GATE AG 2025 Question Paper & Solutions

Verbal Aptitude

Ravi had ______ younger brother who taught at ______ university. He was widely regarded as ______ honorable man. Select the option with the correct sequence of articles to fill in the blanks.

Verbal Aptitude

The CEO's decision to downsize the workforce was considered myopic because it sacrificed long-term stability to accommodate short-term gains. Select the most appropriate option that can replace the word “myopic” without changing the meaning of the sentence.

Quantitative Aptitude

The average marks obtained by a class in an examination were calculated as 30.8. However, the marks of one student were entered incorrectly as 24 instead of 42. After correcting the marks, the average becomes 31.4. How many students does the class have?

Analytical & Spatial Aptitude

P is the brother of Q; S is the daughter of Q; T is the sister of S; R is the mother of Q. Which statement(s) are correct? (1) R is the grandmother of S. (2) P is the uncle of S and T. (3) R has only one son. (4) Q has only one daughter.

Analytical & Spatial Aptitude

According to the map shown (Library & Physics Lab on the NW block; Canteen & Hospital on the NE block, across 1st Main Road; Hostels & Classrooms on the SW block; Chemistry Lab on the SE block, across 5th Cross Road), which statement is correct?

Analytical & Spatial Aptitude

Passage from G.K. Chesterton's “A Piece of Chalk” about objects carried in a pocket. Based only on the passage, which statement is true?

Quantitative Aptitude

Lines QR and ST are parallel; the shortest distance between them is half the shortest distance between point P and line QR. Find the ratio of area(ΔPST) to area(trapezium SQRT).

Quantitative Aptitude

A fair six-faced die is rolled thrice. What is the probability of rolling ‘6’ exactly once?

Analytical & Spatial Aptitude

A square paper is folded twice as shown and then cut; identify the pattern obtained on unfolding.

Quantitative Aptitude

A shop has 4 distinct flavors of ice-cream; scoops of any flavor can be repeated and order doesn't matter. In how many ways can 3 scoops be purchased?

Linear Algebra

If $a, b, c$ are the roots of $2x^3 - 3x^2 + px - 1 = 0$ and the sum of two of the roots is 1, find $p$:

Linear Algebra

If the matrix $\begin{bmatrix} x & -3 \\ 2 & x-5 \end{bmatrix}$ is singular, find the sum of the values of $x$.

Differential Equations

s/(s²+a²) is the Laplace transform of:

Differential Equations

y″ + p(x)y′ + q(x)y = r(x) is a ________ ordinary differential equation.

Probability and Statistics

Find the median of: 154, 130, 144, 137, 156, 146, 138, 149, 160, 138.

Hydrology

Which method is used for the geophysical exploration of groundwater?

Surveying and Levelling

Identify the correct statement related to tape correction in chain surveying:

Farm Power

Find the sphericity (Wadell's, surface-area based) of a cylindrical potato sample with diameter 1.0 cm and length 5.0 cm.

Preservation of Food

The condition of refrigerant at the exit of the compressor in a vapor compression refrigeration system is:

Farm Machinery

Mustard seeds (bulk density = 800 kg/m³) are sown with a four-row fluted roller seed drill, 25 cm row spacing, at 2.5 km/h. For a desired seed rate of 5.0 kg/ha, find the volumetric flow rate of seeds from the machine (m³/h).

Farm Power

By tripling the RMS sound pressure, the resulting increase in sound pressure level (dB) is closest to:

Tractors and Power Tillers

For vertical motion at the tractor seat base, θ (rad) is rotation about the tractor's CG and R is the longitudinal distance from operator's seat to CG. For small θ, 'Rθ' represents vertical motion resulting from tractor's ____________.

Processing of Agriculture Produce

In rice milling, the rubber roll sheller is used for:

Unit Operations in Dairy and Food Engineering

In general, result(s) of blanching fresh fruits and vegetables is/are:

Agricultural Drainage

Identify the adverse effect(s) due to soil salinity or alkalinity or both:

Hydrology

Match the isolines in Column I with the corresponding meteorological or hydrological variables in Column II: | Column I | Column II | |---|---| | P. Isopleth | 1. Rainfall | | Q. Isobath | 2. Pressure | | R. Isohyet | 3. Evapotranspiration | | S. Isochrone | 4. Groundwater | | T. Isobar | 5. Surface runoff |

Irrigation Water Conveyance and Application Methods

Identify correct statement(s) for sprinkler irrigation:

Farm Power

Which method(s) is/are generally used in spark ignition engines for evaluating volatility?

Tractors and Power Tillers

Nominal rear-wheel radius of a 2WD tractor = 0.5 m; rolling radius is 6% less than nominal. Field test: 20 revolutions of the rear wheel cover 56 m. Find rear-wheel slip (%). (Rounded to 2 decimal places)

Tractors and Power Tillers

Front-wheel pivot points of a 2WD tractor are 1.2 m apart. Turning on flat concrete, inner wheel steering angle = 50°, outer wheel steering angle = 35°. For turning without front-wheel skid, find the wheelbase (m). (Rounded to 2 decimal places)

Hydrology

An unconfined aquifer, hydraulic conductivity 12 m/day, covers 1.0 ha. Pumping releases 6000 m³ of water and water table drops from 3 m to 7 m below ground. Find the specific yield (%). (Answer in integer)

Evaporation and Drying

Apple slices dry from 65% (d.b.) to 10% (d.b.) in a hybrid solar dryer, falling rate period, drying rate constant = 1/104 min⁻¹, equilibrium moisture content 2% (d.b.). Find the drying time (min). (Rounded to 2 decimal places)

Evaporation and Drying

Find the water needed to raise the moisture content of 50 kg paddy grains from 13% (d.b.) to 35% (d.b.) in a hydrothermal treatment process (kg). (Rounded to 2 decimal places)

Size Reduction and Material Handling

Find the critical speed (rpm) of a ball mill, mill diameter 3600 mm, ball diameter 160 mm (g = 9.81 m/s², π = 3.14). (Answer in integer)

Heat and Mass Transfer

Three straight metal wires AC, BC, CD (same length, diameter, thermal conductivity) are connected as a Y; heat flows from A and B to C, then from C to D. T_A=100°C, T_B=100°C, T_D=40°C. Find T_C (°C), steady state, no heat loss. (Answer in integer)

Calculus

The series Σ(n=0 to r) qⁿ = 1 + q + q² + ... has the sum:

Calculus

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

Calculus

If $u = x^4 + y^4 + 3x^2y^2$, find the value of $\left(x\frac{\partial u}{\partial x} + y\frac{\partial u}{\partial y}\right)^{-1}$:

Groundwater Hydrology

Steady flow condition in a confined aquifer occurs when:

Soil-Water-Plant Relationship

Lysimeter is an instrument used to measure the following process(es):

Preservation of Food

Identify the assumption(s) which is/are NOT correct for deriving Plank's equation for food freezing time.

Evaporation and Drying

Match psychrometric processes (Sensible cooling; Cooling & dehumidification; Chemical dehumidification; Heating & humidification) with the thermodynamic property changes.

Differential Equations

Find $y$ at $x = 0.3$, given $y(0) = 0$, for $\frac{dy}{dx} = 3y + 2e^x$. (Rounded to 3 decimal places)

Sources of Power

A flat plate solar collector at Bhopal (23°15′N, 77°42′E), tilted 30° from horizontal, facing due South. For hour angle 45° (3:00 PM LAT) on June 30, 2023, find the angle of incidence of beam radiation on the collector (degrees). (Rounded to 2 decimal places)

Wells and Pumps

A six-stage centrifugal pump delivers 150 L/s at a net pressure rise of 5003 kN/m², impeller speed 1450 rpm, g = 9.81 m/s². Find the specific speed. (Answer in integer)

Fluid Mechanics

Water flows through a 90° V-notch weir, Cd = 0.6, head above notch H = 49 cm, g = 9.81 m/s². Find the discharge (m³/s). (Rounded to 2 decimal places)

Soil Mechanics

An undisturbed soil sample: volume 100 cm³, void ratio 0.60. Oven-dry mass reduces from 185 g to 165 g (no volume change). Specific gravity 2.64. Find the degree of saturation (%). (Rounded to 2 decimal places)

Hydrology

A 10 ha watershed: rainfall 15 mm, ET 5 mm, infiltration 4.5 mm, deep percolation 2.2 mm, detention storage 0.5 mm, other abstraction losses 0.3 mm during a storm. Neglecting other surface storages, find the total overland flow (m³). (Answer in integer)

Soil and Water Erosion

A windbreak of height 2.7 m protects a wheat field. Actual wind velocity (perpendicular, at 15 m height) = 9 m/s; minimum velocity to move the most erodible soil fraction = 9.6 m/s. Find the distance of full protection (m). (Rounded to 2 decimal places)

Soil and Water Erosion

A stable drop structure has base length 5.7 m. ΣVertical forces (excl. uplift) = 92.5 kN; Σuplift = 72.5 kN; Σmoments about the mid-section axis = 60 kN·m. Find the eccentricity of the resultant vertical force from the centroid of the base (m). (Rounded to 2 decimal places)

Hydrology

An 8 ha watershed receives rainfall intensities 2.5, 3.6, 5.4, 3.3, 2.6, 1.2 cm/h at successive 30-min intervals. Surface runoff volume = 4800 m³. Neglecting initial abstraction, find the W-index (cm/h). (Rounded to 2 decimal places)

Farm Power

A 4-stroke diesel engine: displacement 6.0 L, 2300 rpm, 75% mechanical efficiency, indicated mean effective pressure 800 kPa, brake-specific fuel consumption 320 g/h/kW, calorific value 44.6 MJ/kg. Find the fuel equivalent power (kW). (Rounded to 2 decimal places)

Tractors and Power Tillers

Engine torque-speed data: T_maxP=125 N·m at N_maxP=2400 rpm; N_HI (high idle)=2600 rpm; T_max=160 N·m at N_maxT=1450 rpm. Find the Governor's regulation (%). (Rounded to 2 decimal places)

Tractors and Power Tillers

An engine at 1200 rpm drives a 1.2 m diameter rigid wheel on a non-deformable surface at 5 km/h forward speed, through a gearbox (3:1), differential (4:1), and final drive (n:1). Neglecting wheel deformation/slip, find n. (Rounded to 2 decimal places)

Machine Design

A solid round uniform-diameter shaft transmits 25 kW at 540 rpm. Allowable shear stress = 35 MPa. Maximum torque exceeds mean torque by 20% (bending neglected). Find the minimum shaft diameter (mm). (Rounded to 2 decimal places)

Tractors and Power Tillers

A 4WD tractor has equal front/rear tread = 1.25 m; CG height = 0.85 m. The tractor overturns during turning at 18 km/h. Neglecting frictional forces on the wheels, find the turning radius (m). (Rounded to 2 decimal places)

Sources of Power

A horizontal-axis wind turbine (24 m diameter blades), average wind velocity 6.0 m/s, average air density 1.23 kg/m³, is used for pumping irrigation water. Cp = 0.3, transmission efficiency 90%, pump efficiency 60%. Find the pump discharge (L/s) for a total head of 20 m. (Rounded to 2 decimal places)

Farm Machinery

A mouldboard plough is operated by a 2WD tractor; the resultant soil-reaction pull is 6.0 kN. Lateral:longitudinal force ratio = 0.30, vertical:longitudinal ratio = 0.50. Driving-wheel diameter = 1.2 m, rear axle speed = 10 rpm, wheel slip = 20%. Find drawbar power (kW). (Rounded to 2 decimal places)

Farm Machinery

For a right-hand offset disc harrow, front and rear gang centers are 2.5 m and 4.5 m (longitudinally) from the hitch point. Longitudinal soil forces on front/rear gangs = 3.0/3.5 kN; lateral soil forces = 2.5/4.0 kN (front/rear gangs throw soil in opposite lateral directions). Find the offset of the center of cut from the hitch point (m). (Rounded to 2 decimal places)

Size Reduction and Material Handling

Locust beans (avg. particle diameter 7 mm) are ground at 10 ton/h to 0.62 mm, consuming 6.7 kW. Using Rittinger's law, find the power (kW) to grind to 0.25 mm at the same rate. (Rounded to 2 decimal places)

Heat and Mass Transfer

N₂ and He mixture in a pipe at 1.0 atm, 298 K. Partial pressure of N₂ = 60.80 kPa at one point and 20.31 kPa at a point 0.22 m away. Diffusion coefficient = 0.612×10⁻⁴ m²/s. R = 8314 m³·Pa/(kgmol·K). Steady-state flux of N₂ = n×10⁻⁶ kgmol/(s·m²). Find n. (Rounded to 2 decimal places)

Heat and Mass Transfer

Milk (25°C) enters the inner pipe of a concentric double-pipe heat exchanger; hot water (82.5°C, 1.2 kg/s) flows countercurrently through the annulus. Inner-pipe diameter 60 mm, length 6 m, overall U = 2100 W/m²K. cp,water=4.18, cp,milk=3.95 kJ/kg·K. Effectiveness = 0.572, NTU = 1.01. Find the hot-water exit temperature (°C). (Rounded to 1 decimal place)

Preservation of Food

Peas (0.5 kg/can) are processed at 121°C. Clostridium spp. spores: initial level 5×10¹⁰/can, D-value 2.5 min. Desired spoilage probability = 5/100 cans. Bacillus spp. D-value 6.0 min, same lethality applied to both. Find the initial number of Bacillus spores per g of peas. (Answer in integer)

Size Reduction and Material Handling

Apple juice (viscosity 1.6 cP) is filtered through a 2 m² filter at constant pressure; solid concentration in filtrate = 0.04 g/mL; total pressure drop = 325.33 kPa; cake resistance α = 1.85×10¹¹ m/kg, filter-medium resistance Rm = 3.50×10¹¹ m⁻¹. Find the time to filter 800 L (hour). (Answer in integer)

Storage Systems

A cylindrical concrete silo (6 m internal diameter, 24 m height) is filled with rough rice (bulk density 635 kg/m³). Wall-friction angle = 30°; lateral/vertical pressure ratio = 0.4. Find the ratio of lateral pressure at 10 m depth to that at 5 m depth. (Rounded to 2 decimal places)