UGC NET — Environmental Sciences (subject code 89) · India · National Testing Agency for the University Grants Commission
Original practice questions written to the published syllabus · not past papersThe mathematics and statistics needed for every numerical question in this track: calculus and differential equations for growth and decay, probability and risk, regression and hypothesis tests, and sampling designs for field data. Experimental design and survey sampling in depth live in the Agricultural Statistics track; this subject covers the environmental applications.
In the exams: GATE ES Section 1 (Mathematics Foundation); ICAR AICE subject 71 Unit 7; UGC NET Environmental Sciences Unit 9
How our questions for UGC NET spread across the units of Mathematics & Statistics for Environmental Science. Difficulty: 7 easy, 26 medium, 17 hard.
| Hypothesis tests: t, F and chi-square | 9 | |
| Environmental sampling designs: random, stratified, systematic | 7 | |
| Diversity indices: Shannon, Simpson and evenness | 7 | |
| Descriptive statistics: central tendency, dispersion, skewness, kurtosis | 6 | |
| Probability, conditional probability and Bayes' theorem | 5 | |
| Probability distributions: binomial, Poisson, normal, log-normal | 4 | |
| Correlation, simple and multiple regression | 4 | |
| Risk and reliability; return periods and exceedance probability | 3 | |
| Experimental designs: CRD, RBD, Latin square, split plot | 3 | |
| Linear algebra: matrices, linear systems, eigenvalues | 1 | |
| Calculus: limits, derivatives, maxima and minima, integrals | 1 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
Principal component analysis of water quality data finds components as
D. covariance-matrix eigenvectors
PCA finds the eigenvectors of the covariance matrix (or of the correlation matrix when variables are standardised), ordered by eigenvalue, the variance each explains. Determinants and regression residuals play no part in defining the components.
Further reading: See the manual sources: Kreyszig; Zar; Gilbert; Gomez & Gomez; Chow et al.; Magurran
Which average is most appropriate for summarising log-normally distributed bacterial counts?
A. Geometric mean
Geometric means suit multiplicative, skewed data; regulations often use them for coliforms.
Further reading: See the manual sources: Kreyszig; Zar; Gilbert; Gomez & Gomez; Chow et al.; Magurran
Adding an outlier of 30 to the data 4, 8, 6, 5, 7 changes the median from 6 to
B. 6.5
Ordered 4, 5, 6, 7, 8, 30: median = (6 + 7)/2 = 6.5; the mean jumps to 10, showing the median's robustness.
Further reading: See the manual sources: Kreyszig; Zar; Gilbert; Gomez & Gomez; Chow et al.; Magurran
Why is the sample variance divided by n − 1 rather than n?
B. To give an unbiased estimate of population variance
Bessel's correction: the sample mean is estimated from the same data, which uses up one degree of freedom, so dividing by n underestimates the population variance and dividing by n − 1 removes that bias.
Further reading: See the manual sources: Kreyszig; Zar; Gilbert; Gomez & Gomez; Chow et al.; Magurran
Bayes' theorem expresses P(B | A) as
D. P(A | B)P(B)/P(A)
Bayes' theorem: P(B | A) = P(A | B)P(B)/P(A), reversing a conditional probability by using the prior P(B). P(A)P(B) is the joint probability only for independent events.
Further reading: See the manual sources: Kreyszig; Zar; Gilbert; Gomez & Gomez; Chow et al.; Magurran
What does the central limit theorem state?
D. Means of large samples are near-normally distributed
The central limit theorem: whatever the parent distribution, means of sufficiently large samples are approximately normally distributed, with standard error σ/√n. It says nothing about the raw data themselves being normal.
Further reading: See the manual sources: Kreyszig; Zar; Gilbert; Gomez & Gomez; Chow et al.; Magurran
Why should regression predictions not be extrapolated far beyond the range of observed data?
A. The data do not support the fit there
A fitted regression is supported only within the range of the data; outside it the relationship may change form, so extrapolated predictions have no empirical basis. Software can compute them, which is exactly the danger.
Further reading: See the manual sources: Kreyszig; Zar; Gilbert; Gomez & Gomez; Chow et al.; Magurran
What are the degrees of freedom for a chi-square test of independence in a 3 × 4 contingency table?
B. 6
Degrees of freedom = (rows − 1)(columns − 1) = (3 − 1)(4 − 1) = 2 × 3 = 6. 12 is the number of cells and 11 is cells minus one, the goodness-of-fit rule.
Further reading: See the manual sources: Kreyszig; Zar; Gilbert; Gomez & Gomez; Chow et al.; Magurran
A sample has 20 species among 500 individuals. What is Margalef's richness index, (S − 1)/ln N?
B. 3.06
19/ln 500 = 19/6.215 ≈ 3.06. 0.89 is Menhinick's index; 0.04 is S/N.
Further reading: See the manual sources: Kreyszig; Zar; Gilbert; Gomez & Gomez; Chow et al.; Magurran
In a sample of 500 individuals, the most abundant species has 200. What is the Berger–Parker dominance index?
A. 0.4
Berger–Parker d = Nmax/N = 200/500 = 0.4. 2.5 is its reciprocal, 1/d, and 300 is the count of the remaining individuals.
Further reading: See the manual sources: Kreyszig; Zar; Gilbert; Gomez & Gomez; Chow et al.; Magurran
Ten here, 50 in the app. The Laisha app has every practice question we have written to UGC NET in this subject, marked as you go, with timed papers, a jump-to-unanswered list and a certificate when you pass at 70 per cent.
Free for ten days, then one subscription of US$10 a month. We would rather say so here than have you find it later.
An AI operating system for agriculture: free guides, manuals and tools written for every country.