GA · GATE CS 2027
10 topics and 20 sheets. Open a topic for its sheets and the topics it depends on.
Grammar rules that decide fill-in and error-spotting options: tenses and sequence of tenses, conditionals, subject-verb agreement (collective nouns, either/neither, none, amounts), articles, adjectives and comparison, prepositions and fixed pairings, conjunctions and correlatives, pronoun case, modifiers and parallel structure.
Meaning from context: signal words and charge, word families and roots, confusable pairs, idioms and phrasal verbs with their meanings, collocations, and one-word substitutes, with the elimination method for synonym, antonym and fill-in questions.
Reading questions by type: stated fact, inference, main idea, author's view and tone, assumption, conclusion, strengthen and weaken, with the scope traps that make options wrong. Narrative sequencing by opener, pronoun and article links, connectors and time order.
Ratios, proportion and percentages as multipliers; successive change, profit, loss, discount and interest; averages, mixtures, work, speed and ages as applications; exponent and logarithm rules, digit counts, unit digits and honest estimation.
Counting with and without order, restrictions, circular and identical arrangements, distributions and derangements; arithmetic, geometric and pattern series; mean, median, mode, range and standard deviation; classical probability, complements, independence, at-least-one and binomial counts.
Reading bar, pie, line and tabular data, 2-D and 3-D plots, maps and contour plots: units and base first, change versus share, percent versus percentage points, pie angles, growth rates and estimation that stays within the gap between options.
Areas, perimeters, surface areas and volumes of plane figures and solids, similar figures and scale factors, triangle and circle properties, polygons, and coordinate geometry for distance, slope, midpoint and area.
Deduction with conditionals, contrapositive, only if and unless; categorical statements and syllogisms checked with Venn diagrams; induction and counterexamples; analogy and coding rules; number puzzles, arrangements, blood relations, directions, clocks and calendars.
Translation, rotation, scaling and reflection of shapes and points, mirror and water images, symmetry, assembling and grouping; paper folding and cutting, cube nets and opposite faces, dice, counting and painted cubes.
The revision sheets: traps grouped by topic with the correct rule, question patterns with the first step and the check, and the master last-day sheet.
The verbal routine for fill-in and error questions, tense choice from time markers, the present perfect and past perfect, sequence of tenses in reported speech, the present tense in future time clauses, the four conditional types and inverted conditionals, stative verbs, subjunctive forms, no sooner and hardly patterns, subject-verb agreement (head noun, intervening phrases, either/neither, none, each and every, collective nouns, a number of, amounts, titles, gerunds), infinitive or gerund after a verb, and active to passive. All example sentences are original.
Articles by sound and by reference, zero article, adjectives and degrees of comparison (irregular forms, double comparatives, than or to, elder and older, fewer and less, like with like, order of adjectives), adverb or adjective after linking verbs, prepositions and fixed pairings, time prepositions, conjunctions and correlatives with parallel structure, connectors by logic (contrast, cause, result, condition), pronoun case, reflexive pronouns, dangling and misplaced modifiers, and an error-spotting order. Example sentences are original.
The context method for meaning, synonym, antonym and fill-in questions (signal words, charge, sense, part of speech), roots and affixes that decode unfamiliar words, word families whose forms differ in meaning, confusable pairs, collocations, idioms and phrasal verbs with meanings, and one-word substitutes. All sentences are original.
Reading questions by type: stated fact, inference, main idea, author's view and tone, assumption, conclusion, strengthen and weaken, and true-false statements; the scope traps that make options wrong (extreme words, outside knowledge, reversed cause, partial truth); a worked original passage; and narrative sequencing by opener, pronoun and article links, connectors, time order and closer, with an original set of sentences.
The quantitative engine of GA: ratios and proportion (combining ratios, dividing in a ratio, direct and inverse proportion, partnership), percentages as multipliers, successive change, undoing a change, profit, loss, marked price and discount, simple and compound interest with the two- and three-year difference formulas, compounding periods, and the fraction-to-percent table used for estimation. Every example is original and recomputed by script.
Ratio and percentage applications that GA word problems use: averages through totals (corrections, newcomers, consecutive numbers), weighted averages, mixtures by alligation and repeated replacement, work and pipes as added rates, man-days, wages, speed, average speed, relative speed for trains and circular tracks, boats and streams, late-early problems and ages. Original examples, every number recomputed by script.
Exponent laws with their conditions, fractional and negative exponents, surds and rationalising, comparing large powers by a common base or exponent, solving exponential equations, logarithm laws and domain, change of base, the four logarithm values worth memorising, digit counts and leading zeros, unit-digit cycles, doubling and half-life, and estimation with a stated error. Original examples, every number recomputed by script.
Counting for GA: multiplication and addition principles, nPr and nCr with their identities, arrangements with restrictions (together, apart, fixed position, gap method), circular arrangements and necklaces, identical objects, selections with at-least conditions by cases and by complement, distributions of identical and distinct objects, grouping, derangements, digit formation and geometric counts. Each formula is checked by brute-force enumeration in the verification script.
Arithmetic and geometric progressions with nth term and sums, infinite geometric series and recurring decimals, standard sums of naturals, squares, cubes, odd and even numbers, telescoping sums, the method for pattern and letter series (differences, ratios, interleaving, squares and cubes, wrong-term questions), and elementary statistics: mean, median, mode, range, variance and standard deviation (population and sample), the shortcut formula, effects of shifting and scaling, and combined means.
Classical probability with equally likely outcomes, standard sample spaces (coins, two dice, a deck), complement and addition rules, mutually exclusive versus independent events, at-least-one by complement, drawing with and without replacement, conditional probability, exactly-k successes (binomial count), expected value, total probability with a two-urn example, odds and geometric probability. All values are exact fractions checked by enumeration.
Method for data interpretation: units, scale and base before arithmetic; change versus share versus value; percent versus percentage points; pie-chart angles and why angles in two pies cannot be compared; line-graph slopes; tables with totals; 2-D plots (scatter, log scale); 3-D surface and contour plots with a worked contour reading; maps with scale and area scale; index numbers; growth rates (CAGR); and estimation by rounding and cross-multiplication. One original data set is shown as a bar chart and a pie chart and worked through.
Areas and perimeters of triangles, quadrilaterals, polygons and circles (sectors, arcs, rings); surface areas and volumes of cubes, cuboids, cylinders, cones, spheres and hemispheres; recasting and rolling problems; scale factors for similar figures; triangle facts (Heron, special triangles, inradius and circumradius, inequality); circle theorems (chords, tangents, angles); polygon angle sums and diagonals; coordinate geometry (distance, midpoint, section point, slope, area by coordinates, centroid).
Deductive logic for GA: the analytical routine (translate, then test every case), conditional statements and their contrapositive, converse and inverse, only if, unless, necessary and sufficient conditions, negations, valid and invalid argument forms, the four categorical statements with Venn diagrams, syllogism checking by least-overlap diagrams and counter-models, complementary (either-or) pairs, and truth-teller puzzles. Every equivalence is checked by truth table and every syllogism by a model search.
Inductive reasoning and its limits (generalisation, counterexamples, why a pattern that holds for many cases can still fail), how to choose between rules that fit the data, analogy by bridge sentences with a table of relation types, odd-one-out by category, number analogies, and letter and number coding: letter positions, opposite letters, shifts, reversal, alternating shifts and position sums.
Number puzzles (digits and reversal, LCM and remainders, divisor counts, trailing zeros, divisibility tests, inclusion-exclusion counts, heads-and-legs), seating puzzles in a row with a worked elimination and a table for left and right in rows and circles, ranking, tournaments, blood relations with a family-tree notation, directions and displacement, clock-hand angles and coincidences, and calendars by odd days. Original examples, each checked by brute force or a date library.
Spatial routine (what a move keeps and what it reverses), translation, rotation by 90 and 180 degrees, reflection in the axes and in y = x, scaling, the coordinate rule for each move with an original point, compositions (two reflections make a rotation or a translation), mirror and water images, mirror images of clocks, symmetry of shapes and letters, pattern completion by rotation steps, assembling pieces into a figure and grouping figures by a shared rule, and counting squares, rectangles and triangles in figures.
Patterns in two and three dimensions: paper folding and punching (unfold by reflecting across fold lines in reverse order, layers double per fold, holes on fold lines), folding a rectangle repeatedly, cube nets (the 11 nets, opposite faces, invalid shapes), dice from two views, counting cubes in stacks, painted cubes and cuboids cut into unit cubes, cuts and pieces, and front, top and side views.
The common mistakes across the General Aptitude pack, grouped from verbal to spatial: each row gives the wrong intuition, the correct rule with an original number or sentence, and the sheet where the rule lives.
One row per recurring General Aptitude question pattern: the recognition cue in the stem, the first step and method, the check or common failure, and the sheet with the full rule. A year is given only for patterns whose past question was verified by script in the earlier edition of this pack.
The General Aptitude pack on one page: the four method families, grammar and reading rules, the arithmetic identities, counting and probability formulas, series and statistics, data interpretation, geometry, logic forms, numerical reasoning and spatial rules, each with a pointer to its sheet.
