Free Practice Questions for Kerala Plus Two Mathematics (DHSE)
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Key Facts: Kerala Plus Two Mathematics (DHSE) Exam
100 marks
Subject total via TE + CE (typically no PE; exact splits as notified)
DHSE Kerala Plus Two assessment pattern
~2.5 h + cool-off
Typical Mathematics theory duration for non-practical subjects
DHSE Plus Two timetable logistics
D+ / ~30%
Common pass grade/aggregate with separate TE floor
Kerala Plus Two grading / pass criteria reporting
TE + CE
Official format is mixed written TE plus CE, not pure MCQ
DHSE Kerala Plus Two Mathematics assessment pattern
English MCQ adaptation
This free local bank is not the official mixed paper format
OpenExamPrep practice policy
DHSE Kerala
Administrator: Directorate of Higher Secondary Education
Government of Kerala Higher Secondary system
Kerala Plus Two Mathematics (DHSE) totals 100 marks via TE + CE (typically no PE); theory is commonly ~2.5 h plus cool-off. Pass is commonly D+/~30% aggregate with ~30% in TE separately as notified. Fees are paid through schools. This free 2026 bank is an English MCQ study adaptation — not an official paper simulation.
Sample Kerala Plus Two Mathematics (DHSE) Practice Questions
Try these sample questions to review concepts for the Kerala Plus Two Mathematics (DHSE) exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.
1Let A = {1, 2, 3, 4} and R = {(1,1), (2,2), (3,3), (4,4), (1,3), (3,1)}. Then R is:
2The number of binary relations on a set with 2 elements is:
3Let f: R to R be defined by f(x) = 2x + 5. Then f is:
4If f(x) = 3x + 1 and g(x) = x squared - 2, then (g compose f)(1) equals:
5Let A = {1, 2, 3, 4} and B = {a, b, c}. The number of onto functions from A to B is:
6If f: R to R is defined by f(x) = 4x - 7, then f inverse of x is:
7A relation R on Z defined by a R b iff a - b is divisible by 3 is:
8If f(x) = cos x and g(x) = x/2, then (f compose g)(pi/3) equals:
9The principal value of cos inverse(1/2) is:
10The domain of f(x) = sin inverse(2x - 3) is:
About the Kerala Plus Two Mathematics (DHSE) Exam
Kerala Plus Two Mathematics is the Class 12 Higher Secondary public examination mathematics paper under the Directorate of Higher Secondary Education (DHSE), Directorate of General Education, Government of Kerala. It assesses NCERT Class 12 Mathematics (as adopted for Kerala HSE / SCERT) for Science and Commerce combinations that include 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. The official assessment is a subject total of 100 marks via Terminal Evaluation (mixed written theory, commonly about 2.5 hours plus cool-off) and Continuous Evaluation — typically no Practical Evaluation — not pure MCQ. Fees and exact schemes are notified by DHSE (beta.hseportal.kerala.gov.in; dhsekerala.gov.in). Pass marks are commonly described as D+ or above (~30% aggregate) with a separate ~30% floor in TE. 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 theory paper or CE evidence.
Exam sponsor: Directorate of Higher Secondary Education (DHSE), Kerala. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.
Assessment
Official Kerala Plus Two Mathematics is assessed as Terminal Evaluation (written theory) + Continuous Evaluation for a subject total of 100 marks. Non-practical subjects such as Mathematics are commonly described under TE 80 + CE 20 (confirm the year’s scheme). Theory duration is commonly about 2.5 hours plus cool-off time as notified (often ~15 minutes). The written paper is mixed format (not pure MCQ) covering NCERT/SCERT 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. English and Malayalam media are typically available. Confirm circulars on beta.hseportal.kerala.gov.in and dhsekerala.gov.in. This practice bank is an English-language MCQ study adaptation for concept and multi-step calculation fluency — it does not simulate official attempt limits, long constructed responses, or CE evidence.
Time Limit
About 2.5 hours theory for Mathematics (plus cool-off time as notified; non-practical subjects commonly ~2.5 h theory)
Passing Score
Commonly reported as grade D+ or above (~30% aggregate across CE and TE where applicable), with a separate minimum of about 30% in Terminal Evaluation (for non-practical Mathematics, TE floor often described near ~24 when TE is 80 marks); verify the current pass criteria for your examination year.
Exam / Certification Fees
As notified by DHSE and paid through Higher Secondary schools for regular Plus Two sittings (no single fixed public subject fee for all categories).
Exam sponsor websiteFees, 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.
Relations and Functions
Equivalence relations, one-one/onto functions, inverse functions, composition, and counting relations/functions on finite sets.
Inverse Trigonometric Functions
Principal values, domain and range, and standard inverse-trig simplifications and identities.
Matrices
Order, addition/multiplication, transpose, symmetric and skew-symmetric matrices, and inverse/identity relations.
Determinants
2×2 and 3×3 evaluation, properties, area of triangle, adjoint and inverse, and consistency of linear systems.
Continuity and Differentiability
Limits and continuity checks, derivatives of composite and inverse functions, logarithmic differentiation, and higher-order derivatives.
Application of Derivatives
Increasing/decreasing intervals, equations of tangents and normals, and maxima–minima word problems.
Integrals
Standard antiderivatives, substitution, partial fractions, integration by parts, and definite-integral properties.
Application of Integrals
Area under a curve and area bounded between two curves using definite integrals.
Differential Equations
Order and degree, variable-separable, homogeneous, and linear first-order equations with particular solutions.
Vector Algebra
Magnitude, unit vectors, dot and cross products, and geometric conditions (perpendicular, parallel, projections).
Three Dimensional Geometry
Direction cosines/ratios, cartesian and vector equations of lines, and plane equations and distances.
Linear Programming
Formulating constraints, identifying feasible regions, and reading optimal values from corner points.
Probability
Conditional probability, independent events, total probability, and Bayes’ theorem multi-step calculations.
Preparing for the Kerala Plus Two Mathematics (DHSE) Exam
What You Need to Know
- Passing score: Commonly reported as grade D+ or above (~30% aggregate across CE and TE where applicable), with a separate minimum of about 30% in Terminal Evaluation (for non-practical Mathematics, TE floor often described near ~24 when TE is 80 marks); verify the current pass criteria for your examination year.
- Assessment: Official Kerala Plus Two Mathematics is assessed as Terminal Evaluation (written theory) + Continuous Evaluation for a subject total of 100 marks. Non-practical subjects such as Mathematics are commonly described under TE 80 + CE 20 (confirm the year’s scheme). Theory duration is commonly about 2.5 hours plus cool-off time as notified (often ~15 minutes). The written paper is mixed format (not pure MCQ) covering NCERT/SCERT 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. English and Malayalam media are typically available. Confirm circulars on beta.hseportal.kerala.gov.in and dhsekerala.gov.in. This practice bank is an English-language MCQ study adaptation for concept and multi-step calculation fluency — it does not simulate official attempt limits, long constructed responses, or CE evidence.
- Time limit: About 2.5 hours theory for Mathematics (plus cool-off time as notified; non-practical subjects commonly ~2.5 h theory)
- Exam / certification fees: As notified by DHSE and paid through Higher Secondary schools for regular Plus Two 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
Kerala Plus Two Mathematics (DHSE): Suggested Study Strategy
Frequently Asked Questions
Is the official Kerala Plus Two Mathematics exam pure multiple-choice?
No. Official Kerala Plus Two Mathematics is mixed Terminal Evaluation (written theory with short/long and objective-style items) plus Continuous Evaluation. This bank is an English-language multiple-choice study adaptation for concepts and multi-step calculations only — not an official paper or CE simulation.
How is Kerala Plus Two Mathematics scored out of 100?
The subject total is commonly 100 marks from Terminal Evaluation + Continuous Evaluation. Non-practical subjects such as Mathematics are often described as TE 80 + CE 20 with no Practical Evaluation — confirm the year’s scheme on beta.hseportal.kerala.gov.in and dhsekerala.gov.in.
How long is the Kerala Plus Two Mathematics theory paper?
Theory for non-practical subjects such as Mathematics is commonly about 2.5 hours, plus cool-off time as notified (often about 15 minutes). Confirm the year’s date sheet and instructions on official DHSE portals.
What is the passing score for Kerala Plus Two Mathematics?
Pass is commonly grade D+ or above (~30% aggregate across CE and TE where applicable), with a separate minimum of about 30% in Terminal Evaluation (for non-practical Mathematics, TE floor often described near ~24 when TE is 80 marks). Always verify the current circular for your examination year.
Which streams offer Plus Two Mathematics?
Mathematics is offered in Science and Commerce Higher Secondary combinations as listed by DHSE for the year. Confirm your school’s approved subject combination and the official HSE subject catalog.
Which languages is Plus Two Mathematics offered in?
English and Malayalam media are commonly available for Kerala Plus Two Mathematics. This practice bank is written in English for concept and calculation revision.
How much does the Kerala Plus Two Mathematics exam cost?
Mathematics is not sold as a separate marketplace product. Fees are notified by DHSE and paid through Higher Secondary schools for regular candidates. Check beta.hseportal.kerala.gov.in for the current fee circular.
What syllabus does this bank follow?
It is aligned to Kerala Higher Secondary / NCERT Class 12 Mathematics (as adopted for SCERT/DHSE): 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 official notices and schemes?
Check the HSE Portal at https://beta.hseportal.kerala.gov.in, DHSE at https://dhsekerala.gov.in, and SCERT Kerala for syllabi, timetables, and related circulars.