GATE CS: Computer Science & Information Technology Paper

Percentages, Profit and Ratios

• Percent change% change = (new − old) / old × 100
• Successive changesa% then b% → net = a + b + ab/100 %
• ProfitProfit = SP − CP; Profit % = Profit / CP × 100
• Shares boughtUnits = money invested / price per unit; value later = units × new price
• Ratio splitSplit N in a : b → Na/(a+b) and Nb/(a+b)

💡 Convert money into number of units first (shares, kg, items); most GATE profit questions are just units × price.

Counting (Permutations and Combinations)

• ArrangementsnPr = n! / (n − r)!
• SelectionsnCr = n! / (r!(n − r)!)
• Circular arrangements(n − 1)! for n distinct objects in a circle
• Knock-out tournamentGames = players − 1 (every game eliminates exactly one player)
• SubsetsA set of n items has 2ⁿ subsets

💡 Look for an invariant (one elimination per game, one handshake per pair) before listing cases.

Probability

• BasicP(E) = favourable / total equally likely outcomes
• ComplementP(not E) = 1 − P(E)
• Independent eventsP(A and B) = P(A) × P(B)
• Exactly k successesP = nCk pᵏ (1 − p)ⁿ⁻ᵏ
• Two dice36 ordered outcomes; sum 7 has 6 ways, sum 2 or 12 has 1 way

💡 For two dice, list pairs by the first roll; it is faster and safer than guessing a formula.

Logic: What Follows from 'If P then Q'

• GivenP → Q (When it rains, peacocks dance)
• Contrapositive (always true)not Q → not P
• Converse (not necessarily true)Q → P
• Inverse (not necessarily true)not P → not Q
• 'Only when''P only when Q' means P → Q

💡 Translate every option into one of these four forms before choosing; the converse is the usual trap.

Reading Inference Questions

• Absolute words'always', 'never', 'all', 'only' are false unless the passage says so
• Hedged words'sometimes', 'some', 'often', 'may' match passages that use similar hedges
• ScopeInfer only from the passage, not from your own knowledge
• Necessarily trueMust hold in every case the passage allows

💡 If the passage says 'sometimes' and a statement says 'always', that statement is false.

Vocabulary and Analogy

• Antonym pairsprotagonist ↔ antagonist, expedite ↔ retard, augment ↔ diminish
• Synonym setsexpedite, hasten, hurry, accelerate
• Analogy methodState the relation of the first pair in a sentence, then test each option in the same sentence
• Common relationsthing : need it satisfies (water : thirst), worker : tool, part : whole

💡 Build a sentence like 'Water quenches thirst'; only one option fits the same sentence.

Spatial Aptitude Checks

• RotationClockwise 90° four times returns the shape; track one corner mark
• Mirror imageLeft and right swap; top and bottom stay for a vertical mirror
• Paper foldingEach fold doubles the holes; unfold in reverse order, mirroring across each fold line
• Cube netsOpposite faces are never adjacent in a net; in a straight row of 3, faces 1 and 3 are opposite

💡 Track one small asymmetric feature (a dot or corner) instead of the whole figure.