List of top Questions asked in GATE Agricultural Engineering

Given that \[ \frac{dy}{dx} = 2x + y, y(0) = 1 \] Using Runge-Kutta fourth order method, the value of \(y\) at \(x = 0.2\) is \underline{\hspace{2cm}} (rounded off to 3 decimal places).

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 \underline{\hspace{4cm}} (rounded off to 2 decimal places).

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 \underline{\hspace{4cm}}.

A 4-stroke diesel engine can be operated with either diesel (HV = 45 MJ/kg) or biodiesel B20 (HV = 42.1 MJ/kg). Brake specific fuel consumption: diesel = 260 g/kWh, B20 = 310 g/kWh. For brake power = 20 kW, the change in brake thermal efficiency of the engine when B20 is used is \underline{\hspace{3cm}}.

A solar photovoltaic system receives radiations between 400–750 W/m\(^2\). Efficiency = 14%. Cell parameters: \(V_{oc} = 21.6 \, V\), \(I_{sc} = 3.22 \, A\), fill factor = 0.72. Find minimum cell area required to generate 10 kW power.

A single disc clutch is used to transmit 10 kW power at 1400 rpm. The axial pressure = 0.07 N/mm\(^2\), coefficient of friction = 0.25, ratio of inner to outer radius = 0.8. If the uniform wear theory applies, the required face width of clutch lining is \underline{\hspace{3cm}}.

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 the 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 \underline{\hspace{2cm}} (rounded off to 2 decimal places).

In a juice filtration process, solid concentration per m\(^3\) of filtrate is 0.2 kg. During filtration of 12.49 m\(^3\) 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: \[ \text{Absolute viscosity of juice} = 2.12 \times 10^{-3} \, \text{kg m}^{-1}\text{s}^{-1}, \text{Specific cake resistance} = 1.2 \times 10^8 \, \text{m kg}^{-1} \]

Cheese is packed in a bilayer plastic package made of low density polyethylene (LDPE) and polyethylene terephthalate (PET). 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 cm\(^2\). The partial pressure difference of oxygen across the package wall is 0.30 atm. The permeability coefficient of oxygen in LDPE and PET are \(4.18 \times 10^{-8} \, \text{cm}^3 \, \text{cm cm}^{-2} \text{s}^{-1}\text{atm}^{-1}\) and \(1.67 \times 10^{-10} \, \text{cm}^3 \, \text{cm cm}^{-2} \text{s}^{-1}\text{atm}^{-1}\), respectively. If the food gets spoiled when it absorbs 0.025 ml oxygen, then the shelf life of food in days is:

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 \(30^\circ C\). 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\(^{-1}\) \(^{\circ}C^{-1}\). If the maximum thickness of ice formed before being scraped off is 10 μm, the minimum speed of the scraper shaft in rpm is:

The percentage absolute humidity of air becomes equal to the percentage relative humidity, when:

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 vector \(\vec{F} = 5\hat{i} - 10\hat{j} + 8\hat{k}\) 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 vertical disc plough with 5 discs is operated at a depth of 0.15 m. The disc angle and disc diameter are \(40^\circ\) 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:

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 rotations 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 is (take \(\pi = 3.14\)):

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 \(75^\circ\). If the height of spraying is reduced to 0.6 m, the change in swath in m is:

The ordinates of a 6-hour S-hydrograph of a catchment are given in the table. The catchment has phi-index of 0.25 cm h\(^{-1}\) and baseflow of 10.5 m\(^3\)/s. The peak of the flood hydrograph generated from this catchment due to a storm of 45 mm received during the first 6 h in m\(^3\)/s is: \[ \begin{array}{|c|c|} \hline \text{Time (h)} & 0 6 12 18 24 30 36 42 48
\hline \text{Ordinate (m}^3/s\text{)} & 0 30 90 180 252 306 342 360 360
\hline \end{array} \]

It is planned to provide irrigation in a crop field having field capacity and permanent wilting point of the soil as 0.21 cm\(^3\)/cm\(^3\) and 0.09 cm\(^3\)/cm\(^3\), respectively. The crop root zone depth is 0.90 m. The growing period of this crop is 1\(^\text{st}\) January to 31\(^\text{st}\) March, during which the observed reference evapotranspiration (ET\(_r\)), effective rainfall (P\(_e\)) and crop coefficients (K\(_c\)) are given: \[ \begin{array}{|c|c|c|c|} \hline \text{Month} & \text{ET}_r \, (\text{mm/day}) & P_e \, (\text{mm/month}) & K_c
\hline \text{January} & 11 & 8 & 0.80
\text{February} & 12 & 25 & 1.10
\text{March} & 14 & 27 & 1.15
\hline \end{array} \] Considering management allowable deficit (MAD) for this crop as 50%, the average irrigation interval during the growing period in days is:

The infiltration capacity of a basin is described by Horton's equation: \[ I = 2 + e^{-3t} \] where \(I\) is in cm/h and \(t\) is in hours. If the duration of the storm event is 2 hours, the depth of infiltration in the last 1 hour of the storm event in mm is:

The probability that a storm event with a return period of 20 years will occur once in a 5-year period is \underline{\hspace{6cm}} (rounded off to 2 decimal places).

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 percent) is \underline{\hspace{6cm}} (rounded off to 2 decimal places).

A trapezoidal grassed waterway with side slope (H:V) of 1:1 carries a design discharge of \(1 \, m^3/s\). 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 \underline{\hspace{3cm}} (rounded off to 2 decimal places).

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 \underline{\hspace{3cm}} (rounded off to 3 decimal places, \(\pi = 3.14\)).

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 \underline{\hspace{3cm}} (rounded off to 3 decimal places, \(\pi = 3.14\)).

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 is \underline{\hspace{3cm}} (rounded off to 3 decimal places).