List of top Questions asked in GATE MN

Consider a five-digit number PQRST that has distinct digits P, Q, R, S, and T, and satisfies the following conditions:
1. $ P<Q $
2. $ S>P>T $
3. $ R<T $
If integers 1 through 5 are used to construct such a number, the value of P is:

Three villages P, Q, and R are located in such a way that the distance PQ = 13 km, QR = 14 km, and RP = 15 km, as shown in the figure. A straight road joins Q and R. It is proposed to connect P to this road QR by constructing another road. What is the minimum possible length (in km) of this connecting road?
Note: The figure shown is representative.

A business person buys potatoes of two different varieties P and Q, mixes them in a certain ratio and sells them at ₹192 per kg.
The cost of the variety P is ₹800 for 5 kg.
The cost of the variety Q is ₹800 for 4 kg.
If the person gets 8% profit, what is the P : Q ratio (by weight)?

For the clock shown in the figure, if
O = O Q S Z P R T, and
X = X Z P W Y O Q,
then which one among the given options is most appropriate for P?

“His life was divided between the books, his friends, and long walks. A solitary man, he worked at all hours without much method, and probably courted his fatal illness in this way. To his own name there is not much to show; but such was his liberality that he was continually helping others, and fruits of his erudition are widely scattered, and have gone to increase many a comparative stranger’s reputation.” (From E.V. Lucas’s “A Funeral”)
Based only on the information provided in the above passage, which one of the following statements is true?

A bag contains Violet (V), Yellow (Y), Red (R), and Green (G) balls. On counting them, the following results are obtained:
(i) The sum of Yellow balls and twice the number of Violet balls is 50.
(ii) The sum of Violet and Green balls is 50.
(iii) The sum of Yellow and Red balls is 50.
(iv) The sum of Violet and twice the number of Red balls is 50.
Which one of the following Pie charts correctly represents the balls in the bag?

In the context of the given figure, which one of the following options correctly represents the entries in the blocks labelled (i), (ii), (iii), and (iv), respectively?

An electricity utility company charges ₹7 per kWh. If a 40-watt desk light is left on for 10 hours each night for 180 days, what would be the cost of energy consumption? If the desk light is on for 2 more hours each night for the 180 days, what would be the percentage-increase in the cost of energy consumption?

The President, along with the Council of Ministers, ............. to visit India next week.
Select the most appropriate option to complete the above sentence.

Even though I had planned to go skiing with my friends, I had to ............. at the last moment because of an injury.
Select the most appropriate option to complete the above sentence.

A double-ended ranging drum (DERD) shearer uni-directionally cuts coal in a longwall panel having the following details:
Shearer drum diameter = 1.4 m
Panel dimension = 1200 m × 200 m × 2.4 m
Web depth = 0.6 m
Average cutting speed = 5 m/minute
Average retreating speed = 10 m/minute
Average operational delay between cuts is 2 hour. There are two production shifts, each of 8 hour duration. The number of days required for complete extraction of the panel is:

Reciprocal levelling is performed for points P and Q by placing the same levelling instrument at A and B. The observations of staff readings are tabulated as below.

If the Reduced Level (RL) of P is 115.246 m, then the true RL of Q, in m, is _______ (rounded off to 3 decimal places)

SO$_2$ is emitted at a rate of 20 kg/s from a 10 km $\times$ 10 km airshed in an industrial area. Wind blows at a speed of 4 m/s from one direction in that area. Radiation inversion restricts the mixing height to 1200 m. Neglect SO$_2$ concentration in the incoming air. Assuming emitted SO$_2$ to be conservative, the steady state SO$_2$ concentration in the airshed, in $\mu g/m^3$, is _______ (rounded off to 2 decimal places).

In a longwall panel, air flows at a velocity of 1.2 m/s through a 900 m long gate road of 2.5 m height and 3 m width. The coefficient of friction is 0.022 Ns$^2$m$^{-4}$. The frictional pressure drop, in Pa, between two ends of the gate road is _______ (rounded off to 3 decimal places).

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

Additional data: Applicable tax rate = 30%
Discount rate = 10%
Depreciation method: Straight line with zero salvage value

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:

The area bounded by the curves $ y = \sqrt{x} $ and $ y = 8x^2 $ is:

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:

The characteristic polynomial of a third order matrix $ A $ is given by \[ f(x) = x^3 - 6x^2 + 11x - 6. \] If one of the eigenvalues of $ A $ is 1, then the sum of the other two eigenvalues is:

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:

In a bord and pillar panel, a square pillar of size 35 m $ \times $ 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 is given by $ S_p = S_1 \left( 0.64 + 0.36 \frac{w}{h} \right) $, where $ S_1 $ is the strength of a 0.9 m$^3$ coal block, $ w $ is the pillar width, and $ h $ is the mining height.

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

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

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 \[ s = \frac{S_{{max}}}{2} \left[ 1.002 - \tanh \left( \frac{4.8x}{H} \right) \right], \] where $ S_{{max}} $ 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:

A 2.5 tonne diesel locomotive hauls 5 mine cars upslope having a gradient of 1 in 20. The constant tractive force of the locomotive is 1800 kN. The gross weight of a car is 3 tonne. Acceleration due to gravity is 10.0 m/s$^2$. If the acceleration of the system is 0.5 m/s$^2$, the rolling resistance in kN/tonne is ________ (rounded off to 3 decimal places).

A direct rope haulage has the following details:
Output = 24 tonne/hour,
Length of trip = 610 m,
Gradient = 1 in 12,
Capacity of mine car = 1.0 tonne,
Tare weight of mine car = 0.5 tonne,
Average rope speed = 1.694 m/s,
Change over time of cars = 3 minutes,
Acceleration due to gravity = 10.0 m/s².
Neglecting all frictional resistance and mass of the rope, the minimum power required, in kW, to raise the loaded mine cars is: