100+ Free ASSEB HSLC General Mathematics Practice Questions

Prepare for the Assam ASSEB HSLC Class 10 General Mathematics (Div-I) exam with instant access — no signup required.

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Key Facts: ASSEB HSLC General Mathematics Exam

90 + 10

Theory + Internal Assessment

ASSEB Div-I HSLC General Mathematics (C2) marking scheme

~3 hours

Typical Theory Duration

ASSEB HSLC examination pattern (confirm timetable)

27 + 3

Typical Pass (Theory + IA)

ASSEB HSLC passing criteria (confirm current circular)

Subject Code

ASSEB Div-I Curriculum & Syllabi

NCERT

Adopted Class 10 Maths Texts

ASSEB Div-I syllabus adoption notice

ASSEB HSLC General Mathematics (C2) is Assam’s Class 10 core maths paper: Theory 90 + IA 10 = 100 marks, NCERT Class 10 syllabus, about 3 hours. Pass typically Theory 27 + IA 3. Fee is part of HSLC form-fill-up. This site offers free English MCQ practice with worked solutions—not a full written-paper simulation.

Sample ASSEB HSLC General Mathematics Practice Questions

Try these sample questions to test your ASSEB HSLC General Mathematics exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1If two positive integers a and b are written as a = x^3 y^2 and b = x y^3, where x, y are prime numbers, then HCF(a, b) is:

A.x y

B.x y^2

C.x^3 y^3

D.x^2 y^2

Explanation: To find the HCF of numbers expressed in prime factors, take the product of the smallest power of each common prime factor. Common factors are x (smallest power 1) and y (smallest power 2). Thus HCF(a, b) = x y^2.

2The LCM of two numbers is 1820 and their HCF is 26. If one of the numbers is 130, what is the other number?

A.364

B.260

C.455

D.182

Explanation: For any two positive integers a and b, HCF(a, b) × LCM(a, b) = a × b. Here 26 × 1820 = 130 × b. Solving for b: b = (26 × 1820) / 130 = 26 × 14 = 364.

3What is the largest number that divides 70 and 125, leaving remainders 5 and 8 respectively?

A.13

B.65

C.117

D.17

Explanation: Subtract the remainders from the given numbers: 70 - 5 = 65, and 125 - 8 = 117. Now find HCF(65, 117). 65 = 5 × 13, 117 = 9 × 13. The highest common factor is 13.

4If n is any natural number, then 6^n always ends with which digit?

A.6

B.0

C.2

D.4

Explanation: 6^1 = 6, 6^2 = 36, 6^3 = 216, 6^4 = 1296, etc. Powers of 6 always have unit digit 6 for all natural numbers n >= 1 because 6 × 6 = 36 (unit digit 6).

5Which of the following rational numbers has a terminating decimal expansion?

A.13 / 3125

B.77 / 210

C.64 / 455

D.29 / 343

Explanation: A rational number p/q in simplest form has a terminating decimal expansion if and only if q is of the form 2^n × 5^m. 3125 = 5^5 = 2^0 × 5^5. Hence 13/3125 terminates (13 / 3125 = 0.00416). 210 has prime factor 3,7; 455 has 7,13; 343 = 7^3.

6If a is an odd integer, then a^2 - 1 is always divisible by:

A.8

B.16

C.6

D.12

Explanation: Any odd integer can be written as a = 2k + 1. Then a^2 - 1 = (2k + 1)^2 - 1 = 4k^2 + 4k = 4k(k + 1). Since k(k + 1) is the product of two consecutive integers, it is always even (divisible by 2). Hence 4 × (even number) is divisible by 8.

7Three alarm clocks ring at intervals of 4, 12, and 20 minutes respectively. If they ring together at 6:00 AM, at what time will they next ring together?

A.7:00 AM

B.6:40 AM

C.7:20 AM

D.8:00 AM

Explanation: The clocks ring together at intervals equal to the LCM of 4, 12, and 20. Prime factorizations: 4 = 2^2, 12 = 2^2 × 3, 20 = 2^2 × 5. LCM = 2^2 × 3 × 5 = 60 minutes = 1 hour. 6:00 AM + 1 hour = 7:00 AM.

8If one zero of the quadratic polynomial (k - 1)x^2 + k x + 1 is -3, then the value of k is:

A.4/3

B.-4/3

C.2/3

D.-2/3

Explanation: Since -3 is a zero, p(-3) = 0. (k - 1)(-3)^2 + k(-3) + 1 = 0 => 9(k - 1) - 3k + 1 = 0 => 9k - 9 - 3k + 1 = 0 => 6k - 8 = 0 => 6k = 8 => k = 8/6 = 4/3.

9If alpha and beta are the zeros of the polynomial p(x) = 2x^2 + 5x + k such that alpha^2 + beta^2 + alpha*beta = 21/4, what is the value of k?

A.2

B.3

C.-2

D.4

Explanation: For p(x) = 2x^2 + 5x + k, sum of zeros alpha + beta = -5/2 and product alpha*beta = k/2. Note that alpha^2 + beta^2 = (alpha + beta)^2 - 2*alpha*beta. So alpha^2 + beta^2 + alpha*beta = (alpha + beta)^2 - alpha*beta = (-5/2)^2 - k/2 = 25/4 - k/2. Set this equal to 21/4: 25/4 - k/2 = 21/4 => k/2 = 25/4 - 21/4 = 4/4 = 1 => k = 2.

10If the sum of the zeros of the quadratic polynomial f(t) = k t^2 + 2t + 3k is equal to their product, then k is:

A.-2/3

B.2/3

C.-3/2

D.3/2

Explanation: Sum of zeros = -b/a = -2/k. Product of zeros = c/a = 3k/k = 3. Given sum = product: -2/k = 3 => 3k = -2 => k = -2/3.

About the ASSEB HSLC General Mathematics Exam

The Assam HSLC General Mathematics examination is the Class 10 core Mathematics paper conducted by the Assam State School Education Board (ASSEB), Division-I (erstwhile SEBA). Subject code C2 assesses NCERT Class 10 mathematics—real numbers, polynomials, linear equations in two variables, quadratic equations, arithmetic progressions, triangles, coordinate geometry, trigonometry and its applications, circles, constructions, areas related to circles, surface areas and volumes, statistics, and probability. Full marks are 100 (Theory 90 + Internal Assessment 10), with a typical theory duration of about 3 hours. The official paper is a written mixed-format exam, not pure multiple-choice. The 100 questions on this page are an English-language multiple-choice study adaptation with step-by-step worked calculations for concept drills and self-assessment.

Assessment

Official: written mixed theory paper, Theory 90 + IA 10 = 100 marks, subject code C2, NCERT Class 10 syllabus, typically about 3 hours. Local bank: English MCQ study adaptation with worked solutions.

Time Limit

About 3 hours for the theory paper (confirm the current ASSEB HSLC timetable)

Passing Score

Theory 27/90 and Internal Assessment 3/10 (30/100 total) under current ASSEB HSLC rules; confirm the latest Board circular.

Exam Fee

Included in the annual ASSEB HSLC examination form-fill-up fees notified by the Board. (Assam State School Education Board (ASSEB), Division-I (erstwhile SEBA))

ASSEB HSLC General Mathematics Exam Content Outline

Real Numbers

Euclid's division lemma and algorithm, fundamental theorem of arithmetic, HCF and LCM using prime factorization, proofs of irrationality (for example √2, √3), and terminating versus non-terminating recurring decimals.

Polynomials

Zeros of linear and quadratic polynomials, relationship between zeros and coefficients, and the division algorithm for polynomials with remainder and quotient interpretation.

Linear Equations in Two Variables

Graphical representation of a pair of linear equations, algebraic solution by substitution, elimination, and cross-multiplication, and conditions for unique, infinite, or no solution.

Quadratic Equations

Standard form ax² + bx + c = 0, solution by factorization, completing the square, and the quadratic formula; nature of roots from the discriminant Δ = b² − 4ac.

Arithmetic Progressions

General term aₙ = a + (n − 1)d, sum Sₙ = n/2 [2a + (n − 1)d], and application problems involving series of payments, seating, or equally spaced quantities.

Triangles

Basic proportionality (Thales) theorem, criteria for similarity (AAA, SAS, SSS), areas of similar triangles, and the Pythagorean theorem with applications.

Coordinate Geometry

Distance formula, section (internal/external) formula, midpoint, area of a triangle from coordinates, and collinearity of three points.

Trigonometry

Trigonometric ratios of acute angles, standard values (0°, 30°, 45°, 60°, 90°), complementary-angle relations, and fundamental identities such as sin²θ + cos²θ = 1.

Applications of Trigonometry

Heights and distances: angle of elevation and depression, two-position problems, and multi-step calculations using right triangles.

Circles

Tangent perpendicular to radius at the point of contact, equal tangents from an external point, and related angle/length properties.

Constructions

Conceptual questions on dividing a line segment in a given ratio, constructing tangents from an external point, and constructing a triangle similar to a given triangle.

Areas Related to Circles

Area and circumference formulas, area of a sector and segment, and areas of combinations of circles with triangles, squares, or other plane figures.

Surface Areas and Volumes

Surface area and volume of cubes, cuboids, cylinders, cones, spheres, and hemispheres, including combinations such as cone on a cylinder or hemisphere on a cuboid.

Statistics

Mean of grouped data (direct, assumed-mean, and step-deviation methods), median and mode of grouped frequency distributions, cumulative frequency, and ogives.

10%

Probability

Classical definition P(E) = n(E)/n(S), complementary events, simple experiments with coins, dice, cards, and equally likely outcomes.

How to Pass the ASSEB HSLC General Mathematics Exam

What You Need to Know

Passing score: Theory 27/90 and Internal Assessment 3/10 (30/100 total) under current ASSEB HSLC rules; confirm the latest Board circular.
Assessment: Official: written mixed theory paper, Theory 90 + IA 10 = 100 marks, subject code C2, NCERT Class 10 syllabus, typically about 3 hours. Local bank: English MCQ study adaptation with worked solutions.
Time limit: About 3 hours for the theory paper (confirm the current ASSEB HSLC timetable)
Exam fee: Included in the annual ASSEB HSLC examination form-fill-up fees notified by the Board.

Keys to Passing

Complete 500+ practice questions
Score 80%+ consistently before scheduling
Focus on highest-weighted sections
Use our AI tutor for tough concepts

ASSEB HSLC General Mathematics Study Tips from Top Performers

1Alternate MCQ drills with timed written answers from NCERT examples so you can show steps for Theory 90 marks.

2Memorize standard trigonometric values and identities; most heights-and-distances errors come from wrong complementary ratios.

3For algebra, always check the discriminant and consistency conditions before solving; label each step clearly for partial-credit style answers.

4In mensuration, write formulas first, substitute carefully, and keep π = 22/7 or 3.14 consistent with the question.

5Build a formula sheet for distance, section, area of triangle, Sₙ of AP, and mean/median/mode of grouped data and revise it weekly.

Frequently Asked Questions

Is the official ASSEB HSLC General Mathematics exam multiple-choice?

No. The official ASSEB Div-I HSLC General Mathematics (C2) paper is a mixed written theory examination out of 90 marks (plus Internal Assessment 10). The 100 questions on this page are an English-language MCQ study adaptation with worked calculations to build speed and accuracy—they are not a full simulation of the official constructed-response format.

What is the full marks split and typical duration for ASSEB HSLC General Mathematics?

Full marks are 100: Theory 90 + Internal Assessment 10. The theory paper is typically about 3 hours; always confirm the exact duration and timetable on the current ASSEB HSLC notification.

What is the passing score for ASSEB HSLC General Mathematics?

Under current ASSEB HSLC practice for this marking scheme, candidates generally need at least 27 marks in Theory (out of 90) and 3 marks in Internal Assessment (out of 10), for 30/100 overall. Verify the latest Board circular for your examination year.

Which syllabus does ASSEB HSLC General Mathematics follow?

ASSEB Division-I has adopted the NCERT Class 10 Mathematics syllabus and textbooks for General Mathematics (subject code C2). Units include real numbers, polynomials, linear equations, quadratic equations, arithmetic progressions, triangles, coordinate geometry, trigonometry and applications, circles, constructions, areas related to circles, surface areas and volumes, statistics, and probability.

How much does the ASSEB HSLC General Mathematics exam cost?

General Mathematics is not separately priced. The fee is included in the annual ASSEB HSLC examination form-fill-up fees notified by the Board. Check site.sebaonline.org for the current fee circular—do not rely on outdated fixed rupee figures from unofficial sources.

How should I use this free MCQ bank for a written HSLC paper?

Use these MCQs for daily concept and calculation drills with worked solutions. Also practise full written answers (short and long) from NCERT exercises and ASSEB-style model papers so you can present steps clearly under theory-paper conditions.