C
CraftExam

CBSE Class 10 Mathematics Sample Paper

Marks:
40
Time:
1½ Hours
Questions:
20
Chapters:
14
Session:
2026-27
Class_10_Mathematics_Sample_Paper_CraftExam.pdfA4 · Set A

Academic Session 2026-27

SAMPLE PAPER

MATHEMATICS

Class X

Time Allowed1½ HoursMaximum Marks40SetA

Assessment: CBSE-Aligned School Assessment

Marks Distribution

SectionQuestion TypeMarks
AMCQs (8×1)8
BShort Answer (9×2)18
CLong Answer (2×5)10
DCase Study (3 parts)4

General Instructions

  1. 1.This question paper has 4 sections.
  2. 2.Marks are shown beside each question.
  3. 3.Read each section instruction carefully.
  4. 4.Attempt only one alternative where internal choice is given.

SECTION A — Objective Type Questions (1×8=8)

Q1 to Q8 are Multiple Choice Questions. Choose the correct option.

Q1. A bag has 3 red balls and 3 blue balls, all identical in size and weight. One ball is drawn without looking. What can be said about the outcomes red and blue?
(1)
  1. (a)Red and blue are equally likely because the bag contains the same number of each colour.
  2. (b)Blue is more likely because blue is listed after red.
  3. (c)Red is more likely because the two colours are different.
  4. (d)They are not equally likely because a random draw always depends on luck.
Q2. A right triangle has one leg of 9 cm and a hypotenuse of 15 cm. What is the length of the other leg?
(1)
  1. (a)12 cm
  2. (b)6 cm
  3. (c)18 cm
  4. (d)9 cm
Q3. The x-intercepts of a cubic graph are at -1, 2, and 3. If the polynomial is monic, what is its expanded form?
(1)
  1. (a)x3 - 4x2 + x + 6
  2. (b)x3 + 4x2 + x - 6
  3. (c)x3 - 4x2 - x + 6
  4. (d)x3 - x2 - 4x + 6
Q4. A sports coach wants to know the most common number of goals scored by players in a training drill. The counts are 1, 2, 2, 3, 2, 4, 5. Which reason best supports choosing mode instead of mean?
(1)
  1. (a)Mode shows the middle score after ordering the data
  2. (b)Mode gives the most frequent score, which matches the question
  3. (c)Mode always uses every value equally, so it is more accurate
  4. (d)Mode is useful only when the data has no repeated values
Q5. A solution line reads “cosec(90° - x)” and the next step should use the complementary-angle rule before substitution. What should it become?
(1)
  1. (a)sec x
  2. (b)cos x
  3. (c)sin x
  4. (d)cot x
Q6. A rectangular park is 28 m long and 21 m wide. A circular pond of radius 7 m is inside it, and only the land around the pond is shaded. What is the shaded area?
(1)
  1. (a)434 m2
  2. (b)588 m2
  3. (c)154 m2
  4. (d)742 m2
Q7. A student writes that two tangents from different outside points must be equal. What is the main error in this statement?
(1)
  1. (a)Tangents from different points need not be equal
  2. (b)Every tangent is always a radius
  3. (c)A circle cannot have tangents
  4. (d)The centre lies on all tangents
Q8. A classmate says 5/14 will terminate because 14 is divisible by 2. Which reply is mathematically correct?
(1)
  1. (a)It will terminate because every even denominator gives a terminating decimal.
  2. (b)It will not terminate because 14 = 2 x 7, and 7 is a prime factor other than 2 or 5.
  3. (c)It will terminate because the numerator is 5, which matches the denominator's factor 5.
  4. (d)It will not terminate only if the numerator and denominator are both even.

SECTION B — Short Answer Questions (2×9=18)

Q9 to Q17 are Short Answer Questions.

Q9. A cylindrical container has radius 21 cm and height 28 cm. It has no lid but has a base. Find the material area, neglecting thickness.
(2)
Q10. Two positive integers differ by 3 and their product is 28. Find them.
(2)
Q11. Determine whether 3,6,9,12 are consecutive terms of an AP and justify.
(2)
Q12. If the midpoint of A(a,6) and B(8,b) is (5,1), find a and b.
(2)
Q13. A point on level ground is 35 m from the foot of a vertical mast. The angle of elevation of its top is 30°. Find the height exactly.
(2)
Q14. A learner gives (7,4) as the solution of x + y = 11, x−y = -3. Check the answer and correct it.
(2)
Q15. PA and PB are tangents from P to a circle. PA = 2x + 2 cm and PB = 5x−4 cm. Find x and both tangent lengths.
(2)
Q16. If a right triangle with opposite side 28, adjacent side 45 and hypotenuse 53 is enlarged by factor 3, do its trigonometric ratios change? Demonstrate with tan A.
(2)
Q17. Find the perimeter of a 90° sector of radius 7 cm.
(2)

SECTION C — Long Answer Questions (5×2=10)

Q18 to Q19 are Long Answer Questions.

Q18. A rectangular floor is 420 cm long and 336 cm wide. It is to be covered by the largest possible identical square tiles, without cutting or gaps. Find the tile side, the number of tiles along each edge, and the total cost if each tile costs ₹85.
(5)
Q19. From the top of a 50 m building, the angles of depression of two points on opposite sides of its foot along one straight level road are 30° and 45°. Find their distances from the foot and their separation. Explain why the distances are added.
(5)

OR

Q19. Use a table of two points for each line to solve x + y = 16 and x−y = 2 graphically. State a suitable scale, the intersection, and verify it algebraically. A student proposes (8,8); explain the error.
(5)

SECTION D — Case-Based Questions (1+1+2=4)

Q20 is a case-based question. Read the case carefully and answer the sub-questions.

Q20

A circular badge of radius 6 cm lies on a drawing. A ruler line touches it at T, and O is the centre. Point S lies on the ruler 8 cm from T. The ruler is perpendicular to OT.
(i) Write the relation among OS2, OT2 and TS2.
(1)
(ii) Is S inside, on or outside the circle?
(1)
(iii) Calculate OS and explain why this confirms that the ruler meets the circle only at T.
(2)

End of Question Paper