CBSE Class 10 Maths Pre-Board Sample Paper 2025-26 with Solutions, Download PDF

The CBSE Class 10 Board Exam is a major milestone for students, and thorough preparation is key to success. To help students gauge their readiness and understand the exam pattern, we are providing a Pre-Board Sample Paper for Mathematics for the 2025-26 academic session. This sample paper is carefully designed based on the latest CBSE curriculum and syllabus, offering an authentic simulation of the actual board exam. Working through this paper will not only test your knowledge across various chapters but also improve your speed and time management skills.

This resource includes the complete sample paper along with detailed solutions. Students are encouraged to first attempt the paper under exam-like conditions and then use the solutions for self-assessment and correction. Download the PDF of this CBSE Class 10 Maths Pre-Board Sample Paper 2025-26 with Solutions to boost your confidence and ensure you are fully prepared to achieve excellent marks in your upcoming board examination.

CBSE Class 10 Maths Pre-Board Sample Paper 2025-26

Exam Instructions: Quick Guide

Section- A

1. The value of k for which the system of equations 3x-ky= 7 and 6x+ 10y =3 is inconsistent, is

A) -10   B) -5   C) 5   D) 7

2. If nth term of an A.P. is 7n-4 then the common difference of the A.P. is

A) 7 B) 7n C) - 4 D) 4

3. Which of the following statements is not true?

A) A number of secants can be drawn at any point on the circle.

B) Only one tangent can be drawn at any point on a circle.

C) A chord is a line segment joining two points on the circle

D) From a point inside a circle only two tangents can be drawn.

4. The radius of the base of a right circular cone and the radius of a sphere are each 5 cm in length. If the volume of the cone is equal to the volume of the sphere then the height of the cone is

A) 5 cm B) 20 cm C) 10 cm D) 4 cm

5. The graph of a quadratic polynomial p(x) passes through the points (-6,0), (0, -30), (4,-20) and (6,0). The zeroes of the polynomial are

A) - 6,0 B) 4, 6 C) - 30,-20 D) - 6,6

6. 

7. The roots of the quadratic equation X2+x-1 = 0 are

A) Irrational and distinct B) not real C ) rational and distinct D) real and equal

8. If 𝜃 = 30𝑜 then the value of 3tan𝜃 is 

A)1   B) 1 √3   C ) 3 √3   (D) not defined

9. 

10. 

11. 

12. 

13. 

14. Which of the following gives the middle most observation of the data?

A) Median B) Mean C) Range D) Mode

15. 

16. The point on the x- axis nearest to the point (-4,-5) is

A) (0, 0)   B) (-4, 0)   C ) (-5, 0)   D) (√41, 0)

17. 

18.  Which of the following gives the middle most observation of the data?

A) Median B) Mean C) Range D) Mode

DIRECTION: In the question number 19 and 20, a statement of Assertion (A) is
followed by a statement of Reason (R).
Choose the correct option
A)Both assertion (A) and reason (R) are true and reason (R) is the correct
explanation of assertion (A)
B)Both assertion (A) and reason (R) are true and reason (R) is not the correct
explanation of assertion (A)
C)Assertion (A) is true but reason (R) is false.
D)Assertion (A) is false but reason (R) is true.

19. Assertion (A): If the radius of sector of a circle is reduced to its half and angle is doubled then the perimeter of the sector remains the same. 1

Reason (R): The length of the arc subtending angle θ at the centre of a circle of radius r = 𝛱𝑟𝜃 180 .

20. Assertion (A): HCF of any two consecutive even natural numbers is always 2.

Reason (R): Even natural numbers are divisible by 2.

Section- B

21. (A) Two dice are rolled together bearing numbers 4, 6, 7, 9, 11, 12. Find the probability that the product of numbers obtained is an odd number

OR

(B) How many positive three digit integers have the hundredths digit 8 and unit’s digit 5? Find the probability of selecting one such number out of all three digit numbers

22. Show that the points A(-5,6), B(3, 0) and C( 9, 8) are the vertices of an isosceles triangle.

23. 

24. Find the point(s) on the x-axis which is at a distance of √41 units from the point (8, -5).

25. (A)Find the H.C.F and L.C.M of 480 and 720 using the Prime factorisation method.

OR

(A) The H.C.F of 85 and 238 is expressible in the form 85m -238. Find the value of m.

Section- C

26. The sum of two numbers is 18 and the sum of their reciprocals is 9/40. Find the numbers.

27. If 𝛼 and 𝛽 are zeroes of a polynomial 6𝑥 2 -5x+1 then form a quadratic polynomial whose zeroes are 𝛼 2 and 𝛽 2 .

28. If cosθ + sinθ = 1 , then prove that cosθ - sinθ = ±1

29. Prove that √3 is an irrational number.

30. 

31. 

Section- D

32. A boy whose eye level is 1.35 m from the ground, spots a balloon moving with the wind in a horizontal line at some height from the ground. The angle of elevation of the balloon from the eyes of the boy at an instant is 60𝑜 . After 12 seconds, the angle of elevation reduces to 30°. If the speed of the wind is 3m/s then find the height of the balloon from the ground. (Use √3= 1.73)

33. 

34. 

35. 

Section- E

36. Metallic silos are used by farmers for storing grains. Farmer Girdhar has decided to build a new metallic silo to store his harvested grains. It is in the shape of a cylinder mounted by a cone.

Dimensions of the conical part of a silo is as follows:
Radius of base = 1.5 m
Height = 2 m
Dimensions of the cylindrical part of a silo is as follows:
Radius = 1.5 m
Height = 7 m

On the basis of the above information answer the following questions.
(i) Calculate the slant height of the conical part of one silo.
(ii) Find the curved surface area of the conical part of one silo.
(iii)(A) Find the cost of metal sheet used to make the curved cylindrical part of 1 silo at the rate of ₹2000 per 𝑚2.

OR

(iii) (B) Find the total capacity of one silo to store grains.

37. Ms. Sheela visited a store near her house and found that the glass jars are arranged one above the other in a specific pattern. A B C P R Q On the top layer there are 3 jars. In the next layer there are 6 jars. In the 3rd layer from the top there are 9 jars and so on till the 8th layer. On the basis of the above situation answer the following questions.

(i) Write an A.P whose terms represent the number of jars in different layers starting from top . Also, find the common difference.

(ii) Is it possible to arrange 34 jars in a layer if this pattern is continued? Justify your answer.

(iii) (A) If there are ‘n’ number of rows in a layer then find the expression for finding the total number of jars in terms of n. Hence find 𝑆8 .

OR

(iii) (B) The shopkeeper added 3 jars in each layer. How many jars are there in the 5th layer from the top?

38. 

CBSE Class 10 Maths Pre-Board Sample Paper 2025-26 Solutions 

Section- A
1. B) -5
2. A) 7
3. D) From a point inside a circle only two tangents can be drawn.
4. B) 20 cm
5. D) -6,6
6. C) 140 Degree
7. A) Irrational and distinct
8. C) 3 /√3
9. A) 11/ 9
10. B) 8𝑥 2 - 20
11. C) 30
12.
13. B) isosceles and similar
14. B) (-4, 0)
15. D) 3/ 26
16. B) (-4, 0)
17. C) (3,0)
18. A) Median
19. D) Assertion (A) is false but reason (R) is true
20. B) Both assertion (A) and reason (R) are true and reason (R) is not the correct
Section- B
21.
22.
23.
24.
25.
Section- C
26.
27.
28.
29.
30.
31.
Section- D
32.
33.
34.
35.
Section - E
36.
37.
38.

Mastering CBSE Class 10 Maths requires consistent practice and understanding the exam format. This Pre-Board Sample Paper (2025-26) with solutions offers a realistic simulation to identify weak areas, refine time management, and build confidence for the board exam. Treat the provided PDF as your final rehearsal. Meticulously analyze the solutions to understand concept application. Consistent practice with authentic material like this is the most effective path to an exceptional Class 10 Board score. Download the PDF to solidify your success preparation.