India · National Testing Agency for ICAR · pg
Computer-based test, 120 minutes, single paper of 120 MCQs, +4 / -1, English. 2026 exam on 4 July 2026. Fills ICAR's all-India quota of Master's seats at agricultural universities.
Eligibility for 7.1 Agricultural Statistics is a BSc in agriculture, horticulture, forestry, sericulture, agricultural marketing, fisheries, veterinary science or agricultural engineering, or a 10+2+3 BSc (alternate eligibility). The 2026 seat table lists Agricultural Statistics seats at about 25 universities, several marked 'NR' (not reported). Group 07 syllabus read in the ICAR AIEEA-PG/AICE syllabus PDF (https://icar.org.in/sites/default/files/Circulars/Syllabus%20AIEEA%20(PG).pdf). Question counts per unit are not published.
Official source: 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 are the supremum and infimum of S = {1 − 1/n : n = 1, 2, 3, …}?
C. sup 1 (not attained), inf 0 (attained)
Terms are 0, 1/2, 2/3, …, increasing towards 1 without reaching it; the minimum 0 occurs at n = 1.
Real Analysis for Statistics · Sets, countability and the real number system
2. The vectors (1, 2, 3) and (2, 4, 6) are:
D. Linearly dependent
The second is twice the first. Their dot product is 28, so they are not orthogonal.
Linear Algebra & Matrix Theory for Statistics · Vector spaces, subspaces, linear independence, basis and dimension
3. A population grows as dN/dt = 0.07N. Its doubling time is about:
B. 9.9 time units
Doubling time = ln 2/r = 0.693/0.07 ≈ 9.9. 14.3 is 1/r, the mean time constant; 70 forgets to divide by the rate in per cent.
Differential Equations, Finite Differences & Numerical Analysis · Ordinary differential equations of first order: exact, linear and Bernoulli equations
4. Which statement describes a genuine limitation of statistics as a science?
D. It studies aggregates and cannot say anything certain about a single individual unit
Statistical laws hold for groups and on average; the mean yield of a variety says nothing certain about one plot. Biological variation is exactly what statistics handles, secondary data are routinely used, and sampling exists precisely to avoid complete enumeration.
Statistical Methods for Agricultural Sciences · Statistics: definition, uses and limitations; frequency distributions and curves
5. As a country's per-capita income rises over decades, what usually happens to agriculture's share of GDP?
A. It falls, while farm output still rises
Structural transformation: Engel's law (food's share of spending falls as income rises) and faster farm productivity growth shrink agriculture's share while output grows.
Agriculture for Statisticians · Importance of agriculture, forestry, livestock and fisheries in national economies
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