The ICAR AIEEA PG 2023 Agricultural Engineering and Technology question paper is now available with detailed solutions for free download. ICAR AIEEA PG 2023 was conducted by the National Testing Agency (NTA) on behalf of ICAR on July 9, 2023, and the Agricultural Engineering and Technology paper carried 120 questions in 2 hours.
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ICAR AIEEA PG 2023 Agricultural Engineering Questions with Solutions
The following are the paddy yields (in kg/plot) for 14 plots: 30, 32, 35, 38, 40, 42, 48, 49, 52, 55, 58, 60, 62, 65. The 25th percentile (Q1) yield in kg/plot will be:
Match List-I with List-II.
| List-I (Nature of data) | List-II (Most appropriate measure) |
|---|---|
| (A) Qualitative data | (I) Geometric mean |
| (B) Raw data with extreme values | (II) Median and Mode |
| (C) Dealing with rates, speeds and prices | (III) Mode |
| (D) Calculating relative change | (IV) Harmonic mean |
Consider the following probability distributions.
(A) Normal distribution
(B) Binomial distribution
(C) Poisson distribution
(D) F-distribution
(E) Chi-square distribution
In which of the above distributions are mean and variance equal:
For two invertible matrices A and B of suitable orders, the value of \((AB)^{-1}\) is:
The angle between vectors \(A = 2i - j + 2k\) and \(B = 6i - 3j + 6k\) is:
Synchronous Speed of an AC induction motor depends on:
(A) Frequency of the supply voltage
(B) Number of poles
(C) Current
(D) Voltage
Choose the correct answer from the options given below:
Hydrometer readings are corrected for:
(A) Temperature correction
(B) Meniscus correction
(C) Dispersing agent correction
(D) Pressure correction
Choose the correct answer from the options given below:
Given below are two statements, one labelled as Assertion (A) and the other labelled as Reason (R).
Assertion (A): In case of soils, compressive normal stresses are taken as positive.
Reason (R): Most of the normal stresses acting on soils are compressive in nature.
In light of the above statements, choose the correct answer from the options given below.
Given below are two statements, one labelled as Assertion (A) and the other labelled as Reason (R).
Assertion (A): The current drawn by the motor lags behind the voltage applied.
Reason (R): Motor is an inductive load.
In light of the above statements, choose the correct answer from the options given below.
Consider the following statements:
(A) Real power is expressed in kW.
(B) Apparent power is expressed in kV.
(C) Reactive power does not provide useful mechanical work.
(D) A motor operating at a given load and supply voltage draws active and reactive power.
(E) Both real power and apparent power are expressed in kW.
Choose the correct answer from the options given below:
Given below are two statements:
Statement (I): The porosity of a soil cannot exceed 100 per cent.
Statement (II): The degree of saturation cannot be zero per cent.
In light of the above statements, choose the most appropriate answer from the options given below.
Which of the following statements are true in case of electric fuse:
(A) It is generally made of materials having low melting point.
(B) It is made of materials having high conductivity.
(C) It has inverse time-current characteristics.
(D) It is inserted in series with the circuit to be protected.
Choose the correct answer from the options given below:
Consider the following statements:
(A) Absolute pressure is always positive.
(B) Vacuum can not exceed local atmospheric pressure.
(C) Gage pressure is the difference between absolute pressure and atmospheric pressure.
(D) Negative gauge pressure is same as vacuum.
Choose the correct answer from the options given below:
Consider the following statements related to Mohr failure hypothesis:
Statement (I): Shear stress on the failure envelope is the maximum shear stress in the element.
Statement (II): The maximum shear stress acts on a plane inclined at 45° to major principle plane.
In light of the above statements, choose the most appropriate answer from the options given below.
Which of the following Law's are based on gradient:
(A) Stefan-Boltzmann law
(B) Fourier's law
(C) Newton's law of cooling
(D) Fick's law
Choose the correct answer from the options given below:
Match List-I with List-II:
| List-I (Process) | List-II (Characteristic) |
|---|---|
| (A) Adiabatic | (I) No volume change takes place |
| (B) Isochoric | (II) No pressure change takes place |
| (C) Isobaric | (III) No temperature change takes place |
| (D) Isothermal | (IV) No heat transfer takes place |
Choose the correct answer from the options given below:
A red brick wall of length 5 m, height 4 m and thickness 0.25 m has a temperature on the inner surface of 40 degree C and on the outer surface of 110 degree C. The thermal conductivity of the red brick is k = 0.70 W/mK. What will be the temperature at an interior point of the wall, 20 cm from the inner wall?
Given below are two statements, one is labelled as Assertion (A) and other one labelled as Reason (R).
Assertion (A): Counter flow heat exchanger is more effective than a parallel flow heat exchanger.
Reason (R): For same temperature limits of hot and cold fluids, the overall heat transfer coefficient of counter flow heat exchanger is more than parallel flow heat exchanger.
In light of the above statements, choose the correct answer from the options given below.
Match List-I with List-II.
| List-I (Property) | List-II (Fluid type) | ||
|---|---|---|---|
| (A) | Apparent viscosity decreases with increasing deformation rate | (I) | Dilatant fluids |
| (B) | Shear stress is directly proportional to rate of deformation | (II) | Newtonian fluids |
| (C) | Behaves as a solid until a minimum yield stress is exceeded and subsequently exhibits a linear relation between stress and rate of deformation | (III) | Pseudoplastic fluids |
| (D) | Viscosity increases with increasing deformation rate | (IV) | Bingham-plastic fluids |
| (E) | Shear stress is not directly proportional to deformation rate | (V) | Non-Newtonian fluids |
Choose the correct answer from the options given below.
Bernoulli's equation is conservation of
If a body is in equilibrium, we may conclude that
(A) No force is acting on the body.
(B) The resultant of all the horizontal forces acting on it is zero.
(C) The resultant of all the vertical forces acting on it is zero.
(D) The moments of the forces about any point is zero.
Choose the correct answer from the options given below.
The centre of gravity of a right circular cone of diameter (d) and height (h) lies at a distance of ____________ from the base measured along the vertical radius.
If the moment of inertia of a body along a perpendicular axis passing through its centre of gravity is 50 kg.m2 and the mass of the body is 30 kg. What will be the moment of inertia (kg.m2) of the same body along another axis, which is 50 cm away from the current axis and parallel to it?
The moment of inertia of a triangular section of base (b) and height (h) about an axis passing through its vertex and parallel to the base is ____________ times as that passing through its centre of gravity and parallel to the base.
Which of the following quantities have unit as Newton-metre (N-m)?
A flywheel starts from rest and revolves with an acceleration of \(0.5\ \text{rad/sec}^2\). What will be its angular displacement after 10 seconds?
Which of the following constitute kinematic link?
Given below are two statements:
Kutzback equation between degrees of freedom (n), number of links (l), number of joints (j) and number of higher pairs (h) of a mechanism having plane motion is given by
Select the correct sequence of increasing size (thickness) of clay minerals
Given below are two statements, one is labelled as Assertion (A) and the other one labelled as Reason (R).
Consider the following statements regarding C.I. engine and S.I. engine
An engine has a swept volume of \(300\ cm^3\), clearance volume of \(25\ cm^3\). Its volumetric efficiency is 0.80 and mechanical efficiency is 0.90. The volume of mixture taken in per stroke is
A two stroke cycle gives ____________ the number of power strokes as compared to four stroke cycle engine at the same engine speed.
The overall mechanization level in India ranges from
Match List-I with List-II.
| List-I (Farm Equipment) | List-II (Action) |
|---|---|
| (A) Turn wrest plough | (I) Moves all the soil towards same side. |
| (B) Disc plough | (II) Moves the soil in opposite directions. |
| (C) Disc harrow | (III) Used for shallow ploughing. |
| (D) Vertical disc plough | (IV) Has an arrangement that the plough bottom can be changed from right hand to left hand by rotating it approximately 180 degree. |
| (E) Off-set disc harrow | (V) Well suited for working under low hanging branches in orchards. |
Which seed metering mechanism in a planter brushes out excess seeds from the cells of the feed mechanism?
Which of the following is primary function of broadcaster?
Match List-I with List-II.
| List-I (Field operation) | List-II (Equipment used) |
|---|---|
| (A) Intercultural operation | (I) Rotavator |
| (B) Deep ploughing | (II) Cultivator |
| (C) Soil pulverization | (III) Sub-soiler |
| (D) Conservation tillage | (IV) Strip-till drill |
| (E) Soil Inversion | (V) MB plough |
A flat fan nozzle is most suitable for
Given below are two statements:
Statement (I): Drift is more serious problem with dusts compared to sprays.
Statement (II): Drift can be minimized by producing sprays having small volume mean diameter (VMD).
In light of the above statements, choose the most appropriate answer from the options given below.
Registration and alignment are the cutting knife adjustments related to
Select the most appropriate sequence of involvement of different parts of combine harvester from crop interception to grain collection
(A) Cutter bar
(B) Auger
(C) Straw walker
(D) Cylinder and concave
(E) Reel
Choose the correct answer from the options given below:
As per BIS, for safe use of threshers
(A) The minimum length of feeding chute should be 90 cm.
(B) The feeding chute should be covered up to a minimum length of 45 cm.
(C) The feeding chute should be inclined to the horizontal at an angle of 5-10 degree.
(D) The feeding chute should be made of stainless steel.
(E) The feeding chute should have an alarming system.
Choose the correct answer from the options given below:
Maximum torque in a tractor is generated at speed
Match List-I with List-II.
| List-I (Harvesting machine) | List-II (Crop) |
|---|---|
| (A) Digger | (I) Cotton |
| (B) Reaper | (II) Potato |
| (C) Picker | (III) Cereal crops |
| (D) Snapper | (IV) Forage crops |
| (E) Mower | (V) Maize |
Choose the correct answer from the options given below:
Which of the following is harvesting machine?
(A) Cotton picker
(B) Potato Digger
(C) Mower
(D) Tree shaker
Choose the correct answer from the options given below:
The acceptable work load for average Indian workers is about
Consider the following statements related to biomass conversion techniques.
Statement (I): Thermo-chemical processes have higher efficiencies than bio-chemical processes.
Statement (II): In comparison to bio-chemical conversion techniques, thermo-chemical conversion techniques have superior ability to decompose lignin.
Choose the correct answer from the options given below.
Which country is having a full-fledged Ministry for Development of New and Renewable Resources?
A tractor operated sprayer has 24 nozzles spaced 50 cm apart. Time lost in turning is 8% and filling the tank takes 7% of the time. If the sprayer is operated at a speed of 5 km/h, calculate the coverage area in ha per hour.
The major drawbacks of conventional tillage are categorized as:
(A) Decrease of soil organic matter
(B) Decrease of soil moisture
(C) Short-term potential for soil compaction
(D) Adversely affect the soil structure
Choose the correct answer from the options given below:
Given below are two statements:
Statement (I): The soil texture is defined as the relative proportion, by weight percentage, of sand, silt and clay in soil.
Statement (II): The aeration in fine textured soil is medium to poor.
In light of the above statements, choose the most appropriate answer from the options given below.
A 2-bottom, 50 cm MB plough is being operated at a speed of 5 km/h. If the time lost in turning is 8 per cent, how many hours will be required to plough 23 ha of land?
A bullock drawn country plough cuts a trapezoidal furrow having 16 cm top width and 4 cm bottom width. The depth of ploughing is 15 cm. If the plough forms an angle of 45° with the horizontal and the average soil resistance is 0.71 kg/cm2, calculate the pull exerted by the bullocks in kgf.
The tractor develops a torque of 35 kg-m at an engine speed of 1350 RPM. Calculate the BHP of the tractor.
The volume of tyre filled with water for ballasting purpose is:
Which is the most appropriate method to measure soil tilth?
Match List-I with List-II
| List-I (Link) | List-II (Type of load) |
|---|---|
| (A) Rock shaft | (I) Bending and shear |
| (B) Lower link | (II) Axial |
| (C) Upper link | (III) Axial, bending and shear |
| (D) Lift arm | (IV) Torsion, bending and shear |
Which of the parameter is affected by the peripheral speed of cylinder in thresher?
The undesirable components which need to be removed during refining of crude vegetable oils include:
Match List-I with List-II
| List-I | List-II |
|---|---|
| (A) Falling rate period | (I) Ratio of humidity with respect to humidity at saturation point |
| (B) Absolute humidity | (II) Critical moisture content |
| (C) Percent humidity | (III) Equilibrium moisture content |
| (D) Constant rate period | (IV) Ratio of kg of water vapour in kg of dry air |
When one ton of grain with 25% (wb) moisture content is to be dried to 20% (wb), then the amount of water to be evaporated will be?
Important functions of a septic tank includes:
In the adiabatic drying process, if there is a decrease in the value of dry bulb temperature, then:
Destoner is a form of separator that separates the:
When a mass of grain having an angle of internal friction of 30 degrees is stored in a bin, what will be the Rankine's earth pressure coefficient?
Given below are two statements, one labelled as Assertion (A) and the other labelled as Reason (R).
The COP of a refrigerator working on reverse Carnot cycle (T2 = higher temperature, T1 = lower temperature) is given by:
Which among the following criteria is used for describing shape of an object?
Given below are two statements, one labelled as Assertion (A) and the other labelled as Reason (R).
The uniformity of grind of a powdered sample is indicated by which of the following index?
Which of the following statement(s) holds correct for a screw press?
The effective tension of a belt conveyor -
Cyclone separator design is based on -
Which among the following is a bag storage structure?
Given below are two statements, one is labelled as Assertion (A) and other one labelled as Reason (R).
What is the amount of heat to be removed from 2 tons of apples when cooled from 25°C to 5°C? Specific heat of apple is 0.1 kcal/kg°C.
Frictional force of granular material is -
Which of the following is related to international trade and promotion?
Given below are two statements, one is labelled as Assertion (A) and other one labelled as Reason (R).
Match List-I with List-II.
| List-I | List-II |
|---|---|
| (A) Deep bin | (I) Pulse milling |
| (B) Shallow bin | (II) Janssen |
| (C) Break roll | (III) Rankine |
| (D) CFTRI method | (IV) Wheat milling |
Agricultural waste from which activated carbon can be manufactured include(s)
Given below are two statements, one is labelled as Assertion (A) and other one labelled as Reason (R).
Given below are two statements, one is labelled as Assertion (A) and other one labelled as Reason (R).
The diameter of largest inscribing circle of an object is observed to be 20 mm. What would be the sphericity of the object if diameter of smallest circumscribing circle is 30 mm?
It is found that the energy required to reduce particle from a mean diameter of 10 mm to 5 mm is 1 kJ/kg. Using Rittinger's law, what is the energy requirement to reduce the same from a diameter of 1 mm to 0.5 mm?
Loose housing barn is one in which
Process of freezing food below eutectic temperature and converting solid ice crystals directly into vapour form is known as
Pyrolysis of biomass at a relatively low temperature produces
Given below are two statements:
Statement (I): Soil and water conservation consists of prevention and control of soil erosion caused due to water. It also includes conserving rain water and soil moisture for the purpose of crop production.
Statement (II): Soil erosion severely affects hilly areas because of steep slopes.
In light of the above statements, choose the most appropriate answer from the options given below.
The major activities of the command area development are:
(A) Modernisation and efficient operation of irrigation systems as well as development of main drainage systems.
(B) Construction of field channels.
(C) Land shaping and levelling job are not required.
(D) Construction of field drains.
Choose the correct answer from the options given below:
Given below are two statements:
Statement (I): In the case of moderate rain at non uniform intensities, \(\Phi\)-index will be somewhat higher than the W-index.
Statement (II): These indices vary with initial soil moisture, changes in the depression storage and interception capacity of the area and amount of precipitation.
In light of the above statements, choose the most appropriate answer from the options given below.
Consider the following statements about H-flumes used for runoff measurement:
(A) H-flumes are well suited for runoff measurement as they have a high capacity and are accurate at different rates of flow.
(B) They are also well suited where sediment sampling of the runoff is done using automatic silt samplers.
(C) The H-flume is useful for flows ranging from 0.009 to 0.85 cumec.
(D) For smaller and greater flows the dimensions of the H-flume are modified and are known as HS flumes for smaller flows and HL flumes for larger flows.
(E) H-flumes need not require calibration and the rating tables are to be used for measuring discharges.
Choose the correct answer from the options given below:
Match List-I with List-II
| List-I | List-II |
|---|---|
| (A) Venturimeter | (I) end of pipe |
| (B) Pitot tube | (II) inverted U-tube |
| (C) Orifice | (III) flow coefficient 0.63 to 0.83 |
| (D) Elbow meter | (IV) discharge measurement |
Which instrument does not measure cumulative flow?
Given below are two statements:
Which parameter is not a soil moisture constant?
Which statements are incorrect?
Given below are five statements:
Match List-I with List-II
| List-I | List-II |
|---|---|
| (A) Hygroscopic water | (I) Number of hydrogen nuclei |
| (B) Capillary water | (II) Mean monthly temperature |
| (C) Neutron moisture meter | (III) Adsorption forces |
| (D) Blaney-Criddle | (IV) Surface tension |
Given below are five statements about soil pH:
Given below are two statements:
Given below are two statements:
The limitations to the use of unit hydrographs are:
(A) Snow melt runoff cannot be satisfactorily represented by unit hydrograph.
(B) The catchment should not have unusually large storages in terms of tanks, ponds, large flood bank storages, etc. which affect the linear relationship between storage and discharge.
(C) If the precipitation is decidedly uniform, unit hydrographs can not be expected to give good results.
(D) The rainfall intensity is assumed constant for the duration of the rainfall excess.
(E) The duration of rainfall should be 1/6 to 1/2 of the basin lag.
Choose the correct answer from the options given below:
A 12-h unit hydrograph of a catchment is triangular in shape with a base width of 144h and a peak discharge of 23 cumec. This unit hydrograph refers to a catchment area of
(A) Floods are exceedingly complex natural events. They are resultant of a number of component parameters and are therefore very difficult to model them analytically.
(B) In the regions having same climatological characteristics, if the available flood data are quite insufficient, the enveloping curve technique can be used to develop a relationship between the minimum flood flow and drainage area.
(C) For design purposes, extreme rainfall situations are used to obtain the design storm.
(D) The rational formula is found to be suitable for a peak flow prediction in small catchments upto 75 km\(^2\) in an area.
(E) The rational formula assumes a homogeneous catchment surface.
Choose the correct answer from the options given below:
Given below are two statements:
Statement (I): Chute spillways carry the flow down the steep slopes through a lined channel rather than by dropping the water in a free overfall.
Statement (II): On steep slopes, chutes are more economical than series of drop structures to take the flow down the slope.
In light of the above statements, choose the most appropriate answer from the options given below.
(A) The plan inspection method of land levelling design is adapted for moderate to flat land slopes.
(B) The profile method of land levelling design consists of plotting the profiles of the grid lines and then laying the desired grade on the profiles.
(C) The contour adjustment method of land levelling design consists of a trial and error adjustment of the contour lines on a plan map.
(D) The contour adjustment method is especially adapted to the smoothening of flat lands that are to be irrigated.
(E) The plane method is rarely used for land levelling design.
Choose the correct answer from the options given below:
Given below are two statements:
Statement (I): Water storage efficiency becomes important when water supplies are limited or when excessive time is required to secure adequate penetration of water into the soil.
Statement (II): Water application efficiency decreases as the amount of water applied during each irrigation increases.
In light of the above statements, choose the most appropriate answer from the options given below.
Given below are two statements:
Statement (I): Isotropic and homogeneous aquifers seldom occur in nature.
Statement (II): Water level measurements during pumping test are made in observation wells installed close to the well or at some distance away from it.
In light of the above statements, choose the most appropriate answer from the options given below.
(A) In levelling, datum surface is an arbitrary surface with reference to which the elevations of the points are measured and compared.
(B) The line of collimation or the line of sight is the line joining the intersection of the cross-hairs to the optical centre of the object glass and its continuation.
(C) A foresight is the first staff reading taken after setting up the instrument in any position.
(D) The height of instrument is the elevation of the plane of collimation when the instrument is levelled.
(E) A change point indicates the shifting of the instrument, both back sight and intermediate sight are taken on this change point.
Choose the correct answer from the options given below:
Match List-I with List-II.
| List-I | List-II |
|---|---|
| (A) Close contour lines | (I) Foot hill |
| (B) Wider contour lines | (II) Higher contour values outside |
| (C) Depression | (III) At right angles |
| (D) Crossing of ridge lines | (IV) Top of hill |
Which points should be kept in mind while selecting the stations?
The design of bench terraces consists in determining the
Which land capability classes are suitable for pastures?
Orchard benched terraces has a width of about
A quantity of 100ml gypsum solution having 36 meq/l concentration as calcium, on reacting with 5gm of an alkali soil showed 32 meq/l of Ca+Mg concentration in the filtrate. Estimate the gypsum requirement in meq/100gm of soil.
Convert 1300 ppm sodium chloride salt concentration into meq/l
Given below are two statements:
ICAR AIEEA PG 2023 Agricultural Engineering Exam Pattern and Marking Scheme Explained
As per the NTA information bulletin on the official website (exams.nta.nic.in/icar), every ICAR AIEEA PG subject paper follows the same fixed format, and Agricultural Engineering and Technology is no different.
- Total questions: 120 MCQs, all from the Agricultural Engineering and Technology subject group
- Duration: 2 hours (120 minutes), computer-based test
- Total marks: 480
- Marking scheme: +4 for a correct answer, -1 for a wrong one, 0 for not attempting
- Question types: single-correct MCQs, several with assertion-reason pairs and match-the-following lists
High-Weightage Subjects in ICAR AIEEA PG 2023 Agricultural Engineering to Focus On First
Going question by question through this paper, three areas alone account for close to half the marks.
- Post-harvest engineering was the single biggest area, with 22 of the 120 questions covering drying, storage, milling, oil expression and refrigeration
- Soil and water conservation engineering followed with 18 questions, including runoff, hydrographs and land levelling
- Farm machinery made up 15 questions, spanning tillage implements, seeding and harvesting equipment
- Farm structures and grain storage design accounted for 7 questions
- Irrigation and drainage engineering added another 7 questions between design and command area development topics
- Farm power, IC engines and theory of machines together made up close to 10 more questions, so engine and mechanism basics are still worth a quick revision
ICAR AIEEA PG 2023 Agricultural Engineering Question Paper Analysis Video
Source: AgriAddict: English Medium
How to Use the ICAR AIEEA PG Agricultural Engineering Question Paper for Practice
Since ICAR AIEEA PG has no sectional cutoff within a subject paper, treat this as one full 2-hour mock rather than solving it topic by topic.
- Solve all 120 questions in one sitting under the real 2-hour limit before you look at the solutions PDF
- Score yourself with the +4/-1 scheme so you know your real net marks out of 480
- Review every post-harvest engineering and soil and water conservation question first, since together they are almost a third of the paper
- Redo the assertion-reason and match-the-following questions separately, they came up more than a dozen times in this paper and reward careful reading over speed
ICAR AIEEA PG Agricultural Engineering Preparation Priority List
- Post-harvest engineering and soil and water conservation together, since they cover a third of the paper
- Farm machinery and tillage implements next, given their steady 12 percent share
- Farm power, IC engines and theory of machines as a supporting block, not the main focus
ICAR AIEEA PG 2023 Agricultural Engineering Question Paper FAQs
Ques. How many questions were there in the ICAR AIEEA PG 2023 Agricultural Engineering and Technology paper?
Ans. The paper had 120 multiple-choice questions worth 480 marks total, with +4 for every correct answer and -1 for every wrong one, in a 2-hour computer-based test.
Ques. Which topics had the highest weightage in ICAR AIEEA PG 2023 Agricultural Engineering?
Ans. Post-harvest engineering led with 22 of 120 questions, followed by soil and water conservation engineering with 18 and farm machinery with 15. These three topics alone made up close to half the paper.
Ques. Are ICAR AIEEA PG Agricultural Engineering questions repeated from previous years?
Ans. Core numerical types, like field capacity calculations, moisture removal problems and parallel axis theorem questions, repeat in concept every year even though the exact numbers change, so solving multiple past papers of this subject is worth your time.
Ques. How is ICAR AIEEA PG 2023 different from the ICAR AIEEA UG exam?
Ans. AIEEA PG is a subject-specific 120-question paper used for admission to ICAR-affiliated master's programmes, while AIEEA UG is a common entrance test for undergraduate agriculture admissions with a different, broader syllabus.
Ques. Where can I download the ICAR AIEEA PG 2023 Agricultural Engineering question paper with solutions PDF for free?
Ans. Use the download table at the top of this page for the free question paper and solutions PDF. For the official question paper and answer key, check the NTA ICAR portal at exams.nta.nic.in/icar.
Ques. What subjects does ICAR AIEEA PG Agricultural Engineering and Technology cover?
Ans. This paper draws from farm machinery, farm power and IC engines, soil and water conservation engineering, irrigation and drainage engineering, post-harvest engineering, farm structures, surveying, and engineering mechanics and mathematics.








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