe (%) grade curve is