IBA Karachi Admission Test Practice Questions — Aptitude Test

These are 50 practice questions in the style of the IBA Admission Test paper, drawn from the official syllabus topics (English grammar/vocabulary/reading and FSc Mathematics). They are practice questions, not real past-paper questions. Every answer is a standard textbook fact. The IBA Admission Test has 95 multiple-choice questions — English 45 and Mathematics 50 — with 50 minutes per part and negative marking. English covers grammar in context, vocabulary in context and reading comprehension; Mathematics covers complex numbers, matrices and determinants, sequences and series, permutation/combination and probability, trigonometry, functions and limits, and analytical geometry. Sectional cut-off marks are set per programme by the Admissions Committee, and SAT/ACT scores can exempt a candidate from the test on a competitive merit list. Pattern checked 8 Nov 2026 — confirm on the official IBA site before your test. For the full pattern and general test preparation, see the general entry test guide.

Q1. Choose the word nearest in meaning to "Meticulous":
A) Careless
B) Thorough
C) Hasty
D) Rough
Correct answer: B — Thorough
Explanation: "Meticulous" means showing great attention to detail, i.e. thorough and careful.
Reference: Standard English vocabulary (Oxford dictionary); IBA-style English word lists.

Q2. Choose the word most nearly opposite in meaning to "Scarce":
A) Rare
B) Abundant
C) Short
D) Limited
Correct answer: B — Abundant
Explanation: "Scarce" means in short supply; its opposite is "abundant" (plentiful).
Reference: Standard English vocabulary (Oxford dictionary); IBA-style English word lists.

Q3. Choose the correct sentence:
A) Each of the students have submitted the assignment.
B) Each of the students has submitted the assignment.
C) Each of the students are submitted the assignment.
D) Each of the students were submitted the assignment.
Correct answer: B — Each of the students has submitted the assignment.
Explanation: "Each" is singular, so it takes the singular verb "has", even though "students" is plural.
Reference: Standard English grammar (subject-verb agreement); FSc English grammar texts.

Q4. Choose the correct verb: "The committee ___ reached a decision."
A) have
B) has
C) are
D) were
Correct answer: B — has
Explanation: "Committee" is a collective noun acting as a single unit here, so it takes the singular verb "has".
Reference: Standard English grammar (collective nouns); FSc English grammar texts.

Q5. "The manager's decision was arbitrary, based on personal preference rather than any rule." The word "arbitrary" here means:
A) Well-reasoned
B) Based on random choice or personal whim
C) Widely approved
D) Legally binding
Correct answer: B — Based on random choice or personal whim
Explanation: "Arbitrary" means based on chance or personal preference rather than reason or a system — exactly as the sentence explains.
Reference: Standard English vocabulary in context (Oxford dictionary); IBA-style reading vocabulary.

Q6. If 2ˣ = 32, then x is:
A) 4
B) 5
C) 6
D) 8
Correct answer: B — 5
Explanation: 2⁵ = 32, so x = 5.
Reference: FSc Mathematics, Indices and Logarithms; standard algebra texts.

Q7. A fair die is rolled once. The probability of getting an even number is:
A) 1/6
B) 1/3
C) 1/2
D) 2/3
Correct answer: C — 1/2
Explanation: The even outcomes are 2, 4 and 6 — 3 out of 6 equally likely outcomes, so 3/6 = 1/2.
Reference: FSc Mathematics, Probability; standard probability texts.

Q8. The sum of the first 10 natural numbers is:
A) 45
B) 50
C) 55
D) 60
Correct answer: C — 55
Explanation: Sum = n(n + 1)/2 = 10 × 11/2 = 55. (1 + 2 + … + 10 = 55.)
Reference: FSc Mathematics, Sequences and Series; standard arithmetic texts.

Q9. The roots of x² − 5x + 6 = 0 are:
A) 2 and 3
B) 1 and 6
C) −2 and −3
D) 2 and −3
Correct answer: A — 2 and 3
Explanation: x² − 5x + 6 = (x − 2)(x − 3) = 0, so x = 2 or x = 3.
Reference: FSc Mathematics, Quadratic Equations; standard algebra texts.

Q10. A shopkeeper buys an item for Rs. 800 and sells it for Rs. 1,000. The profit percentage is:
A) 20%
B) 25%
C) 30%
D) 35%
Correct answer: B — 25%
Explanation: Profit = 1,000 − 800 = Rs. 200; profit % = (200 ÷ 800) × 100 = 25%.
Reference: Matric Mathematics, Profit and Loss; standard arithmetic texts.

Q11. Choose the word nearest in meaning to "Punctual":
A) Late
B) Prompt
C) Slow
D) Careless
Correct answer: B — Prompt
Explanation: "Punctual" means arriving or doing things at the agreed time, i.e. prompt; "late" is its opposite.
Reference: Standard English vocabulary (Oxford dictionary); IBA-style English word lists.

Q12. Choose the word most nearly opposite in meaning to "Brave":
A) Cowardly
B) Bold
C) Strong
D) Fearless
Correct answer: A — Cowardly
Explanation: "Brave" means ready to face danger; its opposite is "cowardly" (lacking courage).
Reference: Standard English vocabulary (Oxford dictionary); IBA-style English word lists.

Q13. Choose the correctly spelt word:
A) Occassion
B) Ocassion
C) Occasionn
D) Occasion
Correct answer: D — Occasion
Explanation: "Occasion" is spelt with double c and a single s: oc-ca-sion.
Reference: Standard English spelling (Oxford dictionary); FSc English vocabulary lists.

Q14. Choose the correct sentence:
A) The number of students are increasing.
B) The number of students is increasing.
C) The number of students were increasing.
D) The number of students have increasing.
Correct answer: B — The number of students is increasing.
Explanation: "The number of" is singular, so it takes the singular verb "is" (contrast with "a number of", which takes a plural verb).
Reference: Standard English grammar (subject-verb agreement); FSc English grammar texts.

Q15. Choose the correct sentence:
A) She speaks English fluent.
B) She speaks English fluency.
C) She speaks English fluently.
D) She speaks English more fluent.
Correct answer: C — She speaks English fluently.
Explanation: The verb "speaks" needs the adverb "fluently"; "fluent" is an adjective and cannot modify a verb.
Reference: Standard English grammar (adjectives and adverbs); FSc English grammar texts.

Q16. Choose the correct preposition: "He apologised ___ his mistake."
A) for
B) to
C) of
D) with
Correct answer: A — for
Explanation: The standard idiom is "apologise for" something (one apologises to a person for a mistake).
Reference: Standard English usage (Oxford dictionary); FSc English grammar texts.

Q17. Choose the correct word: "I have lived here ___ 2015."
A) for
B) since
C) from
D) by
Correct answer: B — since
Explanation: "Since" is used with a point in time (2015) with the present perfect; "for" is used with a length of time.
Reference: Standard English grammar (prepositions of time); FSc English grammar texts.

Q18. Choose the correct sentence:
A) The sun rise in the east.
B) The sun rising in the east.
C) The sun rises in the east.
D) The sun risen in the east.
Correct answer: C — The sun rises in the east.
Explanation: "The sun" is third-person singular, so the present simple verb takes -s: "rises".
Reference: Standard English grammar (present simple tense); FSc English grammar texts.

Q19. "The speaker gave a lucid explanation that everyone understood." The word "lucid" here means:
A) Clear and easy to understand
B) Confusing
C) Long
D) Boring
Correct answer: A — Clear and easy to understand
Explanation: "Lucid" means expressed clearly and easy to understand, which is why everyone understood the explanation.
Reference: Standard English vocabulary in context (Oxford dictionary); IBA-style reading vocabulary.

Q20. Read the passage and answer: "The city museum is free to visit on the first Sunday of every month. On other days, adults pay Rs. 200 while children under twelve enter free. The museum is closed on Mondays." On a Monday, the museum is:
A) Free for everyone
B) Open with normal charges
C) Open only for children
D) Closed
Correct answer: D — Closed
Explanation: The passage states directly that the museum "is closed on Mondays".
Reference: Standard reading-comprehension practice (IBA-style passage questions); worked from the passage itself.

Q21. Read the passage and answer: "Bilal practises the guitar for thirty minutes every day after school. His teacher says regular short practice is better than one long session once a week. After three months, Bilal can play five songs without mistakes." What does the teacher say?
A) Long weekly sessions are best
B) Regular short practice is better than one long weekly session
C) Bilal should stop practising
D) Songs must be memorised
Correct answer: B — Regular short practice is better than one long weekly session
Explanation: The passage states the teacher's view directly: "regular short practice is better than one long session once a week".
Reference: Standard reading-comprehension practice (IBA-style passage questions); worked from the passage itself.

Q22. Choose the correct sentence:
A) If it rains tomorrow, we stay at home.
B) If it rains tomorrow, we stayed at home.
C) If it rains tomorrow, we will stay at home.
D) If it rains tomorrow, we staying at home.
Correct answer: C — If it rains tomorrow, we will stay at home.
Explanation: In a first conditional about a real future possibility, the main clause uses "will" + verb.
Reference: Standard English grammar (conditionals); FSc English grammar texts.

Q23. Choose the correct word: "She is taller ___ her sister."
A) than
B) then
C) that
D) to
Correct answer: A — than
Explanation: Comparisons use "than" ("taller than"); "then" refers to time.
Reference: Standard English grammar (comparatives); FSc English grammar texts.

Q24. Choose the word nearest in meaning to "Sturdy":
A) Weak
B) Fragile
C) Strong
D) Soft
Correct answer: C — Strong
Explanation: "Sturdy" means strongly built and hard-wearing, i.e. strong; "weak" and "fragile" are near-opposites.
Reference: Standard English vocabulary (Oxford dictionary); IBA-style English word lists.

Q25. Choose the word most nearly opposite in meaning to "Generous":
A) Kind
B) Stingy
C) Rich
D) Helpful
Correct answer: B — Stingy
Explanation: "Generous" means giving freely; its opposite is "stingy" (unwilling to give).
Reference: Standard English vocabulary (Oxford dictionary); IBA-style English word lists.

Q26. Choose the correct sentence:
A) The children are playing in the park now.
B) The children is playing in the park now.
C) The children plays in the park now.
D) The children played in the park now.
Correct answer: A — The children are playing in the park now.
Explanation: "Children" is plural, so it takes "are playing"; "now" shows the action is happening at present.
Reference: Standard English grammar (subject-verb agreement and present continuous); FSc English grammar texts.

Q27. Choose the correctly spelt word:
A) Definately
B) Definitly
C) Definetly
D) Definitely
Correct answer: D — Definitely
Explanation: "Definitely" is spelt d-e-f-i-n-i-t-e-l-y (from "finite", not "definate").
Reference: Standard English spelling (Oxford dictionary); FSc English vocabulary lists.

Q28. Choose the correct sentence:
A) He did not come because he is ill.
B) He did not come because he has ill.
C) He did not come because he will be ill.
D) He did not come because he was ill.
Correct answer: D — He did not come because he was ill.
Explanation: The past-tense main clause "did not come" needs the past-tense "was" for the reason at that same past time.
Reference: Standard English grammar (tenses); FSc English grammar texts.

Q29. Read the passage and answer: "The new railway line connects the town to the city in just one hour, half the time the old road journey took. Farmers can now send fresh vegetables to the city market the same morning they are picked. Many people in the town say the railway has changed their daily lives." The railway journey takes:
A) Two hours
B) Half an hour
C) One hour
D) Three hours
Correct answer: C — One hour
Explanation: The passage states the railway connects the town to the city "in just one hour".
Reference: Standard reading-comprehension practice (IBA-style passage questions); worked from the passage itself.

Q30. The conjugate of 4 − 3i is:
A) 4 + 3i
B) −4 + 3i
C) −4 − 3i
D) 3 − 4i
Correct answer: A — 4 + 3i
Explanation: The conjugate of a complex number changes the sign of its imaginary part only, so the conjugate of 4 − 3i is 4 + 3i.
Reference: FSc Mathematics, Complex Numbers; standard algebra texts.

Q31. The sum (2 + 3i) + (1 − 2i) is:
A) 3 + i
B) 3 + 5i
C) 1 + i
D) 3 − i
Correct answer: A — 3 + i
Explanation: Add real parts (2 + 1 = 3) and imaginary parts (3i − 2i = i), giving 3 + i.
Reference: FSc Mathematics, Complex Numbers; standard algebra texts.

Q32. The modulus of 3 + 4i is:
A) 7
B) 5
C) 25
D) 1
Correct answer: B — 5
Explanation: |3 + 4i| = √(3² + 4²) = √(9 + 16) = √25 = 5.
Reference: FSc Mathematics, Complex Numbers; standard algebra texts.

Q33. The determinant of the matrix [[2, 3], [1, 4]] is:
A) 11
B) 3
C) 5
D) 8
Correct answer: C — 5
Explanation: det = 2 × 4 − 3 × 1 = 8 − 3 = 5.
Reference: FSc Mathematics, Matrices and Determinants; standard algebra texts.

Q34. If A = [[1, 2], [3, 4]] and B = [[0, 1], [1, 0]], the (1, 2) entry of A + B is:
A) 2
B) 4
C) 1
D) 3
Correct answer: D — 3
Explanation: Add entries in the same positions: the (1, 2) entry is 2 + 1 = 3.
Reference: FSc Mathematics, Matrices and Determinants; standard algebra texts.

Q35. The 8th term of the arithmetic sequence 3, 7, 11, 15, … is:
A) 27
B) 35
C) 39
D) 31
Correct answer: D — 31
Explanation: First term a = 3, common difference d = 4; 8th term = a + 7d = 3 + 28 = 31. (The terms run 3, 7, 11, 15, 19, 23, 27, 31.)
Reference: FSc Mathematics, Sequences and Series; standard algebra texts.

Q36. The next term of the geometric sequence 3, 6, 12, 24, … is:
A) 48
B) 36
C) 42
D) 96
Correct answer: A — 48
Explanation: The common ratio is 2 (each term is double the previous one), so the next term is 24 × 2 = 48.
Reference: FSc Mathematics, Sequences and Series; standard algebra texts.

Q37. The sum 1 + 2 + 4 + 8 + 16 is:
A) 30
B) 32
C) 31
D) 15
Correct answer: C — 31
Explanation: Adding directly: 1 + 2 = 3, + 4 = 7, + 8 = 15, + 16 = 31. (It is a geometric series with ratio 2.)
Reference: FSc Mathematics, Sequences and Series; standard algebra texts.

Q38. The value of 5! is:
A) 25
B) 60
C) 720
D) 120
Correct answer: D — 120
Explanation: 5! = 5 × 4 × 3 × 2 × 1 = 120.
Reference: FSc Mathematics, Permutation and Combination; standard algebra texts.

Q39. The value of ⁵C₂ (5 choose 2) is:
A) 5
B) 10
C) 20
D) 25
Correct answer: B — 10
Explanation: ⁵C₂ = 5! ÷ (2! × 3!) = 120 ÷ (2 × 6) = 10.
Reference: FSc Mathematics, Permutation and Combination; standard algebra texts.

Q40. Two fair coins are tossed once. The probability of getting two heads is:
A) 1/4
B) 1/2
C) 3/4
D) 1
Correct answer: A — 1/4
Explanation: There are 4 equally likely outcomes (HH, HT, TH, TT) and only one is HH, so the probability is 1/4.
Reference: FSc Mathematics, Probability; standard probability texts.

Q41. Two fair coins are tossed once. The probability of getting at least one head is:
A) 1/4
B) 1/2
C) 3/4
D) 1
Correct answer: C — 3/4
Explanation: The favourable outcomes are HH, HT and TH — 3 out of 4 equally likely outcomes, so 3/4.
Reference: FSc Mathematics, Probability; standard probability texts.

Q42. The value of sin 60° is:
A) 1/2
B) √3/2
C) 1
D) 1/√3
Correct answer: B — √3/2
Explanation: sin 60° = √3/2 is a standard trigonometric value (opposite/hypotenuse in a 30°–60°–90° triangle).
Reference: FSc Mathematics, Trigonometry; standard trigonometry texts.

Q43. The value of sec 60° is:
A) 2
B) 1
C) 1/2
D) √3
Correct answer: A — 2
Explanation: sec 60° = 1 ÷ cos 60° = 1 ÷ (1/2) = 2.
Reference: FSc Mathematics, Trigonometry; standard trigonometry texts.

Q44. The value of sec²θ − tan²θ is:
A) 0
B) tan θ
C) 2
D) 1
Correct answer: D — 1
Explanation: From the identity 1 + tan²θ = sec²θ, rearranging gives sec²θ − tan²θ = 1 for every angle θ.
Reference: FSc Mathematics, Trigonometry; standard trigonometry texts.

Q45. If f(x) = 2x + 1, then f(3) is:
A) 6
B) 8
C) 7
D) 5
Correct answer: C — 7
Explanation: f(3) = 2 × 3 + 1 = 6 + 1 = 7.
Reference: FSc Mathematics, Functions; standard algebra texts.

Q46. The value of lim (x → 2) (x + 3) is:
A) 2
B) 5
C) 3
D) 6
Correct answer: B — 5
Explanation: x + 3 is continuous, so the limit as x approaches 2 is 2 + 3 = 5.
Reference: FSc Mathematics, Functions and Limits; standard calculus texts.

Q47. The value of lim (x → 0) (sin x)/x is:
A) 0
B) ∞
C) Does not exist
D) 1
Correct answer: D — 1
Explanation: This is the standard limit lim (x → 0) (sin x)/x = 1, proved by the squeeze theorem.
Reference: FSc Mathematics, Functions and Limits; standard calculus texts.

Q48. The distance between the points (0, 0) and (6, 8) is:
A) 8
B) 10
C) 14
D) 100
Correct answer: B — 10
Explanation: Distance = √(6² + 8²) = √(36 + 64) = √100 = 10.
Reference: FSc Mathematics, Analytical Geometry; standard geometry texts.

Q49. The midpoint of the line segment joining (2, 4) and (6, 8) is:
A) (3, 5)
B) (4, 6)
C) (4, 5)
D) (8, 12)
Correct answer: B — (4, 6)
Explanation: Midpoint = ((2 + 6)/2, (4 + 8)/2) = (4, 6).
Reference: FSc Mathematics, Analytical Geometry; standard geometry texts.

Q50. The slope of the line joining (1, 2) and (5, 10) is:
A) 1/2
B) 4
C) 2
D) 8
Correct answer: C — 2
Explanation: Slope = (10 − 2) ÷ (5 − 1) = 8 ÷ 4 = 2.
Reference: FSc Mathematics, Analytical Geometry; standard algebra texts.