For a mining company the unit transportation cost from a mine to a washery, and supply and demand are shown below:

The total cost of transportation using the Vogel's approximation method is ______.

In a bord and pillar panel, 6 square pillars are developed as shown in the figure below. The depth of the seam is 300 m and the average unit weight of overburden rock is 25 kN/m$^3$. If the pillar strength is 15 MPa, the safety factor of the shaded pillar zone (round off to two decimal places) is ______.

Water enters a sump having the shape of an inverted frustum at a rate of 500 m$^3$/h. The sump is initially filled up to 2.0 m height. The time taken in days to fill the remaining part of the sump (rounded off to one decimal places) is ______.

The uniaxial stress-strain behavior of a rock sample is shown in the figure. The elastic modulus E is 20,000 MPa. If $\varepsilon_p$ is the plastic strain, the value of the damage parameter D (rounded off to two decimal place) is ______.

The insitu stress field around a circular tunnel is shown in the figure. Points A and B are located at the boundary of the tunnel. If the tangential stress at Point A is 3 times of that at Point B, the value of insitu stress ratio, k is ______.

Data related to explosive and blasthole are given below. Assuming 1 kcal to be 4.2 kJ, the power of explosive in GW in the blasthole (round off to one decimal place) is ______.

• Diameter of the borehole: $200\ \text{mm}$
• Charge length: $8\ \text{m}$
• Density of ANFO: $0.8\ \text{g/cc}$
• Heat of explosion: $912\ \text{cal/g}$
• VOD: $4500\ \text{m/s}$
• Initiation: Bottom

A random variable $X$ is defined by $X = \begin{cases} -2 & \text{probability } \frac{1}{3} \\ 3 & \text{probability } \frac{1}{2} \\ 1 & \text{probability } \frac{1}{6} \end{cases}$

The value of $E(X^2)$ is _____.

A project network consists of the following activities

If the project completion time is 30 days, then the value of 'X', in days, is _______.

Rate of fuel consumption $f_c$ (litres per hour) of a truck varies with truck speed $x$, (kmph) as given below

$f_c = 20 + \frac{x^2}{50}$

The fuel price is Rs. 70 per litre. Other costs amount to Rs. 500 per hour. If the truck travels 100 km from a coal mine to a thermal plant, the speed of the truck, in kmph, that minimizes the total cost is _____.

The grade-tonnage distribution for the ultimate pit of a mine is given below.

The mill cut-off grade is 0.5% Cu. The annual mining capacity (ore + waste) is 4.5 million tonne and milling capacity is 1.0 million tonne. Excavation is planned in such a way that either of the mine or the mill runs at full capacity throughout. The planned life of the mine, in years, is _______ [round off to one decimal place]