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Free Practice Questions for Karnataka II PUC Basic Mathematics (KSEAB)

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Key Facts: Karnataka II PUC Basic Mathematics (KSEAB) Exam

Code 75

Official II PUC Basic Mathematics subject code

KSEAB / DPUE II PUC blueprint 2025–26

≠ Code 35

Distinct from II PUC Mathematics (science-stream full maths)

KSEAB subject codes / DPUE blueprints

~80 theory

Commonly described written theory marks pattern (confirm year notice)

KSEAB II PUC assessment reporting / model papers

~3 hours

Typical II PUC exam duration (confirm date sheet)

KSEAB II PUC exam logistics reporting

~30% / ~33%

Commonly reported per-subject minimum and overall aggregate pass range

KSEAB pass criteria reporting (confirm current circular)

Mixed paper

Official format is objective + subjective, not pure MCQ

KSEAB II PUC Basic Mathematics blueprint Parts A–E style

English MCQ adaptation

This free local bank is not the official mixed paper format

OpenExamPrep practice policy

KSEAB II PUC Basic Mathematics (code 75) is the commerce/arts Class 12 board maths paper — mixed objective + subjective (~3 h), theory commonly ~80 marks plus internal. Pass is commonly ~30% per subject and ~33% aggregate as notified. Distinct from full Maths (35). This free 2026 bank is an English MCQ study adaptation with calculations — not an official paper simulation.

Sample Karnataka II PUC Basic Mathematics (KSEAB) Practice Questions

Try these sample questions to review concepts for the Karnataka II PUC Basic Mathematics (KSEAB) exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1If A = [[2, 3], [1, 4]] and B = [[1, 0], [2, 1]], what is the product matrix AB?
A.[[8, 3], [9, 4]]
B.[[2, 0], [2, 4]]
C.[[5, 3], [9, 4]]
D.[[8, 0], [9, 1]]
Explanation: Matrix multiplication uses row-by-column products: (1,1)=2·1+3·2=8, (1,2)=2·0+3·1=3, (2,1)=1·1+4·2=9, (2,2)=1·0+4·1=4. Therefore AB = [[8, 3], [9, 4]].
2Find the determinant of the matrix [[5, 2], [3, 4]].
A.26
B.14
C.−2
D.20
Explanation: For a 2×2 matrix [[a, b], [c, d]], det = ad − bc = 5·4 − 2·3 = 20 − 6 = 14.
3If A = [[1, 2], [3, 4]], what is A + Aᵀ (the sum of A and its transpose)?
A.[[2, 4], [6, 8]]
B.[[1, 5], [5, 4]]
C.[[2, 5], [5, 8]]
D.[[0, −1], [1, 0]]
Explanation: Aᵀ = [[1, 3], [2, 4]]. Adding entrywise gives (1,1)=2, (1,2)=5, (2,1)=5, (2,2)=8. So A + Aᵀ = [[2, 5], [5, 8]], which is symmetric.
4Solve for x if |[[x, 2], [3, 4]]| = 10.
A.x = 5
B.x = 2
C.x = 1
D.x = 4
Explanation: Determinant condition: 4x − 6 = 10 ⇒ 4x = 16 ⇒ x = 4.
5If A = [[2, 1], [0, 3]], find A⁻¹ using (1/det A)·adj A.
A.[[1/2, −1/6], [0, 1/3]]
B.[[3, −1], [0, 2]]
C.[[1/2, 1/6], [0, 1/3]]
D.[[2, −1], [0, 3]]
Explanation: det A = 2·3 − 1·0 = 6. adj A = [[3, −1], [0, 2]]. So A⁻¹ = (1/6)·[[3, −1], [0, 2]] = [[1/2, −1/6], [0, 1/3]].
6Evaluate the 3×3 determinant |[[1, 2, 3], [0, 4, 5], [0, 0, 6]]|.
A.0
B.24
C.30
D.12
Explanation: An upper-triangular matrix has determinant equal to the product of its diagonal entries: 1·4·6 = 24.
7If A is a 2×2 matrix with det(A) = 5, what is det(3A)?
A.15
B.5
C.45
D.9
Explanation: For an n×n matrix, det(kA) = kⁿ det(A). Here n = 2, so det(3A) = 3²·5 = 9·5 = 45.
8The system 2x + y = 5 and 4x + 2y = 10 has:
A.A unique solution
B.No solution
C.Exactly two solutions
D.Infinitely many solutions
Explanation: The second equation is exactly twice the first, so the equations are dependent. The coefficient determinant |[[2,1],[4,2]]| = 0 with a consistent right-hand side, giving infinitely many solutions.
9If A = [[0, −2], [2, 0]], which statement is true?
A.A is skew-symmetric and det(A) = 4
B.A is symmetric and det(A) = 0
C.A is skew-symmetric and det(A) = −4
D.A is diagonal with det(A) = 4
Explanation: Aᵀ = [[0, 2], [−2, 0]] = −A, so A is skew-symmetric. det(A) = 0·0 − (−2)·2 = 4.
10Using Cramer’s rule, solve x + 2y = 8 and 3x − y = 3 for x.
A.x = 14
B.x = 2
C.x = 3
D.x = −2
Explanation: D = |[[1, 2], [3, −1]]| = −1 − 6 = −7. Dₓ = |[[8, 2], [3, −1]]| = −8 − 6 = −14. Therefore x = Dₓ/D = (−14)/(−7) = 2. Check: y = (8−2)/2 = 3 and 3(2)−3 = 3.

About the Karnataka II PUC Basic Mathematics (KSEAB) Exam

Karnataka II PUC Basic Mathematics is the Class 12 Pre-University public examination Basic Mathematics paper (subject code 75) under the Karnataka School Examination and Assessment Board (KSEAB). It is the commerce/arts-track lighter mathematics paper, distinct from II PUC Mathematics (code 35). Syllabus units cover Algebra (matrices & determinants, permutations & combinations, probability, binomial theorem, partial fractions, mathematical logic), Commercial Arithmetic (ratios & proportions, bill discounting, stocks & shares, learning curve, linear programming, sales tax & VAT), Trigonometry (heights & distances; compound/multiple angles), Analytical Geometry (circles, parabola), and Calculus (limits & continuity, differential calculus, application of derivatives, indefinite integrals, definite integrals & areas). The official assessment is a mixed objective + subjective paper with theory marks commonly described as 80 plus internal assessment. Fees and exact blueprints are notified by KSEAB on kseab.karnataka.gov.in and the DPUE blueprint portal (including the code-75 Basic Maths PDF). The 100 questions on this page are a free English-language multiple-choice study adaptation with step-by-step worked calculations; they are not a full simulation of the official mixed paper.

Exam sponsor: Karnataka School Examination and Assessment Board (KSEAB). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Official KSEAB II PUC Basic Mathematics (subject code 75) is assessed as a mixed paper: 1-mark objective-style items plus multi-mark short and long answers under the year’s blueprint weightage framework, lasting about 3 hours (sometimes described with reading time up to about 3 hours 15 minutes — confirm the date sheet). Theory is widely associated with an 80-mark written component plus 20 internal assessment for non-practical subjects — confirm the year’s circular on kseab.karnataka.gov.in. This practice bank is an English-language MCQ study adaptation for concept and calculation fluency — it does not simulate official attempt limits, Part choices, subjective long answers, or internal assessment. Basic Mathematics is the commerce/arts-track paper and is not the same syllabus as Mathematics (code 35).

Time Limit

About 3 hours (confirm year’s date sheet)

Passing Score

Commonly reported as about 30% minimum per subject (often 24/80 on the theory paper for non-practical subjects) together with about 33% overall aggregate as published by KSEAB for the year; verify the current pass criteria circular.

Exam / Certification Fees

As notified by KSEAB and paid through PU colleges for regular II PUC sittings (no single fixed public subject fee for all categories).

Exam sponsor website

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

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.

~10% of this local bank

Matrices and Determinants

2×2 products, determinants, inverse, transpose/symmetry, Cramer’s rule, and consistency of linear systems.

~5% of this local bank

Permutations and Combinations

Factorials, nPr, nCr, and number-formation without repetition.

~4% of this local bank

Probability

Classical probability on dice, coins, and urns; independent events product rule.

~6% of this local bank

Binomial Theorem

General term, middle/constant terms, coefficients, and simple numerical expansions.

~3% of this local bank

Partial Fractions

Linear-factor decompositions and cover-up evaluation of constants.

~4% of this local bank

Mathematical Logic

Connectives, negation of quantifiers, tautologies, and implication truth cases.

~8% of this local bank

Ratios and Proportions

Compound ratios, division in a ratio, mixtures, proportion properties, and direct variation.

~4% of this local bank

Bill Discounting

Banker's discount, true discount, present worth, and banker's gain calculations.

~3% of this local bank

Stocks and Shares

Cash to buy stock at a market price and dividend income from face value.

~3% of this local bank

Learning Curve

Cumulative average time when output doubles under 80% or 90% learning rates.

~3% of this local bank

Linear Programming

Corner-point evaluation of linear objectives on polygonal feasible regions.

~3% of this local bank

Sales Tax and VAT

Sales tax totals, discount-then-tax, and net VAT payable.

~3% of this local bank

Heights and Distances

Elevation and depression problems with tan of 30°/45°/60°.

~6% of this local bank

Compound and Multiple Angles

sin/cos of 15°/75°, double-angle identities, and tan(A±B).

~5% of this local bank

Circles

Standard and general equations, centre-radius, point position, diameter form.

~3% of this local bank

Parabola

y² = 4ax focus, directrix, and vertex.

~6% of this local bank

Limits and Continuity

Algebraic limits, standard trig limits, infinity limits, and piecewise continuity.

~7% of this local bank

Differential Calculus

Power, chain, product, trig, exponential, and log derivatives.

~5% of this local bank

Application of Derivatives

Critical points, monotonicity, velocity, max/min, and tangent slopes.

~5% of this local bank

Indefinite Integrals

Standard antiderivatives of polynomials, trig, exponential, and 1/x.

~4% of this local bank

Definite Integrals and Areas

Fundamental theorem evaluations and area under y = x-type curves.

Preparing for the Karnataka II PUC Basic Mathematics (KSEAB) Exam

What You Need to Know

  • Passing score: Commonly reported as about 30% minimum per subject (often 24/80 on the theory paper for non-practical subjects) together with about 33% overall aggregate as published by KSEAB for the year; verify the current pass criteria circular.
  • Assessment: Official KSEAB II PUC Basic Mathematics (subject code 75) is assessed as a mixed paper: 1-mark objective-style items plus multi-mark short and long answers under the year’s blueprint weightage framework, lasting about 3 hours (sometimes described with reading time up to about 3 hours 15 minutes — confirm the date sheet). Theory is widely associated with an 80-mark written component plus 20 internal assessment for non-practical subjects — confirm the year’s circular on kseab.karnataka.gov.in. This practice bank is an English-language MCQ study adaptation for concept and calculation fluency — it does not simulate official attempt limits, Part choices, subjective long answers, or internal assessment. Basic Mathematics is the commerce/arts-track paper and is not the same syllabus as Mathematics (code 35).
  • Time limit: About 3 hours (confirm year’s date sheet)
  • Exam / certification fees: As notified by KSEAB and paid through PU colleges for regular II PUC sittings (no single fixed public subject fee for all categories). 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

Karnataka II PUC Basic Mathematics (KSEAB): Suggested Study Strategy

1Practice official KSEAB II PUC Basic Maths model papers under timed conditions so you can switch from MCQ drills to written multi-mark answers with attempt choices.
2Blueprint weight is heavy on Matrices & Determinants, Ratios & Proportions, and Calculus chapters — prioritize those early and revise weekly.
3Commercial arithmetic formulas (BD, TD, stocks income, learning-curve doubling) are high-yield for code 75 and do not appear in the same form on code 35 Maths.
4Keep Basic Maths distinct from full Maths (35): skip vectors/3D/DE-heavy science drills unless they appear in your code-75 syllabus notes.
5Build a formula sheet for compound angles, circle/parabola standard forms, derivative/integral standards, and VAT/bill discount identities.
6Use English-medium wording if you study in English; also review official KSEAB blueprint language and model papers for Part A–E structure.

Frequently Asked Questions

Is the official KSEAB II PUC Basic Mathematics exam pure multiple-choice?

No. Official KSEAB II PUC Basic Mathematics (code 75) is a mixed paper with 1-mark objective-style items and multi-mark short/long answers under the year’s blueprint framework. This bank is an English-language multiple-choice study adaptation for concepts and multi-step calculations only — not an official paper simulation.

What is the subject code for II PUC Basic Mathematics?

KSEAB II PUC Basic Mathematics is subject code 75. It is distinct from II PUC Mathematics, which is subject code 35. Confirm the year’s date sheet and question paper instructions on kseab.karnataka.gov.in and the DPUE blueprint portal.

How is Basic Mathematics (75) different from Mathematics (35)?

Basic Mathematics is the commerce/arts-track paper with commercial arithmetic (bill discounting, stocks & shares, learning curve, sales tax/VAT), mathematical logic, partial fractions, and a lighter calculus/geometry load. Mathematics (35) follows the NCERT Class 12 science-stream outline (relations & functions, inverse trig, vectors, 3D geometry, differential equations, heavier integrals). Do not treat the two banks as interchangeable.

How long is the KSEAB II PUC Basic Mathematics paper?

II PUC papers are commonly scheduled for about 3 hours, and some logistics descriptions still reference about 3 hours 15 minutes including reading time. Confirm the year’s date sheet and instructions on kseab.karnataka.gov.in.

What is the passing score for KSEAB II PUC Basic Mathematics?

Recent reporting commonly describes about 30% minimum per subject (often 24 out of 80 on the theory paper for non-practical subjects) together with about 33% overall aggregate as notified by KSEAB. Always verify the current result/pass criteria circular for your examination year.

What is the theory–internal mark pattern?

II PUC Basic Mathematics is commonly described under an 80 theory + 20 internal assessment pattern for non-practical subjects. Exact section marks and internal weightage are as published by KSEAB for the year — check official circulars on kseab.karnataka.gov.in.

How much does the KSEAB II PUC Basic Mathematics exam cost?

Basic Mathematics is not sold as a separate marketplace product. Fees are notified by KSEAB and paid through PU colleges for regular candidates. Check kseab.karnataka.gov.in for the current fee circular.

Where can I find the official blueprint?

KSEAB publishes II PUC subject-wise blueprints for 2025–26 at https://dpue-exam.karnataka.gov.in/kseabdpueqpue/PUExamBluePrint2026.aspx, including the Basic Mathematics (75) PDF. Also see pue.karnataka.gov.in for syllabus materials.