Class 10 Maths Sample Paper 2024-25, Download Standard & Basic Maths PDF

The Central Board of Secondary Education (CBSE) has officially released the Class 10 Maths Sample Paper 2024-25, allowing students to better prepare for the half-yearly and final board exams. Students who are going to appear in the upcoming board exam in 2025, must download and practice the Maths Sample paper Class 10 2024 25 as much as they can. Scroll down this page for the Sample Paper Class 10 Maths with solution PDF for basis and standard courses.

Class 10 Maths Sample Paper 2024-25

Maths is regarded as the most changeling subject due to its complexity. With proper preparation and strategy, one can successfully achieve the highest score in this paper. The Class 10 Maths Sample Paper 2024-25 is created in compliance with the revised syllabus and using the most recent updated test pattern. These maths sample papers are essential study materials for students who want to understand the expected question paper format and typology of questions. These model question papers help students grasp the format of the question paper and the marking scheme.

Class 10 Maths Sample Paper Pattern

Check out the pattern of the CBSE Class 10 Maths Sample Paper 2024 25 discussed below:

1. This question paper contains 38 questions.
2. This Question Paper is divided into 5 Sections A, B, C, D and E.
3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are Assertion- Reason based questions of 1 mark each.
4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02 marks
each.
5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each.
6. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05 marks each.
7. In Section E, Questions no. 36-38 are case study based questions carrying 4 marks each with
sub parts of the values of 1, 1 and 2 marks each respectively.
8. All Questions are compulsory. However, an internal choice in 2 Question of Section B, 2
Questions of Section C and 2 Questions of Section D has been provided. An internal choice has been provided in all the 2 marks questions of Section E.
9. Draw neat and clean figures wherever required.
10. Take π =22/7 wherever required if not stated.
11. Use of calculators is not allowed.

Maths Sample Paper Class 10 2024-25 with Solutions

Section A
Section A consists of 20 questions of 1 mark each.

1. 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

2. 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

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. 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

5. 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

6.

7. In the given figure, a tangent has been drawn at a point P on the circle centered at O.

If ∠ TPQ= 110𝑂 then ∠POQ is equal to
A) 110º B) 70º C) 140º D)55º

8.. A quadratic polynomial having zeroes – √5/2 and √5/2 is
A) 𝑥²− 5√2 x +1 B) 8𝑥²- 20 C) 15𝑥²- 6 D) 𝑥²- 2√5 x -1

9. Consider the frequency distribution of 45 observations.

The upper limit of median class is
A) 20 B) 10 C) 30 D) 40

10. O is the point of intersection of two chords AB and CD of a circle.

If ∠𝐵𝑂𝐶 = 80𝑂 and OA = OD then 𝛥𝑂𝐷𝐴 𝑎𝑛𝑑 𝛥𝑂𝐵𝐶 are
A) equilateral and similar B) isosceles and similar
C) isosceles but not similar D) not similar

11. 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

12. If 𝜃 = 30𝑜 then the value of 3tan𝜃 is
A)1  B) 1/√3  C )3/ √3 (D) not defined

13. The volume of a solid hemisphere is 396/7 𝑐𝑚³.The total surface area of the solid hemisphere (in sq. cm) is
A)396/7
B)594/ 7
C)549/7
D) 604/ 7

14. In a bag containing 24 balls, 4 are blue, 11 are green and the rest are white. One ball is drawn at random. The probability that the drawn ball is white in colour is
𝐴) 1/6
B) 3/8
C ) 11/ 24
D) 5/8
15. 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)

16. Which of the following gives the middle most observation of the data?
A) Median B) Mean C) Range D) Mode

17. A point on the x-axis divides the line segment joining the points A(2, -3) and B(5, 6) in the ratio 1:2. The point is
A) (4, 0) B) ( 7/2 ,3/2) C) (3, 0) D) (0,3)

18. A card is drawn from a well shuffled deck of playing cards. The probability of getting red face card is
𝐴) 3/ 13
B) 1/ 2
C) 3/ 52
D) 3/ 26

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): HCF of any two consecutive even natural numbers is always 2.
Reason (R): Even natural numbers are divisible by 2.

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

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

Class 10 Maths Sample Paper 2025

Section B
Section B consists of 5 questions of 2 marks each.

21. (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.

22. (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.

23.

24. Find the point(s) on the x-axis which is at a distance of √41 units from the point (8, -5).
25. Show that the points A(-5,6), B(3, 0) and C( 9, 8) are the vertices of an isosceles triangle.

Sample Paper Class 10 Maths Standard

Section C
Section C consists of 6 questions of 3 marks each.

26. (A) In 𝛥ABC, D, E and F are midpoints of BC,CA, and AB respectively. Prove that
△ 𝐹𝐵𝐷 ∼ △ DEF and △ DEF ∼ △ ABC

OR
(B) In 𝛥ABC, P and Q are points on AB and AC respectively such that PQ is parallel to BC. Prove that the median AD drawn from A on BC bisects PQ

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

28. If 𝛼 and 𝛽 are zeroes of a polynomial 6𝑥²-5x+1 then form a quadratic polynomial whose zeroes are 𝛼²  and 𝛽².

29. If cosθ + sinθ = 1 , then prove that cosθ – sinθ = ±1 3
30. (A) The minute hand of a wall clock is 18 cm long. Find the area of the face of the clock described by the minute hand in 35 minutes.
OR
(B) AB is a chord of a circle centered at O such that ∠AOB=60˚. If OA = 14 cm then find the area of the minor segment. (take √3 =1.73)

31. Prove that √3 is an irrational number.

Maths Sample Paper Class 10 2024 25

Section D
Section D consists of 4 questions of 5 marks each

32. (A) Solve the following system of linear equations graphically:
x+2y = 3, 2x-3y+8 = 0
OR
(B) Places A and B are 180 km apart on a highway. One car starts from A and another from B at the same time. If the car travels in the same direction at different speeds, they meet in 9 hours. If they travel towards each other with the same speeds as before, they meet in an hour. What are the speeds of the two cars?

33. Prove that the lengths of tangents drawn from an external point to a circle are equal.

Using the above result, find the length BC of 𝛥ABC. Given that, a circle is inscribed in 𝛥ABC touching the sides AB, BC, and CA at R, P, and Q respectively, and AB= 10 cm, AQ= 7cm, CQ= 5cm.

34. 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)

35. Find the mean and median of the following data:

OR

The monthly expenditure on milk in 200 families of a Housing Society is given below

Find the value of x and also find the mean expenditure.

Sample Paper Class 10 Maths Standard

Section E
Section E consists of 3 case study-based questions of 4 marks each.

36. Ms. Sheela visited a store near her house and found that the glass jars were arranged one above the other in a specific pattern.

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?

37.

Triangle is a very popular shape used in interior designing. The picture given above shows a cabinet designed by a famous interior designer. Here the largest triangle is represented by △ ABC and smallest one with shelf is represented by △ DEF. PQ is parallel to EF.

(i) Show that △ DPQ ∼ △ DEF.  (1)
(ii) If DP= 50 cm and PE = 70 cm then find 𝑃𝑄/𝐸𝐹.
(iii) (A) If 2AB = 5DE and △ ABC ∼ △ DEF then show that 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 △𝐴𝐵𝐶/𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 △𝐷𝐸𝐹 is constant.

OR

(iii) (B) If AM and DN are medians of triangles ABC and DEF respectively then prove that △ ABM ∼ △ DEN.

38. 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 the 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

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