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Free Practice Questions for Karnataka II PUC Mathematics (KSEAB)

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Key Facts: Karnataka II PUC Mathematics (KSEAB) Exam

Code 35

Official II PUC Mathematics subject code

KSEAB / DPUE II PUC blueprint 2025–26

80/120

Marks to earn vs marks in the question framework

KSEAB II PUC Mathematics weightage framework 2025–26

3 h 15 m

Typical II PUC exam duration including reading time

KSEAB II PUC exam logistics / date sheet reporting

~30% / ~33%

Commonly reported per-subject minimum and overall aggregate pass range

KSEAB pass criteria reporting (confirm current circular)

80+20 pattern

Commonly described theory + internal split (confirm year notice)

KSEAB II PUC assessment reporting

Mixed paper

Official format is objective + subjective, not pure MCQ

KSEAB II PUC Mathematics blueprint Parts A–E

English MCQ adaptation

This free local bank is not the official mixed paper format

OpenExamPrep practice policy

KSEAB II PUC Mathematics (code 35) is a Class 12 board subject with a mixed objective + subjective paper (~3 h 15 min) under a 120-mark framework earning 80 theory marks plus ~20 internal. Pass is commonly ~30% per subject and ~33% aggregate as notified. Fees are paid through colleges. This free 2026 bank is an English MCQ study adaptation — not an official paper simulation.

Sample Karnataka II PUC Mathematics (KSEAB) Practice Questions

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

1Let R be a relation on the set A = {1, 2, 3} defined by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}. Then R is:
A.reflexive only
B.symmetric only
C.reflexive and symmetric but not transitive
D.an equivalence relation
Explanation: R contains (1,1), (2,2), (3,3), so it is reflexive. Both (1,2) and (2,1) are present, so it is symmetric. For transitivity, the only non-diagonal pairs involve 1 and 2: (1,2) with (2,1) yields (1,1)∈R and (2,1) with (1,2) yields (2,2)∈R. Thus R is an equivalence relation partitioning A into {1,2} and {3}.
2The number of binary relations on a set with 3 elements is:
A.9
B.27
C.512
D.256
Explanation: A set with 3 elements has 3×3 = 9 ordered pairs in A×A. Each pair may either belong to a relation or not, so there are 2^9 = 512 binary relations.
3Let f: R → R be defined by f(x) = x² + 1. Then f is:
A.one-one and onto
B.one-one but not onto
C.onto but not one-one
D.neither one-one nor onto
Explanation: f(1) = f(−1) = 2, so f is not one-one. Range is [1, ∞), not all of R, so f is not onto R. Hence neither one-one nor onto.
4If f(x) = 2x − 3 and g(x) = x² + 1, then (f ∘ g)(2) equals:
A.3
B.5
C.7
D.11
Explanation: g(2) = 4 + 1 = 5. Then f(g(2)) = f(5) = 2·5 − 3 = 7.
5Let A = {1, 2, 3} and B = {a, b}. The number of onto functions from A to B is:
A.6
B.8
C.9
D.2
Explanation: Total functions: 2³ = 8. Exactly 2 constant functions are not onto. So onto functions = 8 − 2 = 6. Equivalently, 2! · S(3,2) = 2 · 3 = 6.
6If f: R → R is defined by f(x) = 3x + 2, then f⁻¹(x) is:
A.(x − 2)/3
B.(x + 2)/3
C.3x − 2
D.x/3 − 2
Explanation: Set y = 3x + 2 ⇒ x = (y − 2)/3. Replacing y by x gives f⁻¹(x) = (x − 2)/3.
7A relation R on Z defined by aRb iff a − b is divisible by 5 is:
A.reflexive only
B.symmetric only
C.an equivalence relation
D.neither reflexive nor symmetric
Explanation: a − a = 0 is divisible by 5 (reflexive). If 5 | (a−b) then 5 | (b−a) (symmetric). If 5|(a−b) and 5|(b−c) then 5|(a−c) (transitive). Hence R is an equivalence relation (congruence modulo 5).
8If f(x) = sin x and g(x) = x², then (g ∘ f)(π/6) equals:
A.1/4
B.1/2
C.√3/2
D.π²/36
Explanation: f(π/6) = sin(π/6) = 1/2. Then g(f(π/6)) = (1/2)² = 1/4.
9The principal value of sin⁻¹(1/2) is:
A.π/6
B.π/3
C.π/2
D.5π/6
Explanation: The principal range of sin⁻¹ is [−π/2, π/2]. Since sin(π/6) = 1/2 and π/6 lies in that range, sin⁻¹(1/2) = π/6.
10The domain of the function f(x) = cos⁻¹(2x − 1) is:
A.[0, 1]
B.[−1, 1]
C.[0, 2]
D.[−1, 0]
Explanation: cos⁻¹ is defined for arguments in [−1, 1], so −1 ≤ 2x − 1 ≤ 1. Adding 1: 0 ≤ 2x ≤ 2, so 0 ≤ x ≤ 1.

About the Karnataka II PUC Mathematics (KSEAB) Exam

Karnataka II PUC Mathematics is the Class 12 Pre-University public examination mathematics paper (subject code 35) under the Karnataka School Examination and Assessment Board (KSEAB). It assesses NCERT Class 12 Mathematics as adopted in Karnataka: Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants, Continuity and Differentiability, Application of Derivatives, Integrals, Application of Integrals, Differential Equations, Vector Algebra, Three Dimensional Geometry, Linear Programming, and Probability. The official 2025–26 weightage framework allots 120 marks of which candidates earn 80, with heaviest weight on Integrals and Continuity & Differentiability. The official assessment is a mixed objective + subjective paper lasting about 3 hours 15 minutes. Fees and exact blueprints are notified by KSEAB on kseab.karnataka.gov.in and the DPUE blueprint portal; pass marks are commonly described as about 30% per subject with ~33% aggregate. 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 Mathematics (subject code 35) is assessed as a mixed paper: 1-mark objective-style items plus multi-mark short and long answers under a 120-mark framework (candidates earn 80 theory marks), lasting about 3 hours 15 minutes including reading time for many II PUC subjects. Theory is widely associated with an 80 mark written component plus 20 internal assessment — 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 E choices, subjective long answers, or internal assessment.

Time Limit

3 hours 15 minutes

Passing Score

Commonly reported as about 30% minimum per subject (often cited as 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.

~8% of this local bank

Relations and Functions

Equivalence relations, one-one/onto functions, inverse functions, composition, and number of relations/functions on finite sets.

~5% of this local bank

Inverse Trigonometric Functions

Principal values, domain and range, and standard inverse-trig simplifications and identities.

~8% of this local bank

Matrices

Order, addition/multiplication, transpose, symmetric and skew-symmetric matrices, and inverse via elementary operations concepts.

~10% of this local bank

Determinants

2×2 and 3×3 evaluation, properties, area of triangle, adjoint and inverse, and consistency of linear systems.

~14% of this local bank

Continuity and Differentiability

Limits and continuity checks, derivatives of composite and inverse functions, logarithmic differentiation, and higher-order derivatives.

~7% of this local bank

Application of Derivatives

Increasing/decreasing intervals, equations of tangents and normals, and maxima–minima word problems.

~15% of this local bank

Integrals

Standard antiderivatives, substitution, partial fractions, integration by parts, and definite-integral properties.

~4% of this local bank

Application of Integrals

Area under a curve and area bounded between two curves using definite integrals.

~6% of this local bank

Differential Equations

Order and degree, variable-separable, homogeneous, and linear first-order equations with particular solutions.

~6% of this local bank

Vector Algebra

Magnitude, unit vectors, dot and cross products, and geometric conditions (perpendicular, parallel, area of parallelogram).

~5% of this local bank

Three Dimensional Geometry

Direction cosines/ratios, cartesian and vector equations of lines, and plane equations and distances.

~5% of this local bank

Linear Programming

Formulating constraints, identifying feasible regions, and reading optimal values from corner points.

~7% of this local bank

Probability

Conditional probability, independent events, total probability, and Bayes’ theorem multi-step calculations.

Preparing for the Karnataka II PUC Mathematics (KSEAB) Exam

What You Need to Know

  • Passing score: Commonly reported as about 30% minimum per subject (often cited as 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 Mathematics (subject code 35) is assessed as a mixed paper: 1-mark objective-style items plus multi-mark short and long answers under a 120-mark framework (candidates earn 80 theory marks), lasting about 3 hours 15 minutes including reading time for many II PUC subjects. Theory is widely associated with an 80 mark written component plus 20 internal assessment — 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 E choices, subjective long answers, or internal assessment.
  • Time limit: 3 hours 15 minutes
  • 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 Mathematics (KSEAB): Suggested Study Strategy

1Practice official KSEAB II PUC Mathematics model papers under timed ~3 h 15 min conditions so you can switch from MCQ drills to written multi-mark answers with attempt choices.
2Blueprint weight is highest on Integrals (18) and Continuity & Differentiability (17) — prioritize those chapters early and revise weekly.
3Memorize standard integrals, inverse-trig principal values, and derivative formulas; most calculation errors come from wrong substitution limits or sign mistakes.
4For determinants and systems, practice properties before brute-force expansion to save time on 5-mark items.
5Build a formula sheet for vector products, line/plane equations, definite-integral properties, and Bayes’ theorem and revise it before full papers.
6Use English-medium NCERT 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 Mathematics exam pure multiple-choice?

No. Official KSEAB II PUC Mathematics (code 35) is a mixed paper with 1-mark objective-style items and multi-mark short/long answers under a 120-mark framework (80 marks to earn). 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 Mathematics?

KSEAB II PUC Mathematics 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 long is the KSEAB II PUC Mathematics paper?

Many II PUC subjects, including Mathematics, are commonly scheduled for 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 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 Mathematics is commonly described under an 80 theory + 20 internal assessment pattern. The official blueprint uses a 120-mark question framework from which candidates earn 80 theory marks. 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 Mathematics exam cost?

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.

What syllabus does this bank follow?

It is aligned to Karnataka II PUC Mathematics (code 35) as reflected in the official 2025–26 weightage framework and NCERT Class 12 Mathematics: Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants, Continuity and Differentiability, Application of Derivatives, Integrals, Application of Integrals, Differential Equations, Vector Algebra, Three Dimensional Geometry, Linear Programming, and Probability.

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 Mathematics (35) PDF weightage framework. Also see pue.karnataka.gov.in for syllabus materials.