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CBSE Class 10 Mathematics Board Paper Set 2 — 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 2 — 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
The pair of equations x + 2y = 5 and 3x + 6y = 15 has:
A.exactly one solution
B.no solution
C.exactly two solutions
D.infinitely many solutions✓ Correct
Answer: D. infinitely many solutions
Explanation: Comparing the ratios, 1/3 = 2/6 = 5/15, so all three ratios are equal and the two equations represent the same line. Coincident lines overlap at every point, which means infinitely many common solutions rather than a single point of intersection.
Q2Easy
The sum of two numbers is 27 and their difference is 5. The larger of the two numbers is:
A.11
B.22
C.16✓ Correct
D.13.5
Answer: C. 16
Explanation: Let the numbers be x and y with x + y = 27 and x − y = 5. Adding the two equations gives 2x = 32, so x = 16 and then y = 11. Halving only the sum gives 13.5, which ignores the difference altogether.
Q3Easy
The 11th term of the AP −3, −1/2, 2, 9/2, … is:
A.25
B.19.5
C.−22
D.22✓ Correct
Answer: D. 22
Explanation: The common difference is −1/2 − (−3) = 5/2. Using aₙ = a + (n − 1)d, a₁₁ = −3 + 10 × 5/2 = −3 + 25 = 22. Adding only the ten common differences and forgetting the first term gives 25.
Q4Medium
Which of the following rational numbers has a terminating decimal expansion?
A.17/8✓ Correct
B.5/6
C.7/15
D.11/21
Answer: A. 17/8
Explanation: A rational number in its lowest form terminates only when its denominator is of the form 2ᵐ × 5ⁿ. Here 8 = 2³, so 17/8 terminates. The denominators 6 = 2 × 3, 15 = 3 × 5 and 21 = 3 × 7 each carry a prime other than 2 or 5, so those expansions are non-terminating and repeating.
Q5Medium
If α and β are the zeroes of the polynomial x² − 6x + 8, then the value of 1/α + 1/β is:
A.4/3
B.3/4✓ Correct
C.−3/4
D.2/3
Answer: B. 3/4
Explanation: For x² − 6x + 8 the sum of the zeroes is 6 and the product is 8. Since 1/α + 1/β = (α + β)/(αβ), the value is 6/8 = 3/4. Writing the expression as (αβ)/(α + β) by mistake turns the answer upside down to 4/3.
Q6Medium
The quadratic equation kx² − 6x + 1 = 0 has two equal roots when k equals:
A.6
B.9✓ Correct
C.4
D.36
Answer: B. 9
Explanation: Equal roots require the discriminant to be zero: b² − 4ac = 0. Here (−6)² − 4 × k × 1 = 36 − 4k = 0, so k = 9. Setting 36 − 4k equal to the coefficient 6 rather than to zero is what produces the answer 6.
Q7Hard
The point on the x-axis which is equidistant from the points (2, −5) and (−2, 9) is:
A.(−7, 0)✓ Correct
B.(7, 0)
C.(0, −7)
D.(−3, 0)
Answer: A. (−7, 0)
Explanation: Any point on the x-axis has the form (x, 0). Equating the squared distances gives (x − 2)² + 25 = (x + 2)² + 81, which simplifies to −4x + 29 = 4x + 85, so 8x = −56 and x = −7. The required point is therefore (−7, 0); the point (0, −7) lies on the y-axis, not the x-axis.
Q8Hard
If 3 cot θ = 4, then the value of (5 sin θ − 3 cos θ)/(5 sin θ + 3 cos θ) is:
A.9
B.1/9✓ Correct
C.1/3
D.3/5
Answer: B. 1/9
Explanation: From 3 cot θ = 4 we get cot θ = 4/3, so tan θ = 3/4 and the right triangle gives sin θ = 3/5 and cos θ = 4/5. Substituting, the expression becomes (3 − 12/5) ÷ (3 + 12/5) = (3/5) ÷ (27/5) = 1/9. Reading cot θ as 3/4 instead of 4/3 turns the value upside down to 9.

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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.

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