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Sample IBA Karachi Test Practice Questions

Try these sample questions to review concepts for the IBA Karachi Test exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1If a positive integer n is divided by 7, the remainder is 5. What is the remainder when (3n + 8) is divided by 7?
A.1
B.2
C.4
D.5
Explanation: Since n leaves a remainder of 5 upon division by 7, we can write n = 7k + 5 for some integer k. Substituting this into the expression yields 3(7k + 5) + 8 = 21k + 15 + 8 = 21k + 23. Dividing 23 by 7 gives 3 with a remainder of 2 (23 = 3 × 7 + 2). Therefore, the remainder when (3n + 8) is divided by 7 is 2.
2What is the sum of all real values of x that satisfy the equation 2^(2x + 1) - 5(2^x) + 2 = 0?
A.-1
B.0
C.1
D.2.5
Explanation: Rewrite 2^(2x + 1) as 2 · (2^x)^2. Letting y = 2^x, the equation becomes 2y^2 - 5y + 2 = 0. Factoring gives (2y - 1)(y - 2) = 0, which yields y = 1/2 or y = 2. Setting 2^x = 1/2 gives x = -1, and 2^x = 2 gives x = 1. The sum of these real solutions is (-1) + 1 = 0.
3How many integer values of x satisfy the inequality |2x - 7| ≤ 9?
A.8
B.9
C.10
D.11
Explanation: The absolute value inequality |2x - 7| ≤ 9 expands to -9 ≤ 2x - 7 ≤ 9. Adding 7 to all parts gives -2 ≤ 2x ≤ 16. Dividing by 2 yields -1 ≤ x ≤ 8. The integers in this closed interval are -1, 0, 1, 2, 3, 4, 5, 6, 7, and 8, giving a total of 8 - (-1) + 1 = 10 integers.
4For what values of k does the quadratic equation x^2 - (k + 2)x + (2k + 1) = 0 have equal real roots?
A.k = 0 or k = 4
B.k = 2 or k = -2
C.k = 1 or k = 4
D.k = -4 or k = 0
Explanation: A quadratic equation ax^2 + bx + c = 0 has equal real roots when its discriminant Δ = b^2 - 4ac equals 0. Here, Δ = [-(k + 2)]^2 - 4(1)(2k + 1) = (k^2 + 4k + 4) - (8k + 4) = k^2 - 4k. Setting k^2 - 4k = 0 yields k(k - 4) = 0, which gives k = 0 or k = 4.
5When the polynomial P(x) = 2x^3 - 3x^2 + kx - 5 is divided by (x - 2), the remainder is 7. What is the value of k?
A.2
B.3
C.4
D.6
Explanation: According to the Remainder Theorem, dividing P(x) by (x - 2) yields a remainder equal to P(2). Evaluating P(2) gives 2(2)^3 - 3(2)^2 + k(2) - 5 = 2(8) - 3(4) + 2k - 5 = 16 - 12 + 2k - 5 = 2k - 1. Setting this equal to 7 yields 2k - 1 = 7, so 2k = 8, which simplifies to k = 4.
6If 3x + 4y = 18 and 4x + 3y = 17, what is the value of (x - y)?
A.-2
B.-1
C.1
D.5
Explanation: Subtract the first equation directly from the second: (4x + 3y) - (3x + 4y) = 17 - 18. This immediately simplifies to (4x - 3x) + (3y - 4y) = -1, which gives x - y = -1. There is no need to solve for individual values of x and y.
7Given the function f(x) = (2x + 1)/(x - 3) for x ≠ 3, what is the value of f^(-1)(5)?
A.11/3
B.14/3
C.16/3
D.6
Explanation: To find f^(-1)(5), set f(x) = 5 and solve for x: (2x + 1)/(x - 3) = 5. Multiplying both sides by (x - 3) yields 2x + 1 = 5(x - 3) = 5x - 15. Rearranging terms gives 1 + 15 = 5x - 2x, so 16 = 3x, which results in x = 16/3.
8What is the domain of the real-valued function g(x) = sqrt((x - 2)/(5 - x))?
A.[2, 5]
B.[2, 5)
C.(2, 5]
D.(-∞, 2] ∪ (5, ∞)
Explanation: For g(x) to be defined in real numbers, the radicand must be non-negative: (x - 2)/(5 - x) ≥ 0, and the denominator cannot be zero: 5 - x ≠ 0, meaning x ≠ 5. Multiplying numerator and denominator by -1 gives (x - 2)/(x - 5) ≤ 0. The expression is zero at x = 2 and negative between 2 and 5. Because x = 5 makes the denominator zero, x = 5 is excluded, yielding the domain [2, 5).
9Line segment AB joins A(1, 4) and B(5, -2). Which of the following is the equation of the perpendicular bisector of segment AB?
A.2x - 3y - 3 = 0
B.3x + 2y - 11 = 0
C.2x + 3y - 9 = 0
D.3x - 2y - 7 = 0
Explanation: The midpoint M of AB is ((1 + 5)/2, (4 + (-2))/2) = (3, 1). The slope of AB is m_AB = (-2 - 4)/(5 - 1) = -6/4 = -3/2. The slope of the perpendicular bisector is the negative reciprocal: m_perp = 2/3. Using the point-slope form with M(3, 1): y - 1 = (2/3)(x - 3), which gives 3(y - 1) = 2(x - 3) => 3y - 3 = 2x - 6 => 2x - 3y - 3 = 0.
10A circle in the Cartesian plane has the equation x^2 + y^2 - 6x + 8y - 11 = 0. What is the area of this circle?
A.25π
B.36π
C.49π
D.64π
Explanation: Complete the square for both x and y: (x^2 - 6x + 9) + (y^2 + 8y + 16) = 11 + 9 + 16. This factors into (x - 3)^2 + (y + 4)^2 = 36. In standard form (x - h)^2 + (y - k)^2 = r^2, r^2 = 36. The area of the circle is A = πr^2 = 36π.

About the IBA Karachi Test Exam

Independent English-language practice by OpenExamPrep for IBA undergraduate mathematics and English. Published eligibility includes HSSC 65% for BBA and 60% for several BS programs, with program-specific mathematics prerequisites and equivalent-qualification rules. The bank covers selected arithmetic, algebra, geometry, grammar and reading skills; applicants should also review the mathematics scope for their school, especially SMCS advanced topics. Official samples are in English. The current criteria list MCQs, with interviews conditional on the admission route; no mandatory practical or case-study component was identified in those test criteria.

Exam sponsor: Institute of Business Administration (IBA), Karachi. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Mathematics and English-composition MCQs. Fall 2026 uses a common undergraduate test across the three schools, with separate school applications and fees. Program-specific interview or direct-admission criteria also apply; this bank does not simulate interviews.

Time Limit

Confirm the current duration on the IBA test instructions/admit card; a 2026 duration was not independently confirmed.

Passing Score

Program/round-specific English, mathematics and aggregate cutoffs; direct admission and interview thresholds differ. No universal pass mark.

Exam / Certification Fees

Use the current school application voucher; no 2026 amount was independently confirmed. Tuition and admission charges are separate.

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Official sources

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

50% of this study bank; not an official mark weight

Mathematics

Arithmetic, percentages, algebra, functions, geometry and probability; consult the applicable school syllabus.

50% of this study bank; not an official mark weight

English

Grammar, vocabulary, reading comprehension and reasoning about passages.

Preparing for the IBA Karachi Test Exam

What You Need to Know

  • Passing score: Program/round-specific English, mathematics and aggregate cutoffs; direct admission and interview thresholds differ. No universal pass mark.
  • Assessment: Mathematics and English-composition MCQs. Fall 2026 uses a common undergraduate test across the three schools, with separate school applications and fees. Program-specific interview or direct-admission criteria also apply; this bank does not simulate interviews.
  • Time limit: Confirm the current duration on the IBA test instructions/admit card; a 2026 duration was not independently confirmed.
  • Exam / certification fees: Use the current school application voucher; no 2026 amount was independently confirmed. Tuition and admission charges are separate. Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

IBA Karachi Test: Suggested Study Strategy

1Consult the mathematics syllabus for your school.
2Practise reading each passage independently.
3Check separate English, mathematics and interview/direct-admission cutoffs.

Frequently Asked Questions

Is the test separate for every school?

The Fall 2026 schedule specifies a common undergraduate test, while school applications, fees and admission criteria remain separate.

Can historical samples establish current timing or marking?

No. Use them for topic practice and follow the current admit card and test instructions for operational rules.