CBSE Class 10 Maths Practice Paper 2026-27

20 questions · MCQ · Answer key · A4

A 20-question CBSE Class 10 Maths practice paper for 2026-27 on quadratics, triangles, trigonometry & statistics. Free to view and print on A4, no login needed; the answer key with worked solutions is below the questions.

Mathematics — Class 10 Practice Paper

Quadratics, Triangles, Trigonometry & Statistics

  • Board: CBSE
  • Class: 10
  • Time: 60 minutes
  • Max Marks: 80
  • Questions: 20

Instructions: All questions are compulsory. Each question carries 4 marks. There is no negative marking. Choose the most appropriate option.

Scoring on this page: 4 marks per question, 80 in all. In the CBSE board paper, Section A multiple-choice questions carry 1 mark each, so 20 correct answers there are worth 20 marks. This sheet uses four-mark practice scoring instead: divide your score by 4 to see what these 20 questions would be worth on the board paper (for example, 72 out of 80 here is 18 out of 20).

  1. Q1.

    Arjun's probability experiment: P(A) = 0.35, P(B) = 0.45, P(A∩B) = 0.15. P(A∪B)?

    1. (A) 0.50
    2. (B) 0.80
    3. (C) 0.95
    4. (D) 0.65
  2. Q2.

    Quadratic formula for ax² + bx + c = 0: x = ?

    1. (A) (b ± √(b² − 4ac)) / (2a)
    2. (B) (−b ± √(b² + 4ac)) / (2a)
    3. (C) (−b ± √(b² − 4ac)) / (2a)
    4. (D) (b ± √(b² + 4ac)) / a
  3. Q3.

    Discriminant of 3x² − 2x + 1 = 0 is:

    1. (A) −8
    2. (B) 8
    3. (C) 16
    4. (D) −16
  4. Q4.

    In triangle ABC, D lies on AB and E lies on AC, with DE ∥ BC. AD/DB = 3/5 and AE = 6 cm. EC = ?

    1. (A) 8 cm
    2. (B) 9 cm
    3. (C) 12 cm
    4. (D) 10 cm
  5. Q5.

    Arjun calculates: sin 30° + cos 60° = ?

    1. (A) ½
    2. (B) 1
    3. (C) √3/2
    4. (D) √2/2
  6. Q6.

    If tan θ = 3/4 (θ acute), then sin θ = ?

    1. (A) 4/5
    2. (B) 3/4
    3. (C) 3/5
    4. (D) 4/3
  7. Q7.

    Area of equilateral triangle with side a = ?

    1. (A) (√3/2) a²
    2. (B) a²/4
    3. (C) √3 a²
    4. (D) (√3/4) a²
  8. Q8.

    The roots of x² − 7x + 12 = 0 are:

    1. (A) −3, −4
    2. (B) 3, 4
    3. (C) 3, −4
    4. (D) −3, 4
  9. Q9.

    Mean of first n natural numbers:

    1. (A) n
    2. (B) n/2
    3. (C) (n+1)/2
    4. (D) n(n+1)/2
  10. Q10.

    ISRO rocket climbs vertically. From a point 200m away, angle of elevation = 60°. Height?

    1. (A) 100√3 m
    2. (B) 200√3 m
    3. (C) 200/√3 m
    4. (D) 100 m
  11. Q11.

    In ΔABC and ΔPQR, AB/PQ = BC/QR = CA/RP. They are:

    1. (A) Similar
    2. (B) Congruent
    3. (C) Equal area only
    4. (D) Right-angled
  12. Q12.

    If one root of kx² − 5x + 2 = 0 is 2, find k:

    1. (A) 1
    2. (B) 3
    3. (C) 2
    4. (D) 4
  13. Q13.

    Arjun's cricket scores: 85, 92, 78, 96, 88, 74, 90. Median score?

    1. (A) 85
    2. (B) 86
    3. (C) 90
    4. (D) 88
  14. Q14.

    sec²θ − tan²θ = ?

    1. (A) 0
    2. (B) −1
    3. (C) 1
    4. (D) 2
  15. Q15.

    Pythagoras theorem: In right ΔABC (right angle at C), AB² = ?

    1. (A) AC² + BC²
    2. (B) AC + BC
    3. (C) AC × BC
    4. (D) AC² − BC²
  16. Q16.

    Arjun's exam scores: 60, 65, 72, 80, 55, 90, 68. What is his mean score?

    1. (A) 68
    2. (B) 70
    3. (C) 72
    4. (D) 75
  17. Q17.

    For a quadratic ax²+bx+c=0, sum of roots = ?

    1. (A) −b/a
    2. (B) c/a
    3. (C) b/a
    4. (D) −c/a
  18. Q18.

    tan(45°) + cot(45°) = ?

    1. (A) 1
    2. (B) √2
    3. (C) 2√2
    4. (D) 2
  19. Q19.

    A ladder 10m long leans against a wall. Foot is 6m from wall. Height on wall?

    1. (A) 8 m
    2. (B) 4 m
    3. (C) 6 m
    4. (D) 16 m
  20. Q20.

    Which trigonometric ratio is always ≤ 1 for acute angles?

    1. (A) tan θ
    2. (B) sin θ
    3. (C) sec θ
    4. (D) cosec θ

Answer key and solutions

  1. Q1DP(A∪B) = P(A)+P(B)−P(A∩B) = 0.35+0.45−0.15 = 0.65
  2. Q2CStandard quadratic formula: x = (−b ± √(b² − 4ac)) / (2a); the whole of b² − 4ac is under the square root
  3. Q3AD = b²−4ac = 4 − 12 = −8
  4. Q4DBy BPT: AD/DB = AE/EC → 3/5 = 6/EC → EC = 10 cm
  5. Q5Bsin 30° = ½; cos 60° = ½; sum = 1
  6. Q6CHyp = √(9+16) = 5; sin θ = opp/hyp = 3/5
  7. Q7DArea of an equilateral triangle = (√3/4) a²
  8. Q8B(x−3)(x−4) = 0; x = 3 or 4
  9. Q9CSum = n(n+1)/2; Mean = n(n+1)/2 ÷ n = (n+1)/2
  10. Q10Btan 60° = h/200 → √3 = h/200 → h = 200√3 m
  11. Q11ASSS similarity criterion: all corresponding sides proportional → triangles similar
  12. Q12CSubstitute x=2: k(4) − 5(2) + 2 = 0 → 4k − 10 + 2 = 0 → 4k = 8 → k = 2
  13. Q13DSorted: 74,78,85,88,90,92,96. Median (4th) = 88
  14. Q14CPythagorean identity: sec²θ − tan²θ = 1
  15. Q15AHypotenuse² = Sum of squares of other two sides
  16. Q16BSum = 60+65+72+80+55+90+68 = 490. Mean = 490 ÷ 7 = 70
  17. Q17ASum of roots = −b/a
  18. Q18Dtan 45° = 1; cot 45° = 1; sum = 2
  19. Q19Ah² = 10² − 6² = 100 − 36 = 64 → h = 8 m
  20. Q20Bsin θ ranges from 0 to 1 for θ ∈ [0°, 90°]

Maths practice papers, all classes

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 one-mark objective questions in Section A (mostly MCQs, plus assertion-reason items), with no negative marking. This practice set has the same number of questions, but each is worth 4 marks here (80 in all). Divide your score by 4 to compare: 72 or more out of 80 here is the same as 18 or more out of 20 on a one-mark Section A, a good sign you are ready for the objective 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 practice paper to establish your baseline, then use Vybd to generate chapter-specific sets for the topics where you lose marks most often.

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