India · IITs and IISc on rotation (2026: IIT Guwahati) · pg
Computer-based, 3 hours, 100 marks (15 General Aptitude + 85 technical: 25 one-mark and 30 two-mark questions). MCQ, MSQ and NAT; negative marking on MCQ only (−1/3 for one-mark, −2/3 for two-mark); no partial credit on MSQ. On-screen virtual calculator.
Used for M.Tech/PhD admission and some PSU and government screening. The 7-section syllabus dates from the GATE 2021 revision; the 2024 and 2026 texts are word-for-word identical. Only Mathematics has an official weight; Laisha's count of the 2019–2026 papers gives technical-mark averages of about 11 (machinery), 13.5 (power), 16 (soil and water conservation), 9 (irrigation and drainage), 14 (process) and 9 (dairy and food). About 80–88% of technical marks need a calculation. Official reports: 2,362–2,624 candidates appeared each year in 2024–2026, qualifying mark 25 for the general category. Allowed two-paper combination: AG + CE.
Official source: https://gate2026.iitg.ac.in/doc/GATE2026_Syllabus/AG_2026_Syllabus.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)?
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?
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. A 3000 kg tractor stands on level ground. Its wheelbase is 2.4 m and its centre of gravity is 0.8 m ahead of the rear axle. What is the static load on the front axle?
C. 9.81 kN
W = 3000 x 9.81 = 29.43 kN. Moments about the rear-wheel contact: Rf x 2.4 = 29.43 x 0.8, Rf = 9.81 kN. 19.62 kN is the rear-axle load; 14.71 kN assumes an even split; 1.00 kN uses mass in kg as if it were force.
Engineering Mechanics (Statics & Dynamics) · Free-body diagrams and equilibrium
4. A round steel implement bar tapers uniformly from 40 mm to 20 mm diameter over a length of 1 m and carries an axial load of 60 kN. With E = 200 GPa, its elongation is closest to:
D. 0.477 mm
For a linearly tapered circular bar, δ = 4PL/(πE d₁ d₂) = 4 × 60,000 × 1000/(π × 200,000 × 40 × 20) = 0.477 mm. Using the average diameter of 30 mm gives 0.424 mm, which underestimates because stress rises faster than linearly towards the small end. Using the small-end area (20 mm) throughout gives 0.955 mm, and the large-end area (40 mm) gives 0.239 mm.
Strength of Materials · Stress, strain and Hooke's law
5. How many links does a 20 m metric chain have, and what is the length of one link?
D. 100 links of 0.2 m
A 20 m metric chain has 100 links, so each link is 20/100 = 0.2 m. The 30 m chain has 150 links of 0.2 m, which is where 150 links comes from; Gunter's chain also has 100 links but is 66 ft long. 200 links of 0.1 m describes a tape graduated in decimetres, not a chain.
Surveying & Levelling · Chain and tape surveying, including tape corrections
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