Change log: page 5
New topics, content updates, published corrections, syllabus checks and new versions of the privacy policy and terms, newest first. Typo fixes are not listed: they do not change what a page teaches.
2092 changes Latest 7 Nov 2026
Page 5 of 11 · 200 changes on this page
November 2026
-
Integrated rate equations
Scope integrated laws and pressure equations; clarify disappearance constants, saturation limits and pseudo-first-order interpretation.
-
Temperature dependence of rate
Correct Arrhenius/Maxwell interpretation, transition-state language and catalyst thermodynamics; scope temperature and parameter assumptions.
-
Collision theory
Separate collision counts, molar rates and rate coefficients; clarify energy-factor, threshold and orientation-model limits.
-
Group 13 elements
OpenAI Codex read the full published lesson, FAQs and practice; corrected factual errors and overclaims, distinguished traditional exam models from modern bonding, checked sources and recomputed answers. New unpublished draft; simulations unchanged.
-
Group 14 elements
OpenAI Codex read the full published lesson, FAQs and practice; corrected factual errors and overclaims, distinguished traditional exam models from modern bonding, checked sources and recomputed answers. New unpublished draft; simulations unchanged.
-
Group 15 elements
OpenAI Codex read the full published lesson, FAQs and practice; corrected factual errors and overclaims, distinguished traditional exam models from modern bonding, checked sources and recomputed answers. New unpublished draft; simulations unchanged.
-
Group 16 elements
OpenAI Codex read the full published lesson, FAQs and practice; corrected factual errors and overclaims, distinguished traditional exam models from modern bonding, checked sources and recomputed answers. New unpublished draft; simulations unchanged.
-
Group 17 elements
OpenAI Codex read the full published lesson, FAQs and practice; corrected factual errors and overclaims, distinguished traditional exam models from modern bonding, checked sources and recomputed answers. New unpublished draft; simulations unchanged.
-
Group 18 elements
OpenAI Codex read the full published lesson, FAQs and practice; corrected factual errors and overclaims, distinguished traditional exam models from modern bonding, checked sources and recomputed answers. New unpublished draft; simulations unchanged.
-
Position in the periodic table
OpenAI Codex reviewed the full published lesson, FAQs and practice, corrected factual errors and overclaims, verified primary sources and recomputed answers. New unpublished draft; simulations unchanged.
-
Electronic configurations
OpenAI Codex reviewed the full published lesson, FAQs and practice, corrected factual errors and overclaims, verified primary sources and recomputed answers. New unpublished draft; simulations unchanged.
-
Occurrence
OpenAI Codex reviewed the full published lesson, FAQs and practice, corrected factual errors and overclaims, verified primary sources and recomputed answers. New unpublished draft; simulations unchanged.
-
General properties
OpenAI Codex reviewed the full published lesson, FAQs and practice, corrected factual errors and overclaims, verified primary sources and recomputed answers. New unpublished draft; simulations unchanged.
-
Important compounds
OpenAI Codex reviewed the full published lesson, FAQs and practice, corrected factual errors and overclaims, verified primary sources and recomputed answers. New unpublished draft; simulations unchanged.
-
Experiment: KMnO₄ titrations
OpenAI Codex reviewed the full published lesson, FAQs and practice, corrected factual errors and overclaims, verified primary sources and recomputed answers. New unpublished draft; simulations unchanged.
-
Lanthanoids
OpenAI Codex reviewed the full published lesson, FAQs and practice, corrected factual errors and overclaims, verified primary sources and recomputed answers. New unpublished draft; simulations unchanged.
-
Actinoids
OpenAI Codex reviewed the full published lesson, FAQs and practice, corrected factual errors and overclaims, verified primary sources and recomputed answers. New unpublished draft; simulations unchanged.
-
Applications
OpenAI Codex reviewed the full published lesson, FAQs and practice, corrected factual errors and overclaims, verified primary sources and recomputed answers. New unpublished draft; simulations unchanged.
-
Werner’s theory
OpenAI Codex read the complete published lesson, FAQs and practice; corrected factual errors and overclaims, verified sources and recomputed answers and isomer counts. New unpublished draft; simulations unchanged.
-
Experiment: double salts
OpenAI Codex read the complete published lesson, FAQs and practice; corrected factual errors and overclaims, verified sources and recomputed answers and isomer counts. New unpublished draft; simulations unchanged.
-
Ligands and other terms
OpenAI Codex read the complete published lesson, FAQs and practice; corrected factual errors and overclaims, verified sources and recomputed answers and isomer counts. New unpublished draft; simulations unchanged.
-
Nomenclature
OpenAI Codex read the complete published lesson, FAQs and practice; corrected factual errors and overclaims, verified sources and recomputed answers and isomer counts. New unpublished draft; simulations unchanged.
-
Isomerism
OpenAI Codex read the complete published lesson, FAQs and practice; corrected factual errors and overclaims, verified sources and recomputed answers and isomer counts. New unpublished draft; simulations unchanged.
-
Bonding: VBT and CFT
OpenAI Codex read the complete published lesson, FAQs and practice; corrected factual errors and overclaims, verified sources and recomputed answers and isomer counts. New unpublished draft; simulations unchanged.
-
Metal carbonyls
OpenAI Codex read the complete published lesson, FAQs and practice; corrected factual errors and overclaims, verified sources and recomputed answers and isomer counts. New unpublished draft; simulations unchanged.
-
Importance and applications
OpenAI Codex read the complete published lesson, FAQs and practice; corrected factual errors and overclaims, verified sources and recomputed answers and isomer counts. New unpublished draft; simulations unchanged.
-
Carbonyl group: names and structure
Restricted aldehyde definition to H plus carbon/H, avoiding inclusion of formic acid and formamide.
-
Preparation of aldehydes and ketones
Corrected Gattermann–Koch usual AlCl3 WITH CuCl catalyst system; limited substrate scope.
-
Physical properties of aldehydes and ketones
Corrected ethanal state at 25 C/1 atm from NIST boiling data, including practice and summary.
-
Reactions of aldehydes and ketones
Distinguished anionic and acid-catalysed neutral-nucleophile mechanisms and non-universal slow/fast labels.
-
Experiment: tests for aldehydes and ketones
Removed contradictory aldehyde-only claims throughout explanations, table, summary and quick answer; included reducing sugars/alpha-hydroxy ketones.
-
Experiment: preparation of iodoform
Clearly labelled Remsen recipe historical rather than a modern validated protocol; retained source distinction from NCERT identification test.
-
Uses of aldehydes and ketones
Clarified formalin concentration basis, commercial stabiliser purpose and 10% formalin dilution convention; retained explicitly assumed 40wt numerical exercises.
-
Carboxyl group: names and structure
Corrected C12–C18 as a common fatty-acid range rather than a definition.
-
Preparation of carboxylic acids
Corrected carbon accounting and benzylic-H condition in side-chain oxidation, including quick answer; clarified Jones reagent.
-
Physical properties of carboxylic acids
Restricted physical-state trend to straight-chain saturated monoacids and stated temperature dependence.
-
Chemical reactions of carboxylic acids
Corrected soda-lime carboxyl-carbon fate as carbonate, contrasting Kolbe CO2; qualified coupling-product expectations.
-
Experiment: tests for the carboxyl group
Corrected phenol/litmus oversimplification across lesson and practice; all acid tests interpreted with specificity limits.
-
Uses of carboxylic acids
Corrected water as vinegar largest constituent, formic acid kitchen-staple implication and total-acid inference from pH alone.
-
Structure of amines
Qualified pyramidal/sp3 model, removed advice to give an incorrect measured angle, distinguished rapid nitrogen inversion from carbon-centred chirality.
-
Classification of amines
Expanded arylamine definition to all amine classes and aryl systems; clarified neutral amino-acid structures versus zwitterions.
-
Nomenclature of amines
Scoped alkanamine naming to appropriate parent structures and principal groups, corrected arylamine definition.
-
Preparation of amines
Corrected selective N-methylation implication, excess-ammonia purity claim, acid-reduction work-up and carbon-count wording.
-
Physical properties of amines
Corrected incorrect exam advice on butan-1-amine solubility; added NIOSH measured miscibility and a NIST branched-primary boiling counterexample.
-
Chemical reactions of amines
Corrected pyridine stronger-than-amine claim, resonance-structure counting argument and proton affinity versus Gibbs basicity.
-
Experiment: tests for the amino group
Added test specificity, controls, acid-mole requirement and actual aniline solubility; qualified azo colour and negative interpretation.
-
Experiment: preparation of acetanilide and p-nitroacetanilide
Corrected anhydride-limited theoretical yield and unsupported extra acetylation by solvent; clarified pyridine role.
-
Preparation of diazonium salts
Scoped aryl versus alkyl diazonium definitions, corrected exact Celsius conversion and removed a universal 283 K decomposition threshold.
-
Physical properties of diazonium salts
Removed easy-to-handle/dry implication for diazonium tetrafluoroborates; distinguished relative persistence from explosive hazard.
-
Chemical reactions of diazonium salts
Distinguished reagent-specific substitution pathways from universal simple displacement and qualified Sandmeyer yield generalisation.
-
Experiment: preparation of aniline yellow
Corrected acid dilution sequence, limited aniline solubility, weakly acidic medium versus weak acid, and source-only carbon tetrachloride purification.
-
Diazonium salts in the synthesis of aromatic compounds
Replaced impossible-product claims with selectivity/condition limits for cyanation and directing effects.
-
The empty set
Content-quality review: Example 3 asked for n(A) although four set cardinalities were intended; revised the prompt.
-
Finite and infinite sets
Content-quality review: FAQ misleadingly suggested an infinite set has no cardinal number at Class 11 level; separated NCERT notation from mathematical cardinality.
-
Subsets
Content-quality review: FAQ counterexample needs distinct a,b; added this hypothesis. Added a<b to the quick-answer interval convention.
-
Power set
Content-quality review: Non-empty proper-subset formula wrongly applied at n=0 and produced −1. Added n≥1 guard, empty-set count0, explanation and synchronized formula sheet.
-
Universal set
Content-quality review: Definition/summary/metadata used ambiguous contains sets language; clarified that U contains elements and has the sets as subsets.
-
Venn diagrams
Content-quality review: Wrong partial-overlap instruction omitted reverse containment. Added equal/proper-subset cases and distinguished simplified Euler pictures from a general Venn diagram with empty regions.
-
Cartesian product
Content-quality review: Explicitly limited n(A) counting notation to finite sets and retained the direct empty-product proof for infinite sets. Softened an absolute Venn-diagram claim about element types.
-
Relations
Content-quality review: FAQ incorrectly claimed relations in opposite directions are necessarily different. Added empty relation and A=B exceptions. Made projection formula existential quantifiers explicit.
-
Functions
Content-quality review: Extra Q6 incorrectly equated a function on all integers with a four-pair set. Reframed as four known values of an integer-domain function. Added finite non-empty hypothesis to counting and equal-axis scales to45° claim.
-
Angles
Content-quality review: Clarified signed rotation versus nonnegative arc length, corrected approximate equality, and answered the wheel question in radians during one second rather than only radians per second.
-
Trigonometric functions
Content-quality review: The quoted reciprocal rule could imply cot is undefined where tan is undefined. Added the common-domain restriction and cot(π/2)=0 counterexample.
-
Sum and difference formulas
Content-quality review: Replaced a geometric-angle step that only directly fits a restricted diagram with a rotation argument valid for all real angles. Explicitly retained domains after cancellation and defined A,B in the formula sheet.
-
Modulus and conjugate
Content-quality review: Added missing real-variable hypotheses to extra practice Q6/Q8; their modulus-square steps require real components.
-
Argument and polar form
Content-quality review: Excluded both axes from the acute reference-angle algorithm, including in quick answer. Softened an unnecessarily absolute claim about proof prerequisites.
-
Quadratic equations
Content-quality review: Rational-coefficient discriminant test needed square of a rational number rather than ambiguous perfect square. Added a worked complex-coefficient equation and explicit limit of discriminant sign classification.
-
Inequalities
Content-quality review: Corrected claim that mixed chains cannot be inequalities; explained that3<x>1 is two lower bounds. Distinguished genuinely two-variable examples from axis-parallel linear inequalities. Replaced unnecessary legal/medical generalizations with explicit hypothetical specification
-
Solving linear inequalities
Content-quality review: Temperature prompts used ambiguous between although solutions were strict; made endpoint exclusion explicit in example5 and extraQ9.
-
Fundamental principle of counting
Content-quality review: Quick answer omitted the fixed number of second-stage choices and disjointness of added cases; aligned it with the correct full explanation.
-
Permutations
Content-quality review: Added n≥1 to factorial recurrence and circular arrangement formula. Replaced unsupported specific past-paper and categorical school-exam claims with precise scope of the extension.
-
Combinations
Content-quality review: Ball-selection questions needed individual distinguishability to justify binomial coefficients; made the assumption explicit. Added m≥3 to the collinear-point formula case.
-
Binomial theorem
Content-quality review: Clarified formal n+1 term count before substitutions, fixed blanket not2terms claim at n=1, and supplied nonzero/radical domain conditions in extra practice.
-
General and middle terms
Content-quality review: Greatest-term FAQ failed at x=0 (T0 and zero denominators) and called opposite-sign terms equal for negative x. Added zero-input and a=0 cases, absolute-value language and ratio-domain restrictions.
-
Sequences
OpenAI Codex content review: clarified domains, indexing or model assumptions; independently checked worked examples and practice. See per-topic review findings.
-
Series
OpenAI Codex content review: clarified domains, indexing or model assumptions; independently checked worked examples and practice. See per-topic review findings.
-
Arithmetic progression
OpenAI Codex content review: clarified domains, indexing or model assumptions; independently checked worked examples and practice. See per-topic review findings.
-
Geometric progression
OpenAI Codex content review: clarified domains, indexing or model assumptions; independently checked worked examples and practice. See per-topic review findings.
-
A.M. and G.M.
OpenAI Codex content review: clarified domains, indexing or model assumptions; independently checked worked examples and practice. See per-topic review findings.
-
Coordinate geometry basics
OpenAI Codex review: corrected domain, degenerate-case and geometry explanations; independently solved examples and practice. Detailed per-topic findings retained in content-quality audit.
-
Locus
OpenAI Codex review: corrected domain, degenerate-case and geometry explanations; independently solved examples and practice. Detailed per-topic findings retained in content-quality audit.
-
Slope of a line
OpenAI Codex review: corrected domain, degenerate-case and geometry explanations; independently solved examples and practice. Detailed per-topic findings retained in content-quality audit.
-
Forms of the equation of a line
OpenAI Codex review: corrected domain, degenerate-case and geometry explanations; independently solved examples and practice. Detailed per-topic findings retained in content-quality audit.
-
Distance of a point from a line
OpenAI Codex review: corrected domain, degenerate-case and geometry explanations; independently solved examples and practice. Detailed per-topic findings retained in content-quality audit.
-
Intersection of lines and triangle centres
OpenAI Codex review: corrected domain, degenerate-case and geometry explanations; independently solved examples and practice. Detailed per-topic findings retained in content-quality audit.
-
Sections of a cone
OpenAI Codex content review: checked conic equations, domains, worked examples and all practice. See per-topic audit for improvements and independent calculations.
-
Circle
OpenAI Codex content review: checked conic equations, domains, worked examples and all practice. See per-topic audit for improvements and independent calculations.
-
Parabola
OpenAI Codex content review: checked conic equations, domains, worked examples and all practice. See per-topic audit for improvements and independent calculations.
-
Ellipse
OpenAI Codex content review: checked conic equations, domains, worked examples and all practice. See per-topic audit for improvements and independent calculations.
-
Hyperbola
OpenAI Codex content review: checked conic equations, domains, worked examples and all practice. See per-topic audit for improvements and independent calculations.
-
Coordinate axes and planes
OpenAI Codex content review: independently checked coordinates, distances, examples and practice; clarified degenerate and signed-ratio cases where needed.
-
Coordinates of a point in space
OpenAI Codex content review: independently checked coordinates, distances, examples and practice; clarified degenerate and signed-ratio cases where needed.
-
Section formula in 3D
OpenAI Codex content review: independently checked coordinates, distances, examples and practice; clarified degenerate and signed-ratio cases where needed.
-
Intuitive idea of derivatives
OpenAI Codex content review: independently solved examples and practice; corrected velocity, limit cancellation and derivative-domain conditions. Simulations excluded.
-
Limits
OpenAI Codex content review: independently solved examples and practice; corrected velocity, limit cancellation and derivative-domain conditions. Simulations excluded.
-
Limits of trigonometric functions
OpenAI Codex content review: independently solved examples and practice; corrected velocity, limit cancellation and derivative-domain conditions. Simulations excluded.
-
Derivatives
OpenAI Codex content review: independently solved examples and practice; corrected velocity, limit cancellation and derivative-domain conditions. Simulations excluded.
-
Mean, median and mode
OpenAI Codex content review: recalculated examples and practice; corrected grouped-data assumptions, median theorem scope, mode and dispersion edge cases. Simulations excluded.
-
Mode
OpenAI Codex content review: recalculated examples and practice; corrected grouped-data assumptions, median theorem scope, mode and dispersion edge cases. Simulations excluded.
-
Measures of dispersion
OpenAI Codex content review: recalculated examples and practice; corrected grouped-data assumptions, median theorem scope, mode and dispersion edge cases. Simulations excluded.
-
Range
OpenAI Codex content review: recalculated examples and practice; corrected grouped-data assumptions, median theorem scope, mode and dispersion edge cases. Simulations excluded.
-
Mean deviation
OpenAI Codex content review: recalculated examples and practice; corrected grouped-data assumptions, median theorem scope, mode and dispersion edge cases. Simulations excluded.
-
Variance and SD
OpenAI Codex content review: recalculated examples and practice; corrected grouped-data assumptions, median theorem scope, mode and dispersion edge cases. Simulations excluded.
-
Events
OpenAI Codex content review: solved all event/probability examples and practice; clarified finite-space, independence, uniform-selection and replacement assumptions.
-
Axiomatic probability
OpenAI Codex content review: solved all event/probability examples and practice; clarified finite-space, independence, uniform-selection and replacement assumptions.
-
Types of relations
OpenAI Codex content review: checked proofs, counterexamples, domains and counts; corrected model assumptions, empty-set counting and inverse/composition scope.
-
Types of functions
OpenAI Codex content review: checked proofs, counterexamples, domains and counts; corrected model assumptions, empty-set counting and inverse/composition scope.
-
Composition and inverse
OpenAI Codex content review: checked proofs, counterexamples, domains and counts; corrected model assumptions, empty-set counting and inverse/composition scope.
-
Principal value branches
OpenAI Codex content review: checked principal branches, all examples and practice; corrected a hidden division by zero, endpoint cases and domain explanations.
-
Properties
OpenAI Codex content review: checked principal branches, all examples and practice; corrected a hidden division by zero, endpoint cases and domain explanations.
-
Matrix and order
OpenAI Codex content review: read complete lesson, FAQs and practice; independently verified matrix calculations and definitions. Corrected diagonal, power and cancellation scope where required; retained verified lessons unchanged.
-
Types of matrices
OpenAI Codex content review: read complete lesson, FAQs and practice; independently verified matrix calculations and definitions. Corrected diagonal, power and cancellation scope where required; retained verified lessons unchanged.
-
Operations on matrices
OpenAI Codex content review: read complete lesson, FAQs and practice; independently verified matrix calculations and definitions. Corrected diagonal, power and cancellation scope where required; retained verified lessons unchanged.
-
Transpose of a matrix
OpenAI Codex content review: read complete lesson, FAQs and practice; independently verified matrix calculations and definitions. Corrected diagonal, power and cancellation scope where required; retained verified lessons unchanged.
-
Symmetric and skew symmetric
OpenAI Codex content review: read complete lesson, FAQs and practice; independently verified matrix calculations and definitions. Corrected diagonal, power and cancellation scope where required; retained verified lessons unchanged.
-
Invertible matrices
OpenAI Codex content review: read complete lesson, FAQs and practice; independently verified matrix calculations and definitions. Corrected diagonal, power and cancellation scope where required; retained verified lessons unchanged.
-
Determinant
OpenAI Codex content review: read and verified lesson, FAQs and practice. Recomputed determinants, cofactors, inverses and systems; clarified exceptional cases, signs and proof conditions.
-
Area of a triangle
OpenAI Codex content review: read and verified lesson, FAQs and practice. Recomputed determinants, cofactors, inverses and systems; clarified exceptional cases, signs and proof conditions.
-
Minors and cofactors
OpenAI Codex content review: read and verified lesson, FAQs and practice. Recomputed determinants, cofactors, inverses and systems; clarified exceptional cases, signs and proof conditions.
-
Adjoint and inverse
OpenAI Codex content review: read and verified lesson, FAQs and practice. Recomputed determinants, cofactors, inverses and systems; clarified exceptional cases, signs and proof conditions.
-
Solving linear systems
OpenAI Codex content review: read and verified lesson, FAQs and practice. Recomputed determinants, cofactors, inverses and systems; clarified exceptional cases, signs and proof conditions.
-
Continuity
OpenAI Codex review: read full lesson, FAQs and practice; independently checked derivatives and limits. Corrected domain/endpoint and zero-denominator cases, with complete product derivatives where logarithms fail.
-
Differentiability
OpenAI Codex review: read full lesson, FAQs and practice; independently checked derivatives and limits. Corrected domain/endpoint and zero-denominator cases, with complete product derivatives where logarithms fail.
-
Exponential and log functions
OpenAI Codex review: read full lesson, FAQs and practice; independently checked derivatives and limits. Corrected domain/endpoint and zero-denominator cases, with complete product derivatives where logarithms fail.
-
Logarithmic differentiation
OpenAI Codex review: read full lesson, FAQs and practice; independently checked derivatives and limits. Corrected domain/endpoint and zero-denominator cases, with complete product derivatives where logarithms fail.
-
Parametric derivatives
OpenAI Codex review: read full lesson, FAQs and practice; independently checked derivatives and limits. Corrected domain/endpoint and zero-denominator cases, with complete product derivatives where logarithms fail.
-
Second order derivative
OpenAI Codex review: read full lesson, FAQs and practice; independently checked derivatives and limits. Corrected domain/endpoint and zero-denominator cases, with complete product derivatives where logarithms fail.
-
Rate of change
OpenAI Codex review: checked full lesson, FAQs and all examples/practice. Corrected derivative-test logic and rate/domain conditions; verified optimum values and retained sound content unchanged.
-
Maxima and minima
OpenAI Codex review: checked full lesson, FAQs and all examples/practice. Corrected derivative-test logic and rate/domain conditions; verified optimum values and retained sound content unchanged.
-
Anti derivatives
OpenAI Codex review: read lesson, FAQs and practice; independently checked integrals, domains and convergence. Corrected material conditions and false divergent-integral answer; preserved sound content.
-
Substitution and identities
OpenAI Codex review: read lesson, FAQs and practice; independently checked integrals, domains and convergence. Corrected material conditions and false divergent-integral answer; preserved sound content.
-
Particular integrals
OpenAI Codex review: read lesson, FAQs and practice; independently checked integrals, domains and convergence. Corrected material conditions and false divergent-integral answer; preserved sound content.
-
Partial fractions
OpenAI Codex review: read lesson, FAQs and practice; independently checked integrals, domains and convergence. Corrected material conditions and false divergent-integral answer; preserved sound content.
-
Integration by parts
OpenAI Codex review: read lesson, FAQs and practice; independently checked integrals, domains and convergence. Corrected material conditions and false divergent-integral answer; preserved sound content.
-
Definite integral
OpenAI Codex review: read lesson, FAQs and practice; independently checked integrals, domains and convergence. Corrected material conditions and false divergent-integral answer; preserved sound content.
-
Fundamental theorem
OpenAI Codex review: read lesson, FAQs and practice; independently checked integrals, domains and convergence. Corrected material conditions and false divergent-integral answer; preserved sound content.
-
Properties of definite integrals
OpenAI Codex review: read lesson, FAQs and practice; independently checked integrals, domains and convergence. Corrected material conditions and false divergent-integral answer; preserved sound content.
-
Area under curves
OpenAI Codex review: read full lesson and FAQs; independently checked region boundaries, intersections and all areas. Clarified area formula domains, absolute values and ordering conditions.
-
Area between curves
OpenAI Codex review: read full lesson and FAQs; independently checked region boundaries, intersections and all areas. Clarified area formula domains, absolute values and ordering conditions.
-
Order and degree
OpenAI Codex review: checked definitions, FAQs and every solution by differentiation. Added domain/branch restrictions, restored divided-out solutions, and corrected impossible-condition exam advice.
-
General and particular solutions
OpenAI Codex review: checked definitions, FAQs and every solution by differentiation. Added domain/branch restrictions, restored divided-out solutions, and corrected impossible-condition exam advice.
-
Solving first order equations
OpenAI Codex review: checked definitions, FAQs and every solution by differentiation. Added domain/branch restrictions, restored divided-out solutions, and corrected impossible-condition exam advice.
-
Vectors: basic concepts
OpenAI Codex review: read all notes, FAQs and practice; recalculated vector components, dot/cross products, sections and geometry. Clarified zero/parallel exceptions, direction signs and projection domains.
-
Types of vectors
OpenAI Codex review: read all notes, FAQs and practice; recalculated vector components, dot/cross products, sections and geometry. Clarified zero/parallel exceptions, direction signs and projection domains.
-
Addition of vectors
OpenAI Codex review: read all notes, FAQs and practice; recalculated vector components, dot/cross products, sections and geometry. Clarified zero/parallel exceptions, direction signs and projection domains.
-
Scalar multiple and components
OpenAI Codex review: read all notes, FAQs and practice; recalculated vector components, dot/cross products, sections and geometry. Clarified zero/parallel exceptions, direction signs and projection domains.
-
Dot and cross products
OpenAI Codex review: read all notes, FAQs and practice; recalculated vector components, dot/cross products, sections and geometry. Clarified zero/parallel exceptions, direction signs and projection domains.
-
Direction cosines and ratios
OpenAI Codex review: checked all line/direction examples, FAQs and practice; independently solved feet and distances. Corrected reversed angles and degenerate-direction conditions; retained two sound lessons unchanged.
-
Equation of a line in space
OpenAI Codex review: checked all line/direction examples, FAQs and practice; independently solved feet and distances. Corrected reversed angles and degenerate-direction conditions; retained two sound lessons unchanged.
-
Angle between two lines
OpenAI Codex review: checked all line/direction examples, FAQs and practice; independently solved feet and distances. Corrected reversed angles and degenerate-direction conditions; retained two sound lessons unchanged.
-
Linear programming problems
OpenAI Codex review: read full lesson and FAQs; independently solved vertices, objective values, integer plans and unbounded cases. Added feasibility qualifications and missing practice constraints.
-
Conditional probability
OpenAI Codex review: read full lesson, FAQs and practice; independently recomputed probabilities and checked hypotheses. Corrected missing assumptions and misleading claims; preserved published content pending review.
-
Multiplication theorem
OpenAI Codex review: read full lesson, FAQs and practice; independently recomputed probabilities and checked hypotheses. Corrected missing assumptions and misleading claims; preserved published content pending review.
-
Independent events
OpenAI Codex review: read full lesson, FAQs and practice; independently recomputed probabilities and checked hypotheses. Corrected missing assumptions and misleading claims; preserved published content pending review.
-
Bayes’ theorem
OpenAI Codex review: read full lesson, FAQs and practice; independently recomputed probabilities and checked hypotheses. Corrected missing assumptions and misleading claims; preserved published content pending review.
-
Probability distribution
OpenAI Codex review: read full lesson, FAQs and practice; independently recomputed probabilities and checked hypotheses. Corrected missing assumptions and misleading claims; preserved published content pending review.
-
What is living?
Clarify life-cycle features, inactive seeds and responsiveness; correct non-living size increase and dead-versus-never-living explanations.
-
Diversity in the living world
Attribute the species estimate to NCERT and clarify accepted names, synonyms and the scope of nomenclatural codes.
-
Taxonomic categories
Qualify the seven-rank hierarchy, developmental chordate features and comparisons of nested taxa.
-
Five kingdom classification
Clarify yeast placement, group-specific exceptions and the distinction between three domains and NCERT’s six-kingdom mapping.
-
Kingdom Monera
Correct bacterial multiplication versus survival and gene transfer; qualify cell walls and repair the economic-use exercise.
-
Kingdom Protista
Clarify Protista exceptions, diatom-wall persistence, euglenoid heterotrophy and harmful-bloom terminology.
-
Kingdom Fungi
Qualify traditional fungal groups and walls; correct plasmogamy, spore structures and refrigeration wording.
-
Kingdom Plantae
Clarify plant-cell chloroplasts, nutritional exceptions and gametophyte gamete formation; improve the classification reasoning question.
-
Kingdom Animalia
Correct animal reproduction and digestion generalisations, cellular organisation in sponges and plant-dependence exceptions.
-
Viruses, viroids, prions and lichens
Correct CJD versus variant CJD, viral genome/replication distinctions, smallpox context and lichen pollution/taxonomy generalisations.
-
Algae
Correct oogamy, stored-food chemistry, flagellated-cell scope and thallus terminology; qualify aquatic food-web claims.
-
Bryophytes
Correct bryophyte transport explanation and qualify rhizoid function and typical sporophyte morphology.
-
Pteridophytes
Qualify the typical pteridophyte body, homosporous prothallus and habitat generalisations; include rootless whisk ferns.
-
Gymnosperms
Clarify naked seeds, pollen dispersal and Cycas female structures; attribute the cycad study precisely.
-
Angiosperms
Clarify diplontic terminology and reproductive-resource explanation; preserve typical-trait qualifications.
-
Basis of classification
Clarify body-cavity definitions, flatworm digestive exceptions and non-chordate neural diversity.
-
Classification of animals
Correct animal-group generalisations and the offspring-number exercise; distinguish textbook summaries from biological exceptions.
-
The root
Clarify root-system form versus origin and root/shoot identity independently of above/below-ground position.
-
Modifications of root
Correct mangrove worked answer and turnip storage-organ anatomy; remove unsupported exam-choice advice.
-
The stem
Clarify underground stems, shoot-system definition and limits of growth direction as an identification test.
-
Modifications of stem
Correct grape-tendril position and distinguish a phylloclade from any ordinary green stem.
-
The leaf
Correct guava phyllotaxy and unreliable leaf/leaflet orientation test; qualify identification rules.
-
Modifications of leaf
Clarify phyllodes, pitcher development and carnivorous-plant mineral nutrition.
-
The flower
Distinguish perigyny terminology and compound pistils; qualify literal any-plane symmetry.
-
The fruit
Align fruit definition and quick answer with parthenocarpy, seedlessness and accessory fruit tissues.
-
Semi-technical description
Clarify that a plus sign can separate groups within a whorl as well as distinct whorls.
-
Family Malvaceae
Scope cotton-hibiscus characters correctly and avoid universal claims for modern Malvaceae.
-
Family Cruciferae
Correct Brassicaceae habit, fruit and residual-endosperm generalisations; clarify turnip storage tissue.
-
Family Leguminosae
Clarify nitrogen return and pea-type versus whole-family traits; label traditional subfamilies.
-
Family Compositae
Clarify Asteraceae variation, fruit terminology and outdated evolutionary ranking; improve quick answer.
-
Family Gramineae
Correct grass carpel formula, bamboo stamen generalisation and pollination assertion; qualify typical structures.
-
Plant tissues
Correct meristem-origin and living-tissue generalisations; clarify permanent cells, collenchyma and source–sink transport.
-
Tissue systems
Clarify seasonal lenticel closure, cuticle function, periderm and optional subsidiary cells.
-
Dicot and monocot anatomy
Clarify representative anatomy, Casparian-strip chemistry, living bulliform cells and root-thickening inference.
-
Animal tissues
Correct junction permeability, epithelial examples and muscle coordination; remove unsupported glial precision.
-
Frog
Clarify frog thrombocytes, lymphoid anatomy, partial blood mixing and species/life-stage scope.
-
What is a cell?
Clarify cell-life criteria, cellular dependence, yeast classification and zygote scope.
-
Cell theory
Clarify cell theory scope, historical wall comparison and acellular-virus exception.
-
Overview of the cell
Clarify typical cell plans, enucleate eukaryotes and wall/ribosome exceptions.
-
Prokaryotic cells
Correct pili motility, mesosome scope, wall and DNA generalisations; align practice/FAQ.
-
Eukaryotic cells
Correct membrane transport, mitochondrial ribosomes, spindle origin and chromosome scope.
-
Chemical composition
Clarify shared elements, fatty-acid saturation/range, oil melting and amino-acid charge.
-
Primary and secondary metabolites
Clarify primary/secondary distinction, overlapping categories and alkaloid scope.
-
Biomacromolecules
Qualify size thresholds, lipid exception and cell-composition arithmetic.