MP Board Class 10 New Pattern Practice Paper 2027 — No Choice 2 Mark Questions With Solutions

In short: MPBSE has changed the Class 10 exam pattern for 2027 — 2-mark questions are now compulsory with no internal choice. This means approximately 16 marks in every subject depend on 2-mark questions where every single question must be answered. This practice paper set covers all five main subjects (Maths, Science, Hindi, English, Social Science) with questions aligned to the new pattern. Each paper follows the official MPBSE blueprint: objective (1 mark) + compulsory very short answer (2 marks) + short answer with choice (3 marks) + long answer with choice (4 marks) + very long answer with choice (5 marks).

What Changed in 2027 — The New Pattern

Impact: Under the old pattern, you could skip 4 out of 8 two-mark questions by choosing the easier ones. Now, all 8 must be answered. This means EVERY chapter must be prepared for 2-mark type questions. No skipping chapters for 2-mark prep.

Practice Paper 1 — Mathematics (गणित) — 80 Marks

Time: 3 Hours | Maximum Marks: 80

Section A — Objective Questions (1 mark each × 15 = 15 marks)

Q1-Q8: Multiple Choice Questions (MCQ)

Q1. The HCF of 12, 21, and 15 is: (a) 3 (b) 6 (c) 12 (d) 1

Q2. If one zero of the polynomial p(x) = 2x² + 3x + k is 1/2, then the value of k is: (a) -2 (b) 2 (c) -1 (d) 1

Q3. For what value of k, the pair of equations 2x + 3y = 7 and (k-1)x + (k+2)y = 3k has infinitely many solutions? (a) k = 7 (b) k = 4 (c) k = 2 (d) k = 8

Q4. The 10th term of AP: 2, 7, 12, 17, ... is: (a) 45 (b) 47 (c) 50 (d) 52

Q5. In △ABC, DE ∥ BC. If AD = 2 cm, DB = 3 cm, and AE = 3 cm, then EC = (a) 4 cm (b) 4.5 cm (c) 5 cm (d) 3.5 cm

Q6. If tan θ = 3/4, then sin θ = (a) 3/5 (b) 4/5 (c) 3/4 (d) 5/3

Q7. The distance between points (3, 4) and (0, 0) is: (a) 5 (b) 7 (c) 25 (d) 12

Q8. The probability of an impossible event is: (a) 1 (b) 0 (c) 1/2 (d) -1

Q9-Q12: Fill in the Blanks

Q9. The product of a non-zero rational number and an irrational number is always _______.

Q10. If the discriminant of a quadratic equation is 0, the roots are _______.

Q11. The total surface area of a hemisphere of radius r is _______.

Q12. If P(E) = 0.6, then P(not E) = _______.

Q13-Q15: True or False

Q13. Every natural number is a whole number. (True / False)

Q14. Two triangles are similar if their corresponding sides are proportional. (True / False)

Q15. The tangent at any point of a circle is perpendicular to the radius through the point of contact. (True / False)

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Section B — Very Short Answer (2 marks each × 8 = 16 marks) ⚠️ ALL COMPULSORY

Q16. Prove that √3 is irrational.

Q17. Find the zeroes of the polynomial x² - 3 and verify the relationship between zeroes and coefficients.

Q18. Solve: x + y = 14, x - y = 4.

Q19. Find the 20th term of the AP: 3, 8, 13, 18, ...

Q20. State and prove the Basic Proportionality Theorem (BPT) for the case where DE ∥ BC in triangle ABC with D on AB and E on AC.

Q21. If sin A = 3/4, find cos A and tan A.

Q22. Find the distance between the points (-1, 5) and (3, 2).

Q23. Find the mean of the following data by direct method:

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Section C — Short Answer (3 marks each × 8 = 24 marks) [Choice in some]

Q24. Find the LCM and HCF of 26 and 91 by prime factorization method.

Q25. A train covered a certain distance at a uniform speed. If the speed had been 6 km/h more, it would have taken 4 hours less. If the speed had been 6 km/h less, it would have taken 6 hours more. Find the distance and original speed.

OR

Q25. The sum of areas of two squares is 468 m². If the difference of their perimeters is 24 m, find the sides of the two squares.

Q26. Find the sum of first 15 terms of the AP: 7, 13, 19, 25, ...

Q27. Prove that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

OR

Q27. In a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides. Prove.

Q28. Evaluate: (sin 30° + tan 45° - cosec 60°) / (sec 30° + cos 60° + cot 45°)

Q29. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

Q30. A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

OR

Q30. A toy is in the shape of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

Q31. The following table gives the distribution of heights (in cm) of 50 students in a class. Find the median height.

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Section D — Long Answer (4 marks each × 4 = 16 marks)

Q32. The first term of an AP is 5, the last term is 45, and the sum is 400. Find the number of terms and the common difference.

OR

Q32. How many terms of the AP 24, 21, 18, ... must be taken so that their sum is 78?

Q33. 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.

Q34. Draw a circle of radius 3 cm. From a point 7 cm away from its centre, construct a pair of tangents to the circle. Measure the length of each tangent.

Q35. A die is thrown once. Find the probability of getting: (a) a prime number, (b) a number lying between 2 and 6, (c) an odd number.

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Section E — Very Long Answer (5 marks each × 2 = 10 marks)

Q36. A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.

OR

Q36. Prove that the lengths of tangents drawn from an external point to a circle are equal.

Q37. The following frequency distribution gives the monthly consumption of electricity of 68 consumers in a locality. Find the median, mean, and mode.

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Solutions — Section A (Objective)

Solutions — Section B (2-Mark Compulsory)

Q16 Solution: Prove √3 is irrational

Assume √3 is rational. Let √3 = a/b where a, b are co-prime integers, b ≠ 0.

Squaring: 3 = a²/b² → a² = 3b²

This means a² is divisible by 3, so a is divisible by 3. Let a = 3c.

Then (3c)² = 3b² → 9c² = 3b² → b² = 3c²

So b² is also divisible by 3, meaning b is divisible by 3.

But if both a and b are divisible by 3, they are not co-prime — contradiction.

Therefore √3 is irrational.

Q17 Solution: Zeroes of x² - 3

x² - 3 = 0 → x² = 3 → x = ±√3

Zeroes: √3 and -√3

Verification: Sum of zeroes = √3 + (-√3) = 0 = -b/a = 0/1 ✓ Product of zeroes = (√3)(-√3) = -3 = c/a = -3/1 ✓

Q18 Solution: Solve x + y = 14, x - y = 4

Adding both equations: 2x = 18 → x = 9 Substituting: 9 + y = 14 → y = 5

Solution: x = 9, y = 5

Q19 Solution: 20th term of AP 3, 8, 13, 18, ...

a = 3, d = 8 - 3 = 5

T₂₀ = a + (n-1)d = 3 + 19(5) = 3 + 95 = 98

Q20 Solution: BPT Statement and Application

Statement: If a line is drawn parallel to one side of a triangle, it divides the other two sides in the same ratio.

In △ABC, if DE ∥ BC where D is on AB and E is on AC, then: AD/DB = AE/EC

(For 2 marks: stating the theorem clearly and writing the proportionality result with a labeled diagram is sufficient.)

Q21 Solution: sin A = 3/4, find cos A and tan A

sin A = 3/4 → opposite = 3, hypotenuse = 4

By Pythagoras: adjacent = √(4² - 3²) = √(16 - 9) = √7

cos A = √7/4

tan A = 3/√7 = 3√7/7

Q22 Solution: Distance between (-1, 5) and (3, 2)

d = √[(3-(-1))² + (2-5)²] d = √[(4)² + (-3)²] d = √[16 + 9] d = √25 = 5 units

Q23 Solution: Mean by Direct Method

Mean = Σfᵢxᵢ / Σfᵢ = 580/20 = 29

Practice Paper 2 — Science (विज्ञान) — 80 Marks

Time: 3 Hours | Maximum Marks: 80

Section A — Objective (1 mark × 15 = 15 marks)

Q1. The chemical formula of baking soda is: (a) Na₂CO₃ (b) NaHCO₃ (c) NaCl (d) NaOH

Q2. Which gas is produced when zinc reacts with dilute hydrochloric acid? (a) Oxygen (b) Hydrogen (c) Chlorine (d) Nitrogen

Q3. The SI unit of electric current is: (a) Volt (b) Ohm (c) Ampere (d) Watt

Q4. In a concave mirror, when the object is at the centre of curvature, the image is formed: (a) At infinity (b) At F (c) At C (d) Between F and C

Q5. Which of the following is not a part of the human excretory system? (a) Kidneys (b) Ureters (c) Lungs (d) Urinary bladder

Q6. The process of nutrition in Amoeba is called: (a) Autotrophic (b) Holozoic (c) Parasitic (d) Saprotrophic

Q7. A ray of light travelling from a denser medium to a rarer medium bends: (a) Towards the normal (b) Away from the normal (c) Along the normal (d) Does not bend

Q8. Resistors connected in parallel have the same: (a) Current (b) Resistance (c) Potential difference (d) Power

Q9. The functional group present in ethanol is _______. (Fill in the blank)

Q10. In humans, the sex of the baby is determined by the _______ chromosome of the father. (Fill in the blank)

Q11. Decomposition of vegetable matter into compost is a _______ reaction. (Fill in the blank)

Q12. The power of accommodation of the eye decreases with ageing due to _______. (Fill in the blank)

Q13. All metals are good conductors of electricity. (True / False)

Q14. Photosynthesis is an endothermic reaction. (True / False)

Q15. The refractive index of a medium is always greater than 1. (True / False)

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Section B — Very Short Answer (2 marks × 8 = 16 marks) ⚠️ ALL COMPULSORY

Q16. What is a chemical equation? Write the balanced equation for the reaction of iron with water.

Q17. Define pH. What is the pH value of pure water?

Q18. What is the difference between biodegradable and non-biodegradable waste? Give one example of each.

Q19. State Ohm's law and write its mathematical expression.

Q20. Define the term "power of a lens." What is its SI unit?

Q21. What is a food chain? Give an example of a food chain with four trophic levels.

Q22. Differentiate between arteries and veins (any two differences).

Q23. What is meant by "homologous series" in carbon compounds? Give two characteristics.

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Section C — Short Answer (3 marks × 8 = 24 marks)

Q24. An element X has atomic number 12. (a) Write its electronic configuration. (b) State the group and period to which it belongs. (c) Is it a metal or non-metal?

Q25. An electric heater is rated 1500 W. How much energy does it use in 10 hours? Express in kWh and joules.

OR

Q25. Three resistors of 5 Ω, 10 Ω, and 30 Ω are connected in parallel. Find the equivalent resistance and the current through the circuit if connected to a 15 V battery.

Q26. Explain the process of photosynthesis. Include the chemical equation and the role of chlorophyll.

Q27. What is atmospheric refraction? How does it explain the twinkling of stars?

OR

Q27. Draw a ray diagram showing image formation by a convex lens when the object is placed between F and 2F.

Q28. Explain the extraction of metals of medium reactivity from their ores with an example.

Q29. What is the significance of DNA copying in reproduction? What are the advantages of sexual reproduction over asexual reproduction?

OR

Q29. Explain vegetative propagation with two examples. State its advantages.

Q30. What is a solenoid? Draw the magnetic field pattern around a current-carrying solenoid. How does it resemble a bar magnet?

Q31. Explain the formation of rainbow. Which phenomenon of light is responsible?

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Section D — Long Answer (4 marks × 4 = 16 marks)

Q32. Explain the human digestive system with a labeled diagram. Describe the role of enzymes in digestion.

OR

Q32. Describe the human respiratory system. Explain the mechanism of breathing (inhalation and exhalation).

Q33. A student focused sunlight on a sheet of paper using a convex lens. The sharp bright spot formed on the paper is 15 cm from the lens. (a) What is the focal length of the lens? (b) What is the power of the lens? (c) If the student holds the lens 10 cm from the paper, will the spot be sharp? Why?

Q34. What are the different methods of contraception? Classify them into barrier, chemical, and surgical methods.

Q35. Explain Mendel's experiment on pea plants with reference to monohybrid cross. Show the F1 and F2 generations with a Punnett square.

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Section E — Very Long Answer (5 marks × 2 = 10 marks)

Q36. Explain the human nervous system. Describe the structure and function of a neuron with a labeled diagram. What is a reflex arc? Give an example.

OR

Q36. Describe the structure of the human eye with a labeled diagram. Explain the defects of vision (myopia and hypermetropia) and their correction.

Q37. (a) Explain the electrolytic refining of metals. Draw a labeled diagram. (b) What is corrosion? How can it be prevented?

Science Section B — Solutions (2-Mark Compulsory)

Q16 Solution

A chemical equation is a symbolic representation of a chemical reaction using chemical formulas and symbols.

Balanced equation: 3Fe + 4H₂O → Fe₃O₄ + 4H₂

Q17 Solution

pH is a measure of the concentration of hydrogen ions (H⁺) in a solution. It indicates whether a solution is acidic, basic, or neutral.

pH of pure water = 7 (neutral).

Q18 Solution

Biodegradable waste: Waste that can be broken down by biological processes (decomposers). Example: vegetable peels.

Non-biodegradable waste: Waste that cannot be broken down by biological processes. Example: plastic bags.

Q19 Solution

Ohm's Law: At constant temperature, the current flowing through a conductor is directly proportional to the potential difference across its ends.

V = IR (where V = potential difference, I = current, R = resistance)

Q20 Solution

Power of a lens: The degree of convergence or divergence of light rays achieved by a lens. It is defined as the reciprocal of the focal length in metres.

P = 1/f (SI unit: Dioptre, symbol: D)

Q21 Solution

A food chain is a series of organisms in which each organism feeds on the one before it, transferring energy from one trophic level to the next.

Example: Grass → Grasshopper → Frog → Snake (Producers → Primary Consumer → Secondary Consumer → Tertiary Consumer)

Q22 Solution

Q23 Solution

A homologous series is a group of organic compounds having the same general formula, same functional group, and similar chemical properties, with successive members differing by a -CH₂- group.

Two characteristics: (1) Successive members differ by a molecular mass of 14 u. (2) All members have similar chemical properties due to the same functional group.

How to Use These Practice Papers

2-Mark Section Strategy

Since 2-mark questions are now compulsory, follow this approach:

Critical rule: Never leave a 2-mark question blank. Even a partially correct answer can get 1 mark. Under the old pattern, you could skip. Under the new pattern, a blank = guaranteed 0.

Time Management for Full Paper

Frequently Asked Questions

What exactly changed in MP Board 2027 exam pattern?

MPBSE removed internal choice from 2-mark very short answer questions for all main subjects (Maths, Science, Hindi, English, Social Science) for Classes 9-12. Previously, students could choose 4 out of 8 two-mark questions. Now all 8 are compulsory. The change affects approximately 16 marks per subject. Choice continues in 3-mark, 4-mark, and 5-mark questions.

How many marks are affected by the no-choice rule?

Approximately 16 marks per subject are affected (8 questions × 2 marks = 16 marks). This is 20% of the 80-mark theory paper. While 16 marks may seem small, the impact is significant because these questions cover ALL chapters. Previously, you could strategically skip some chapters for 2-mark prep. Now you cannot.

Is the blueprint (marks distribution) same as before?

Yes. The chapter-wise marks distribution has not changed. Only the internal choice rule for 2-mark questions has changed. The total marks, exam duration, and overall paper structure remain the same.

Which chapters are most likely to have 2-mark questions?

Every chapter can have 2-mark questions. Based on previous year patterns and the MP Board Blueprint 2027, 2-mark questions typically test: definitions, single-step calculations, one-line proofs, diagram labels, and direct formula applications. Prepare these for ALL chapters without exception.

How should I change my preparation strategy?

Three key changes: (1) Do not skip any chapter — even low-weightage chapters can have compulsory 2-mark questions. (2) Create a chapter-wise list of 2-mark type questions (definitions, short formulas, quick applications) and practice them separately. (3) Practice writing precise, 30-40 word answers for 2-mark questions — be brief but complete.

Are these practice papers aligned to the official MPBSE blueprint?

Yes. The question types, marks distribution, and chapter coverage follow the official MPBSE blueprint for 2027. The 2-mark section specifically tests every unit to reflect the new compulsory pattern. However, these are practice papers — the actual board paper may vary in specific questions while following the same structure.

Related Guides

MP Board Blueprint 2027 Hindi PDF | MP Board English vs Hindi Medium | MP Board Ganit Weightage Hindi | MP Board Vigyan Weightage Hindi | MP Board New Pattern Score Strategy

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