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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:
A.reflexive only
B.symmetric only
C.reflexive and symmetric but not transitive
D.an equivalence relation
Explanation: R includes all diagonal pairs, so it is reflexive. (1,3) and (3,1) are both present, so it is symmetric. Compositions involving only 1 and 3 stay in R, so R is transitive — an equivalence relation with classes {1,3}, {2}, {4}.
2The number of binary relations on a set with 2 elements is:
A.4
B.8
C.16
D.32
Explanation: A set with n elements has n squared ordered pairs. Each may or may not belong to a relation, so there are 2 to the power n squared relations. For n=2, 2^4 = 16.
3Let f: R to R be defined by f(x) = 2x + 5. Then f is:
A.one-one but not onto
B.onto but not one-one
C.both one-one and onto
D.neither one-one nor onto
Explanation: If f(x1)=f(x2) then 2x1+5=2x2+5 implies x1=x2, so one-one. For any y in R, x=(y-5)/2 is a preimage, so onto. Hence f is bijective.
4If f(x) = 3x + 1 and g(x) = x squared - 2, then (g compose f)(1) equals:
A.7
B.14
C.2
D.-1
Explanation: f(1)=3(1)+1=4. Then g(f(1))=g(4)=16-2=14.
5Let A = {1, 2, 3, 4} and B = {a, b, c}. The number of onto functions from A to B is:
A.24
B.81
C.36
D.6
Explanation: By inclusion-exclusion: 3^4 - C(3,1)*2^4 + C(3,2)*1^4 = 81 - 48 + 3 = 36. Equivalently 3! * S(4,3) = 6*6 = 36.
6If f: R to R is defined by f(x) = 4x - 7, then f inverse of x is:
A.(x - 7)/4
B.4x + 7
C.(7 - x)/4
D.(x + 7)/4
Explanation: Set y = 4x - 7 so x = (y+7)/4. Swapping variables, f inverse(x) = (x+7)/4.
7A relation R on Z defined by a R b iff a - b is divisible by 3 is:
A.reflexive only
B.symmetric only
C.an equivalence relation
D.neither reflexive nor symmetric
Explanation: a-a=0 is divisible by 3 so reflexive. If 3 divides (a-b) then 3 divides (b-a) so symmetric. If 3 divides (a-b) and (b-c) then 3 divides (a-c) so transitive. Congruence mod 3 is an equivalence relation.
8If f(x) = cos x and g(x) = x/2, then (f compose g)(pi/3) equals:
A.1/2
B.sqrt(3)/2
C.0
D.1
Explanation: g(pi/3)=pi/6. Then f(g(pi/3))=cos(pi/6)=sqrt(3)/2.
9The principal value of cos inverse(1/2) is:
A.pi/6
B.pi/3
C.pi/4
D.2pi/3
Explanation: cos inverse maps [-1,1] to [0,pi]. cos(pi/3)=1/2, so cos inverse(1/2)=pi/3.
10The domain of f(x) = sin inverse(2x - 3) is:
A.[0, 1]
B.[1, 2]
C.[-1, 1]
D.[2, 3]
Explanation: Need -1 <= 2x-3 <= 1 so 2 <= 2x <= 4 so 1 <= x <= 2. Domain is [1,2].

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 website

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 counting 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/identity relations.

~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, projections).

~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 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

1Practice official DHSE/school Mathematics model papers under timed ~2.5 h conditions so you can switch from MCQ drills to written multi-mark answers with attempt choices.
2Weight revision toward Integrals and Continuity & Differentiability — they dominate multi-step marks on Class 12 papers.
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 long 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/Malayalam textbooks as directed by your school; this free bank is an English MCQ adaptation only.

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.