CBSE Class 10 Mathematics Board Paper — MCQs with Answers
Original paper · CBSE patternWritten by our subject team, not a reprint of an official sample paper.
- Questions
- 30
- Time
- 60 min
- Marking
- +1, no negative marking
- Mix
- 14 Easy · 17 Medium
Board Paper — CBSE Class 10 Mathematics is a full 30-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 picks 30 objective questions from a pool of 31 questions covering the whole Class 10 Mathematics syllabus. So when you take it again, you get a different paper, not the same questions.
The difficulty mix is 14 Easy · 17 Medium, balanced the way the board balances Section A. You get 60 minutes, about 120 seconds a question, which is the speed the real paper needs. 6 of the questions are solved in full below, each with the correct option and a worked explanation. Sign in free to attempt the other 24, timed and scored.
From 2026-27, CBSE Class 10 has two board exams a year. The first, around 15 February – 10 March 2027, is compulsory. An optional improvement exam in May 2027 lets you take up to three subjects again, and the better score counts. So you get two real attempts, and timed practice between February and May matters far more than it used to.
6 solved questions from this paper
Answer and worked explanation shown for each. The remaining 24 are timed and scored when you sign in free.
- Q1Easy
The HCF of 96 and 404 is:
A.4✓ CorrectB.2C.8D.101Answer: A. 4
Explanation: 96 = 2⁵ × 3 and 404 = 2² × 101, so the common factor is 2² = 4.
- Q2Easy
If α and β are the zeroes of the polynomial x² − 5x + 6, then α + β equals:
A.6B.−5C.−6D.5✓ CorrectAnswer: D. 5
Explanation: Sum of zeroes = −(coefficient of x)/(coefficient of x²) = −(−5)/1 = 5.
- Q3Easy
The pair of equations x + 2y = 4 and 2x + 4y = 12 has:
A.a unique solutionB.no solution✓ CorrectC.infinitely many solutionsD.exactly two solutionsAnswer: B. no solution
Explanation: a₁/a₂ = b₁/b₂ = 1/2 but ≠ c₁/c₂ = 4/12, so the lines are parallel and there is no solution.
- Q4Medium
After how many decimal places will the decimal expansion of 23/(2³ × 5²) terminate?
A.2B.1C.4D.3✓ CorrectAnswer: D. 3
Explanation: For a denominator 2ᵐ × 5ⁿ the expansion terminates after max(m, n) places; here max(3, 2) = 3.
- Q5Medium
Assertion (A): √2 is an irrational number. Reason (R): The square root of every prime number is irrational. Choose the correct option.
A.Both A and R are true and R is the correct explanation of A✓ CorrectB.Both A and R are true but R is not the correct explanation of AC.A is true but R is falseD.A is false but R is trueAnswer: A. Both A and R are true and R is the correct explanation of A
Explanation: 2 is prime and the square root of any prime is irrational, which directly proves √2 is irrational — so R correctly explains A.
- Q6Medium
A quadratic polynomial whose zeroes are 3 and −2 is:
A.x² + x − 6B.x² − x + 6C.x² − x − 6✓ CorrectD.x² + x + 6Answer: C. x² − x − 6
Explanation: Polynomial = x² − (sum)x + (product) = x² − (1)x + (−6) = x² − x − 6.
Sit the full paper — free
All 30 questions on a 60-minute timer, scored automatically, with a worked solution for every one — including the 24 not shown above. Sign in with Google — no card needed.
Attempt this paper free →More Class 10 Mathematics board papers
- Board Paper — you are here
- Board Paper Set 1 — 20 questions
- Board Paper Set 2 — 20 questions
- Board Paper Set 3 — 20 questions
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 on purpose. This is an original paper written by our subject team in the CBSE board pattern. It is not a copy of CBSE's official Sample Question Paper. So you get fresh questions you have not already seen on a dozen other sites, with instant scoring and worked solutions instead of 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. A board paper takes nothing away for a wrong answer, and leaving a question blank can only cost you.
How long should this paper take?
60 minutes for 30 questions, about 120 seconds each. The timer keeps running whether you watch it or not, and that is the point. Students lose board marks to poor timing at least as often as to gaps in what they know.
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 makes timed practice more useful. The better of your two scores counts, so a February attempt that goes badly is no longer final. But that only helps if you know exactly which topics cost you marks. A scored full-length paper tells you that. Re-reading the chapter does not.