Haryana Board HBSE Model Paper 2027 — Class 10 Solved Practice Paper With Solutions

In short: This is a solved HBSE (BSEH) Class 10 practice paper set for the 2027 board exam. It includes a complete 80-mark Maths paper with step-by-step solutions, plus Science and Social Science question sets with answers. The structure follows the recent BSEH pattern: a 1-mark objective section (MCQ, assertion-reason, fill in the blanks), followed by 2-mark, 3-mark, 5-mark and case-based questions. Use it for timed practice, then check your answers against the solutions. Official model papers are published on bseh.org.in. Our HBSE model paper strategy guide explains how to plan your model paper practice.

HBSE Class 10 Exam Pattern 2027 — Quick Recap

Note: Subjects with a practical component can have a different theory/practical split. Always check the latest BSEH marking scheme for your subject before the exam.

Maths Practice Paper — 80 Marks

Time: 3 hours | Maximum Marks: 80

This paper follows a typical BSEH layout. The exact number of questions per section can vary slightly year to year.

Section A — Objective (20 × 1 = 20 marks)

1. The LCM of 6 and 20 is: (a) 30 (b) 60 (c) 120 (d) 2
2. The sum of the zeroes of x² − 5x + 6 is: (a) −5 (b) 6 (c) 5 (d) −6
3. The pair 2x + 3y = 5 and 4x + 6y = 10 has: (a) no solution (b) one solution (c) infinitely many solutions (d) two solutions
4. The discriminant of x² + 4x + 4 = 0 is: (a) 0 (b) 4 (c) 8 (d) 16
5. The common difference of the AP 3, 7, 11, ... is: (a) 3 (b) 4 (c) 7 (d) 10
6. The 11th term of the AP 5, 8, 11, ... is: (a) 32 (b) 35 (c) 38 (d) 41
7. The distance of the point (6, 8) from the origin is: (a) 6 (b) 8 (c) 10 (d) 14
8. The midpoint of (2, 4) and (6, 8) is: (a) (4, 6) (b) (8, 12) (c) (2, 2) (d) (3, 4)
9. sin 60° cos 30° + cos 60° sin 30° equals: (a) 0 (b) 1/2 (c) √3/2 (d) 1
10. The value of tan 45° is: (a) 0 (b) 1 (c) √3 (d) 1/√3
11. If sin θ = cos θ, then θ is: (a) 0° (b) 30° (c) 45° (d) 60°
12. Two similar triangles have sides in the ratio 1 : 2. The ratio of their areas is: (a) 1 : 2 (b) 1 : 4 (c) 2 : 1 (d) 1 : 8
13. The number of tangents that can be drawn to a circle from an external point is: (a) 1 (b) 2 (c) 3 (d) infinite
14. The area of a circle of radius 7 cm is (π = 22/7): (a) 44 cm² (b) 154 cm² (c) 49 cm² (d) 308 cm²
15. The volume of a cube of side 3 cm is: (a) 9 cm³ (b) 18 cm³ (c) 27 cm³ (d) 54 cm³
16. The probability of getting a head when a coin is tossed once is: (a) 0 (b) 1/2 (c) 1 (d) 2
17. The empirical relation between mean, median and mode is: 3 Median = Mode + ____ Mean. (Fill in the blank)
18. The sum of the first 10 natural numbers is ____. (Fill in the blank)
19. Assertion (A): HCF × LCM of 12 and 18 is 216. Reason (R): For any two positive integers a and b, HCF(a, b) × LCM(a, b) = a × b. (a) Both A and R are true and R explains A (b) Both true, R does not explain A (c) A true, R false (d) A false, R true
20. The probability of a sure event is ____. (Fill in the blank)

Section B — Very Short Answer (6 × 2 = 12 marks)

21. Find the HCF and LCM of 96 and 404 by prime factorisation.
22. Find a quadratic polynomial whose sum of zeroes is −3 and product of zeroes is 2.
23. Solve: 2x + y = 7 and x − y = 2.
24. Find the value of k for which x² − 4x + k = 0 has two equal roots.
25. Find the coordinates of the point that divides the join of (−1, 7) and (4, −3) in the ratio 2 : 3.
26. If tan A = 4/3, find sin A and cos A.

Section C — Short Answer (6 × 3 = 18 marks)

27. Prove that √5 is irrational.
28. Find the sum of the first 20 terms of the AP 1, 4, 7, 10, ...
29. Prove that (1 + tan²A) cos²A = 1.
30. Find the area of a sector of a circle of radius 21 cm with central angle 60°.
31. Two dice are thrown together. Find the probability that the sum of the numbers is 8.
32. A 10 m long ladder reaches a window 8 m above the ground. Find the distance of the foot of the ladder from the wall.

Section D — Long Answer (4 × 5 = 20 marks)

33. A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less. Find the speed of the train.
34. State and prove the Basic Proportionality Theorem (Thales' theorem).
35. From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed on top of a 20 m high building are 45° and 60°. Find the height of the tower.
36. Find the mean and median of the following data:

Section E — Case-Based (2 × 5 = 10 marks)

37. School garden. Students plant saplings in rows. The first row has 3 saplings, the second has 5, the third has 7, and so on.

• (i) How many saplings are in the 10th row? (1 mark)
• (ii) How many saplings are in the first 10 rows together? (2 marks)
• (iii) How many rows are needed to plant 195 saplings in total? (2 marks)

38. Water tank. A village water tank is a cylinder of radius 1.4 m and height 2 m.

• (i) Find the volume of the tank. (2 marks)
• (ii) Find its curved surface area. (1 mark)
• (iii) How many litres of water can it hold? (2 marks)

Maths Solutions

Section A Answers

Quick checks: Q3 — ratios 2/4 = 3/6 = 5/10, so the lines coincide. Q6 — 5 + 10 × 3 = 35. Q9 — this is sin(60° + 30°) = sin 90° = 1. Q19 — 12 × 18 = 216, and the reason states the rule correctly.

Section B Solutions

Q21. 96 = 2⁵ × 3 and 404 = 2² × 101. HCF = 2² = 4. LCM = 2⁵ × 3 × 101 = 9696. Check: 4 × 9696 = 38784 = 96 × 404 ✓

Q22. Polynomial = x² − (sum)x + product = x² + 3x + 2.

Q23. Adding: 3x = 9, so x = 3. Then y = 7 − 6 = 1. x = 3, y = 1.

Q24. Equal roots means D = 0: 16 − 4k = 0, so k = 4.

Q25. x = (2 × 4 + 3 × (−1)) / 5 = 1. y = (2 × (−3) + 3 × 7) / 5 = 3. Point = (1, 3).

Q26. Opposite = 4, adjacent = 3, hypotenuse = 5. sin A = 4/5, cos A = 3/5.

Section C Solutions

Q27. Assume √5 = a/b with a, b co-prime. Then a² = 5b², so 5 divides a², hence 5 divides a. Let a = 5c. Then 25c² = 5b², so b² = 5c², and 5 divides b. Both a and b are divisible by 5, which contradicts co-primeness. So √5 is irrational.

Q28. a = 1, d = 3, n = 20. S₂₀ = 20/2 × [2(1) + 19(3)] = 10 × 59 = 590.

Q29. 1 + tan²A = sec²A. So LHS = sec²A × cos²A = (1/cos²A) × cos²A = 1 = RHS.

Q30. Area = (θ/360) × πr² = (60/360) × (22/7) × 441 = (1/6) × 1386 = 231 cm².

Q31. Favourable outcomes: (2,6), (3,5), (4,4), (5,3), (6,2) = 5. Total = 36. P = 5/36.

Q32. Distance = √(10² − 8²) = √36 = 6 m.

Section D Solutions

Q33. Let speed = x km/h. 360/x − 360/(x + 5) = 1. This gives 1800 = x² + 5x, so x² + 5x − 1800 = 0, which factors as (x + 45)(x − 40) = 0. Speed cannot be negative, so speed = 40 km/h.

Q34. Statement: if a line is drawn parallel to one side of a triangle and intersects the other two sides at distinct points, it divides those sides in the same ratio. Proof outline: In △ABC with DE ∥ BC, join BE and CD, and draw DM ⊥ AC and EN ⊥ AB.

• ar(ADE)/ar(BDE) = AD/DB (same height EN)
• ar(ADE)/ar(DEC) = AE/EC (same height DM)
• ar(BDE) = ar(DEC) (same base DE, between the same parallels DE and BC)
• Therefore AD/DB = AE/EC.

Draw a neat labelled diagram. Diagrams carry marks in BSEH evaluation.

Q35. Let the tower height be h and the distance from the point to the building be x.

• From the 45° angle: tan 45° = 20/x, so x = 20 m.
• From the 60° angle: tan 60° = (20 + h)/20, so 20√3 = 20 + h.
• h = 20(√3 − 1) ≈ 20 × 0.732 = 14.64 m.

Q36.

Mean = 1350/50 = 27. Median: n/2 = 25, so the median class is 20-30 (l = 20, cf = 13, f = 15, h = 10). Median = 20 + [(25 − 13)/15] × 10 = 20 + 8 = 28.

Section E Solutions

Q37. This is an AP with a = 3 and d = 2.

• (i) a₁₀ = 3 + 9 × 2 = 21 saplings
• (ii) S₁₀ = 10/2 × [6 + 9 × 2] = 5 × 24 = 120 saplings
• (iii) Sₙ = n/2 × [6 + 2(n − 1)] = n(n + 2) = 195. So n² + 2n − 195 = 0, giving (n + 15)(n − 13) = 0. n = 13 rows

Q38.

• (i) V = πr²h = (22/7) × 1.96 × 2 = 12.32 m³
• (ii) CSA = 2πrh = 2 × (22/7) × 1.4 × 2 = 17.6 m²
• (iii) 1 m³ = 1000 L, so the tank holds 12,320 litres

Science Practice Set (With Answers)

Use this set to practise each question type. Check the current BSEH Science marking scheme for the exact theory marks and section split.

1-Mark Questions

2-Mark Questions

Q1. Why should a magnesium ribbon be cleaned before burning? Magnesium reacts with oxygen in air and forms a layer of magnesium oxide on its surface. This layer stops the ribbon from burning properly, so it is rubbed with sandpaper first.

Q2. State two differences between a convex and a concave lens. A convex lens is thicker at the centre and converges light. A concave lens is thinner at the centre and diverges light. A convex lens can form real images. A concave lens always forms virtual, erect, diminished images.

Q3. What is the function of the placenta? It supplies glucose and oxygen from the mother to the embryo. It also removes waste products from the embryo into the mother's blood.

Q4. Why is the series arrangement not used for domestic circuits? In series, the same current flows through all appliances, so they cannot run independently. If one fails, the whole circuit breaks. The total resistance also increases, which reduces the current.

3-Mark Questions

Q1. Three resistors of 2 Ω, 3 Ω and 6 Ω are connected in parallel to a 6 V battery. Find the equivalent resistance and the total current. 1/R = 1/2 + 1/3 + 1/6 = (3 + 2 + 1)/6 = 1, so R = 1 Ω. I = V/R = 6/1 = 6 A.

Q2. An object is placed 30 cm in front of a convex lens of focal length 20 cm. Find the image position and nature. 1/v − 1/u = 1/f, with u = −30 and f = +20. So 1/v = 1/20 − 1/30 = 1/60, and v = +60 cm. The image is real, inverted and magnified (m = v/u = −2).

Q3. Explain double circulation in humans. Blood passes through the heart twice in one complete cycle. In pulmonary circulation (right ventricle → lungs → left atrium), blood picks up oxygen. In systemic circulation (left ventricle → body → right atrium), oxygen is delivered to the body. This keeps oxygenated and deoxygenated blood separate, which gives efficient oxygen supply.

5-Mark Question

Draw a labelled diagram of the human excretory system and explain how urine is formed in a nephron. Diagram labels: kidneys, ureters, urinary bladder, urethra, renal artery, renal vein.

How urine forms:

• (1) Filtration: blood is filtered in the glomerulus into Bowman's capsule
• (2) Selective reabsorption: glucose, amino acids, salts and most water go back into the blood through the tubule
• (3) Tubular secretion: extra wastes are secreted into the tubule
• The remaining fluid is urine. It passes through the collecting duct and ureter to the bladder.

Social Science Practice Set (With Answers)

How to Use This Paper

Frequently Asked Questions

Where can I download the official HBSE model papers for 2027?

BSEH publishes model papers and marking schemes on its official website, bseh.org.in, usually during the academic session. Check the "Model Papers" or "Downloads" section. This practice paper is a supplement for extra timed practice. Always solve the official papers too.

Is this practice paper the same as the actual HBSE board paper?

No. This is a practice paper modelled on the recent BSEH pattern and NCERT syllabus. The real paper will have different questions. However, the question types, chapter coverage and difficulty level are similar, so it is useful for practice.

How many model papers should I solve before the HBSE exam?

Aim for at least 5 full papers per main subject: the official BSEH model papers, previous year papers, and practice papers like this one. Solve them under timed conditions in the last 6-8 weeks before the exam.

Does HBSE give marks for steps in Maths?

Yes. BSEH marking schemes award marks for correct steps, formulas and method, even if the final answer has a small error. Always show your working, write the formula, and box your final answer.

What is the passing mark in HBSE Class 10?

You need 33% in each subject to pass. Internal assessment marks are added to your theory marks, so performing well in school assessments throughout the year makes passing easier.

Should I write answers in Hindi or English?

You can write in the medium you chose during registration. Most HBSE students write in Hindi. Keep your technical terms consistent. If you use "प्रतिरोध" for resistance, use it throughout.

Related Guides

HBSE Model Paper Strategy Guide | HBSE Class 10 Chapter-Wise Weightage | HBSE Class 10 Maths Weightage | HBSE Class 10 Important Questions Hindi | Haryana Board Class 10 Taiyari

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