This free CBSE Class 10 Maths sample paper 2026-27 is designed to help board exam aspirants practise the MCQ section of the CBSE Class 10 Mathematics paper. The 20 questions span the highest-weightage topics in the board syllabus: real numbers and Euclid's division algorithm, quadratic equations and their discriminant, similarity and congruence of triangles, trigonometric identities and heights-and-distances applications, and statistics including mean, median and mode. CBSE Class 10 board exams now carry Section A with 20 one-mark MCQs — this paper replicates that format exactly, including carefully crafted distractors that reflect common student errors. Reviewing your answers against the detailed solution key helps identify the precise gaps to address before the board examination. Free to try and print on A4 — no login needed.
✅ Answer Key & Solutions
Q1
B
P(A∪B) = P(A)+P(B)−P(A∩B) = 0.35+0.45−0.15 = 0.65
Q2
A
Standard quadratic formula: x = (−b ± √(b²−4ac)) / 2a
Q3
A
D = b²−4ac = 4 − 12 = −8
Q4
C
By BPT: AD/DB = AE/EC → 3/5 = 6/EC → EC = 10 cm
Q5
B
sin 30° = ½; cos 60° = ½; sum = 1
Q6
A
Hyp = √(9+16) = 5; sin θ = opp/hyp = 3/5
Q7
B
Area of equilateral triangle = (√3/4)a²
Q8
A
(x−3)(x−4) = 0; x = 3 or 4
Q9
B
Sum = n(n+1)/2; Mean = n(n+1)/2 ÷ n = (n+1)/2
Q10
B
tan 60° = h/200 → √3 = h/200 → h = 200√3 m
Q11
B
SSS similarity criterion: all corresponding sides proportional → triangles similar
Q12
B
Substitute x=2: k(4) − 5(2) + 2 = 0 → 4k − 10 + 2 = 0 → 4k = 8 → k = 2
Q13
C
Sorted: 74,78,85,88,90,92,96. Median (4th) = 88
Q14
C
Pythagorean identity: sec²θ − tan²θ = 1
Q15
B
Hypotenuse² = Sum of squares of other two sides
Q16
A
Deviations from 70: -10,-5,2,10,-15,20,-2. Sq: 100,25,4,100,225,400,4. Sum=858. Var=858/7≈122.6≈124 (closest)
Q17
B
Sum of roots = −b/a
Q18
C
tan 45° = 1; cot 45° = 1; sum = 2
Q19
C
h² = 10² − 6² = 100 − 36 = 64 → h = 8 m
Q20
D
sin θ ranges from 0 to 1 for θ ∈ [0°, 90°]
Frequently Asked Questions
How many MCQ questions appear in the CBSE Class 10 Maths board exam?
The CBSE Class 10 Mathematics board paper (standard and basic) contains 20 MCQ questions in Section A, each worth 1 mark with no negative marking. This paper matches that count and format exactly. Scoring 18+ on this sample paper is a strong indicator of readiness for the board exam MCQ section.
What is the difference between CBSE Maths Basic and Maths Standard at Class 10?
Maths Standard (code 041) has more complex questions and is required for students planning science or commerce streams in Class 11-12. Maths Basic (code 241) is slightly easier and suitable for students who will not take Maths further. This paper is appropriate preparation for both, as it covers the core syllabus common to both papers.
How many sample papers should a Class 10 student complete before boards?
Most toppers and teachers recommend completing 8-10 full-length sample papers in the 6 weeks before the board exam, plus targeted chapter-wise practice for weak areas. Start with this free sample paper to establish your baseline, then use Vybd to generate chapter-specific sets for the topics where you lose marks most often.