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100+ Free GATE ST Practice Questions

Pass your Graduate Aptitude Test in Engineering — Statistics (ST) exam on the first try — instant access, no signup required.

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ANCOVA differs from ANOVA primarily because ANCOVA:

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2026 Statistics

Key Facts: GATE ST Exam

100 marks

Total marks (15 GA + 85 Statistics)

gate2026.iitg.ac.in

65 questions

Total questions in 3 hours

GATE 2026 Information Brochure

−1/3 mark

Negative marking for a 1-mark MCQ

GATE Information Brochure

INR 1800

Regular registration fee (General)

GATE 2026 official notification

100

Free practice questions here

OpenExamPrep

GATE ST is a 3-hour Computer-Based Test with 65 questions for 100 marks (15 GA + 85 subject). MCQs carry −1/3 to −2/3 negative marking; MSQ and NAT carry none. Scores feed MTech/PhD admission at IITs, IISc, NITs and PSU recruitment.

Sample GATE ST Practice Questions

Try these sample questions to test your GATE ST exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1In the GATE 2026 exam, what is the negative marking for an incorrect multiple-choice question (MCQ) carrying 2 marks?
A.−1/3 mark
B.−2/3 mark
C.−1 mark
D.No negative marking
Explanation: GATE applies 1/3 negative marking on MCQs: for a 1-mark MCQ the penalty is −1/3, and for a 2-mark MCQ the penalty is −2/3. MSQ and NAT questions carry no negative marking. This rule is stated in the official GATE 2026 information brochure.
2A train travels the first half of the distance at 40 km/h and the second half at 60 km/h. What is the average speed for the whole journey?
A.48 km/h
B.50 km/h
C.52 km/h
D.55 km/h
Explanation: For equal distances at speeds v₁ and v₂, the average speed is the harmonic mean 2v₁v₂/(v₁+v₂) = 2(40)(60)/(40+60) = 4800/100 = 48 km/h. The arithmetic mean overestimates because more time is spent at the slower speed.
3Choose the most appropriate word to complete the sentence: The committee's decision was widely ______ by stakeholders who felt it was unjust.
A.lauded
B.endorsed
C.criticized
D.ratified
Explanation: The clause 'who felt it was unjust' signals a negative response. 'Criticized' fits because stakeholders who view a decision as unjust would express disapproval, not praise or approval.
4If 5 workers complete a task in 12 days working 8 hours a day, how many days will 8 workers take to complete the same task working 6 hours a day?
A.8 days
B.10 days
C.12 days
D.15 days
Explanation: Total work in man-hours = 5 × 12 × 8 = 480 man-hours. With 8 workers at 6 hours/day, daily output = 48 man-hours. Days required = 480/48 = 10 days. The work-equivalence formula M₁D₁H₁ = M₂D₂H₂ gives the same result.
5A statement and two conclusions follow. Statement: All students who study regularly score well. Conclusion I: Some who score well do not study regularly. Conclusion II: Students who do not study regularly may still score well. Which follows?
A.Only Conclusion I follows
B.Only Conclusion II follows
C.Both conclusions follow
D.Neither conclusion follows
Explanation: The statement asserts a sufficient condition (regular study → scoring well) but does not claim it is necessary. So scoring well without regular study is logically possible (Conclusion II), but the statement does not assert that any such cases exist (Conclusion I is unsupported).
6In the series 3, 6, 11, 18, 27, ?, what comes next?
A.36
B.38
C.40
D.42
Explanation: Differences are 3, 5, 7, 9, 11 — increasing odd numbers. Adding 11 to 27 yields 38. Equivalently the general term is n² + 2 for n = 1, 2, 3, ...
7A bag contains 4 red, 5 blue, and 6 green balls. If two balls are drawn at random without replacement, what is the probability both are blue?
A.1/21
B.2/21
C.5/42
D.1/6
Explanation: P(both blue) = C(5,2)/C(15,2) = 10/105 = 2/21. Equivalently, (5/15)(4/14) = 20/210 = 2/21.
8Identify the grammatically correct sentence.
A.Neither the manager nor the employees was present.
B.Neither the manager nor the employees were present.
C.Neither the manager or the employees were present.
D.Neither the manager nor the employees is present.
Explanation: In 'neither...nor' constructions, the verb agrees with the nearer subject. 'Employees' is plural and nearer, so 'were' is correct. Also, 'nor' (not 'or') must follow 'neither'.
9If 30% of a number is 45, what is 80% of the same number?
A.100
B.110
C.120
D.135
Explanation: The number is 45/0.30 = 150. Then 80% of 150 = 120. Alternatively, 80/30 × 45 = 120 directly.
10A figure has 5 lines of symmetry and rotational symmetry of order 5. Which polygon is it?
A.Regular pentagon
B.Regular hexagon
C.Equilateral triangle
D.Square
Explanation: A regular n-gon has exactly n axes of symmetry and rotational symmetry of order n. With 5 axes and order 5, the polygon is a regular pentagon.

About the GATE ST Exam

GATE Statistics (paper code ST) is the Graduate Aptitude Test in Engineering's dedicated paper for statistics graduates, conducted jointly by IISc Bangalore and the seven older IITs. GATE 2026 is being organised by IIT Guwahati. The Computer-Based Test runs 3 hours and contains 65 questions for 100 marks: 10 General Aptitude questions (15 marks) and 55 subject-specific Statistics questions (85 marks) spanning Calculus, Matrix Theory, Probability, Stochastic Processes, Inference, Regression, Multivariate Analysis, and Design of Experiments. Questions are a mix of MCQ, Multiple Select (MSQ), and Numerical Answer Type (NAT); MCQs carry 1/3 negative marking while MSQ and NAT do not. The score is used for MTech/MSc/PhD admission to IITs, IISc, NITs, IIITs, and CFTIs, and for PSU recruitment.

Questions

100 scored questions

Time Limit

180 minutes (3 hours)

Passing Score

Qualifying cutoff varies — typically ~25/100 for General, ~22.5 for OBC (NCL), and ~16.6 for SC/ST/PwD

Exam Fee

INR 900 (Female/SC/ST/PwD); INR 1800 (all other candidates) for regular registration (IISc Bangalore and seven IITs on rotation (GATE 2026 organised by IIT Guwahati))

GATE ST Exam Content Outline

15%

General Aptitude (GA)

Verbal ability, vocabulary, quantitative aptitude, data interpretation, and analytical/logical reasoning — common to every GATE paper

~8%

Calculus

Functions of one and several real variables, limits, continuity, differentiability, mean value theorem, Taylor's theorem, sequences, uniform convergence, Riemann integration, multiple integrals

~8%

Matrix Theory

Vector spaces, matrix rank, determinants, eigenvalues and eigenvectors, positive definite quadratic forms

~20%

Probability

Axioms, conditional probability, Bayes' theorem, random variables, standard distributions (Bernoulli, binomial, Poisson, hypergeometric, geometric, negative binomial, uniform, exponential, normal, gamma, beta, chi-square), joint distributions, expectation, MGF and characteristic functions, transformations

~10%

Stochastic Processes

Markov chains, transition probability matrix, classification of states, stationary distributions, Poisson and birth-death processes

~15%

Inference

Point estimation (MLE, MoM, sufficiency, completeness, UMVUE, Cramer-Rao), interval estimation, hypothesis testing (NP lemma, LRT, UMP, chi-square, t, F), nonparametric tests (sign, Wilcoxon, Mann-Whitney)

~10%

Regression Analysis

Simple and multiple linear regression, least squares, Gauss-Markov theorem, residual analysis, ANOVA, logistic regression, nonparametric regression

~8%

Multivariate Analysis

Multivariate normal, Hotelling's T², Wishart distribution, discriminant analysis, PCA, canonical correlation, cluster analysis, factor analysis

~6%

Design of Experiments

Randomized block, Latin square, and factorial designs; analysis of variance; analysis of covariance

How to Pass the GATE ST Exam

What You Need to Know

  • Passing score: Qualifying cutoff varies — typically ~25/100 for General, ~22.5 for OBC (NCL), and ~16.6 for SC/ST/PwD
  • Exam length: 100 questions
  • Time limit: 180 minutes (3 hours)
  • Exam fee: INR 900 (Female/SC/ST/PwD); INR 1800 (all other candidates) for regular registration

Keys to Passing

  • Complete 500+ practice questions
  • Score 80%+ consistently before scheduling
  • Focus on highest-weighted sections
  • Use our AI tutor for tough concepts

GATE ST Study Tips from Top Performers

1Build a strong probability and distributions base first — roughly 20% of the paper centres on probability and another 15% on inference, both of which lean heavily on distribution theory
2Practice MSQ and NAT questions aggressively because they carry no negative marking — every reasonable attempt is upside
3Solve the past 5-10 years of GATE ST official papers from the GATE archives; question patterns and numerical scales repeat across cycles
4Make a personal formula sheet for moment generating functions, common distribution moments, MLE/MoM derivations, and ANOVA/F-test degrees of freedom
5Schedule timed mocks of 3 hours each in the final two months; pacing the 65 questions and managing the on-screen virtual calculator is itself a skill
6Read at least the syllabus PDF on gate2026.iitg.ac.in line by line before you finalise the topic list — examiners stick close to the printed syllabus

Frequently Asked Questions

What is the GATE 2026 ST exam pattern?

GATE 2026 ST is a 3-hour Computer-Based Test with 65 questions worth 100 marks. The paper has 10 General Aptitude questions (15 marks) and 55 Statistics-subject questions (85 marks), with a mix of MCQ, Multiple Select Questions (MSQ), and Numerical Answer Type (NAT). MCQs carry 1/3 negative marking; MSQ and NAT have no negative marking.

Who conducts GATE 2026 and where is the official ST syllabus?

GATE 2026 is being organised by IIT Guwahati on behalf of the National Coordination Board, with IISc Bangalore and seven IITs (Bombay, Delhi, Guwahati, Kanpur, Kharagpur, Madras, Roorkee) jointly responsible. The official ST syllabus, brochure, and registration links are published on gate2026.iitg.ac.in.

What is the GATE 2026 registration fee for the ST paper?

Regular registration fees are INR 900 for Female, SC, ST, and PwD candidates and INR 1800 for all other Indian candidates. A late fee of INR 500 applies after the regular deadline. Fees for foreign candidates are higher and listed in the GATE 2026 information brochure.

What subjects does GATE Statistics (ST) cover?

The ST paper covers Calculus, Matrix Theory, Probability, Stochastic Processes, Inference, Regression Analysis, Multivariate Analysis, and Design of Experiments. General Aptitude (verbal, quantitative, analytical, spatial) is common to every GATE paper and contributes 15 marks.

What is the negative marking rule on GATE ST?

For multiple-choice questions (MCQs), one-third negative marking applies: −1/3 for a 1-mark MCQ and −2/3 for a 2-mark MCQ. Multiple Select Questions (MSQ) and Numerical Answer Type (NAT) questions have no negative marking, so candidates should attempt all MSQ and NAT items.

What is the GATE ST qualifying cutoff and how is the score used?

Qualifying marks vary by year and category but typically hover near 25/100 for General candidates and lower for reserved categories. A GATE ST score is used for MTech/MSc/PhD admission to IITs, IISc, NITs, IIITs, and CFTIs, as well as for recruitment by select Public Sector Undertakings (PSUs).

Is there a JEST or IIT JAM equivalent for statistics, or only GATE ST?

For postgraduate admissions IIT JAM has a Mathematical Statistics (MS) paper at the MSc level, while GATE ST is generally used for MTech/PhD admission and PSU recruitment. The two exams have overlapping but distinct syllabi; GATE ST is broader in inference, regression and multivariate analysis.