Controller of Mines • 2026 • Technical Paper-III
An equipment costs Rs. 5,00,000. Salvage value after 10 years is Rs. 50,000. Yearly depreciation under straight-line method is:
A)
45,000
B)
50,000
C)
55,000
D)
60,000
Under the straight-line method, yearly depreciation = (Cost of equipment - Salvage value) / Useful life. Here, (5,00,000 - 50,000) / 10 = 4,50,000 / 10 = 45,000. So the correct answer is 45,000. The other options are not equal to the annual straight-line depreciation.
Controller of Mines • 2026 • Technical Paper-III
An “Exponential Distribution” is frequently used in mine reliability engineering to represent:
A)
Time between equipment failures.
B)
The shape of a blast fragment.
C)
The depth of a borehole.
D)
The market price of minerals.
The exponential distribution is commonly used in reliability engineering to model the waiting time between successive random events, especially failures. In mining, it is often applied to represent time between equipment failures or breakdowns. The other options are unrelated to this distribution: blast fragment shape, borehole depth, and market price of minerals are not standard uses of the exponential model.
Controller of Mines • 2026 • Technical Paper-III
If you are facing North-West and turn 225 degrees clockwise, which direction are you facing?
A)
East
B)
South-West
C)
North
D)
South
North-West is halfway between North and West. Turning 225° clockwise means moving 180° + 45°, i.e., 4.5 direction steps of 45° each. From North-West, clockwise: North-West → North → North-East → East → South-East → South. Equivalently, 225° clockwise from North-West lands on South-West. So the correct direction is South-West.
Controller of Mines • 2026 • Technical Paper-III
The coefficient of variation is given by:
A)
M / 100
B)
/ M 100
C)
/ N 100
D)
M.N 100
The coefficient of variation (CV) is defined as the ratio of standard deviation to mean, expressed as a percentage: CV = (σ / M) × 100, where σ is the standard deviation and M is the mean. Option (a) is the reciprocal of the correct formula, while (c) and (d) are not standard definitions of coefficient of variation.
Controller of Mines • 2026 • Technical Paper-III
Karl Pearson’s coefficient of skewness is zero when:
A)
Mean Mode
B)
Mean = Mode
C)
Mean > Mode
D)
Mode > Mean
Karl Pearson’s coefficient of skewness is given by (Mean − Mode) / Standard Deviation. It becomes zero only when the numerator is zero, i.e., Mean = Mode. Therefore, the distribution is perfectly symmetrical. The other options would give a non-zero skewness.
Controller of Mines • 2026 • Technical Paper-III
In the sequence of numbers 5, 8, 13, x, 34, 55, 89. The value of x is:
A)
20
B)
21
C)
23
D)
29
This is a Fibonacci-type sequence, where each term is the sum of the previous two terms: 5, 8, 13 (=5+8), 21 (=8+13), 34 (=13+21), 55 (=21+34), 89 (=34+55). Therefore, x = 21. The other options do not satisfy the pattern.
Controller of Mines • 2026 • Technical Paper-III
Write a short note on Depreciation, Redemption and Depletion.
Controller of Mines • 2026 • Technical Paper-III
“To burn the candle at both ends” means:
A)
To be very resourceful.
B)
To waste energy on a useless project.
C)
To work or play excessively without enough rest.
D)
To light a room efficiently.
The idiom “to burn the candle at both ends” means to use up one’s energy too quickly by working, studying, or socializing excessively, often with too little rest. Option (c) matches this meaning. The other options do not reflect the idiomatic sense.
Controller of Mines • 2026 • Technical Paper-III
If the radius of sphere is decreased by 24%, by what per cent does the surface area decrease?
A)
44%
B)
49%
C)
42.24%
D)
46.2%
Surface area of a sphere is proportional to r². If the radius is decreased by 24%, the new radius becomes 76% of the original. So the new surface area becomes (0.76)² = 0.5776 of the original. Therefore, the decrease in surface area = 1 - 0.5776 = 0.4224 = 42.24%. Hence, the correct option is (c).
Controller of Mines • 2026 • Technical Paper-III
Discuss the role of Indian Bureau of Mines under MCDR, 2017.
Controller of Mines • 2026 • Technical Paper-III
If the “Coefficient of Variation” of ore grade in two different blocks is 15% and 30% respectively, which block has higher relative variability?
A)
The block with 15%
B)
The block with 30%
C)
Both have equal variability
D)
Coefficient of variation does not measure variability
The coefficient of variation (CV) measures relative variability. A higher CV means greater dispersion relative to the mean. Since 30% is greater than 15%, the block with 30% coefficient of variation has higher relative variability. Option (a) is lower, option (c) is false because the values are different, and option (d) is incorrect because CV is specifically used to measure relative variability.
Controller of Mines • 2026 • Technical Paper-III
Explain the general safety provisions under Coal Mines Regulations, 2017.
Controller of Mines • 2026 • Technical Paper-III
Choose the word most nearly opposite in meaning to ABSTEMIOUS:
A)
Self-indulgent
B)
Frugal
C)
Temperate
D)
Moderate
ABSTEMIOUS means restrained, sparing, or self-denying, especially in eating and drinking. The word most nearly opposite is Self-indulgent, which means indulging one's desires excessively. Frugal, temperate, and moderate are all close in meaning to abstemious, not opposites.
Controller of Mines • 2026 • Technical Paper-III
Analogy — LURID: DISMAL::
A)
Lucid: Obscure
B)
Gaudy: Drab
C)
Adroit: Skilful
D)
Ephemeral: Eternal
The pair "lurid : dismal" is an antonym pair: lurid means glaring/harsh or unpleasantly vivid, while dismal means gloomy. Among the options, "gaudy : drab" is also an antonym pair. The other options are either synonyms or do not match the same relationship. Hence, the correct analogy is Gaudy: Drab.
Controller of Mines • 2026 • Technical Paper-III
Synonym of ‘OBSTINATE’:
A)
Flexible
B)
Humble
C)
Cheerful
D)
Stubborn
‘Obstinate’ means stubbornly refusing to change one’s opinion or course of action. Among the options, ‘Stubborn’ is the closest synonym. ‘Flexible’ is the opposite, while ‘Humble’ and ‘Cheerful’ are unrelated.
Controller of Mines • 2026 • Technical Paper-III
What sum lent out at simple interest will amount to Rs. 3400 in 3 years at 1% per month?
A)
Rs. 2400
B)
Rs. 1800
C)
Rs. 1600
D)
Rs. 2500
Simple interest rate = 1% per month = 12% per year. For 3 years, the total simple interest = 12% × 3 = 36% of the principal. So, Amount = Principal + Interest = 136% of Principal. Given amount = Rs. 3400, so Principal = 3400 × 100 / 136 = Rs. 2500? Wait, that does not match the options. Since the rate is given per month, we should use months directly: 3 years = 36 months, interest = 1% × 36 = 36%. Thus Amount = 136% of principal. Principal = 3400 / 1.36 = Rs. 2500. Therefore the correct answer is Rs. 2500, option (d).
Controller of Mines • 2026 • Technical Paper-III
Briefly outline the basic safety precautions that must be strictly followed during the storage and transport of explosives in a mine, referencing the Explosives Rules, 2008.
Controller of Mines • 2026 • Technical Paper-III
As Per the Mizoram Minor Concession Rule, 2000 the lessee shall pay royalty on minor minerals at the rate specified in the:
A)
First Schedule
B)
Second Schedule
C)
Third Schedule
D)
Gazette Notification
Under the Mizoram Minor Mineral Concession Rules, 2000, royalty on minor minerals payable by the lessee is specified in the First Schedule. The other schedules deal with different matters such as forms, fees, or related provisions, not the royalty rates.
Controller of Mines • 2026 • Technical Paper-III
As Per the Mizoram Minor Concession Rule, 2000 the maximum ordinary period for which a mining lease may be granted under these rules is:
A)
2 years
B)
3 years
C)
4 years
D)
5 years
Under the Mizoram Minor Mineral Concession Rules, 2000, the maximum ordinary period for which a mining lease may be granted is 5 years. This is the standard ordinary term prescribed under the rules, unless renewed or otherwise extended as permitted by the rules. Therefore, option (d) is correct.
Controller of Mines • 2026 • Technical Paper-III
Who is held ultimately responsible for the overall financial and safety compliance of the mine under the Mines Act?
A)
The Mine Foreman
B)
The Manager
C)
The Owner / Agent
D)
The Blaster
Under the Mines Act, the owner/agent has the ultimate responsibility for the mine, including overall financial control and ensuring compliance with statutory safety requirements. The Manager is responsible for day-to-day operation and supervision, but that responsibility is subject to the owner/agent’s overall accountability. A Mine Foreman or Blaster has only limited operational duties and is not ultimately responsible for the mine as a whole.
Controller of Mines • 2026 • Technical Paper-III
Explain the role and primary functions of the Directorate General of Mines Safety (DGMS) in regulating safety in Indian mines.
Controller of Mines • 2026 • Technical Paper-III
100 students appeared for two examinations, 60 passed the first, 50 passed the second and 30 passed both. The probability that a student selected at random has failed in both the examination, is:
A)
0.3
B)
0.2
C)
0.4
D)
0.1
Let A = passed the first exam and B = passed the second exam.
Given:
- |A| = 60
- |B| = 50
- |A ∩ B| = 30
- Total students = 100
Students who passed at least one exam:
|A ∪ B| = |A| + |B| - |A ∩ B| = 60 + 50 - 30 = 80
So, students who failed in both exams = 100 - 80 = 20.
Therefore, the required probability = 20/100 = 0.2.
Why others are wrong:
- 0.3, 0.4, and 0.1 do not match the complement of the union of those who passed at least one exam.
Controller of Mines • 2026 • Technical Paper-III
Which of the following authorities is responsible for granting licenses for the bulk storage of explosives under the Explosives Rules, 2008?
A)
DGMS
B)
Indian Bureau of Mines (IBM)
C)
Petroleum and Explosives Safety Organization (PESO)
D)
State Pollution Control Board
Under the Explosives Rules, 2008, the licensing authority for storage of explosives, including bulk storage, is the Petroleum and Explosives Safety Organization (PESO), functioning under the Chief Controller of Explosives. DGMS deals mainly with mining safety, not explosive storage licensing. IBM regulates mining and mineral matters, and the State Pollution Control Board handles environmental clearances, not explosive licenses.
Controller of Mines • 2026 • Technical Paper-III
If ROAD=URDG, then TOWN=?
A)
WSAS
B)
WSRA
C)
ZRBS
D)
WQRA
Look at the pattern in ROAD → URDG:
- R → U: shift forward by 3
- O → R: shift forward by 3
- A → D: shift forward by 3
- D → G: shift forward by 3
So each letter is moved 3 positions ahead in the alphabet.
Applying the same rule to TOWN:
- T → W
- O → R
- W → Z
- N → Q
This gives WRZQ. However, since WRZQ is not among the options, we must check whether the coded example is using a different arrangement.
Notice that ROAD → URDG can also be seen as:
- first three letters shifted +3: R→U, O→R, A→D
- last letter shifted +3: D→G
For TOWN:
- T→W, O→R, W→Z, N→Q, which still gives WRZQ.
Since WRZQ is absent, the options appear inconsistent with the given coding rule. Therefore the question as stated cannot be solved with certainty from the provided options.
Controller of Mines • 2026 • Technical Paper-III
Which one of the following has a greater perimeter than the rest?
A)
A square with an area of 36 sq cm
B)
An equilateral triangle with a side of 9 cm
C)
A rectangle with 10 cm as length and 40 sq cm as area
D)
A circle with a radius of 4 cm
Find the perimeter/circumference of each figure:
(a) Square area = 36 sq cm, so side = √36 = 6 cm. Perimeter = 4 × 6 = 24 cm.
(b) Equilateral triangle side = 9 cm. Perimeter = 3 × 9 = 27 cm.
(c) Rectangle length = 10 cm and area = 40 sq cm, so breadth = 40/10 = 4 cm. Perimeter = 2(10 + 4) = 28 cm.
(d) Circle radius = 4 cm. Circumference = 2πr = 8π ≈ 25.13 cm.
The greatest perimeter is 28 cm, so the correct option is (c), not (d).
