Computer-based test, 2 hours, 120 MCQs, +4 / -1 (Part A general, Part B core group, Part C subject). 2026 exam held with AIEEA-PG in July 2026.
Sections
Subject 68 Agricultural Statistics - Unit 1 Statistical Methods I: probability, distributions, limit theorems, point and interval estimation (Cramer-Rao, Rao-Blackwell, Lehmann-Scheffe), Neyman-Pearson, UMP and likelihood-ratio tests
Unit 2 Statistical Methods II: correlation and regression, model adequacy, compound and truncated distributions, order statistics, non-parametric tests, contingency tables, log-linear models, SPRT, time-series components, multivariate analysis, linear programming
Unit 3 Statistical Genetics: segregation and linkage, population genetics, polygenic variance, inbreeding, G x E and stability, heritability, path analysis, diallel and line x tester, selection response and selection indices
Unit 4 Design of Experiments: linear models, Gauss-Markoff, uniformity trials, CRD, RCBD, Latin square, factorials and confounding, split- and strip-plot, crossover, multiple comparisons, missing plots, ANCOVA, transformations, BIBD, PBIBD, lattice, Youden square, groups of experiments
Unit 5 Sample Surveys: SRS, stratified, ratio and regression, systematic, cluster and multistage, PPS, double sampling, successive occasions, non-sampling errors, randomised response, imputation, large-scale surveys, the agricultural statistics system and crop estimation surveys
Subject 69 Bioinformatics: molecular biology, bioinformatics databases and alignment, genome assembly, evolutionary biology and phylogenetics, statistical genomics
Subject 70 Computer Application: architecture, programming (C++/Java), internet programming, data structures, software engineering, networking, compilers, operating systems, DBMS, numerical analysis and statistical methods
Over the years
Unit lists read in the ICAR AICE-JRF/SRF syllabus PDF (https://icar.org.in/sites/default/files/Circulars/Syllabus%20AICE%20JRF_SRF%20(PhD).pdf). The core-group number that holds these subjects in the 2026 bulletin could not be read (the bulletin PDF is a scanned image), so the Part B core-group content is not verified.
Original questions written to this exam's published syllabus and pattern. Not past papers.
1. In the one-way model yᵢⱼ = μ + τᵢ + εᵢⱼ with 4 treatments, the design matrix has 5 columns. Its rank is:
4
5
3
6
Answer and working
A. 4
The μ column equals the sum of the four treatment columns, so the rank is 4; only contrasts in τ are estimable.
Linear Algebra & Matrix Theory for Statistics · Rank, nullity and row-reduced echelon form
2. The equilibrium of a linear system x′ = Ax is stable when the eigenvalues of A:
Are all positive
Are all equal to one
All have negative real parts
Are purely imaginary with large magnitude
Answer and working
C. All have negative real parts
Solutions combine e^(λt) terms, which decay only if Re(λ) < 0.
Differential Equations, Finite Differences & Numerical Analysis · Higher-order linear equations: complementary function and particular integral
3. About which value is the sum of absolute deviations Σ|x − a| of a data set smallest?
The median
The arithmetic mean
The mode
The mid-range
Answer and working
A. The median
Σ|x − a| is minimised when a is the median, while Σ(x − a)² is minimised at the mean. Confusing the two properties is the common error.
Statistical Methods for Agricultural Sciences · Measures of central tendency: arithmetic, geometric and harmonic means, median and mode
4. A pathologist reports the mean disease score (0-9 scale) of each fungicide as 4.37 ± 0.21. What assumption does this summary make?
That the scores are measured on a nominal scale with no order
That the scores follow a Poisson distribution with equal mean and variance
That the steps between successive scores are equal in size
That every plot was scored by more than one observer independently
Answer and working
C. That the steps between successive scores are equal in size
Averaging treats the scores as interval data with equal gaps. That is often only approximately true for visual scales, so medians or rank and ordinal-model methods are alternatives.
Exploratory Data Analysis & Statistical Graphics · Types of data and measurement scales
5. Which is not one of Knuth's properties of an algorithm?
Finiteness: it must stop after finitely many steps
It must be written in a compiled language
Definiteness
Effectiveness
Answer and working
B. It must be written in a compiled language
An algorithm is language-independent; finiteness, definiteness, input, output and effectiveness are its properties.
Programming for Statistics & Data (R and Python) · Algorithms, flowcharts and pseudocode
Practise it, and prove it
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