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GATE AG 2023: Agricultural Engineering

  • Paper code: AG
  • Language: English
  • 28 pages
GATE AG 2023 question paper, GATE 2023, Agricultural Engineering, page 1 of 28
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Agricultural Engineering (AG)


General Aptitude (GA)
Q.1 – Q.5 Carry ONE mark Each

 Q.1       “You are delaying the completion of the task. Send _______ contributions at the
           earliest.”




 (A)       you are


 (B)       your


 (C)       you’re


 (D)       yore




 Q.2       References : ______ : : Guidelines : Implement

           (By word meaning)




 (A)       Sight


 (B)       Site


 (C)       Cite


 (D)       Plagiarise




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 Q.3       In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and
           PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)

                                                      7
                                   P                                    S

                                                      5     90°
                                           4
                                               90°                  V
                         Q             T                        R


 (A)       20
            7

 (B)       28
            5

 (C)       9
           2

 (D)       35
            4




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Agricultural Engineering (AG)



 Q.4       In 2022, June Huh was awarded the Fields medal, which is the highest prize in
           Mathematics.

           When he was younger, he was also a poet. He did not win any medals in the
           International Mathematics Olympiads. He dropped out of college.

           Based only on the above information, which one of the following statements can be
           logically inferred with certainty?




 (A)       Every Fields medalist has won a medal in an International Mathematics Olympiad.


 (B)       Everyone who has dropped out of college has won the Fields medal.


 (C)       All Fields medalists are part-time poets.


 (D)       Some Fields medalists have dropped out of college.




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Agricultural Engineering (AG)



 Q.5       A line of symmetry is defined as a line that divides a figure into two parts in a way
           such that each part is a mirror image of the other part about that line.

           The given figure consists of 16 unit squares arranged as shown. In addition to the
           three black squares, what is the minimum number of squares that must be coloured
           black, such that both PQ and MN form lines of symmetry? (The figure is
           representative)

                                              P                  N




                         M
                                              Q

 (A)       3


 (B)       4


 (C)       5


 (D)       6




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Agricultural Engineering (AG)


Q.6 – Q.10 Carry TWO marks Each

 Q.6       Human beings are one among many creatures that inhabit an imagined world. In
           this imagined world, some creatures are cruel. If in this imagined world, it is given
           that the statement “Some human beings are not cruel creatures” is FALSE, then
           which of the following set of statement(s) can be logically inferred with certainty?

                 (i)     All human beings are cruel creatures.
                 (ii)    Some human beings are cruel creatures.
                 (iii)   Some creatures that are cruel are human beings.
                 (iv)    No human beings are cruel creatures.




 (A)       only (i)


 (B)       only (iii) and (iv)


 (C)       only (i) and (ii)


 (D)       (i), (ii) and (iii)




 Q.7       To construct a wall, sand and cement are mixed in the ratio of 3:1. The cost of sand
           and that of cement are in the ratio of 1:2.

           If the total cost of sand and cement to construct the wall is 1000 rupees, then what
           is the cost (in rupees) of cement used?




 (A)       400


 (B)       600


 (C)       800


 (D)       200


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Agricultural Engineering (AG)


           The World Bank has declared that it does not plan to offer new financing to Sri
 Q.8       Lanka, which is battling its worst economic crisis in decades, until the country has
           an adequate macroeconomic policy framework in place. In a statement, the World
           Bank said Sri Lanka needed to adopt structural reforms that focus on economic
           stabilisation and tackle the root causes of its crisis. The latter has starved it of
           foreign exchange and led to shortages of food, fuel, and medicines. The bank is
           repurposing resources under existing loans to help alleviate shortages of essential
           items such as medicine, cooking gas, fertiliser, meals for children, and cash for
           vulnerable households.

           Based only on the above passage, which one of the following statements can be
           inferred with certainty?




 (A)       According to the World Bank, the root cause of Sri Lanka’s economic crisis is that
           it does not have enough foreign exchange.


 (B)       The World Bank has stated that it will advise the Sri Lankan government about how
           to tackle the root causes of its economic crisis.


 (C)       According to the World Bank, Sri Lanka does not yet have an adequate
           macroeconomic policy framework.


 (D)       The World Bank has stated that it will provide Sri Lanka with additional funds for
           essentials such as food, fuel, and medicines.




 Q.9       The coefficient of x 4 in the polynomial (x − 1)3 (x − 2)3 is equal to _______.




 (A)       33


 (B)       ̶ 3


 (C)       30


 (D)       21


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 Q.10      Which one of the following shapes can be used to tile (completely cover by
           repeating) a flat plane, extending to infinity in all directions, without leaving any
           empty spaces in between them? The copies of the shape used to tile are identical
           and are not allowed to overlap.




 (A)       circle


 (B)       regular octagon


 (C)       regular pentagon


 (D)       rhombus




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Q.11 – Q.35 Carry ONE mark Each

 Q.11      If A and B are square matrices of order 3 such that |A| = −1, |B| = 3, then |3AB|
           equals


 (A)       -81


 (B)       -27


 (C)       -9


 (D)       81




 Q.12          √1+x−1
           lim        is equal to
           x→0    x


 (A)       0


 (B)       1
           2


 (C)       1


 (D)       2




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                                   π
 Q.13                                (sinx+cosx)2
           The value of I = ∫      2                dx is
                             0        √1+sin2x


 (A)       0


 (B)       1


 (C)       2


 (D)       3




 Q.14      y = ae mx + be −mx is the solution of the differential equation

 (A)       dy
                − my = 0
           dx


 (B)       dy
                + my = 0
           dx


 (C)       d2y
                  + m2 y = 0
           dx 2


 (D)       d2y
                  − m2 y = 0
           dx 2




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 Q.15      In rotary tiller, the total energy requirement for carrying out tillage will decrease if


 (A)       the bite length is increased


 (B)       the bite length is decreased


 (C)       the cone index of soil is higher


 (D)       forward speed of the machine is reduced




 Q.16      The effectiveness of the turbocharger of a diesel engine increases when


 (A)       the ambient temperature increases


 (B)       the pressure ratio across the compressor decreases


 (C)       the load on the engine increases


 (D)       the displacement volume of the engine decreases




 Q.17      In a thresher, the cylinder separation efficiency can be improved by increasing


 (A)       cylinder diameter


 (B)       cylinder speed


 (C)       cylinder-concave clearance


 (D)       feed rate




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 Q.18      In a 4-stroke single cylinder diesel engine, the inlet valve opens at 10⁰ before TDC
           and closes at 40⁰ after BDC. The exhaust valve opens at 25⁰ before BDC and closes
           at 15⁰ after TDC. The percentage of time for which both the valves remain closed
           in one cycle of the engine is


 (A)       32.29


 (B)       40.97


 (C)       46.53


 (D)       75.01




 Q.19      The torque available at maximum power developed by the tractor is 150 N m. If the
           reserve torque is 20%, the peak torque that can be developed by the tractor in N m
           is


 (A)       100


 (B)       120


 (C)       180


 (D)       210




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 Q.20      The statement which is not correct for the porous medium is


 (A)       Seepage velocity is always greater than the Darcy’s velocity


 (B)       Darcy’s velocity is not exclusively controlled by soil porosity


 (C)       Seepage velocity increases with increasing surface ponding of water


 (D)       Darcy’s velocity in unsaturated soil is always greater than that in saturated soil




 Q.21      A sprinkler irrigation system has been designed for a crop with the water application
           rate of 1.17 cm h-1 and sprinkler discharge of 1.3 L s-1. The coefficient of discharge
           and uniformity coefficient are 0.9 and 0.8, respectively. If the sprinkler spacing
           along the lateral is 20 m, the lateral spacing in m is


 (A)       14.4


 (B)       16.0


 (C)       18.0


 (D)       20.0




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 Q.22      The average discharge, operating pressure and emitter constant of a drip emitter are
           4 L h-1, 110 kPa and 0.3, respectively. The type of emitter is


 (A)       orifice


 (B)       long path


 (C)       pressure compensating


 (D)       disc




 Q.23      If the departure and latitude of a line are 70 m and −130 m, respectively, then the
           whole circle bearing of the line in degrees is


 (A)       28


 (B)       62


 (C)       152


 (D)       208




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 Q.24      Match the Columns:
                    I                                    II
                1. Tensiometer                       a. Consumptive use
                2. Piezometer                        b. Bernoulli’s equation
                3. Lysimeter                         c. Soil moisture
                4. Elbow meter                       d. Hydrostatic pressure
                5. Pitot tube                        e. Volumetric flow rate

           .


 (A)       1 – c, 2 – b, 3 – a, 4 – e, 5 – d


 (B)       1 – c, 2 – d, 3 – a, 4 – e, 5 – b


 (C)       1 – d, 2 – c, 3 – e, 4 – a, 5 – b


 (D)       1 – c, 2 – d, 3 – a, 4 – b, 5 – e




 Q.25      The information needed for estimating the design flood using Rational formula is


 (A)       cumulative infiltration


 (B)       antecedent moisture condition of soil


 (C)       shape factor of the catchment


 (D)       time of concentration of the catchment




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 Q.26      The microbial death kinetics for a food suspension follows the equation:

                                                 N0     t − tl
                                           log      =1+
                                                 N        D
           where No= initial microbial load, N = microbial load after time t, tl = lag time and
           D = decimal reduction time.

           The correct statement for this equation is


 (A)       the time required to reduce 10% of the initial population is lag time.


 (B)       the time required to reduce the initial 90% of population is lag time


 (C)       time required to kill the first 90% population is lower than D value at the same
           temperature


 (D)       lag time approaches D value as N0 becomes smaller and temperature decreases.




 Q.27      If the diameter of fat globule in a cream separator is reduced to half and the
           rotational speed of the centrifuge increased to three times, the terminal settling
           velocity of fat globule is


 (A)       decreased to 0.44 times


 (B)       increased to 0.44 times


 (C)       decreased to 2.25 times


 (D)       increased to 2.25 times




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 Q.28      The log mean temperature difference (LMTD) correction factor is not required
           during heat transfer rate calculation in


 (A)       plate heat exchanger


 (B)       1 shell pass and 1 tube pass heat exchanger


 (C)       1 shell pass and 2 tube pass heat exchanger


 (D)       2 shell pass and 4 tube pass heat exchanger




 Q.29      Identify the dimensionless parameter(s) from the following:


 (A)       Cone index


 (B)       Puddling index


 (C)       Performance index


 (D)       Reel index




 Q.30      The probability that a storm event with a return period of 20 years will occur once
           in 5-year period is ____________________(rounded off to 2 decimal places).




 Q.31      Considering declining balance method, the constant rate of depreciation at which
           the value of the tractor will come down to 50% of its purchase price at the end of
           4th year in per cent is _____________________(rounded off to 2 decimal places).




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 Q.32      A trapezoidal grassed waterway with side slope (H:V) of 1:1 carries a design
           discharge of 1 m3 s-1. The bed slope and Manning’s roughness coefficient of this
           channel are 1% and 0.04, respectively. The design depth of the best hydraulic
           trapezoidal grassed waterway section in m is ______________ (rounded off to 2
           decimal places).




 Q.33      The minimum fluidization height of 1.20 m is maintained during fluidized bed
           drying of carrots. The bed diameter of the fluidized bed dryer is 0.6 m. If mass and
           solid density of carrots are 250 kg and 1040 kg m-3, respectively, then the porosity
           of the bed at the minimum fluidization condition is ____________ (rounded off to
           3 decimal places, Consider π = 3.14).




 Q.34      The lighter liquid layer and the interphase layer in a basket centrifuge, rotating at a
           speed of 1000 rpm, are 0.1025 m and 0.105 m away from the center, respectively.
           Considering the densities of lighter and heavier liquids as 920 kg m-3 and
           1015 kg m-3, the differential pressure in horizontal direction required to maintain
           the interphase layer in kPa is ______________ (rounded off to 3 decimal places,
           Consider π = 3.14).




 Q.35      The upstream and downstream pressures in a homogenizer during homogenization
           of milk are maintained at 250 bar and 10 bar, respectively. If density of milk is
           1030 kg m-3, then the velocity at which milk comes out of the homogenizing valve
           in m s-1 is ________________________ (rounded off to 3 decimal places).




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Q.36 – Q.65 Carry TWO marks Each

 Q.36                 1 −1        a     1
           If A = [       ], B = [        ] and (A + B)2 = A2 + B2, then the values of a and b
                      2 −1         b   −1
           are:




   (A)     a = 4, b = 1


   (B)     a = 1, b = 4


   (C)     a = 0, b = 4


   (D)     a = 2, b = 4




  Q.37     A vector F⃗ = 5î − 10ĵ + 8k̂ is passing through the origin of a 3-D frame.
           Considering the tendency of rotation in the counter clockwise direction as positive,
           the moment about a point A: (3, 4, 8) is


   (A)     −16î + 112ĵ + 50k̂


   (B)     112î + 16ĵ − 50k̂


   (C)     50î − 112ĵ + 16k̂


   (D)     −112î −16ĵ + 50k̂




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 Q.38      A vertical disc plough with 5 discs is operated at a depth of 0.15 m. The disc angle
           and disc diameter are 40⁰ and 0.6 m, respectively. If overlap between two
           consecutive discs is 0.12 m at 0.15 m depth of cut, the total width of cut at the
           specified depth in m is




 (A)       1.19


 (B)       1.55


 (C)       2.11


 (D)       2.36




 Q.39      In a 9×20 cm fluted roller type seed drill, each fluted roller is discharging 4.25 g of
           seed per revolution of fluted roller shaft. The fluted roller shaft rotates once for two
           complete rotation of the ground drive wheel of the seed drill. The rolling diameter
           of the ground drive wheel is 0.35 m. Considering no skid of the ground drive wheel,
           the seed rate in kg ha-1 is

           Consider π = 3.14


 (A)       96.62


 (B)       141.55


 (C)       187.35


 (D)       386.42




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 Q.40      A field sprayer with 12 nozzles fitted to the boom at a spacing of 0.5 m is used for
           spraying at a height of 0.75 m from the ground. The angle of spraying is 75⁰. If the
           height of spraying is reduced to 0.6 m, the change in swath in m is


 (A)       0.23


 (B)       0.48


 (C)       0.65


 (D)       0.91




 Q.41      The ordinates of a 6-hour S-hydrograph of a catchment are given in Table below.
           The catchment has phi-index of 0.25 cm h-1 and baseflow of 10.5 m3 s-1. The peak
           of the flood hydrograph generated from this catchment due to a storm of 45 mm
           received during the first 6 h in m3 s-1 is


            Time (h)               0    6       12     18    24    30     36    42    48
            Ordinate (m3 s-1)      0   30       90    180   252   306    342   360 360

   (A)     259.5


   (B)     270.0


   (C)     280.5


   (D)     349.5




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  Q.42     It is planned to provide irrigation in a crop field having field capacity and permanent
           wilting point of the soil as 0.21 cm3 cm-3 and 0.09 cm3 cm-3, respectively. The crop
           root zone depth is 0.90 m. The growing period of this crop is 1st January to 31st
           March, during which the observed reference evapotranspiration (ETr), effective
           rainfall (Pe) and crop coefficients (Kc) are listed below. Considering management
           allowable deficit (MAD) for this crop as 50%, the average irrigation interval during
           the growing period in days is

           .
               Month                     January               February                March
               ETr (mm day-1)               11                     12                     14
               Pe (mm month-1)              8                      25                     27
               Kc                          0.80                   1.10                  1.15




 (A)       4


 (B)       6


 (C)       8


 (D)       11




 Q.43      The infiltration capacity of a basin is described by the Horton’s equation,
           I = 2 + e −3t , where I is in cm h-1 and the duration, t is in hours. If the duration of the
           storm event is 2 hours, the depth of the infiltration in the last 1 hour of the storm
           event in mm is


 (A)       5


 (B)       10


 (C)       20


 (D)       25


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 Q.44      In a juice filtration process, solid concentration per m3 of filtrate is 0.2 kg. During
           filtration of 12.49 m3 of juice, 0.02 m thick cake (porosity of 0.32) is deposited. If
           2.5 kg of solid is collected in 180 s, the pressure drop across the cake in kPa is

           [Absolute viscosity of juice is 2.12 ×10-3 kg m-1 s-1, and specific cake resistance is
           1.2 × 108 m kg-1]




 (A)       0.18


 (B)       1.81


 (C)       18.06


 (D)       180.60




 Q.45      Cheese is packed in a bilayer plastic package made up of low density polyethylene
           (LDPE) and polyethylene terephthalate (PET). The thickness of LDPE and PET in
           the package are 1.5 mm and 1.3 mm, respectively. The surface area of the plastic
           package is 6.25 cm2. The partial pressure difference of oxygen across the package
           wall is 0.30 atm. The permeability coefficient of oxygen in LDPE and PET are
           4.18×10-8 cm3 cm cm-2 s-1 atm-1 and 1.67×10-10 cm3 cm cm-2 s-1 atm-1, respectively.
           If the food gets spoiled when it absorbs 0.025 ml of oxygen, then the shelf life of
           food in days is


 (A)       121


 (B)       103


 (C)       73


 (D)       61




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 Q.46      The rotor shaft of an ice cream freezer consists of 3 scraper blades. The temperature
           difference between the ice cream mix and the refrigerant during freezing of ice
           cream is 30 ⁰C. Density and latent heat of fusion of ice are 917 kg m-3 and 335 kJ
           kg-1, respectively. The overall heat transfer coefficient is 2000 kJ m-2 h-1 ⁰C-1. If
           the maximum thickness of ice formed before being scraped off is 10 µm, the
           minimum speed of the scraper shaft in rpm is




 (A)       88


 (B)       109


 (C)       121


 (D)       149




 Q.47      The percentage absolute humidity of air becomes equal to the percentage relative
           humidity, when




 (A)       absolute humidity of air is equal to relative humidity


 (B)       saturated humidity of air is equal to relative humidity


 (C)       air is almost or completely dry


 (D)       air is almost or completely saturated




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 Q.48      Dimensionless numbers play an important role in correlating transfer coefficients
           during forced convection. In relation to the dimensionless numbers, the correct
           statement(s) is/are


 (A)       Prandtl number in heat transfer is analogous to Schmidt number in mass transfer


 (B)       Small value of Prandtl number signifies lower thermal diffusion as compared to
           momentum diffusion


 (C)       Prandtl number is the ratio of momentum diffusivity to the thermal diffusivity of
           the fluid


 (D)       Lewis number is the product of Schmidt number and Prandtl number




 Q.49      In a locality ‘A’, the probability of a convective storm event is 0.7 with a density
           function, fX1 (x1 ) = e −x1 , x1 > 0. The probability of tropical cyclone-induced
           storm in the same location is given by the density function
           fX2 (x2 ) = 2e −2x2 , x2 > 0. The probability of occurring more than 1 unit of storm
           event is ______________ (rounded off to 2 decimal places).




 Q.50                  dy
           Given that dx = 2x + y and y = 1, when x = 0. Using Runge-Kutta fourth order
           method, the value of y at x = 0.2 is __________(rounded off to 3 decimal places).




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 Q.51      A power operated chaff cutter with a mean cutting radius of 0.25 m is fitted with
           two cutting knives and is rotating at 300 rpm. Thirty maize stalks with a mean
           diameter of 12 mm are fed through the throat at a time. The dynamic shear strength
           of the stalk is 0.05 N mm-2. The mass and radius of gyration of the flywheel
           (including knives) are 40 kg and 0.27 m, respectively. The total shaft power
           requirement in kW is _____________ (rounded off to 2 decimal places).




 Q.52      A two-wheel drive tractor with a total weight of 24 kN has a static weight
           distribution of 30% and 70% at the front and rear axles, respectively. When the
           tractor is operated on a level ground of pure sand, the maximum tractive force
           developed is 13 kN. If external weight of 1.5 kN is added to the rear axle, neglecting
           weight transfer, the change in maximum tractive force in kN is __________
           (rounded off to 2 decimal places).




 Q.53      A 4-stroke diesel engine can be operated with either diesel (heating value
           45 MJ kg-1) or biodiesel blend, B20 (heating value 42.1 MJ kg-1). The brake specific
           fuel consumption of the engine when operated with diesel and B20 is
           260 g kW-1 h-1 and 310 g kW-1 h-1, respectively. For developing a brake power of
           20 kW, the change in brake thermal efficiency of the engine when B20 is used in
           place of diesel is __________ (rounded off to 2 decimal places).




 Q.54      A solar photovoltaic system is used to generate power from total solar radiations
           varying from 400 to 750 W m-2. The maximum conversion efficiency of solar
           photovoltaic system is 14%. The open circuit voltage, short circuit current and fill
           factor of solar cells are 21.6 V, 3.22 A and 0.72, respectively. To generate maximum
           power, the minimum cell area required in m2 is _____________ (rounded off to 3
           decimal places).




 Q.55      A single disc clutch is used to transmit 10 kW power at 1400 rpm. The axial pressure
           exerted on the contact surface is 0.07 N mm-2 and the coefficient of friction is 0.25.
           Considering the ratio of diameter to face width of the clutch lining as 8 and
           assuming uniform wear theory, the required face width of friction lining in mm is
           __________________ (rounded off to 2 decimal places).



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 Q.56      In a tractor seat system, the chassis frequency and seat suspension damping rate are
           20 rad s-1 and 400 N m-1 s, respectively. The critical damping rate of tractor seat
           system is 1600 N m-1 s. If the combined mass of the seat and operator is 80 kg, the
           transmissibility of vibration is __________ (rounded off to 2 decimal places).




 Q.57      Two cylindrical reservoirs ‘A’ and ‘B’ are connected by a 30 m long pipe of
           250 mm internal diameter as shown in Figure below. The Darcy-Weisbach friction
           factor for the pipe is 0.025. Initially the reservoir ‘A’ was full at the indicated level
           and reservoir ‘B’ was empty. If the entrance and exit losses in this pipe are
           neglected, the time required to empty the reservoir ‘A’ in hour is ___________
           (rounded off to 3 decimal places).

           Consider π = 3.14 and acceleration due to gravity, g = 9.81 m s-2.




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 Q.58      A homogenous anisotropic earthen dam of height 52 m with a free board of 2 m is
           constructed on an impermeable foundation. The horizontal and vertical hydraulic
           conductivities of soil used for the construction of the dam are 4.5×10-8 m s-1 and
           2.0×10-8 m s-1, respectively. There are 6 flow channels and 25 equipotential drops
           in a square flownet drawn in the transformed dam section. If the downstream dam
           side is dry, the quantity of seepage per unit length through the dam in m 3 day-1 m-1
           is ____________ (rounded off to 3 decimal places).




 Q.59      A salt affected crop field is to be leached with irrigation water having salt
           concentration of 3.5 meq L-1. Salt concentration in the saturation extract of soil is
           15.2 meq L-1. Leaching efficiency of the field is 55%. In the month of March, the
           observed reference evapotranspiration and effective rainfall in this area are 150 mm
           and 75 mm, respectively. If the average crop coefficient in this month is 1.05, the
           leaching requirement for the entire month in mm is __________ (rounded off to 2
           decimal places).




 Q.60      A 10 m long concrete pipe is required to carry a peak discharge of 1.0 m3 s-1 in a
           drop inlet spillway with a head of 4 m. The entrance loss coefficient is 0.5 and the
           friction loss coefficient is 0.02. Consider acceleration due to gravity = 9.81 m s-2.
           The neutral slope of the water level in per cent is __________ (rounded off to 2
           decimal places).




 Q.61      Discharge from a centrifugal pump operating at 1000 rpm with a total head of 30 m
           is 300 L min-1. The pump efficiency is 65%. If speed of the pump is increased to
           1200 rpm, the power required to operate the pump in kW is _______________
           (rounded off to 2 decimal places).

           Consider acceleration due to gravity = 9.81 m s-2.




 Q.62      A 0.30 m diameter well penetrates an unconfined aquifer with a saturated depth of
           40 m. After 8 hours of pumping at a steady rate of 0.03 m3 s-1, the drawdown in two
           observation wells located at 20 m and 50 m away from the pumping well are found
           to be 3 m and 2 m, respectively. The drawdown in the pumping well in m is
           ___________ (rounded off to 1 decimal place, Consider π = 3.14).


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 Q.63      The apparent wall shear stress in a 0.6 m long pipe line carrying refined oil is
           12.5 Pa. If the pressure drop along the length is 300 Pa and flow rate is 0.25 m3 s-1,
           the absolute viscosity of oil in 10-3 Pa s is ______________ (rounded off to 3
           decimal places).




 Q.64      The carrot slices (water activity = 0.89) are to be preserved using osmo-dehydration.
           Addition of salt (NaCl) to 20% sucrose solution (water activity = 0.987) reduces the
           water activity to 0.85. Percentage of NaCl added to the solution is ______________
           (rounded off to 2 decimal places).

           Consider molecular mass of Sucrose = 342 and molecular mass of NaCl = 58.44




 Q.65      A copper ball and a steel ball having diameters d1 and d2, respectively, are initially
           at a uniform temperature of 200 oC. Both the balls are exposed to the atmosphere at
           30 oC. If both the balls attain a temperature of 120 ⁰C after equal exposure duration,
           then the ratio of d1 to d2 is ___________________ (rounded off to 3 decimal
           places).

           Assume Biot Number to be less than 0.1. The thermo-physical properties of copper
           and steel are given below:

               Material            Density         Specific heat    Thermal conductivity
                                   (kg m-3)         (J kg-1 ⁰C-1)       (W m-1 ⁰C-1)

                Copper              8950                383                 386
                 Steel              7800                460                  36




                                   END OF QUESTION PAPER




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Source: GATE. Question paper published by GATE.