Unit VII: Surveying, hydrology, irrigation, soil and water conservation, groundwater and pumps, drainage, salinity
Over the years
Admission to M.Tech in agricultural universities and the ICAR-PG scholarship. Sub-subjects for counselling: 10.1 SWCE, 10.2 IDE, 10.3 Processing and Food Engineering, 10.4 FMPE, 10.5 REE. Wider than GATE AG: electric motors (Unit II) and farmstead planning are examined here but not in GATE AG. Question papers are not published, so no topic-frequency data exists. 2026 bulletin: https://cdnbbsr.s3waas.gov.in/s388a839f2f6f1427879fc33ee4acf4f66/uploads/2026/05/202605091397132773.pdf
Original questions written to this exam's published syllabus and pattern. Not past papers.
1. What is the determinant of the matrix A = [[2, 1, 3], [0, 4, 5], [1, 0, 6]] (rows listed in order)?
31
41
48
65
Answer and working
B. 41
Expand along the first row with the sign pattern + − +: det = 2(4·6 − 5·0) − 1(0·6 − 5·1) + 3(0·0 − 4·1) = 48 + 5 − 12 = 41. Taking every cofactor sign as + gives 31; flipping the sign of the third term as well gives 65; multiplying only the diagonal (48) is valid only for a triangular matrix.
Engineering Mathematics · Matrices, determinants and systems of linear equations
2. Six grain samples from one bin give moisture contents (per cent, wet basis) of 12.1, 13.4, 11.8, 12.9, 13.6 and 12.4. What is the sample standard deviation?
0.658
0.520
0.721
0.600
Answer and working
C. 0.721
Mean = 76.2/6 = 12.7000. Sum of squared deviations = 2.6000. Sample variance = 2.6000/(n − 1) = 2.6000/5 = 0.5200, so s = 0.721. Dividing by n = 6 gives the population SD 0.658; 0.520 is the variance, not the SD; 0.600 is the mean absolute deviation.
Probability, Statistics & Data Analysis · Measures of central tendency and dispersion
3. Varignon's theorem, used to simplify moment calculations, states that:
The moment of a force about a point equals the sum of the moments of its components about that point
Three concurrent forces in equilibrium are each proportional to the sine of the angle between the other two
A force may be slid along its own line of action without changing its external effect on a rigid body
The resultant of two forces is the diagonal of the parallelogram drawn with the two forces as adjacent sides
Answer and working
A. The moment of a force about a point equals the sum of the moments of its components about that point
Varignon's theorem is the principle of moments: resolve the force into components and add their moments. The Lami statement, the principle of transmissibility and the parallelogram law are separate results that are often confused with it.
Engineering Mechanics (Statics & Dynamics) · Force systems and resultants
4. One megapascal (MPa), the unit most used for stress in machine design, is equal to:
1 N/m²
1 kN/mm²
1 N/mm²
1 kN/cm²
Answer and working
C. 1 N/mm²
1 MPa = 10⁶ N/m² and 1 m² = 10⁶ mm², so 1 MPa = 1 N/mm². That is why working in N and mm gives stress directly in MPa. 1 N/m² is 1 Pa; 1 kN/mm² is 1 GPa; 1 kN/cm² is 10 MPa.
Strength of Materials · Stress, strain and Hooke's law
5. In a program flowchart drawn to ISO 5807, which symbol shows a point where the flow splits according to a yes/no test, such as 'Is soil moisture below the refill point?'
A diamond with one entry line and two labelled exit lines
A rounded oval placed only at the start and the end
A parallelogram with one entry line and one exit line
A rectangle with double vertical lines on its two sides
Answer and working
A. A diamond with one entry line and two labelled exit lines
The decision symbol is a diamond with labelled exits (yes/no). A parallelogram is input/output, a rectangle with double side lines is a predefined process (subroutine), and the oval is the terminal symbol.
Computer Programming, Data Structures & Agricultural Informatics · Algorithms and flowcharts
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