GATE MN year:2025 PYQs & Answers — Page 6

Questions 51–60 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 6 of 7

A longwall panel is to be developed in a flat seam at a depth of H m. The surface subsidence profile (s) of the area with the horizontal distance x is estimated as

where, S_ is the maximum subsidence at the centre of the panel, x is measured from the inflection point. The value of x is negative towards the panel centre and positive towards the panel boundary.

The ratio between the critical width of the panel and the depth is_____ (rounded off to 2 decimal places).

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The percent Fe content of a random sample consisting of five observations is shown.

62 | 64 | 63 | 60 | 61

If mean grade of the stockpile is estimated using the above data, the standard error of mean grade, in %, is _____ (rounded off to 3 decimal places).

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In a bord and pillar panel, a square pillar of size 35 m × 35 m (centre to centre) is extracted to form four equal square-shaped stooks as shown. The width of each gallery and crosscut is 5 m. The height of the working seam is 3 m. The reduction in safety factor after pillar splitting by using Bieniawski’s pillar strength formula, in %, is____ (rounded off to 2 decimal places)

Bieniawski’s pillar strength formula,

; where,

= strength of 0.9 m^3 of coal block,

= pillar width and

= mining height

Diagram for Mining Engineering question 53

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A five-member truss system is shown in the figure. The maximum vertical force P in kN that can be applied so that loads on the member CD and BC do NOT exceed 50 kN and 30 kN, respectively is________ (rounded off to 2 decimal places).

Diagram for Mining Engineering question 54

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The characteristic polynomial of a third order matrix, A, is given by

If one of the eigen values of A is 1, then sum of the other two eigen values is ______ (in integer)

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The directional derivative of a function

at the point P (3, 4, 5) in the direction vector

is___ (rounded off to 1 decimal place)

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Average noise level at a working place is 80 dB(A) for the first 10 minutes and 60 dB(A) for the next 30 minutes. The energy equivalent continuous noise level at the place for the entire period of 40 minutes, in dB(A), is_____ (rounded off to 2 decimal places)

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The area bounded by the curves,

, and

is ___ (rounded off to 3 decimal places)

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Data from a borehole log with collar elevation at 590 mRL are given below. Composite grade is calculated using cores of 5 m above and below the reference bench at 580 mRL. The composite grade, in %, is ___ (rounded off to 1 decimal place)

Sequence of cores (top to bottom)	Core length (m)	Grade (%)
1	3.0	40
2	3.0	42
3	2.0	41
4	3.0	43
5	2.0	42
6	3.0	41
7	3.0	44

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The information of a mining project for a life of three years is given below:

	Year 0	Year 1	Year 2	Year 3
Revenue (Crore Rupees)		200	300	400
Capital cost (Crore Rupees)	300
Operating cost (Crore Rupees)		30	40	35

Applicable tax rate = 30 %

Discount rate = 10 %

If straight line depreciation with zero salvage value is applicable, the NPV, in Crore Rupees, is ____ (rounded off to 2 decimal places)

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GATE MN year:2025 PYQs

Question 51

Question 52

Question 53

Question 54

Question 55

Question 56

Question 57

Question 58

Question 59

Question 60