CUET-PG - Statistics

India · National Testing Agency · pg · unverified source

914practice questions written to this syllabus
18subjects

Format

Computer-based MCQ test used by central and participating universities for MSc Statistics admission.

Sections

Over the years

Built from Laisha's knowledge because the official page could not be opened or was not found during research (web search quota exhausted); confirm against the body's current notification before relying on it. Paper codes and question counts change between years.

Official source: https://exams.nta.ac.in/CUET-PG/

Subjects this exam draws on

Real Analysis for Statistics26 questionsLinear Algebra & Matrix Theory for Statistics13 questionsDifferential Equations, Finite Differences & Numerical Analysis10 questionsStatistical Methods for Agricultural Sciences80 questionsExploratory Data Analysis & Statistical Graphics18 questionsProbability Theory85 questionsProbability Distributions & Sampling Distributions66 questionsStochastic Processes33 questionsStatistical Inference I: Estimation70 questionsStatistical Inference II: Testing of Hypotheses & Sequential Analysis70 questionsNonparametric & Rank-Based Methods69 questionsMultivariate Analysis60 questionsCategorical Data Analysis & Generalized Linear Models75 questionsBayesian Inference59 questionsDemography & Vital Statistics21 questionsBioassay, Survival & Epidemiological Statistics61 questionsOptimization Techniques for Statisticians35 questionsStatistical Quality Control & Reliability63 questions

Five practice questions, worked

Original questions written to this exam's published syllabus and pattern. Not past papers.

1. Which of these sets is uncountable?

  1. The real numbers in (0, 1)
  2. The rational numbers (fractions p/q)
  3. The integers
  4. The set of all finite subsets of N
Answer and working

A. The real numbers in (0, 1)

Cantor's diagonal argument shows (0, 1) is uncountable. Q and Z are countable, and finite subsets of N can be listed by size and largest element.

Real Analysis for Statistics · Sets, countability and the real number system

2. Which subset of R³ is a subspace?

  1. The plane x + y + z = 1
  2. The plane x + y + z = 0
  3. The set of vectors with x ≥ 0
  4. The union of the x-axis and the y-axis
Answer and working

B. The plane x + y + z = 0

A subspace must contain 0 and be closed under addition and scaling; x + y + z = 1 misses 0, x ≥ 0 fails under negation, and the union of two axes is not closed under addition.

Linear Algebra & Matrix Theory for Statistics · Vector spaces, subspaces, linear independence, basis and dimension

3. The equation (2xy + 3)dx + (x² + 4y)dy = 0 is exact because:

  1. M and N are both polynomials
  2. ∂M/∂y = ∂N/∂x = 2x
  3. ∂M/∂x = ∂N/∂y
  4. M = N at the origin
Answer and working

B. ∂M/∂y = ∂N/∂x = 2x

M = 2xy + 3 gives ∂M/∂y = 2x; N = x² + 4y gives ∂N/∂x = 2x.

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?

  1. It cannot be applied to biological data because living organisms vary too much
  2. It can only handle data collected by the investigator personally, never secondary data
  3. It requires every unit of a population to be measured before any conclusion is drawn
  4. It studies aggregates and cannot say anything certain about a single individual unit
Answer and working

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. Disease severity on wheat leaves is scored 0 to 9 by eye. On which measurement scale are these scores?

  1. Nominal
  2. Interval
  3. Ratio
  4. Ordinal
Answer and working

D. Ordinal

The scores are ordered (9 is worse than 5) but the gaps between scores are not known to be equal, which is the definition of an ordinal scale. Nominal categories have no order at all.

Exploratory Data Analysis & Statistical Graphics · Types of data and measurement scales

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