# Question batches 36,000 questions have bilingual step-by-step derivations. Browse original batches or search and filter in the question explorer. [Search all questions & derivations →](/en/explore/) [← Previous](/en/practice/?page=4#results)[1](/en/practice/?page=1#results) … [4](/en/practice/?page=4#results) 5 [6](/en/practice/?page=6#results) … [15](/en/practice/?page=15#results)[Next →](/en/practice/?page=6#results) 360 results · Page 5 of 15 Question batch · 100 questions ## [Valid Cliques, Independent Sets, Inclusion-Maximality and Global Extrema](/en/practice/batch-20261014-advance-20261106-r02-clique-and-independent-set-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D5) Cliques and independent sets batch-20261014-advance-20261106-r02-clique-and-independent-set-foundations Question batch · 100 questions ## [Proper Palettes, Exact Chromatic Minima and Independent Certificate Flags](/en/practice/batch-20261014-advance-20261106-r01-chromatic-number-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D5) Chromatic number batch-20261014-advance-20261106-r01-chromatic-number-foundations Question batch · 100 questions ## [Declared IID Premises, Chebyshev Upper Bounds and Strict All-n Tails](/en/practice/batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D5) Weak law of large numbers batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations Question batch · 100 questions ## [Complete Fibre Pushforwards, Parameter Families and Nonclaim Markers](/en/practice/batch-20261014-advance-20261105-r06-sampling-distribution-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D5) Sampling distribution batch-20261014-advance-20261105-r06-sampling-distribution-foundations Question batch · 100 questions ## [Both Continuity Directions, Finite Discrete Scope and Metric Boundaries](/en/practice/batch-20261014-advance-20261105-r05-homeomorphism-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D5) Homeomorphism batch-20261014-advance-20261105-r05-homeomorphism-foundations Question batch · 100 questions ## [Single-Use Edges, Degree Parity, Support Connectivity and Zero Circuits](/en/practice/batch-20261014-advance-20261105-r04-eulerian-trail-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D5) Euler trails and circuits batch-20261014-advance-20261105-r04-eulerian-trail-foundations Question batch · 100 questions ## [Exact Division Chains, Signed Bezout Witnesses and Zero Boundaries](/en/practice/batch-20261014-advance-20261105-r03-euclidean-algorithm-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D5) Euclidean algorithm batch-20261014-advance-20261105-r03-euclidean-algorithm-foundations Question batch · 100 questions ## [Functional Pairings, Dual Bases and Opposite Coordinate Laws](/en/practice/batch-20261014-advance-20261105-r02-dual-vector-space-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D5) Dual vector space batch-20261014-advance-20261105-r02-dual-vector-space-foundations Question batch · 100 questions ## [Unique Decompositions, Ambient Coverage and Multi-Summand Independence](/en/practice/batch-20261014-advance-20261105-r01-direct-sum-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D5) Direct sum of subspaces batch-20261014-advance-20261105-r01-direct-sum-foundations Question batch · 100 questions ## [Exact Finite-Atomic p-Moments, Moment Tolerances and Symbolic Tails](/en/practice/batch-20261014-advance-20261104-r07-lp-convergence-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D5) Lp convergence batch-20261014-advance-20261104-r07-lp-convergence-foundations Question batch · 100 questions ## [Full-Vertex Connectivity, Acyclicity, Edge Counts and Unweighted Boundaries](/en/practice/batch-20261014-advance-20261104-r06-spanning-tree-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D5) Spanning tree batch-20261014-advance-20261104-r06-spanning-tree-foundations Question batch · 100 questions ## [Normalized CRT Solutions, Product Uniqueness and Noncoprime Compatibility](/en/practice/batch-20261014-advance-20261104-r05-chinese-remainder-theorem-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D5) Chinese remainder theorem batch-20261014-advance-20261104-r05-chinese-remainder-theorem-foundations Question batch · 100 questions ## [One Total Statistic, Observed Estimates, Expectations and Nonclaim Markers](/en/practice/batch-20261014-advance-20261104-r04-statistical-estimator-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D5) Statistical estimator batch-20261014-advance-20261104-r04-statistical-estimator-foundations Question batch · 100 questions ## [Absolute Geometric Sums, Conditional Harmonic Tails and Finite Boundaries](/en/practice/batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D5) Absolute convergence of series batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations Question batch · 100 questions ## [Common Strict Finite-Domain Witnesses, Supremum Gaps and Evidence Limits](/en/practice/batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D5) Uniform convergence of functions batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations Question batch · 100 questions ## [Rectangular Map Direction, Exact Kernel/Image Bases and Rank-Nullity](/en/practice/batch-20261014-advance-20261104-r01-rank-nullity-theorem-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D5) Rank-nullity theorem batch-20261014-advance-20261104-r01-rank-nullity-theorem-foundations Question batch · 100 questions ## [Signed Extended Euclid, Normalized Inverses and Nonunit Boundaries](/en/practice/batch-20261014-advance-20261103-r07-modular-inverse-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D5) Modular inverse batch-20261014-advance-20261103-r07-modular-inverse-foundations Question batch · 100 questions ## [Maximum Matchings: Validity before Global Optimality](/en/practice/batch-20261014-advance-20261103-r06-maximum-matching-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D5) Maximum matching batch-20261014-advance-20261103-r06-maximum-matching-foundations Question batch · 100 questions ## [Connected Topological Spaces: Actual Spaces and Independent Reference Conventions](/en/practice/batch-20261014-advance-20261103-r05-connected-topological-space-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D5) Connected topological space batch-20261014-advance-20261103-r05-connected-topological-space-foundations Question batch · 100 questions ## [Complete Law Tables, Likelihoods and Parameter-Observation Roles](/en/practice/batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D5) Parametric statistical model batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations Question batch · 100 questions ## [Exact Partial Sums, Geometric and Telescoping Tails, Harmonic Boundaries](/en/practice/batch-20261014-advance-20261103-r03-infinite-series-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D5) Infinite series batch-20261014-advance-20261103-r03-infinite-series-foundations Question batch · 100 questions ## [Signed Pointwise Values, Strict Epsilon Tails and Finite-Domain Maxima](/en/practice/batch-20261014-advance-20261103-r02-pointwise-convergence-of-functions-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D5) Pointwise convergence of functions batch-20261014-advance-20261103-r02-pointwise-convergence-of-functions-foundations Question batch · 100 questions ## [Exact RREF Rank, Minor Bounds and Singular-Determinant Limits](/en/practice/batch-20261014-advance-20261103-r01-matrix-rank-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D5) Matrix rank batch-20261014-advance-20261103-r01-matrix-rank-foundations Question batch · 100 questions ## [Arbitrary-Word Mod-Count Invariants and Exact Prefix-Trie DFA Constructions](/en/practice/batch-20261014-advance-20261102-r07-regular-language-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D5) Regular language batch-20261014-advance-20261102-r07-regular-language-foundations [← Previous](/en/practice/?page=4#results)[1](/en/practice/?page=1#results) … [4](/en/practice/?page=4#results) 5 [6](/en/practice/?page=6#results) … [15](/en/practice/?page=15#results)[Next →](/en/practice/?page=6#results) 360 results · Page 5 of 15