GSEB Std 10 Model Question Papers (English and Gujarati Medium)

Model papers are the closest thing to a rehearsal of the GSEB board exam. Practising them under time shows you which chapters need work and trains you to finish the paper. This page explains how the GSEB Std 10 paper is structured, where to find official papers, and gives you an original 50-mark Maths model paper with a full answer key. A Gujarati-medium version of this page is also available.

How the GSEB Std 10 paper is structured

• Marks: in most subjects, 80 marks for the written board exam plus 20 marks for internal assessment.
• Question mix: objective questions (such as MCQs, fill in the blanks and one-word answers), short answers and long answers.
• Maths levels: GSEB offers Standard and Basic Mathematics in Std 10. Choose with your teacher, based on whether you will study Maths in Std 11.
• Mediums: papers are available in Gujarati, English and other mediums.

The exact sections, number of questions and internal choices are set by the board each year. Always check the current paper style and notices on the official GSEB website before you plan your practice.

Where to find official papers

The Gujarat Secondary and Higher Secondary Education Board publishes notices, paper styles and question papers on gseb.org. GSEB's Std 10 Maths and Science textbooks follow the NCERT syllabus, so the NCERT textbooks and NCERT Exemplar problems are also useful for extra practice. Chapter numbers can differ slightly between editions, so match chapters by name.

How to use a model paper

1. Sit it under time: no book, no phone, a clock in front of you.
2. Mark it honestly using the answer key, giving step marks only where the step is correct.
3. Note every lost mark: concept gap, calculation slip, time or presentation.
4. Revise those chapters before the next paper.

GSEB Std 10 Maths model paper (Standard level, 50 marks, 2 hours)

Section A: 1 mark each (10 marks)

1. Find the HCF of 26 and 91.
2. If 2 is a zero of x² − 5x + k, find k.
3. How many solutions does the pair 2x + 3y = 5 and 4x + 6y = 10 have?
4. Find the discriminant of 2x² − 4x + 3.
5. Find the 11th term of the AP 3, 8, 13, …
6. Find the distance of the point (−6, 8) from the origin.
7. Find the value of sin²60° + cos²60°.
8. A point is 10 cm from the centre of a circle of radius 6 cm. Find the length of the tangent from the point.
9. A die is thrown once. Find the probability of getting a prime number.
10. Find the mode of 5, 7, 7, 9, 5, 7, 8.

Section B: 2 marks each (10 marks)

11. Express 156 as a product of its prime factors.
12. Find the zeroes of x² − 2x − 8.
13. Find the midpoint of the line segment joining (−2, 5) and (4, −1).
14. A 10 m ladder leans against a wall, making an angle of 60° with the ground. How high up the wall does it reach? (√3 ≈ 1.732)
15. Find the area of a sector of angle 60° in a circle of radius 7 cm. (π = 22/7)

Section C: 3 marks each (15 marks)

16. Solve: x + y = 14 and x − y = 4.
17. Find the sum of the first 15 terms of the AP 6, 10, 14, …
18. Solve the quadratic equation 6x² − x − 2 = 0 by factorisation.
19. Prove that √5 is irrational.
20. A toy is a cone of height 12 cm mounted on a hemisphere, both of radius 3.5 cm. Find the volume of the toy. (π = 22/7)

Section D: 5 marks each (15 marks)

21. From the top of a 7 m high building, the angle of elevation of the top of a tower is 60° and the angle of depression of its foot is 45°. Find the height of the tower. (√3 ≈ 1.732)
22. Find the mean and the median of this data: marks 0-10: 4 students, 10-20: 6, 20-30: 10, 30-40: 6, 40-50: 4.
23. Prove that the lengths of the tangents drawn from an external point to a circle are equal.

Answer key

Show the full answer key

Section A. 1) 13. 2) 4 − 10 + k = 0, so k = 6. 3) Infinitely many (the equations are proportional). 4) 16 − 24 = −8. 5) 3 + 10 × 5 = 53. 6) √(36 + 64) = 10. 7) 1. 8) √(100 − 36) = 8 cm. 9) Primes 2, 3, 5: 3/6 = 1/2. 10) 7.

Section B. 11) 156 = 2² × 3 × 13. 12) (x − 4)(x + 2) = 0, so x = 4 or −2. 13) (1, 2). 14) 10 × sin 60° = 5√3 ≈ 8.66 m. 15) (60/360) × (22/7) × 49 = 154/6 ≈ 25.67 cm².

Section C. 16) Adding: 2x = 18, x = 9; y = 5. 17) S₁₅ = 15/2 × (2 × 6 + 14 × 4) = 15/2 × 68 = 510. 18) 6x² − 4x + 3x − 2 = 2x(3x − 2) + 1(3x − 2) = (3x − 2)(2x + 1) = 0, so x = 2/3 or x = −1/2. 19) Assume √5 = a/b in lowest terms. Then 5b² = a², so 5 divides a² and hence a; write a = 5c, giving b² = 5c², so 5 divides b too. This contradicts a/b being in lowest terms, so √5 is irrational. 20) Cone: ⅓ × (22/7) × 3.5² × 12 = 154 cm³; hemisphere: ⅔ × (22/7) × 3.5³ ≈ 89.83 cm³; total ≈ 243.83 cm³.

Section D. 21) Let the distance be d. tan 45° = 7/d, so d = 7 m. Height of the tower above the building = 7 tan 60° = 7√3 m. Tower height = 7 + 7√3 = 7(1 + √3) ≈ 19.12 m. 22) Class marks 5, 15, 25, 35, 45; Σfx = 20 + 90 + 250 + 210 + 180 = 750; mean = 750/30 = 25. n/2 = 15; cumulative frequencies 4, 10, 20, so the median class is 20-30: median = 20 + [(15 − 10)/10] × 10 = 25. 23) Draw tangents PQ and PR from P to the circle with centre O; join OQ, OR and OP. ∠OQP = ∠ORP = 90° (radius ⊥ tangent), OQ = OR (radii) and OP is common, so ΔOQP ≅ ΔORP (RHS). Hence PQ = PR.

Practise chapter by chapter, then full papers

Model papers work best after chapter-wise practice. Start with our GSEB Class 10 question bank, then come back to full papers in the last month. Our 8-week board exam plan works for GSEB as well as CBSE, and how to get good marks in Class 10 Maths covers the mistakes that cost the most marks.

Intellicamp supports GSEB Std 5 to 10 in English and Gujarati medium (see boards and standards). You can take chapter-wise practice tests, get them marked instantly and see which chapters cost you marks. See how it works for students and our personalised study material for weak chapters.

Frequently asked questions

Where can I download official GSEB Std 10 question papers?

Official papers, paper styles and notices are published by the Gujarat Secondary and Higher Secondary Education Board on gseb.org. Always use the current year's paper style for practice.

How many marks is the GSEB Std 10 board exam?

In most subjects, 80 marks are for the written board exam and 20 marks for internal assessment, making 100. Check the current notification for each subject.

Is the GSEB Std 10 syllabus the same as NCERT?

GSEB's Std 10 Maths and Science textbooks follow the NCERT syllabus, so chapters match by name. Chapter numbers can differ slightly in the Gujarat textbook edition.

What are Basic and Standard Maths in GSEB Std 10?

GSEB offers two levels of Std 10 Mathematics. Standard Maths is for students who plan to study Maths in Std 11 Science; Basic Maths is for others. The papers differ in difficulty.

Are these model papers available in Gujarati medium?

Yes. A Gujarati version of this page is available, and Intellicamp supports Gujarati-medium practice tests for GSEB.