CBSE Class 10 Mathematics Board Paper Set 3 — MCQs with Answers
Original paper · CBSE patternWritten by our subject team, not a reprint of an official sample paper.
- Questions
- 20
- Time
- 25 min
- Marking
- +1, no negative marking
- Mix
- 8 Easy · 8 Medium · 4 Hard
Board Paper Set 3 — CBSE Class 10 Mathematics is a full 20-question objective paper for Class 10 Mathematics, written in the CBSE board pattern and marked the way the board marks: +1 for a correct answer and 0 for a wrong one — no negative marking, exactly like the real board paper. It follows Section A of a real CBSE paper: Q1–Q16 are single-correct MCQs, Q17–Q18 are case-based questions built on a short source, and Q19–Q20 are assertion–reason items using the board's own four option strings.
Difficulty is 8 Easy · 8 Medium · 4 Hard, weighted the way the board weights Section A. You get 25 minutes — about 75 seconds a question, the pace the real paper demands. 8 of the questions are solved in full below, with the correct option and a worked explanation for each; the remaining 12 are timed and scored when you sign in free.
From 2026-27 CBSE Class 10 has two board exams a year: the first around 15 February – 10 March 2027 is compulsory, and an optional improvement exam in May 2027 lets you re-attempt up to three subjects with the better score counting. That gives you two genuine attempts — and makes timed practice between February and May worth far more than it used to be.
8 solved questions from this paper
Answer and worked explanation shown for each. The remaining 12 are timed and scored when you sign in free.
- Q1Easy
A quadratic polynomial whose zeroes are 3 and −5 is:
A.x² − 2x − 15B.x² + 2x + 15C.x² − 2x + 15D.x² + 2x − 15✓ CorrectAnswer: D. x² + 2x − 15
Explanation: A quadratic polynomial with given zeroes is x² − (sum of zeroes)x + (product of zeroes). The sum is 3 + (−5) = −2 and the product is 3 × (−5) = −15, giving x² + 2x − 15. Missing the minus sign already built into the formula flips the middle term to −2x.
- Q2Easy
The roots of the equation x² − 3x − 10 = 0 are:
A.−5 and 2B.5 and 2C.5 and −2✓ CorrectD.−5 and −2Answer: C. 5 and −2
Explanation: Factorising, x² − 3x − 10 = (x − 5)(x + 2), so the roots are 5 and −2. Both 5, −2 and −5, 2 give a product of −10, so check the sum: it must be −(−3) = 3, and 5 + (−2) = 3 while −5 + 2 = −3.
- Q3Easy
In ΔABC, AB = 6√3 cm, AC = 12 cm and BC = 6 cm. The measure of ∠B is:
A.60°B.45°C.90°✓ CorrectD.120°Answer: C. 90°
Explanation: Test the Pythagoras relation: AB² + BC² = (6√3)² + 6² = 108 + 36 = 144, and AC² = 12² = 144. The square on AC equals the sum of the squares on the other two sides, so the angle opposite AC, which is ∠B, is a right angle.
- Q4Medium
The pair of equations 3x − y = 5 and 6x − 2y = k has no solution when:
A.k ≠ 10✓ CorrectB.k = 10C.k = 5D.k ≠ 5Answer: A. k ≠ 10
Explanation: A pair of linear equations has no solution when a₁/a₂ = b₁/b₂ but c₁/c₂ is different. Here 3/6 = (−1)/(−2) = 1/2, so we need 5/k ≠ 1/2, that is k ≠ 10. At k = 10 the two equations describe the same line and would have infinitely many solutions instead of none.
- Q5Medium
Which term of the AP 21, 18, 15, … is −81?
A.34thB.35th✓ CorrectC.36thD.30thAnswer: B. 35th
Explanation: Here a = 21 and d = 18 − 21 = −3. Setting aₙ = a + (n − 1)d = −81 gives 21 − 3(n − 1) = −81, so n − 1 = 34 and n = 35. Stopping at n − 1 = 34 reports the number of gaps rather than the term number.
- Q6Medium
The diagonals of a rhombus measure 16 cm and 12 cm. The length of each side of the rhombus is:
A.10 cm✓ CorrectB.14 cmC.28 cmD.20 cmAnswer: A. 10 cm
Explanation: The diagonals of a rhombus bisect each other at right angles, so each side is the hypotenuse of a right triangle with legs 8 cm and 6 cm. The side is √(64 + 36) = √100 = 10 cm. Using the full diagonals 16 and 12 instead of their halves gives 20 cm.
- Q7Hard
Two positive integers are written as p = a²b³ and q = a³b, where a and b are prime numbers. Then HCF(p, q) is:
A.a³b³B.a²b✓ CorrectC.abD.a²b³Answer: B. a²b
Explanation: The HCF takes each common prime raised to the lower of the two powers. Comparing a² with a³ the lower power is a², and comparing b³ with b¹ the lower power is b, so the HCF is a²b. Taking the higher powers instead gives a³b³, which is the LCM.
- Q8Hard
The quadratic equation (k + 4)x² + (k + 1)x + 1 = 0 has equal roots for:
A.k = −5 and k = 3B.k = 5 and k = 3C.k = −5 and k = −3D.k = 5 and k = −3✓ CorrectAnswer: D. k = 5 and k = −3
Explanation: Equal roots mean the discriminant is zero, so (k + 1)² − 4(k + 4) = 0. Expanding gives k² + 2k + 1 − 4k − 16 = k² − 2k − 15 = 0, which factorises as (k − 5)(k + 3) = 0, so k = 5 or k = −3. Reversing the signs of the factors reverses both answers.
Sit the full paper — free
All 20 questions on a 25-minute timer, scored automatically, with a worked solution for every one — including the 12 not shown above. Sign in with Google — no card needed.
Attempt this paper free →More Class 10 Mathematics board papers
- Board Paper — 31 questions
- Board Paper Set 1 — 20 questions
- Board Paper Set 2 — 20 questions
- Board Paper Set 3 — you are here
Prefer chapter-by-chapter revision first? Class 10 Mathematics notes & chapter MCQs →
Questions students ask about this paper
Is this an official CBSE sample paper?
No — and that is deliberate. This is an original paper written in the CBSE board pattern by our subject team, not a copy of CBSE's official Sample Question Paper. It means you get fresh questions you have not already seen on a dozen other sites, with instant scoring and worked solutions rather than a PDF.
How is this Class 10 Mathematics paper marked?
+1 for a correct answer and 0 for a wrong one — no negative marking, exactly like the real board paper. So attempt every question — there is no penalty for a wrong answer on a board paper, and leaving a question blank can only cost you.
How long should this paper take?
25 minutes for 20 questions, roughly 75 seconds each. The timer runs whether or not you are watching it, which is the point: board marks are lost to pacing at least as often as to gaps in knowledge.
Do I need to pay to attempt it?
No. Sign in free with Google and the full paper opens with a live timer, automatic scoring and a worked solution for every question — including the ones not shown on this page.
Does the May 2027 improvement exam change how I should practise?
It raises the value of timed practice. Because the better of your two scores counts, a February attempt that goes badly is no longer final — but only if you know precisely which topics cost you the marks. A scored full-length paper tells you that; re-reading the chapter does not.