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Exam Review

Key Facts: CHSE Odisha Elective Mathematics Exam

200 marks

Elective Mathematics total across Year 1 (100) + Year 2 (100) pure theory

CHSE Odisha Arts Courses of Studies

5 × 20

Year-2 unit marks: Relations–LP, Algebra–Probability, Diff. Calc., Int. Calc., Vectors–3D

CHSE Odisha Mathematics (+2 2nd year) course structure

10+60+30

Official Group A/B/C mark split on the Year-2 theory paper

CHSE Odisha Mathematics general instructions

No practical

Mathematics is pure theory 100 marks (unlike Statistics 70+30)

CHSE Odisha Arts/Science Mathematics syllabus

In AHSE fee

No separate elective marketplace fee; included in session exam fee

CHSE Odisha AHSE fee structure via colleges

CHSE Odisha Elective Mathematics is a +2 elective (200 marks: 100+100 pure theory). Year-2 AHSE uses five equal 20-mark units and Group A/B/C written format—not a pure MCQ board paper. This free 2026 bank is a calculation-heavy English MCQ study adaptation covering topics from official units.

Sample CHSE Odisha Elective Mathematics Practice Questions

Try these sample questions to review concepts for the CHSE Odisha Elective Mathematics 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} given by R = {(1,1), (2,2), (3,3), (1,2), (2,1)}. Which property does R satisfy that makes it an equivalence relation when combined with the other required properties?
A.R is only reflexive
B.R is reflexive, symmetric, and transitive on A
C.R is only symmetric
D.R is neither reflexive nor symmetric
Explanation: R contains all diagonal pairs (reflexive), is closed under swap of ordered pairs (symmetric), and checking chains (e.g. 1R2 and 2R1 gives 1R1 already present; no path forces missing pairs) shows transitivity. Hence R is an equivalence relation on A.
2A relation R on Z is defined by a R b if and only if a − b is divisible by 5. How many equivalence classes does R determine on Z?
A.1
B.5
C.10
D.Infinitely many with no modular structure
Explanation: a ≡ b (mod 5) is the standard congruence relation. The equivalence classes are the residue classes [0], [1], [2], [3], [4] — exactly 5 classes.
3Let f: R → R be defined by f(x) = 2x + 3. Which statement is correct?
A.f is one-one but not onto
B.f is onto but not one-one
C.f is neither one-one nor onto
D.f is both one-one and onto
Explanation: If f(x1)=f(x2) then 2x1+3=2x2+3 ⇒ x1=x2 (one-one). For any y∈R, x=(y−3)/2 is a real preimage (onto). Linear functions with nonzero slope are bijections R→R.
4If f(x) = x + 1 and g(x) = 2x − 3, then (f ∘ g)(2) equals:
A.2
B.3
C.1
D.5
Explanation: g(2)=2(2)−3=1. Then f(g(2))=f(1)=1+1=2. So (f∘g)(2)=2.
5If f: R → R is given by f(x) = 3x − 5, then f⁻¹(x) is:
A.(x − 5)/3
B.3x + 5
C.(x + 5)/3
D.1/(3x − 5)
Explanation: Set y = 3x − 5 ⇒ x = (y + 5)/3. Swapping variables, f⁻¹(x) = (x + 5)/3. Check: f(f⁻¹(x)) = 3·(x+5)/3 − 5 = x.
6The principal value of sin⁻¹(1/2) is:
A.π/3
B.π/2
C.π/6
D.π/4
Explanation: sin(π/6)=1/2 and π/6 lies in the principal range [−π/2, π/2] of sin⁻¹. Hence sin⁻¹(1/2)=π/6.
7The principal value of cos⁻¹(−1/2) is:
A.2π/3
B.π/3
C.π/6
D.5π/6
Explanation: cos(2π/3)=−1/2 and 2π/3 ∈ [0, π], the principal range of cos⁻¹. Note 5π/6 has cos = −√3/2, not −1/2.
8If tan⁻¹ x + tan⁻¹ y = π/4 and xy < 1, then:
A.x + y = 1 + xy
B.x − y = 1 + xy
C.x + y = 1 − xy
D.xy = 1
Explanation: tan(tan⁻¹x + tan⁻¹y) = (x+y)/(1−xy) when xy<1. This equals tan(π/4)=1, so (x+y)/(1−xy)=1 ⇒ x+y=1−xy.
9The domain of the function f(x) = sin⁻¹(2x − 1) is:
A.[0, 1]
B.[−1, 1]
C.[1/2, 1]
D.[0, 2]
Explanation: sin⁻¹ is defined for argument in [−1,1], so −1 ≤ 2x−1 ≤ 1 ⇒ 0 ≤ 2x ≤ 2 ⇒ 0 ≤ x ≤ 1.
10In a linear programming problem, the feasible region is the set of points that:
A.Satisfy only the objective function
B.Lie only outside all half-planes
C.Maximise the objective without any constraint
D.Satisfy all the constraints simultaneously
Explanation: By definition, the feasible region is the intersection of all constraint half-planes (including non-negativity if present). Optimal solutions, when they exist, occur at corner points of this region for linear objectives.

About the CHSE Odisha Elective Mathematics Exam

Odisha CHSE Higher Secondary Elective Mathematics follows the Arts Courses of Studies (aligned Science Mathematics unit map): Year 1 covers sets and functions, algebra (induction, complex numbers, inequalities, permutations, binomial, sequences), coordinate geometry, introductory limits and derivatives, mathematical reasoning, and statistics/probability foundations. Year 2 emphasises relations and functions, inverse trigonometric functions, linear programming, matrices and determinants, probability (conditional, Bayes, binomial), continuity and differentiability with applications of derivatives, integrals and applications, differential equations, and vectors with three-dimensional geometry. Electives total 200 marks; the Council Year-2 paper counts toward the pass certificate.

Exam sponsor: Council of Higher Secondary Education, Odisha (CHSE Odisha). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

CHSE Odisha Higher Secondary Elective Mathematics carries 200 marks (100 Year-1 college level + 100 Year-2 Council AHSE). Year-2 units each carry 20 marks: (I) Relations & Functions and Linear Programming, (II) Algebra and Probability, (III) Differential Calculus, (IV) Integral Calculus, (V) Vectors and 3-D Geometry. Official paper pattern: Group A (1×10=10), Group B (4×15=60), Group C (6×5=30). Unlike Statistics, Mathematics has no 70+30 practical split—theory is 100 marks. This free bank is an English MCQ study adaptation—not a full long-answer simulation.

Time Limit

3 hours (per 100-mark paper)

Passing Score

~30% minimum in theory (confirm current AHSE circular)

Exam / Certification Fees

Included in the CHSE Odisha AHSE examination fee for the session (collected through the affiliated college/H.S. school; no separate public per-elective marketplace fee).

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.

~20% of this local bank

Relations, Functions, Inverse Trig & LP

Types of relations; one-one/onto; inverse trig; graphical LP.

~20% of this local bank

Matrices, Determinants & Probability

Matrix algebra, systems, conditional probability, Bayes, binomial.

~20% of this local bank

Differential Calculus

Continuity, derivatives, MVT ideas, maxima-minima, rates.

~20% of this local bank

Integral Calculus & DE

Standard integrals, definite integrals, area, first-order DE.

~20% of this local bank

Vectors & 3-D Geometry

Vector products; lines and planes in space.

Preparing for the CHSE Odisha Elective Mathematics Exam

What You Need to Know

  • Passing score: ~30% minimum in theory (confirm current AHSE circular)
  • Assessment: CHSE Odisha Higher Secondary Elective Mathematics carries 200 marks (100 Year-1 college level + 100 Year-2 Council AHSE). Year-2 units each carry 20 marks: (I) Relations & Functions and Linear Programming, (II) Algebra and Probability, (III) Differential Calculus, (IV) Integral Calculus, (V) Vectors and 3-D Geometry. Official paper pattern: Group A (1×10=10), Group B (4×15=60), Group C (6×5=30). Unlike Statistics, Mathematics has no 70+30 practical split—theory is 100 marks. This free bank is an English MCQ study adaptation—not a full long-answer simulation.
  • Time limit: 3 hours (per 100-mark paper)
  • Exam / certification fees: Included in the CHSE Odisha AHSE examination fee for the session (collected through the affiliated college/H.S. school; no separate public per-elective marketplace fee). 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

CHSE Odisha Elective Mathematics: Suggested Study Strategy

1Drill equal time across the five Year-2 units—each is 20 marks on the official scheme.
2Master inverse trigonometric principal-value ranges and elementary identities before AHSE.
3Practise 2×2 and 3×3 determinants, adjoints, and inverse-matrix solutions of linear systems daily.
4Link probability theorems (conditional, total, Bayes) to binomial mean np and variance npq.
5For calculus, alternate derivative applications (maxima, tangents) with standard integral forms and area problems.
6Use Bureau's Higher Secondary (+2) Elements of Mathematics and current circulars from chseodisha.nic.in.

Frequently Asked Questions

How is CHSE Odisha Higher Secondary Elective Mathematics examined?

Elective Mathematics carries 200 marks (100 Year-1 college + 100 Year-2 Council AHSE). The Year-2 paper is pure theory 100 marks with Group A very short answers (10 marks), Group B mid-length bits (60 marks), and Group C long bits (30 marks). There is no Statistics-style 70 theory + 30 practical split for Mathematics. Papers last about 3 hours.

What are the five Year-2 Mathematics units?

Each unit is 20 marks: (I) Relations and Functions & Linear Programming (including inverse trigonometric functions), (II) Algebra (matrices, determinants) and Probability, (III) Differential Calculus, (IV) Integral Calculus (integrals, applications, differential equations), (V) Vectors and Three-Dimensional Geometry.

Is this practice bank the same format as the official CHSE paper?

No. Official papers mix very short, short, and long constructed-response mathematical solutions. This bank is an English-language multiple-choice study adaptation for concept and calculation revision—not an official blueprint replica.

Does Elective Mathematics include a practical exam?

No. Under the CHSE Arts Courses of Studies Mathematics syllabus, assessment is theory-based (100 marks per year). Practical components appear in subjects such as Statistics, not in Elective Mathematics.

What is the pass mark?

CHSE Odisha AHSE practice commonly requires about 30% as the minimum pass floor in theory. Confirm the current AHSE notification on chseodisha.nic.in.

What does the exam cost?

Examination charges are included in the CHSE Odisha AHSE fee structure notified for the session and collected through the affiliated college/H.S. school—no separate public per-elective marketplace fee.