GATE AG 2026 Question Paper & Solutions

Verbal Aptitude

Suresh said, “I did it yesterday.” Which one of the following options is the correct form of this sentence in indirect speech?

Analytical & Spatial Aptitude

To continue the sequence of tiles shown, the tile indicated by the question mark should be: Figure Q.2 — sequence of dot-tiles and the four options

Analytical & Spatial Aptitude

Consider an art gallery whose walkways are shown as lines in the diagram. A black dot represents a junction of two walkways. A guard may be placed at a junction to watch over the walkways that join at that junction. The minimum number of guards needed to watch all the walkways is ________. Figure Q.3 — walkway network of the art gallery

Quantitative Aptitude

The 2ⁿᵈ of June is a Thursday in a certain year. Which day of the week is the 3ʳᵈ of July in that year?

Analytical & Spatial Aptitude

A coin with heads facing up is shown as H, and a coin with tails facing up is shown as T. Six coins are placed in the Starting Arrangement shown below. A “step” is defined as interchanging a pair of adjacent coins without flipping them. The minimum number of steps needed to go from the Starting Arrangement to the Final Arrangement is ________. Figure Q.5 — starting and final coin arrangements

Analytical & Spatial Aptitude

Exacerbate : Mitigate :: ___________ Choose the option with the correct pair of words to fill the blank.

Analytical & Spatial Aptitude

A paper shown in Panel I is folded along the dashed lines to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to cubes shown in Panel II, which one of the options is correct? Figure Q.7 — Panel I (net) and Panel II (cubes) — approximate reconstruction

Analytical & Spatial Aptitude

In a population, patients who have high cholesterol also have high blood-pressure (BP). Some patients with high BP also have diabetes. There are no patients who have both high cholesterol and diabetes. Furthermore, 1. the total number of patients with at least one of these conditions is 75, 2. the number of patients with high cholesterol is 10, 3. the number of patients with high BP is 45, and 4. the number of patients with only high BP and no other conditions is 20. Then the number of patients who have both diabetes and high BP is _______

Analytical & Spatial Aptitude

Four people P, Q, R, and S, of different ages, make the following observations. P — I am younger than S. Q — I am neither the youngest nor the oldest. R — P is older than me. Based on these observations, the youngest person is ______.

Analytical & Spatial Aptitude

Circles $C_1$, $C_2$, and $C_3$, with centres $O_1$, $O_2$, and $O_3$, and radii $r_1$, $r_2$, and $r_3$ respectively, touch each other as shown in the figure. Given $r_1 = 2\text{ cm}$, $r_2 = 1\text{ cm}$ and the angle $\angle O_1O_3O_2 = 90^\circ$, $r_3 = \text{_____ cm}.$

Differential Equations

Identify the following partial differential equations in the given order based on their generic form $A\frac{\partial^2 u}{\partial x^2} + B\frac{\partial^2 u}{\partial x \partial y} + C\frac{\partial^2 u}{\partial y^2} + D\frac{\partial u}{\partial x} + E\frac{\partial u}{\partial y} + Fu = G$:

Probability and Statistics

A box contains one red ball and two blue balls. One ball is drawn at random, its colour is noted and the ball is returned to the box. The process is repeated. In the first two draws, a blue ball appears each time. The probability of drawing a blue ball again in the third draw is

Differential Equations

The general solution to the ordinary differential equation $\frac{d^2y}{dx^2} = \cos 2x$ is:

Linear Algebra

Two square matrices A and B of the same order are such that det[A·B] = −80 and det[A] = 5. Here A·B is the product of A and B. The value of det[Bᵀ] is

Numerical Methods

Consider the simultaneous equations 2x + 4y = −7; 3x + 5y = 1 While solving using Gauss elimination without pivoting, after the forward elimination, the diagonal elements of the coefficient matrix are

Farm Machinery

A plough attachment, which is a miniature plough bottom that cuts a narrow, shallow furrow ahead of the shin and moves trash and roots toward the main furrow so that they are completely covered by the mouldboard, is called as

Farm Power

Fuel property that predominantly governs ‘hard / cold starting’ in an SI engine is P; and the property that predominantly governs ‘ignition delay’ in a CI engine is Q. Identify the correct option for the P and Q combination.

Farm Power

A tractor engine delivers 382 N·m brake torque at a rated speed of 2000 rpm. The radiator cooling fan draws 5% of the engine brake power. The fan pushes 2.8 m³·s⁻¹ of air against a 0.9 kPa static pressure rise. Assuming air as incompressible and ignoring other losses, the fan efficiency, in %, is nearest to (Take π = 3.14)

Tractors and Power Tillers

A 2WD tractor’s driving axle experiences a total dynamic normal load of 28 kN. The driving wheels have 0.60 m rolling radius. The total driving axle torque measured is 10.7 kN·m. At 18% wheel slip, the coefficient of net traction is 0.35. Tractive efficiency of the driving wheels, in %, is nearest to

Tractors and Power Tillers

The RMS sound pressure is increased by 50%. This increases the sound pressure level, in dB, nearly by

Fluid Mechanics

A trapezoidal channel carries 5 m³·s⁻¹ of water under uniform flow condition. The channel has a bottom width of 2 m, side slope of 2:1 (horizontal : vertical), and a bed slope of 1%. If the Manning roughness coefficient is 0.03, the conveyance of the channel, in m³·s⁻¹, is

Soil and Water Erosion

In wind erosion, the amount of soil transported varies

Soil and Water Erosion

When the bed slope of the discharge carrier in a chute spillway changes from steeper to milder, we provide a

Soil-Water-Plant Relationship

A natural colloidal clay, having the characteristics of absorbing water and swelling 8 to 15 times its dry size, used as an efficient and effective sealing material for farm ponds, is

Hydrology

By depth-area-duration analysis, the maximum average depth of rainfall over a 10³ km² catchment due to a 6-hour storm is 80 mm. For the same storm, the maximum average depth of rainfall for a 10⁴ km² catchment, in mm, is

Heat and Mass Transfer

Dimensionless parameter among the following options is

Heat and Mass Transfer

It is given that the water activity of a food is equal to the relative humidity of the atmosphere that is in equilibrium with the food. The partial pressure of water vapour of the food at a specific temperature is

Size Reduction and Material Handling

Air carrying dust particles enters a cyclone separator of 800 mm diameter at a tangential velocity of 30 m·s⁻¹ near the wall. The average diameter of the dust particles is 100 µm. The separation factor is nearest to (Take g = 9.81 m·s⁻²)

Storage Systems

A circular mild steel storage bin of 8 m height contains wheat having bulk density of 800 kg·m⁻³. The coefficient of static friction between wheat grain and bin wall is 0.40 and hydraulic radius of the bin is 1 m. Equivalent diameter of the bin, in m, is

Heat and Mass Transfer

Specific heat, coefficient of viscosity, and thermal conductivity are related in the

Engineering Properties of Agriculture Produce

Mechanical model/method NOT related to rheological behaviour of food products is known as

Farm Power

At an initial pressure of 100 kPa, 1 kg of air is compressed reversibly from 15 litres to 1 litre at a final pressure of 2000 kPa. Neglecting other losses, the Polytropic Exponent (n) is ________. (Rounded off to three decimal places)

Irrigation Water Conveyance and Application Methods

A tubewell operating 10 hours per day discharges water at a rate of 25 m³·h⁻¹. The average irrigation depth is 80 mm, and the irrigation interval is 20 days. If the intensity of irrigation is 80%, the culturable command area (in hectares) is ________. (Rounded off to two decimal places)

Agricultural Drainage

A tile drainage system having a drainage coefficient of 25 mm drains an area of 0.2 km². The average discharge from the system (in m³·s⁻¹) is ________. (Rounded off to three decimal places)

Wells and Pumps

Impeller speed of a centrifugal pump is increased by 30%. The power requirement of the pump increases by n times. The value of n is ________. (Rounded off to two decimal places)

Calculus

The value of the integral $I = \int_{0}^{1} \int_{0}^{1} x \cos(xy) \, dx \, dy$ is:

Linear Algebra

The determinant of a 2 × 2 square matrix is 1.6. If the sum of the eigen values is −2.8, the eigen values are

Machine Design

A flat belt of negligible mass and thickness drives an output pulley of 0.6 m diameter, constantly rotating at 500 rpm without slip. The arc of contact is 190° for this pulley, while it is 170° for the smaller input pulley. The coefficient of friction between the belt and pulleys is 0.30. The measured slack-side tension is 250 N. Neglecting other losses, the power transmitted by the belt drive, in kW, is nearest to (Take π = 3.14)

Machine Design

A tractor PTO runs at a constant speed of 540 rpm to drive a rotary tiller via a flange coupling having a shear pin parallel to the shaft. The shear pin axis is located at 60 mm from the PTO shaft axis. The allowable shear stress of the pin material is 200 MPa. For overload safety, it must fail at 150% of the rated torque to protect the gearbox. The tiller requires 40 kW under normal load at rated PTO speed. Neglecting bending, stress concentration effects and other losses, the pin diameter, in mm, is nearest to (Take π = 3.14)

Sources of Power

A small horizontal-axis wind turbine (HAWT) is being designed to deliver 2 kW shaft power at a steady wind speed of 7 m·s⁻¹. The HAWT operates with an aerodynamic power coefficient of 0.36, drivetrain efficiency of 0.90, and air density of 1.225 kg·m⁻³. Neglecting other losses, the required rotor diameter is X m. When the wind speed drops to 6 m·s⁻¹, the shaft power is Y kW. Identify the nearest correct option for the X and Y combination. (Take π = 3.14)

Evaporation and Drying

The ratio of moisture content on wet basis to moisture content on dry basis for wheat grain is 4:5. The ratio of weight of dry matter to weight of water in the grain is

Preservation of Food

A refrigeration system based on the reverse Carnot cycle operates between −30 °C and 20 °C. The refrigeration capacity of the system is 70 kW. Heat rejected at the condenser to the atmosphere (hot reservoir), in kW, is nearest to

Heat and Mass Transfer

A 2 mm diameter electric wire is insulated with 2 mm thick plastic. The plastic has a thermal conductivity of 0.5 W·m⁻¹·K⁻¹. The wire is exposed to air at 320 K and the outside convective heat transfer coefficient is 25 W·m⁻²·K⁻¹. Wire surface temperature is constant at 420 K and remains unaffected by the covering. Assuming steady state heat transfer conditions, the ratio of heat loss per metre of wire length with insulation to that without insulation is nearest to (Take π = 3.14)

Size Reduction and Material Handling

In grinding of black pepper, 80% of the feed passes through a 6 mm screen, and 80% of the product passes through a 0.5 mm screen. The gross energy required is 10 kW·h per ton of material. Assuming Bond’s law holds good, and for the same feed conditions, if 80% of the product passes through a 0.2 mm screen, the energy required, in kW·h per ton of material, is nearest to

Evaporation and Drying

A single effect evaporator is used to concentrate orange fruit juice with a 2.7:1 concentration ratio of product solid to feed solid. The juice is fed to the evaporator at 100 kg·h⁻¹ and 30 °C, where the product moisture evaporates at 60 °C. The specific heat of juice is 3.9 kJ·kg⁻¹·°C⁻¹. The latent heat of vaporisation at 60 °C is 2450 kJ·kg⁻¹. Heat to accomplish the evaporation, in MJ·h⁻¹, is nearest to

Evaporation and Drying

At 60 °C dry bulb temperature, saturated water vapour pressure is 20 kPa and relative humidity is 20%. The corresponding absolute humidity of air at atmospheric pressure is nearest to (Take molecular weight of water = 18.02 g·mol⁻¹, molecular weight of air = 28.97 g·mol⁻¹, and atmospheric pressure = 101.325 kPa)

Unit Operations in Dairy and Food Engineering

Pasteurisation of milk can be carried out either at 91 °C for 3 s or at 73 °C for 30 s to inactivate vegetative cells of microorganism(s). The sterilisation value is 10 in both the cases. Thermal death time constant (z value) for reference temperatures of 73 °C and 91 °C, in °C, is nearest to -type split: MCQ — 48 questions; NAT — 17 questions (no MSQ in this paper). Farm Power and Soil & Water Conservation Engineering jointly carry 34 marks — the highest-yield pair. Within Farm Power, Tractors and Power Tillers alone contributed 5 questions (traction theory, ergonomics/noise, final drives, steering hydraulics). Hydrology (Q.25, 58, 59) and Fluid Mechanics — flow in open channels (Q.21, 60) dominated Section 4. Engineering Mathematics stayed formula-direct: Linear Algebra (2), Differential Equations (2), Numerical Methods (2), Calculus (1), Vector Calculus (1), Probability and Statistics (1). Several 1-mark questions (Q.21, Q.28, Q.29) deliberately contained redundant data. Recognising the governing definition — rather than computing with every number given — was the real test. Three high-value NAT questions demanded a non-obvious refinement of the standard formula: Q.54 (Taborek’s kingpin torque relation), Q.59 (Snyder’s duration correction) and Q.62 (riser projection deducted from bench width). Solving with the basic formula alone lands outside the official range in each case.

Engineering Properties of Agriculture Produce

Mass fractions of carbohydrate, protein, fat, ash, and water in banana are 0.220, 0.010, 0.005, 0.015, and 0.750 respectively. The density of carbohydrate, protein, fat, ash, and water are 1550, 1220, 900, 610, and 1000 kg·m⁻³ respectively. The density of banana, in kg·m⁻³, is nearest to

Vector Calculus

The following two vectors are adjacent sides of a parallelogram: $\vec{A} = 2\hat{i} + 3\hat{j} - \hat{k}$ and $\vec{B} = 5\hat{i} - 4\hat{k}$. The area of the parallelogram is ______

Numerical Methods

While solving an equation e⁻ˣ − x = 0 for x, using the Newton-Raphson method with initial guess x₀ = 2, the solution after the first iteration (x₁) is ________ (Rounded off to two decimal places)

Farm Power

A four-cylinder four-stroke engine (100 mm bore and 120 mm stroke) runs at 1800 rpm mean speed with 0.9 MPa indicated mean effective pressure (IMEP). The flywheel constant (ratio of the energy fluctuation to the indicated work per crankshaft revolution) is 0.30. All other losses are neglected. For an allowable speed fluctuation of ±1% about the mean, the required flywheel mass moment of inertia (in kg·m²) is ________. (Rounded off to two decimal places) (Take π = 3.14)

Tractors and Power Tillers

A 2WD tractor has to develop 30 kN gross tractive force at the ground. Rolling radius of the rear wheels is 0.73 m. Each rear wheel is driven by a simple planetary final-drive in which the sun gear (26 teeth) is input, the ring gear (78 teeth) is fixed, and the carrier is bolted to the rear-wheel hub. The sun-planet external mesh efficiency is 98.5%, while the planet-ring internal mesh efficiency is 99%. Losses upstream of the final-drive are neglected. The required sun-shaft input torque per rear wheel (in kN·m) is ________. (Rounded off to two decimal places)

Farm Machinery

A tractor-mounted boom sprayer carries a horizontal row of 12 identical flat-fan nozzles (spray angle 110°). To achieve uniform coverage, the required lateral overlap between adjacent nozzle footprints at the target plane is 30% of a single nozzle footprint. Boom height is 0.60 m above the target plane. The tractor is set to travel at a theoretical forward speed of 8 km·h⁻¹. Wheel slip is 8% and the field efficiency is 75%. All other losses are neglected. The total time (in minutes) required to spray a 25 ha field is ________. (Rounded off to the nearest integer)

Tractors and Power Tillers

A stationary Ackerman-steer tractor on a dry, clean concrete surface carries 12 kN vertical load on each front steered wheel of 0.28 m nominal tyre width (b). Assume uniform pressure distribution on the circular tyre-print area having diameter b. Effective friction coefficient between tyre and surface is 0.30. The steering is individually power-assisted by a single-rod hydraulic cylinder, acting through a pitman arm resulting in a 60 mm effective moment arm. The hydraulic relief valve is set to 8 MPa, and the cylinder bore is 32 mm (ignore rod area). Neglect other losses. The maximum kingpin offset (in mm), which does not cause the maximum allowable kingpin torque to be exceeded, is ________. (Rounded off to the nearest integer) (Take π = 3.14)

Farm Machinery

An 8 × 20 cm seed drill has a 0.60 m diameter ground wheel. On a hard-surface calibration stand, the drill delivers 814 g of seeds in 30 wheel revolutions. When operated in a field having soft soil, the wheel’s effective rolling circumference reduces by 4%. Neglecting other losses, the actual-field seed application rate (in kg·ha⁻¹) is ________. (Rounded off to two decimal places) (Take π = 3.14)

Machine Design

A tractor PTO shaft, through a spur-gear reduction, drives a small grain auger at 540 rpm. The driving gear on the PTO shaft has 0.18 m pitch circle diameter. The auger requires 3.5 kW, transmitted through this gear. Normal force along the line of action between the meshing teeth is 760 N. Assume involute spur gears, single tooth contact, and neglect friction. The pressure angle (in degrees) is ________. (Rounded off to two decimal places) (Take π = 3.14)

Soil Mechanics

A homogeneous earthen embankment has an upstream water level of 12 m. The top width of the embankment is 3 m, and its upstream and downstream slopes (horizontal : vertical) are 2:1 and 2.5:1 respectively. A freeboard of 2 m is provided. The coefficient of permeability of the fill material is 2.5 × 10⁻⁵ m·s⁻¹. If a 20 m long horizontal filter is placed inward from the downstream toe, the seepage discharge per unit length of the embankment is n × 10⁻⁵ m³·s⁻¹·m⁻¹. The value of n is ________. (Rounded off to two decimal places)

Hydrology

A 0.80 km² agricultural watershed has a slope of 0.30% and the maximum length of travel of water is 1 km. The 10-year maximum depth of rainfall is tabulated below: Half of the watershed has row crops (runoff coefficient = 0.40), whilst the other half of the watershed has pasture (runoff coefficient = 0.35). The peak flow rate for the watershed (in m³·s⁻¹) for the 10-year return period is ________. (Rounded off to two decimal places)

Hydrology

Two catchments M and N are meteorologically similar. The basin length (L), length to the centroid (L_ca), and the drainage area (A) of catchment M are 36 km, 18 km, and 250 km² respectively. The L, L_ca and A for catchment N are 50 km, 30 km, and 400 km² respectively. For the 6-h unit hydrograph in catchment M, the peak discharge of 50 m³·s⁻¹ occurs at 12 h from the beginning of the rainfall excess. Using Snyder’s method, the peak of the 6-h unit hydrograph for catchment N (in m³·s⁻¹) is ________. (Rounded off to two decimal places)

Fluid Mechanics

Two rectangular channels, A and B, join to form a large rectangular channel, C. Each rectangular channel is lined with the same material and has the same bottom slope. The bottom widths of Channels A and B are 2 m and 1 m respectively. If the flow depth in each channel is 2 m, the bottom width of Channel C (in m) is ________. (Rounded off to two decimal places)

Groundwater Hydrology

A well fully penetrates a 30 m thick confined aquifer. After a long period of pumping at a constant rate of 0.06 m³·s⁻¹, drawdowns of 3.6 m and 2.0 m are found at distances 60 m and 120 m away from the well respectively. The hydraulic conductivity of the aquifer is n × 10⁻⁴ m·s⁻¹. The value of n is ________ (Rounded off to two decimal places)

Soil and Water Erosion

Bench terraces are planned on a 15% hill slope. The vertical interval is 2.5 m, and the riser has a slope of 1:1. The earthwork in cutting is equal to the earthwork in filling. The volume of earthwork per hectare (in m³·ha⁻¹) is ________ (Rounded off to the nearest integer)

Soil-Water-Plant Relationship

An undisturbed soil sample is collected from a field with a core cylinder having an internal diameter of 60 mm and length of 100 mm. The weights of moist soil and oven dried soil are 0.48 kg and 0.44 kg respectively. Assuming density of water as 1000 kg·m⁻³, the water depth (in metres per metre depth of soil) is ________ (Rounded off to two decimal places)

Soil-Water-Plant Relationship

The crop period is divided into four stages — initial, grand growth, mid-season, and late-season — with each stage spanning 25 days. The crop coefficient varies linearly from 0.4 at the initial stage to 1.2 at the mid-season stage. The reference crop evapotranspiration on the 40ᵗʰ day is 8 mm. The corresponding actual crop evapotranspiration (in mm) is ________ (Rounded off to two decimal places)

Irrigation Water Conveyance and Application Methods

Uniformity of irrigation is checked in a border strip by measuring water penetration depth at 16 equally spaced stations along a border strip. The depths of penetration of water recorded are: 0.65, 0.83, 0.79, 0.87, 0.67, 0.85, 0.86, 0.68, 0.88, 0.77, 0.73, 0.59, 0.89, 0.63, 0.72, 0.70 The distribution uniformity low-quarter (DU_LQ) (in fraction) is ________ (Rounded off to two decimal places)