GATE AG 2020 Question Paper & Solutions

Verbal Aptitude

The untimely loss of life is a cause of serious global concern as thousands of people get killed ____ accidents every year while many other die ____ diseases like cardio vascular disease, cancer, etc.

Verbal Aptitude

He was not only accused of theft ____ of conspiracy.

Analytical & Spatial Aptitude

Select the word that fits the analogy: Explicit : Implicit :: Express : ______

Analytical & Spatial Aptitude

Air Canada lost a lawsuit over a French-speaking couple's complaint about formal in-flight announcements in English (15 s) vs. informal ones in French (5 s). The French-speaking couple were upset at ____.

Quantitative Aptitude

A superadditive function f(·) satisfies f(x₁+x₂) ≥ f(x₁)+f(x₂). Which of the following functions is superadditive for x > 1?

Analytical & Spatial Aptitude

Based on the passage on the 2008 global financial crisis (sub-prime lending crisis in USA following the East Asian crisis, leading to banking crisis and collapse of Lehman Brothers), which sequence shows the correct precedence?

Quantitative Aptitude

It is quarter past three (3:15). Find the angle between the hour hand and the minute hand.

Quantitative Aptitude

A rectangle PQRS of maximum possible area is inscribed in a circle of radius a. Find the area of the shaded (remaining) portion of the circle.

Quantitative Aptitude

a, b, c are real numbers. The quadratic equation ax²−bx+c=0 has equal roots, β. Then:

Quantitative Aptitude

Bar chart gives enrollment (thousands) for School P and Q, 2014–2018: P = 3,5,5,6,4; Q = 4,7,8,7,5. Find the ratio of the average number of students in P to the average of the difference of students enrolled in P and Q.

Calculus

The function $f(x) = x^4 - 4x^3 + 6x^2 - 4x + 1$ has a:

Linear Algebra

A linear system with n unknowns has coefficient-matrix rank r₁ and augmented-matrix rank r₂. The condition for the system to be consistent with a UNIQUE solution is:

Differential Equations

Find the general solution to $\frac{d^3y}{dx^3} - 6\frac{d^2y}{dx^2} + 11\frac{dy}{dx} - 6y = 0$:

Tractors and Power Tillers

In a tractor steering system, the angle made by the kingpin axis projected on the longitudinal plane of the tractor with the vertical axis is known as:

Farm Machinery

A tractor-operated 9-row precision planter has 16 cells on the metering plates. The speed ratio of the metering plates to the ground drive wheel is 1:2; rolling diameter of the drive wheel = 40 cm. Assuming no skid, find the plant-to-plant spacing in rows (mm).

Tractors and Power Tillers

A self-propelled wheel does not have:

Hydrology

Match the aquifer properties in Column I with the terms in Column II: | Column I | Column II | |---|---| | P. Properties of confined & semi-confined aquifers | 1. Perched aquifer | | Q. Property of an unconfined aquifer | 2. Coefficient of storage | | R. Property of semi-confined aquifer | 3. Specific yield | | S. Special case of an unconfined aquifer | 4. Leakage factor |

Irrigation Water Conveyance and Application Methods

From dripper performance evaluation, the discharge exponent = 0.5 and coefficient of variation = 0.04. The drippers are categorized as:

Hydrology

Five stations A, B, C, D, E have average annual rainfall 1020, 810, 675, 940, 780 mm. In a particular year, station A was non-operational; B, C, D, E recorded 890, 725, 980, 850 mm. Estimate the rainfall at A that year (mm).

Soil-Water-Plant Relationship

A field crop is irrigated when available soil water is depleted to 60%. Field capacity=32%, wilting point=12% (by weight); bulk density=1.5 g/cm³; field application efficiency=75%; root zone depth=50 cm. Find the gross depth of irrigation to bring soil moisture to field capacity (cm).

Preservation of Food

A cold storage takes 5 hours to bring down the temperature of 100 metric tons of potato from 35°C to 8°C. Specific heat of potato = 3.1 kJ/kg·°C. COP = 3.66; latent heat of vaporization of R-22 (at −10°C evaporation) = 230 kJ/kg. Neglecting respiration heat load and power loss, find the refrigerant flow rate and compressor power input.

Evaporation and Drying

Hydrothermal treatment of paddy makes:

Evaporation and Drying

Both particle formation and drying processes are carried out by:

Linear Algebra

If one of the two eigenvalues of the matrix $\begin{bmatrix} 3 & 2 \\ 2 & 1 \end{bmatrix}$ is 4.236, find the other eigenvalue. (Rounded to 3 decimal places)

Calculus

Find $\lim_{x \to 0} \frac{e^x - e^{-x} - 2x}{x - \sin x}$:

Sources of Power

At maximum power output of a solar panel, voltage = 18 V, current = 5.56 A. Open-circuit voltage = 21.6 V, short-circuit current = 6.11 A. Find the fill factor. (Rounded to 2 decimal places)

Tractors and Power Tillers

The sound pressure level on the operator's seat of a tractor is 80 dB. If the reference sound pressure is 2×10⁻⁵ N/m², find the RMS sound pressure (N/m²). (Rounded to 2 decimal places)

Tractors and Power Tillers

A towed pneumatic wheel with unloaded radius 330 mm covers 9.9 m in 5 revolutions without skid. Assuming rolling radius = static loaded radius, find the tire deflection (mm). (Rounded to 1 decimal place)

Farm Machinery

Grain-to-straw ratio of 500 kg feed material is 3:2. Blown grain loss = 0.05%, separation loss = 0.5%, cleaning efficiency = 99.1%. Considering 100% threshing efficiency, find grain recovery at the main grain outlet (kg). (Rounded to 2 decimal places)

Wells and Pumps

A tubewell discharges 40 m³/h and operates 20 h/day during the irrigation season. Irrigation interval = 20 days, depth of irrigation = 8 cm. Find the command area of the tubewell (ha).

Agricultural Drainage

The drainage coefficient of a 720 ha watershed is 1.2 cm. Find the design discharge of the drain (m³/s).

Soil and Water Erosion

Watershed erosion data: R=280 MJ·mm/(ha·h·yr), K=0.38 t·ha·h/(MJ·mm), slope length=200 m, average slope=8%, LS-steepness factor=0.85, C=0.35, P=0.60. If slope length is halved, find the percentage reduction in soil loss (using the USLE slope-length exponent m=0.5 for slopes ≥5%). (Rounded to 2 decimal places)

Evaporation and Drying

Fresh tomato juice (6% w/w total solids) enters a single-effect evaporator at 500 kg/h to be concentrated to 36% w/w solids. Find the rate of water removal (kg/h). (Rounded to 1 decimal place)

Heat and Mass Transfer

Heat gain through a composite cold-storage wall of brick (100 mm, k=0.30 W/m°C) and polyurethane foam insulation (150 mm, k=0.05 W/m°C); exposed surface temperatures are 45°C (brick) and 10°C (insulation). Find the temperature at the brick-insulation interface (°C). (Rounded to 1 decimal place)

Preservation of Food

A milk plant pasteurizes 12,500 L whole milk to inactivate Coxiella burnetii (D=14 s at 72°C), packed in 500 mL pouches, initial count 10/mL. Find the process F-value (s) required so that no package contains a survivor.

Vector Calculus

A particle moves along the path $\vec{R}(t) = (2t^3+4t^2)\hat{i} + (3t^2-5t)\hat{j} + (7t^2+6t)\hat{k}$. Find the velocity component in the direction of $\hat{i} + \hat{j} + 3\hat{k}$ at $t = 1$:

Differential Equations

For f(t) = 4cos2t + 6e⁻⁸ᵗ, find F(s) = L{f(t)}.

Fluid Mechanics

In an irrigation channel, water passes through a 90° triangular weir with 36 cm head, then (with no loss) through a 1.0 m long rectangular weir further downstream. Using Francis' formula, find the head over the rectangular weir (cm).

Fluid Mechanics

A differential mercury manometer connected across two points on a pipe carrying oil shows a 20 cm mercury-level difference. Specific gravity of oil = 0.8, mercury = 13.6; ρwater=1000 kg/m³ at 4°C, g=9.81 m/s². Find the pressure difference at the two points (N/m²).

Soil Mechanics

Match the soil and fluid properties in Column I with their physical definitions in Column II: | Column I | Column II | |---|---| | P. Hydraulic Conductivity | 1. Upper limit of moisture available to plant | | Q. Permeability | 2. All soil pores filled with water | | R. Viscosity | 3. Soil capillarity | | S. Surface Tension | 4. Property of fluid and soil | | T. Saturation Capacity | 5. Property of the medium | | U. Field Capacity | 6. Internal friction resisting flow |

Soil Mechanics

A retaining wall of height 5 m retains cohesionless dry soil (density 1.9 Mg/m³, angle of internal friction 28°). Backfill surface is horizontal. Find the active and passive earth pressures per meter length of the wall (kN). [g=9.81 m/s²]

Wells and Pumps

A 40 cm diameter tubewell in a 10 m thick confined aquifer (K=25 m/day); piezometric surface 40 m above impervious stratum at radius of influence 500 m; drawdown = 30 m. If aquifer thickness is doubled and well diameter halved (other parameters unchanged), find the change in discharge. [π=3.14]

Machine Design

Match the milling process in Column I with the corresponding machine component in Column II: | Column I | Column II | |---|---| | P. Paddy dehusking | 1. Abrasive emery roll cylinder | | Q. Wheat milling | 2. Attrition disk | | R. Pulse dehusking | 3. Rubber rolls | | S. Spice grinding | 4. Break roll and reduction roll |

Unit Operations in Dairy and Food Engineering

Saturated steam at 121°C sterilizes pineapple juice by direct steam injection. Initial juice temperature = 80°C; blended juice exits at 95°C. Enthalpies: hf(95°C)=397.9, hg(121°C)=2707.1 kJ/kg; specific heat of juice = 3.9 kJ/kg·°C. Find the ratio of juice sterilized to steam utilized.

Heat and Mass Transfer

Hot refined oil at 120°C enters a concentric tube-in-tube heat exchanger at 20 kg/min; oil is cooled by water entering at 30°C from the other end at 50 kg/min. Specific heats: oil=1.9, water=4.2 kJ/kg°C. Effectiveness of the HE = 0.7. Assuming steady state, no heat loss, find the exit temperature of water (°C).

Numerical Methods

Using six intervals of $\pi/12$ each and Simpson's $1/3$ rule, evaluate $\int_{0}^{\pi/2} \sqrt{\cos\theta} \, d\theta$. (Rounded to 3 decimal places)

Probability and Statistics

Two cards are drawn in succession (without replacement) from a pack of red cards only (26 cards). The probability of drawing a king first, followed by a queen, is P×10⁻³. Find P. (Rounded to 3 decimal places)

Farm Machinery

A hydraulic sprayer at 10 km/h and 420 kPa covers a width of 4.5 m; pump power = 0.75 kW, pump efficiency = 70%; 10% of discharge is bypassed for agitation. Working pressure is increased to 500 kPa. Assuming no change in coverage width, find the application rate (L/ha) at the new pressure. (Rounded to 1 decimal place)

Farm Machinery

A tractor PTO-operated rotary disc mower has 4 rotating discs, each cutting 60 cm width (no overlap). Specific power loss (air/stubble/gear friction) = 2.5 kW per m cutting width; specific cutting energy = 2.0 kJ/m². At forward speed 6 km/h, find the PTO power requirement (kW). (Rounded to 2 decimal places)

Surveying and Levelling

The underside beam of a railway bridge, a permanent Bench Mark with RL 85.168 m, is used for a leveling operation. The Back Sight (staff held inverted against the BM) = 3.645 m. For a Fore Sight of 1.523 m at a construction-site point, find its RL in m (rounded to 2 decimal places). *(Note: This question was officially CANCELLED / WITHDRAWN by the organizing institute (IIT Delhi) in the official GATE 2020 evaluation, and MARKS TO ALL (MTA) were awarded to all candidates).*

Tractors and Power Tillers

A 2WD tractor, total weight 25 kN, wheelbase 2.2 m, CG 0.7 m ahead of the rear axle. A steady horizontal pull is applied at drawbar hitch height 0.5 m such that front-axle weight becomes 20% of static weight. Find the coefficient of net traction. (Rounded to 2 decimal places)

Farm Power

A tractor's diesel engine cooling system rejects 0.58 kW of heat per kW of brake power; it requires 0.16 L/s of water per kW of heat rejection to maintain a 6 °C temperature drop across the radiator. If the engine develops 45 kW brake power, find the required water flow rate in the radiator (L/s). (Rounded to 2 decimal places)

Machine Design

A V-belt drive transmits 10 kW at belt velocity 8 m/s. Angle of contact on smaller pulley = 170°, groove angle = 38°, coefficient of friction = 0.28, maximum permissible stress = 4 MPa (neglect centrifugal effect). Find the minimum cross-sectional area of the belt (mm²). (Rounded to 1 decimal place)

Farm Machinery

A chaff cutter's electric motor runs at 1440 rpm; speed reduction motor→main shaft = 4:1. Feed rollers (10 cm diameter) are driven by the main shaft with a further reduction of 15:1. The cutting unit (on the main shaft) has two knives. Find the theoretical length of cut chaff (mm). (Rounded to 2 decimal places)

Farm Machinery

A tractor-drawn right-hand offset disc harrow: front gang longitudinal/lateral soil reactions = 3.0/2.5 kN at 2.5 m behind hitch; rear gang = 3.5/4.0 kN at 4.0 m behind hitch. Find the required offset of the disc harrow (m). (Rounded to 2 decimal places)

Farm Power

A diesel engine operating with B20 biodiesel blend (20% biodiesel, 80% diesel by volume) develops 10 kW brake power at brake-specific fuel consumption 0.26 kg/kWh. Density of biodiesel = 880 kg/m³, diesel = 850 kg/m³. Find the volume of biodiesel required to run the engine for 3 hours (L). (Rounded to 2 decimal places)

Surveying and Levelling

Area enclosed by contours of a pond: Contour (m) 100–106 with Area (m²): 440, 580, 640, 740, 960, 1100, 1240. Using the trapezoidal formula, find the total estimated capacity of the pond (m³).

Wells and Pumps

At 1800 rpm, a centrifugal pump discharges 50 L/s at its best-efficiency point for a total head of 25 m. Find the specific speed of the pump (rpm). (Rounded to 2 decimal places)

Hydrology

Curve Number (CN) of a 40 ha watershed (AMC-II) is 80; initial abstraction = 20% of maximum retention S. For a 40 mm rainfall event, find the direct runoff (mm). (Rounded to 2 decimal places)

Surveying and Levelling

The underside beam of a railway bridge, a permanent Bench Mark with RL 85.168 m, is used for a leveling operation. The Back Sight (staff held inverted against the BM) = 3.645 m. For a Fore Sight of 1.523 m at a construction-site point, find its RL (m).

Evaporation and Drying

Air-water vapor mixture at 30°C DBT, 40% RH is heated to 65°C DBT, 30°C WBT and used as drying medium in the constant-rate period for spinach leaves. Given saturation vapor pressures and latent heats at 30/45/65°C, find the absolute humidity (kg water vapor/kg dry air) for the dryer-exit air at 45°C DBT (same wet-bulb line). (Rounded to 3 decimal places)

Size Reduction and Material Handling

A tray-type paddy separator separates paddy from a paddy/brown-rice mixture at feed rate 1200 kg/h. Mass fractions of paddy in feed, separated-paddy stream, and brown-rice stream = 0.2, 0.75, 0.02. Find the amount of paddy in the separated-paddy stream (kg/h). (Rounded to 2 decimal places)

Storage Systems

A cylindrical silo (3.0 m diameter, height:diameter ratio 5:1) holds 60 metric tons of wheat (bulk density 725 kg/m³). Wall friction coefficient = 0.42; lateral:vertical pressure ratio = 0.5. Find the vertical pressure at the bottom of the silo (kPa). [1 kgf = 9.81 N] (Rounded to 2 decimal places)

Size Reduction and Material Handling

A bucket elevator lifts parboiled paddy (bulk density 840 kg/m³) at belt speed 2 m/s. Bucket width = 25.4 cm; its cross-section subtends 75° at the center of a 12.7 cm radius circle. Bucket spacing = 40 cm; buckets filled to 80% of capacity. Find the lifting capacity (kg/min). (Rounded to 2 decimal places)

Preservation of Food

A contact plate freezer extracts heat from a 24 mm thick slab of boneless meat (85% w/w water). Initial slab temperature = freezing point = 272.5 K; latent heat of freezing = 335 kJ/kg water. Plate temperature = 247.5 K (steady). Bulk density = 750 kg/m³; thermal conductivity of frozen meat = 1.5 W/m·K. Find the minimum duration for complete freezing (s).