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Free Practice Questions for Assam ASSEB Higher Secondary Mathematics

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Key Facts: Assam ASSEB Higher Secondary Mathematics Exam

100

Practice Questions

OpenExamPrep

3 hours

Board Exam Duration

ASSEB

33%

Minimum Pass Mark

ASSEB Board Regulations

Class 11-12

Curriculum Standard

ASSEB / NCERT

The ASSEB Higher Secondary Mathematics exam tests key areas of Class 11 and 12 mathematics curriculum. This 100-question practice set covers calculus, algebra, vectors, 3D geometry, and probability with detailed step-by-step worked solutions for every problem.

Sample Assam ASSEB Higher Secondary Mathematics Practice Questions

Try these sample questions to review concepts for the Assam ASSEB Higher Secondary 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 of integers Z defined by R = {(a, b) : a - b is divisible by 5}. What type of relation is R?
A.Reflexive only
B.Symmetric only
C.Transitive only
D.Equivalence relation
Explanation: R is reflexive since a - a = 0 is divisible by 5 for all a in Z. It is symmetric because if 5 divides (a - b), it also divides -(a - b) = (b - a). It is transitive because if 5 divides (a - b) and (b - c), it divides (a - b) + (b - c) = a - c. Hence, R is an equivalence relation.
2If f: R -> R is defined by f(x) = 3x - 4, which of the following best describes f?
A.One-one but not onto
B.Onto but not one-one
C.One-one and onto (Bijective)
D.Neither one-one nor onto
Explanation: For one-one: f(x1) = f(x2) implies 3x1 - 4 = 3x2 - 4, so x1 = x2. For onto: for any y in R, taking x = (y + 4)/3 yields f(x) = y. Since f is both injective and surjective, f is bijective.
3Let A = {1, 2, 3} and B = {a, b}. How many total functions can be defined from set A to set B?
A.6
B.8
C.9
D.5
Explanation: The total number of functions from a finite set A to a finite set B is given by |B|^|A|. Here |A| = 3 and |B| = 2, so the number of functions is 2^3 = 8.
4If f(x) = (4x + 3) / (6x - 4) for x != 2/3, find (f o f)(x).
A.x
B.1 / x
C.4x - 3
D.-x
Explanation: (f o f)(x) = f(f(x)) = f((4x + 3)/(6x - 4)). Substituting yields [4((4x + 3)/(6x - 4)) + 3] / [6((4x + 3)/(6x - 4)) - 4] = (16x + 12 + 18x - 12) / (24x + 18 - 24x + 16) = 34x / 34 = x.
5Let f: R -> R be defined by f(x) = x^2. Why is f NOT an injective (one-one) function?
A.Because f(x) >= 0 for all x
B.Because f(1) = f(-1) = 1 while 1 != -1
C.Because f is continuous everywhere
D.Because the domain is the set of real numbers
Explanation: A function is injective if f(x1) = f(x2) implies x1 = x2. For f(x) = x^2, we have f(1) = 1 and f(-1) = 1, but 1 != -1. Distinct domain elements produce the same output, so f is not one-one.
6If a relation R on set A = {1, 2, 3, 4} is given by R = {(1,1), (2,2), (3,3), (4,4), (1,2), (2,1), (2,3)}, which property does R FAIL to satisfy?
A.Reflexivity
B.Symmetry
C.Transitivity
D.Completeness
Explanation: R contains (2, 3), but it does not contain (3, 2). For symmetry, (a, b) in R must imply (b, a) in R. Since (2, 3) in R but (3, 2) not in R, symmetry fails.
7Let f: [0, infinity) -> [0, infinity) be given by f(x) = x^2. What is the inverse function f^(-1)(x)?
A.x^2
B.sqrt(x)
C.1 / x^2
D.-sqrt(x)
Explanation: To find the inverse of y = x^2 on [0, infinity), we solve for x: x = sqrt(y) (taking the positive root since x >= 0). Swapping variables gives f^(-1)(x) = sqrt(x).
8Let A = {1, 2, 3}. What is the total number of equivalence relations containing (1, 2) that can be formed on set A?
A.1
B.2
C.3
D.4
Explanation: Any equivalence relation must contain (1,1), (2,2), (3,3). Containing (1,2) forces it to contain (2,1). The smallest such relation is R1 = {(1,1),(2,2),(3,3),(1,2),(2,1)}. Adding any additional pair like (2,3) forces (3,2), (1,3), (3,1) by transitivity, giving the universal relation A x A. Thus, exactly 2 equivalence relations exist.
9If f: R -> R is defined by f(x) = 2x + cos(x), 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'(x) = 2 - sin(x) >= 1 > 0 for all x in R. Since f'(x) > 0 everywhere, f is strictly increasing, hence one-one. Also, as x -> infinity, f(x) -> infinity, and as x -> -infinity, f(x) -> -infinity. By continuity, range of f is R, so f is onto.
10What is the domain of the real-valued function f(x) = sqrt(9 - x^2)?
A.(-3, 3)
B.[-3, 3]
C.[0, 3]
D.(-infinity, -3] U [3, infinity)
Explanation: For sqrt(9 - x^2) to be real, the radicand must be non-negative: 9 - x^2 >= 0, which means x^2 <= 9. Solving gives -3 <= x <= 3, or domain = [-3, 3].

About the Assam ASSEB Higher Secondary Mathematics Exam

The Assam ASSEB Higher Secondary Mathematics examination assesses Class 11 and Class 12 students on foundational and advanced mathematics topics. Content includes relations and functions, inverse trigonometric functions, matrices, determinants, continuity, differentiability, applications of derivatives, indefinite and definite integrals, application of integrals, differential equations, vector algebra, three-dimensional geometry, linear programming, and probability including Bayes' Theorem.

Exam sponsor: Assam State School Education Board (ASSEB / AHSEC). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

100 practice MCQs (Board exam includes MCQs and long answer numericals)

Time Limit

3 hours

Passing Score

30% - 33%

Exam / Certification Fees

Board registration fee

Exam sponsor website

Reported exam pass rate: ~80%. overall Science stream pass percentage This describes exam candidates, not OpenExamPrep users or results from using our resources. 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.

15%

Relations & Functions and Inverse Trigonometry

Types of relations (reflexive, symmetric, transitive, equivalence), one-one and onto functions, composition of functions, domain/range and principal value branches of inverse trigonometric functions.

18%

Algebra: Matrices & Determinants

Matrix operations, transpose, symmetric and skew-symmetric matrices, determinant expansion, properties, area of triangles, minors, cofactors, matrix inverse, and solving system of linear equations.

25%

Calculus: Continuity, Differentiability & Applications

Continuity, differentiability, chain rule, implicit functions, logarithmic differentiation, second order derivatives, rate of change, increasing/decreasing functions, tangents and normals, maxima and minima.

22%

Calculus: Integrals & Differential Equations

Integration by substitution, partial fractions, integration by parts, definite integrals and properties, area under simple curves, order and degree of differential equations, variable separable, homogeneous, and linear DEs.

20%

Vectors, 3D Geometry, Linear Programming & Probability

Vector dot and cross products, direction cosines and ratios, line equations in 3D, shortest distance, linear programming graphical method, conditional probability, and Bayes' Theorem.

Preparing for the Assam ASSEB Higher Secondary Mathematics Exam

What You Need to Know

  • Passing score: 30% - 33%
  • Assessment: 100 practice MCQs (Board exam includes MCQs and long answer numericals)
  • Time limit: 3 hours
  • Exam / certification fees: Board registration 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

Assam ASSEB Higher Secondary Mathematics: Suggested Study Strategy

1Master standard differentiation and integration formulas and substitution techniques.
2Practice matrix multiplication, adjoint, and inverse formulas without manual arithmetic errors.
3Understand principal value branches for inverse trigonometric functions.
4Focus on properties of definite integrals to simplify complex definite integration problems.
5Practice 3D geometry line vector equations and shortest distance formulas.
6Memorize Bayes' Theorem conditional probability formulas and tree diagram setups.

Frequently Asked Questions

What is the ASSEB Higher Secondary Mathematics Exam?

The ASSEB HS Mathematics examination is the official Class 12 board assessment conducted by the Assam State School Education Board (formerly AHSEC) for senior secondary students in Assam.

What syllabus is covered in this question bank?

The question bank aligns with the Class 11 and Class 12 ASSEB / NCERT Mathematics syllabus, covering relations & functions, inverse trig, matrices, determinants, differential & integral calculus, differential equations, vectors, 3D geometry, linear programming, and probability.

Are mathematical calculation problems included in this practice set?

Yes, the practice set includes detailed calculation questions across calculus, matrix algebra, 3D geometry, and probability, each accompanied by step-by-step worked solutions.

What is the passing criteria for ASSEB Class 12 Mathematics?

Students must secure at least 30% to 33% marks overall (in theory and internal assessments) to pass the ASSEB HS Mathematics examination.

How can this practice set help with state entrance exams like Assam CEE?

The core concepts tested in ASSEB Class 11-12 Mathematics form the primary foundation for entrance exams like Assam CEE and JEE Main. Practicing these 100 MCQs strengthens conceptual speed and accuracy.