GATE Statistics 2025
65 questions, booklet ST2025.
Section GA · General Aptitude (Q1–Q10) · Q1–10
Practise this section →- 1Phrasal verb: backing out of a planGeneral AptitudeVerbal AptitudeEasy
- 2Subject-verb agreement with 'along with'General AptitudeVerbal AptitudeEasy
- 3Energy cost and percentage increaseGeneral AptitudeQuantitative AptitudeEasy
- 4Letter-number grid pattern completionGeneral AptitudeSpatial AptitudeMedium
- 5Pie chart from ball countsGeneral AptitudeQuantitative AptitudeMedium
- 6Inference from a funeral passageGeneral AptitudeVerbal AptitudeEasy
- 7Clock-face letter cipher for PGeneral AptitudeAnalytical AptitudeMedium
- 8Five-digit number with ordered digitsGeneral AptitudeQuantitative AptitudeMedium
- 9Mixture ratio with fixed profitGeneral AptitudeQuantitative AptitudeMedium
- 10Shortest road from village to QRGeneral AptitudeSpatial AptitudeMedium
Section ST · Statistics (Q11–Q65) · Q11–65
Practise this section →- 11Functional equation for f on the half-lineAnalysisCalculusMedium
- 12Countability of digit-defined setsAnalysisCalculusHard
- 13Orthogonal complement of a punctured planeLinear AlgebraMatrix TheoryEasy
- 14MGF of Poisson at log 3ProbabilityProbabilityEasy
- 15Conditional mean in a multinomialProbabilityJoint DistributionsEasy
- 16SLLN for Cauchy-transformed sampleProbabilityConvergence of Random VariablesMedium
- 17Covariances of Poisson process incrementsStochastic ProcessesStochastic ProcessesMedium
- 18Properties of complete sufficient statisticsStatistical InferenceEstimationHard
- 19LRT for two-sided normal meanStatistical InferenceTesting of HypothesesMedium
- 20MP test on adjacent supportsStatistical InferenceTesting of HypothesesHard
- 21MP test properties in generalStatistical InferenceTesting of HypothesesHard
- 22Asymptotics of the empirical cdfProbabilityConvergence of Random VariablesHard
- 23Correlation from conditional meanMultivariate AnalysisMultivariate AnalysisEasy
- 24Regression through origin after reparametrisationLinear Models & RegressionRegression AnalysisMedium
- 25Double integral with cosine kernelAnalysisCalculusMedium
- 26Determinant of a matrix polynomialLinear AlgebraMatrix TheoryMedium
- 27Rank of a linear mapLinear AlgebraMatrix TheoryEasy
- 28Point mass from a cdf jumpProbabilityProbabilityEasy
- 29Second moment of a binomialProbabilityProbabilityEasy
- 30MGF of log chi-squareMultivariate AnalysisMultivariate AnalysisHard
- 31Second moment of summed BrownianStochastic ProcessesStochastic ProcessesEasy
- 32MLE of binomial p under a boundStatistical InferenceEstimationEasy
- 33Cramer-Rao bound times 15Statistical InferenceEstimationEasy
- 34Spearman coefficient on ordered pairsNon-parametric InferenceJoint DistributionsEasy
- 35Adjusted R-squared from R-squaredLinear Models & RegressionRegression AnalysisEasy
- 36Lipschitz, secants and Darboux propertyAnalysisCalculusHard
- 37Minimum of quartic over half-planeAnalysisCalculusMedium
- 38Rank of an equi-correlation-type matrixLinear AlgebraMatrix TheoryMedium
- 39Constant in a cdf with a jumpProbabilityProbabilityMedium
- 40Lognormal moments and variance of the logProbabilityProbabilityMedium
- 41Poisson-binomial mixture identificationProbabilityJoint DistributionsMedium
- 42Minimal sufficiency in N(-theta, theta)Statistical InferenceEstimationMedium
- 43Tests sharing the same power functionStatistical InferenceTesting of HypothesesMedium
- 44Expected ranks among mixed exponentialsProbabilityProbabilityMedium
- 45Variance of a Wishart quadratic formMultivariate AnalysisMultivariate AnalysisMedium
- 46F-test statistic for the slopeLinear Models & RegressionRegression AnalysisMedium
- 47Convergence of a harmonic-type sequenceAnalysisCalculusHard
- 48Eigenvalues of rotation matricesLinear AlgebraMatrix TheoryHard
- 49Independence and t, F constructionsProbabilityJoint DistributionsHard
- 50Consequences of almost sure convergenceProbabilityConvergence of Random VariablesMedium
- 51Stationary distribution of a 3-state chainStochastic ProcessesStochastic ProcessesMedium
- 52Estimation for symmetric uniform distributionStatistical InferenceEstimationMedium
- 53Quadratic forms of a singular multivariate normalMultivariate AnalysisMultivariate AnalysisMedium
- 54Properties of the ridge estimatorLinear Models & RegressionRegression AnalysisMedium
- 55Saddle points of a quartic surfaceAnalysisCalculusMedium
- 56Product of eigenvalues of skew-symmetric PLinear AlgebraMatrix TheoryMedium
- 57Trace of matrix powersLinear AlgebraMatrix TheoryMedium
- 58P(X Y+Z) from mgfsProbabilityProbabilityMedium
- 59Rate from a mixed survival probabilityProbabilityProbabilityMedium
- 60Limit distribution of a dyadic sumProbabilityConvergence of Random VariablesHard
- 61Bias of the gamma rate MLEStatistical InferenceEstimationMedium
- 62Power of the UMP test at log 0.36Statistical InferenceTesting of HypothesesHard
- 63Size of an extreme-value testStatistical InferenceTesting of HypothesesMedium
- 64Partial correlation with a zero linkMultivariate AnalysisMultivariate AnalysisMedium
- 65Bivariate normal orthant probabilityMultivariate AnalysisMultivariate AnalysisMedium