# 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=2#results)[1](/en/practice/?page=1#results) [2](/en/practice/?page=2#results) 3 [4](/en/practice/?page=4#results) … [15](/en/practice/?page=15#results)[Next →](/en/practice/?page=4#results) 360 results · Page 3 of 15 Question batch · 100 questions ## [Complete Subgroup Closure, Conjugation and All-Element Coset Equality](/en/practice/batch-20261015-advance-20261113-r01-finite-normal-subgroup-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D3) Finite normal subgroup batch-20261015-advance-20261113-r01-finite-normal-subgroup-foundations Question batch · 100 questions ## [Epsilon-Closed Starts, Move-Closure Transitions and Prefix Invariants](/en/practice/batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D3) Subset construction from an NFA to a DFA batch-20261014-advance-20261112-r07-subset-construction-nfa-to-dfa-foundations Question batch · 100 questions ## [Complete Odd-Prime Three-Valued Classification and Method Boundaries](/en/practice/batch-20261014-advance-20261112-r06-legendre-symbol-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D3) Legendre symbol batch-20261014-advance-20261112-r06-legendre-symbol-foundations Question batch · 100 questions ## [Whole Coefficient Laws, Independent Endpoints and Zero-Infinity-Prefix Radii](/en/practice/batch-20261014-advance-20261112-r05-power-series-radius-of-convergence-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D3) Radius of convergence of a power series batch-20261014-advance-20261112-r05-power-series-radius-of-convergence-foundations Question batch · 100 questions ## [Declared Power Integrands, Independent One-Sided Limits and Principal-Value Boundaries](/en/practice/batch-20261014-advance-20261112-r04-improper-integral-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D3) Improper integral batch-20261014-advance-20261112-r04-improper-integral-foundations Question batch · 100 questions ## [Hausdorff Separation, Finite Subcovers and Ambient Closedness](/en/practice/batch-20261014-advance-20261112-r03-compact-subset-closed-in-hausdorff-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D3) A compact subset of a Hausdorff space is closed batch-20261014-advance-20261112-r03-compact-subset-closed-in-hausdorff-foundations Question batch · 100 questions ## [Complete Centered Jets, Exact Factorial Coefficients and Finite Taylor Boundaries](/en/practice/batch-20261014-advance-20261112-r02-taylor-polynomial-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D3) Taylor polynomial batch-20261014-advance-20261112-r02-taylor-polynomial-foundations Question batch · 100 questions ## [Prime Divisors, Exact Element Orders and Composite-Order Nonconverses](/en/practice/batch-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D3) Cauchy theorem for finite groups batch-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-foundations Question batch · 100 questions ## [Finite Epsilon Closures, Existential Accepting Paths and Bounded-Search Limits](/en/practice/batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D3) Nondeterministic finite automaton batch-20261014-advance-20261111-r07-nondeterministic-finite-automaton-foundations Question batch · 100 questions ## [Complete Nonzero Square Tables, Opposite Roots and Odd-Prime Conventions](/en/practice/batch-20261014-advance-20261111-r06-quadratic-residue-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D3) Quadratic residue batch-20261014-advance-20261111-r06-quadratic-residue-foundations Question batch · 100 questions ## [Zero-Based Catalan Recurrence, Exact Divisibility and Both Closed Forms](/en/practice/batch-20261014-advance-20261111-r05-catalan-numbers-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D3) Catalan numbers batch-20261014-advance-20261111-r05-catalan-numbers-foundations Question batch · 100 questions ## [Whole Continuous CDFs, Zero Jumps, Flat Intervals and Singular Boundaries](/en/practice/batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D3) Continuous real distribution function batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations Question batch · 100 questions ## [Complete Point-Pair Separators, Vacuous Cases and Sample Nonconclusions](/en/practice/batch-20261014-advance-20261111-r03-hausdorff-space-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D3) Hausdorff space batch-20261014-advance-20261111-r03-hausdorff-space-foundations Question batch · 100 questions ## [Recursive Derivative Orders, Exact Polynomial Coefficients and Existence Boundaries](/en/practice/batch-20261014-advance-20261111-r02-higher-order-derivative-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D3) Higher-order derivative batch-20261014-advance-20261111-r02-higher-order-derivative-foundations Question batch · 100 questions ## [Complete Left-Coset Partitions, Divisibility and Precisely Scoped Converses](/en/practice/batch-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D3) Lagrange theorem for finite groups batch-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-foundations Question batch · 100 questions ## [Explicit PDA Stack Runs, Full-Input Acceptance and Bounded-Search Nonconclusions](/en/practice/batch-20261014-advance-20261110-r07-pushdown-automaton-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D3) Pushdown automaton batch-20261014-advance-20261110-r07-pushdown-automaton-foundations Question batch · 100 questions ## [Complete Divisor Transforms, Consistent Mobius Indexing and Roundtrips](/en/practice/batch-20261014-advance-20261110-r06-mobius-inversion-finite-divisors-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D3) Mobius inversion on finite divisor sets batch-20261014-advance-20261110-r06-mobius-inversion-finite-divisors-foundations Question batch · 100 questions ## [Oldest-to-Newest State Updates, Complete Initials and Unique Prefixes](/en/practice/batch-20261014-advance-20261110-r05-recurrence-relation-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D3) Recurrence relation batch-20261014-advance-20261110-r05-recurrence-relation-foundations Question batch · 100 questions ## [Nonempty Partition Cells, Exact Within-Between Variance and Null Weights](/en/practice/batch-20261014-advance-20261110-r04-law-of-total-variance-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D3) Law of total variance batch-20261014-advance-20261110-r04-law-of-total-variance-foundations Question batch · 100 questions ## [Qualified Maps, Relative Cover Pullbacks and Compact-Image Nonconverses](/en/practice/batch-20261014-advance-20261110-r03-continuous-image-of-compact-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D3) Continuous image of a compact set batch-20261014-advance-20261110-r03-continuous-image-of-compact-foundations Question batch · 100 questions ## [Exact Polynomial Secants, Interior MVT Witnesses and Mode-Specific Boundaries](/en/practice/batch-20261014-advance-20261110-r02-mean-value-theorem-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D3) Mean value theorem batch-20261014-advance-20261110-r02-mean-value-theorem-foundations Question batch · 100 questions ## [Same-Point Orbit-Stabilizer Counts, Fibers and Left-Coset Certificates](/en/practice/batch-20261014-advance-20261110-r01-orbit-stabilizer-theorem-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D3) Orbit-stabilizer theorem batch-20261014-advance-20261110-r01-orbit-stabilizer-theorem-foundations Question batch · 100 questions ## [Complete Grammars, Explicit Derivations and Bounded-Search Nonconclusions](/en/practice/batch-20261014-advance-20261109-r07-context-free-grammar-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D3) Context-free grammar batch-20261014-advance-20261109-r07-context-free-grammar-foundations Question batch · 100 questions ## [Complete Prime Multiplicities, Positive-Domain Mobius Values and Divisor Sums](/en/practice/batch-20261014-advance-20261109-r06-mobius-function-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D3) Mobius function batch-20261014-advance-20261109-r06-mobius-function-foundations [← Previous](/en/practice/?page=2#results)[1](/en/practice/?page=1#results) [2](/en/practice/?page=2#results) 3 [4](/en/practice/?page=4#results) … [15](/en/practice/?page=15#results)[Next →](/en/practice/?page=4#results) 360 results · Page 3 of 15