GATE AG 2023 Question Paper & Solutions

Verbal Aptitude

"You are delaying the completion of the task. Send _______ contributions at the earliest."

Analytical & Spatial Aptitude

References : ______ : : Guidelines : Implement (By word meaning)

Analytical & Spatial Aptitude

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.)

Analytical & Spatial Aptitude

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?

Analytical & Spatial Aptitude

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)

Analytical & Spatial Aptitude

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.

Quantitative Aptitude

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?

Verbal Aptitude

The World Bank has declared that it does not plan to offer new financing to Sri 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?

Quantitative Aptitude

The coefficient of x⁴ in the polynomial (x − 1)³(x − 2)³ is equal to _______.

Analytical & Spatial Aptitude

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.

Linear Algebra

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

Calculus

$\lim_{x \to 0} \frac{\sqrt{1+x} - 1}{x}$ is equal to:

Calculus

The value of $I = \int_{0}^{\pi/2} \frac{(\sin x + \cos x)^2}{\sqrt{1+\sin 2x}} \, dx$ is:

Differential Equations

$y = a e^{mx} + b e^{-mx}$ is the solution of the differential equation:

Farm Machinery

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

Farm Power

The effectiveness of the turbocharger of a diesel engine increases when

Farm Machinery

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

Farm Power

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

Tractors and Power Tillers

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

Soil Mechanics

The statement which is not correct for the porous medium is

Irrigation Water Conveyance and Application Methods

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

Irrigation Water Conveyance and Application Methods

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

Farm Power

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

Hydrology

Match the instruments in Column I with the corresponding measurement variables in Column II: | Column I | Column 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 |

Hydrology

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

Preservation of Food

The microbial death kinetics for a food suspension follows the equation: log(N0/N) = 1 + (t−t_l)/D, where N0=initial microbial load, N=microbial load after time t, t_l=lag time, D=decimal reduction time. The correct statement for this equation is

Unit Operations in Dairy and Food Engineering

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

Heat and Mass Transfer

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

Machine Design

Identify the dimensionless parameter(s) from the following:

Probability and Statistics

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).

Farm Machinery

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).

Soil and Water Erosion

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).

Evaporation and Drying

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).

Size Reduction and Material Handling

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).

Unit Operations in Dairy and Food Engineering

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).

Linear Algebra

If $A = \begin{bmatrix} 1 & -1 \\ 2 & -1 \end{bmatrix}$, $B = \begin{bmatrix} a & 1 \\ b & -1 \end{bmatrix}$ and $(A+B)^2 = A^2 + B^2$, then the values of $a$ and $b$ are:

Machine Design

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

Farm Machinery

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

Farm Machinery

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]

Farm Machinery

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

Hydrology

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 m³s⁻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 m³s⁻¹ is [Time(h): 0,6,12,18,24,30,36,42,48; Ordinate(m³/s): 0,30,90,180,252,306,342,360,360]

Soil-Water-Plant Relationship

It is planned to provide irrigation in a crop field having field capacity and permanent wilting point of the soil as 0.21 cm³cm⁻³ and 0.09 cm³cm⁻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 ET_r, effective rainfall (P_e) and crop coefficients (K_c) are listed (Jan: ET_r=11,P_e=8,K_c=0.80; Feb: ET_r=12,P_e=25,K_c=1.10; Mar: ET_r=14,P_e=27,K_c=1.15). Considering MAD for this crop as 50%, the average irrigation interval during the growing period in days is

Hydrology

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

Size Reduction and Material Handling

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⁻¹s⁻¹, and specific cake resistance is 1.2×10⁸ m kg⁻¹]

Storage Systems

Cheese is packed in a bilayer plastic package made up of LDPE and 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 and 1.67×10⁻¹⁰ cm³ cm cm⁻²s⁻¹atm⁻¹, respectively. If the food gets spoiled when it absorbs 0.025 ml of oxygen, then the shelf life of food in days is

Unit Operations in Dairy and Food Engineering

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 30⁰C. 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⁻²h⁻¹⁰C⁻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

Evaporation and Drying

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

Heat and Mass Transfer

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

Probability and Statistics

In a locality 'A', the probability of a convective storm event is 0.7 with a probability density function $f_{X_1}(x) = 0.1 e^{-0.1x}$, and the probability of a frontal storm event is 0.3 with a density function $f_{X_2}(x) = 0.2 e^{-0.2x}$ ($x > 0$). The combined probability that storm depth $X$ exceeds 10 mm is ______

Numerical Methods

Given that $\frac{dy}{dx} = 2x + y$ and $y(0) = 1$. Using the Runge-Kutta fourth order method with step size $h = 0.1$, the value of $y(0.1)$ is ______

Farm Machinery

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).

Tractors and Power Tillers

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).

Sources of Power

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⁻¹h⁻¹ and 310 g kW⁻¹h⁻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).

Sources of Power

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).

Tractors and Power Tillers

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).

Tractors and Power Tillers

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).

Fluid Mechanics

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 g = 9.81 m s⁻². Reconstructed figure for Q.57 (schematic; not to scale — as stated in the original).

Soil Mechanics

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 m³ day⁻¹ m⁻¹ is ____________ (rounded off to 3 decimal places).

Agricultural Drainage

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).

Soil and Water Erosion

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 g = 9.81 m s⁻². The neutral slope of the water level in per cent is __________ (rounded off to 2 decimal places).

Wells and Pumps

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 g = 9.81 m s⁻².

Hydrology

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).

Fluid Mechanics

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).

Heat and Mass Transfer

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

Heat and Mass Transfer

A copper ball and a steel ball having diameters d1 and d2, respectively, are initially at a uniform temperature of 200⁰C. Both the balls are exposed to the atmosphere at 30⁰C. If both the balls attain a temperature of 120⁰C 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.