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Key Facts: BSEB Inter Mathematics Exam

3h 15m

BSEB Intermediate Mathematics theory exam duration

BSEB Intermediate Mathematics model-paper style logistics (codes 121/327)

100 marks theory-only

MATHEMATICS (ELECTIVE) full marks; no practical component

BSEB Intermediate model-paper style materials (121/327-MATH)

50 + 30 + 20

Model-paper style split: any 50 objectives + 15 short×2 + 4 long×5

BSEB Intermediate Mathematics model paper pattern reporting

English MCQ adaptation

This free local bank is not the official Intermediate paper format

OpenExamPrep practice policy

BSEB Intermediate Mathematics (Elective, codes 121/327) is a Class 12 theory-only public exam subject: 100 marks, 3 hours 15 minutes, mixed objective + short + long answers (model-paper style any 50 of 100 objectives + 15×2 + 4×5). This free 2026 bank is an English MCQ study adaptation for NCERT/BSEB-focused Class 12 Mathematics — not an official paper simulation.

Sample BSEB Inter Mathematics Practice Questions

Try these sample questions to review concepts for the BSEB Inter Mathematics exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1A relation R on the set A = {1, 2, 3} is defined by R = {(1,1), (2,2), (3,3), (1,2)}. Which property does R fail?
A.Reflexivity
B.Symmetry
C.Transitivity
D.It is an equivalence relation
Explanation: R is reflexive (all (a,a) present) and transitive, but (1,2) ∈ R while (2,1) ∉ R, so R is not symmetric.
2If f: R → R is given by f(x) = 3x + 5, then f is:
A.One-one but not onto
B.Onto but not one-one
C.Bijective
D.Neither one-one nor onto
Explanation: Strictly increasing linear functions with nonzero slope are one-one and onto R, so f is bijective. Inverse is f⁻¹(y) = (y−5)/3.
3If f(x) = x² and g(x) = sin x, then (f ∘ g)(x) equals:
A.sin(x²)
B.sin² x
C.x² sin x
D.sin x²
Explanation: (f ∘ g)(x) = f(g(x)) = f(sin x) = (sin x)² = sin² x.
4The function f: N → N defined by f(n) = n² 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: If n₁² = n₂² for natural numbers then n₁ = n₂, so f is one-one. It is not onto because 2 has no natural square root preimage under f.
5Let R be the relation on Z defined by a R b iff a − b is divisible by 5. Then R 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); a−b divisible by 5 ⇒ b−a is (symmetric); and divisibility by 5 is transitive. So R is an equivalence relation (congruence mod 5).
6If f(x) = |x| − x, then f is:
A.One-one on R
B.Onto R
C.Neither one-one nor onto R
D.Bijective on R
Explanation: For x ≥ 0, f(x)=0; for x < 0, f(x)=−x−x=−2x > 0. So the range is [0, ∞), not all of R (not onto), and many positives map to 0 (not one-one).
7Number of binary operations on a set with 3 elements is:
A.3³
B.3⁹
C.9³
D.2⁹
Explanation: A binary operation is a function A×A → A. |A×A|=9, and each of 9 pairs can map to any of 3 elements, so 3⁹ operations.
8If f: R → R, f(x) = x³ − x, then f is:
A.One-one
B.Onto
C.Both one-one and onto
D.Neither one-one nor onto
Explanation: f′(x)=3x²−1 changes sign, so f is not monotonic and not one-one (e.g. f(0)=f(1)=0). As a cubic with leading coefficient 1, lim±∞ f = ±∞ so f is onto R by intermediate value theorem.
9The principal value of sin⁻¹(1/2) is:
A.π/6
B.π/3
C.π/2
D.5π/6
Explanation: Range of sin⁻¹ is [−π/2, π/2]; sin(π/6)=1/2, so sin⁻¹(1/2)=π/6.
10The principal value of cos⁻¹(−1/2) is:
A.π/3
B.2π/3
C.π/6
D.−π/3
Explanation: Range of cos⁻¹ is [0, π]. cos(2π/3)=−1/2, so cos⁻¹(−1/2)=2π/3.

About the BSEB Inter Mathematics Exam

Bihar Intermediate Mathematics (Elective) under BSEB covers Class 12 Mathematics aligned to the Board’s Intermediate syllabus and NCERT Class 12 Mathematics. Core topics include relations and functions, inverse trigonometric functions, matrices, determinants, continuity and differentiability, applications of derivatives, integrals, applications of integrals, differential equations, vectors, three-dimensional geometry, linear programming, and probability. Official assessment is a theory-only 100-mark mixed objective–subjective paper of 3 hours 15 minutes (model-paper style 121/327-MATH: answer any 50 of 100 objectives, plus short and long choice blocks). This free local bank provides English four-option MCQs for revision and calculation practice; pair it with official model papers via biharboardonline.com.

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

Assessment

BSEB Intermediate Mathematics (Elective; codes 121/327) is a theory-only 100-mark subject for I.Sc. & I.A. streams with a public examination paper of 3 hours 15 minutes. Model-paper style structure (e.g., 121/327-MATH): Section A — 100 objective questions, answer any 50 for 1 mark each (50 marks); Section B — 30 short-answer questions, answer any 15 for 2 marks each (30 marks), and 8 long-answer questions, answer any 4 for 5 marks each (20 marks). Official papers are bilingual Hindi/English. Exact section splits and internal options are set by BSEB for each academic year; always confirm the current model paper and circulars on biharboardonline.com. This practice bank is an English-language MCQ study adaptation for concept and calculation fluency — it does not simulate the official mixed-format Intermediate paper.

Time Limit

3 hours 15 minutes (theory public examination; confirm year’s timetable)

Passing Score

Subject pass criteria follow the current BSEB Intermediate notification; secondary reporting commonly describes a floor near about 30% — verify the official circular for the year.

Exam / Certification Fees

As notified by BSEB and paid through Intermediate colleges/schools for regular and compartment/improvement 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.

~14% of this local bank

Relations, Functions & Inverse Trigonometry

Relation/function types, composition, invertibility, principal values, and inverse trig identities.

~16% of this local bank

Matrices & Determinants

Matrix algebra, inverse and adjoint, determinants, and solving linear systems.

~18% of this local bank

Continuity, Differentiability & AOD

Limits continuity differentiability checks, standard derivatives, maxima-minima, tangent/normal, and rate problems.

~17% of this local bank

Integrals, Area & Differential Equations

Indefinite/definite integrals, properties, area under curves, and first-order DE.

~16% of this local bank

Vectors & Three-Dimensional Geometry

Dot and cross products, lines and planes, angles, and shortest distance.

~14% of this local bank

Linear Programming & Probability

LPP formulation and corner points; conditional probability, Bayes, and binomial ideas.

~5% of this local bank

Mixed Calculation & Concept Checks

Cross-topic numericals typical of Intermediate objective revision.

Preparing for the BSEB Inter Mathematics Exam

What You Need to Know

  • Passing score: Subject pass criteria follow the current BSEB Intermediate notification; secondary reporting commonly describes a floor near about 30% — verify the official circular for the year.
  • Assessment: BSEB Intermediate Mathematics (Elective; codes 121/327) is a theory-only 100-mark subject for I.Sc. & I.A. streams with a public examination paper of 3 hours 15 minutes. Model-paper style structure (e.g., 121/327-MATH): Section A — 100 objective questions, answer any 50 for 1 mark each (50 marks); Section B — 30 short-answer questions, answer any 15 for 2 marks each (30 marks), and 8 long-answer questions, answer any 4 for 5 marks each (20 marks). Official papers are bilingual Hindi/English. Exact section splits and internal options are set by BSEB for each academic year; always confirm the current model paper and circulars on biharboardonline.com. This practice bank is an English-language MCQ study adaptation for concept and calculation fluency — it does not simulate the official mixed-format Intermediate paper.
  • Time limit: 3 hours 15 minutes (theory public examination; confirm year’s timetable)
  • Exam / certification fees: As notified by BSEB and paid through Intermediate colleges/schools for regular and compartment/improvement 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

BSEB Inter Mathematics: Suggested Study Strategy

1Memorize standard derivatives and integrals (including inverse trig forms) and practise chain rule / substitution before timed drills.
2For matrices and determinants, always write intermediate steps (cofactors, adjoint) even when practising MCQs — the same algebra wins long-answer marks.
3Sketch feasible regions for LPP and draw line/plane diagrams for 3D geometry; visual checks catch sign errors fast.
4After each MCQ set, rewrite one related short or long Intermediate-style solution so you transfer MCQ speed into official written format.
5Use current BSEB model papers (121/327-MATH style) from biharboardonline.com to allocate revision time by objective vs short vs long section weight for your year.

Frequently Asked Questions

How is BSEB Intermediate Mathematics officially examined?

Mathematics (Elective; codes 121/327) is examined under the Bihar Intermediate Public Examination at Class 12 as a theory-only 100-mark paper of 3 hours 15 minutes for I.Sc. & I.A. Model-paper style materials describe Section A with 100 objectives (answer any 50 × 1 mark) and Section B short (answer 15 of 30 × 2) plus long answers (answer 4 of 8 × 5). Confirm the year’s model paper and circulars on biharboardonline.com.

Is this practice bank the same format as the official Intermediate Mathematics paper?

No. Official BSEB Intermediate Mathematics theory papers mix a large objective section with short- and long-answer subjective work and are bilingual Hindi/English. This bank is an English-language multiple-choice study adaptation for concepts and calculations only — not an official translation, blueprint replica, or full paper simulation.

What syllabus does this bank follow?

It is aligned to Bihar Intermediate (BSEB) Class 12 Mathematics — the standard NCERT Class 12 scope: relations and functions, inverse trigonometric functions, matrices, determinants, continuity and differentiability, applications of derivatives, integrals, applications of integrals, differential equations, vectors, 3D geometry, linear programming, and probability.

What is the pass mark for BSEB Intermediate Mathematics?

Passing criteria are set in the current BSEB Intermediate notification. Secondary reporting often describes a subject floor near about 30%. Always verify the official circular for exact wording and mark requirements for your year.

Where should I check official model papers and circulars?

Use the Bihar School Examination Board website at biharboardonline.com for Intermediate model papers (including Mathematics codes such as 121/327-MATH style materials), syllabi, and exam circulars.

Does Intermediate Mathematics include a practical exam?

No. BSEB Intermediate Mathematics (Elective) is theory-only (100 marks). Unlike science subjects with laboratory components, there is no separate practical examination for Mathematics under the standard Intermediate pattern described here.