List of top Questions asked in GATE MN

The straight line shown depicts the failure criterion of a rock type. The values of stress at points A and B are as shown. The safety factor at the points A and B respectively are 

The Mohr circle of stress of a dry porous rock is shown in the figure. If the rock is fully saturated with a pore pressure \( p \), then the Mohr circle takes the form of 

The pit bottom in a correlation survey is shown in the figure. Points C and D represent two suspended wires. The bearing of line CD is 286°00'00'' and its length is 4.64 m. The angle CED is measured as 00°00'40''. The length of line DE is 5.46 m. Considering the Weisbach triangle method, the bearing of the line CE is 

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

\[ \begin{array}{|c|c|} \hline \text{Cu grade (\%)} & \text{Cumulative million tonnes below the grade} \\ \hline 0.1 & 0 \\ 0.4 & 15.0 \\ 0.5 & 17.0 \\ 0.6 & 18.0 \\ 0.7 & 19.0 \\ 0.9 \text{ and above} & 23.0 \\ \hline \end{array} \] 

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 the mine or the mill runs at full capacity throughout. The planned life of the mine, in years, is \(\underline{\hspace{1cm}}\). (round off to one decimal place)

A project network consists of the following activities

\[\begin{array}{|c|c|c|} \hline \textbf{Activity} & \textbf{Immediate Predecessors} & \textbf{Duration (days)} \\ \hline \text{A} & \text{--} & 3 \\ \hline \text{B} & \text{--} & 4 \\ \hline \text{C} & \text{A, B} & 5 \\ \hline \text{D} & \text{B} & 6 \\ \hline \text{E} & \text{D} & 7 \\ \hline \text{F} & \text{C, E} & 8 \\ \hline \text{G} & \text{D} & 9 \\ \hline \text{H} & \text{F, G} & X \\ \hline \end{array}\]
 

If the project completion time is 30 days, then the value of \( X \), in days, is \(\underline{\hspace{2cm}}\) (in integer).

A random variable \( X \) is defined by \[ X = \begin{cases} -2 & \text{with probability} \, \frac{1}{3}, \\ 3 & \text{with probability} \, \frac{1}{2}, \\ 1 & \text{with probability} \, \frac{1}{6}. \end{cases} \] The value of \( E(X^2) \) is \(\underline{\hspace{2cm}}\) (round off to one decimal place).

Injury experience is studied in an underground coal mine with a random sample of 132 workers. The results of the study are tabulated below. 

\[ \begin{array}{|c|c|c|c|} \hline \text{Injured} & \text{Non-injured} & \text{Total workers} \\ \hline \text{Roof-bolter operators} & 13 & 12 & 25 \\ \text{Loader operators} & 35 & 72 & 107 \\ \hline \text{Total workers} & 48 & 84 & 132 \\ \hline \end{array} \] The odds ratio of experiencing an injury by the roof-bolter operators when compared to the loader operators is \(\underline{\hspace{1cm}}\). (round off to 2 decimal places)

The value of \[ \lim_{x \to \infty} \left(x \sqrt{x^2 + b^2} - \sqrt{x^4 + b^4}\right) \text{ is} \]

Production planning of a small quarry having 3 years of life is shown in the figure. The following information of revenue and cost data are available. 

Selling price of ore = Rs. 1500/tonne 
Ore mining cost = Rs. 500/tonne 
Waste mining cost = Rs. 500/m\(^3\) 
Initial capital = Rs. 1000 million 
Discount rate = 10% 
By neglecting depreciation, salvage value and corporate tax, the NPV of the mining project, in million Rs., is \(\underline{\hspace{2cm}}\). [round off to 2 decimal places]

With reference to the figure related to rock cutting by point attack tool, match the angle with corresponding name. 

The CORRECT curve showing the relationship between vertical stress on a coal pillar and extraction ratio of a bord and pillar panel in a horizontal seam is 

The value of the integral \( I = \int_{0}^{4} \sqrt{x}\, dx \) computed using Simpson's 1/3 rule with 2 subintervals is \(\underline{\hspace{1cm}}\). (round off to 3 decimal places)

The vectors $\vec{a}$ and $\vec{b}$ act in a plane as shown below. The magnitude of the vector} \[ \vec{c} = (\vec{a} + \vec{b}) \times (\vec{a} - \vec{b}) \] is

A coal mine operating in three shifts produces 400 tonnes of coal per day with a face OMS of 1.0 from panel A, and 200 tonnes of coal with face OMS of 1.0 from panel B. The panel A and panel B are in parallel with resistance 0.6 Ns^2\text{m}^8 and 0.5 Ns^2\text{m}^8, respectively. If the panels are supplied with minimum permissible quantity as per CMR 2018, the requisite regulator resistance to meet the conditions in Ns^2\text{m}^8 is \(\underline{\hspace{2cm}}\) (round off to 2 decimal places).
In an analysis of fragmented blast muck, the mean fragment size is found to be 60 cm with uniformity index of 1.25. Considering Rosin-Ramler equation, the cumulative mass fraction, in percent, to pass the grizzly screen size of 100 cm is \(\underline{\hspace{1cm}}\). (round off to 2 decimal places)
A single-acting reciprocating ram pump, while running at 120 rpm, delivers water at a rate of 10 litres per second. Considering the ram diameter is 150 mm and stroke length is 300 mm, the volumetric efficiency of the pump, in percent, is \(\underline{\hspace{1cm}}\). (round off to one decimal place)
In a sand stowing arrangement, the slurry has a sand concentration of 35% by volume. The specific gravity of sand grain is 2.6. The concentration of sand by weight, in percent, in the slurry is \(\underline{\hspace{1cm}}\). (round off to one decimal place)
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 \(\underline{\hspace{2cm}}\) (round off to one decimal place).
In order to check whether iron ore is supplied to the specification of 62% Fe, a steel company has conducted a hypothesis test with the null hypothesis as \( H_0: \mu_{\text{Fe}} = 62% \) and alternative hypothesis \( H_a: \mu_{\text{Fe}} < 62% \). A random sample of 5 observations reveal the following grade values of the lot: 58%, 56%, 60%, 64%, 62%. The t-test statistic for the hypothesis is
For a dumpy level, the bubble tube has sensitivity of 40" for one division. While taking a staff reading at a distance of 60 m, the bubble is out of centre by 2 divisions. The error in staff reading in mm is \(\underline{\hspace{1cm}}\). (round off to one decimal place)
On an old plan of scale 1:1000, leasehold area of a mine is now measured as 802 cm^2 using a planimeter. The plan is found to have shrunk, such that the original line of 10 cm is now measured as 9.8 cm on the plan. True lease hold mine area, in m^2 is \(\underline{\hspace{2cm}}\) (round off to the nearest integer).
CO is released from a point source on a level ground at a rate of 25 g/s. The average wind speed is 5 m/s. The dispersion coefficients are 150 m and 200 m in horizontal and vertical directions, respectively, at a receiver station located on the ground along the downwind direction. Assuming the plume follows Gaussian dispersion model, the concentration of CO, in \, \mu g/m^3 at the station is \(\underline{\hspace{2cm}}\) (round off to 2 decimal places).
Assume that COVID-19 growth rate of number of infections per day (c) in a certain population is represented by the following differential equation. \[ 100 \frac{dc}{dt} - 7c = 0 \] Where, t stands for time in days. Time taken for the number of infections per day to double, in days, is \(\underline{\hspace{2cm}}\) (round off to the nearest integer).
Ore is hoisted from 620 m depth using a single skip of 7 tonne pay load. The skip winding system has constant acceleration/deceleration of 1 m/s\(^2\) and a constant speed of 10 m/s. The skip loading time and unloading time are 120 s and 60 s, respectively. Considering the overall utilization of the skip as 70%, the maximum daily capacity of the winding system, in tonne, is \(\underline{\hspace{1cm}}\). (round off to the nearest integer)
A dump truck moves up an incline of 5° with constant tractive force of 800 kN. The gross mass of the truck is 250 tonne and its rolling resistance is 545 kN. The acceleration due to gravity is 10 m²/s. The time required, in s, to reach a speed of 3.3 m/s from 1.0 m/s is