RBSE Class 10th Mathematics Board Paper 2025

Secondary Examination, 2025

Mathematics — English Medium (Question Paper)

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SECTION – A

(Multiple Choice Questions)

1. The sum of powers of prime factors of 400 is
   A) 4   B) 9   C) 6   D) 8
2. If 3 is a zero of the polynomial 2x² + x + k, then k =
   A) -12   B) 21   C) -21   D) 12
3. In a two-digit number, the unit digit is x and the tens digit is y. Then the number is
   A) 10x + y   B) 10y + x   C) x + y   D) 10xy
4. If ΔABC ~ ΔDEF and AB = 10 cm, DE = 8 cm, then BC : EF is
   A) 8 : 18   B) 4 : 5   C) 9 : 4   D) 5 : 4
5. Distance of P(-3, 4) from O(0, 0) is
   A) 5   B) √41   C) 7   D) 1
6. cosec 245° – cot 245° equals
   A) √2   B) 1   C) 0   D) 2√2
7. The shadow of a vertical pillar is equal to its height. Angle of elevation of the sun is
   A) 60°   B) 30°   C) 90°
8. From a point P, the tangent to a circle is 24 cm, distance from centre = 25 cm. Radius = ?
   A) 7 cm   B) 14 cm   C) 3.5 cm   D) 1 cm
9. Area of a quadrant of a circle of radius 7 cm =
   A) 38.5 cm²   B) 77 cm²   C) 15π cm²   D) 7π cm²
10. Radius = 14 cm, slant height = 10 cm. Curved surface area of cone =
    A) 220 cm²   B) 110 cm²   C) 440 cm²   D) 140 cm²
11. Which cannot be a probability?
    A) 2   B) 1   C) 0.7   D) 0.53
12. If HCF = LCM for two rational numbers, then numbers are always
    A) Composite   B) Equal   C) Prime   D) Co-prime
13. If sum and product of zeros of a quadratic polynomial are 5 and 6, then polynomial is
    A) x² + 5x + 6 B) x² + 6x + 5 C) x² – 6x + 5 D) x² – 5x + 6
14. For which value of k, equations x + y – 4 = 0 and 2x + ky – 3 = 0 have no solution?
    A) 0   B) 6   C) 8   D) None
15. AB = 2 cm, ∠A = 50°, AC = 4 cm, DE = 3 cm, ∠D = 50°, DF = 6 cm. If BC = 3 cm, then EF = ?
    A) 4.5 cm   B) 6 cm   C) 8 cm   D) 5 cm
16. sin²A = 2 sin A is true when A =
    A) 0°   B) 30°   C) 45°   D) 90°
17. If cos A = 12/13, then sin A =
    A) 5/12   B) 12/13   C) 5/13   D) 13/5
18. Angle subtended at the centre by minute hand in 5 minutes =
    A) 30°   B) 60°   C) 2.5°   D) 10°

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Fill in the blanks:

19. If 18, a, 10 are in A.P., then a = ______.
20. Midpoint of P(7, -3) and Q(3, 9) is ______.
21. Value of sin60°·cosec60° + cos30°·sec30° = ______.
22. Diameter of solid hemisphere = 14 cm. Total surface area = ______.
23. Mode of 1, 4, 5, 6, 4, 7, 9, 2, 4, 3, 5 = ______.
24. Class mark = 17, upper class limit = 24, then lower limit = ______.

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SECTION – A (Very Short Answer Type)

25. If radius of a circle = 14 cm, length of arc = 12 cm, find angle at centre.
26. Total surface area of a cube = 864 cm². Find surface area of one face.
27. Find median of the following distribution:

    x	3	7	9	11	13
    f	6	7	5	6	7

28. Probability of getting number > 5 in a single throw of die.
29. A cone and cylinder have equal radius and height. Volume of cone = 66 cm³. Find volume of cylinder.
30. Find median of 19, 17, 25, 27, 18, 20, 29.
31. Ram’s probability of winning = 4/9. Find Shyam’s probability of winning.
32. A cuboid formed by joining two cubes of side 2 cm. Find its volume.
33. Find mean of first 10 odd natural numbers.
34. A bag has 6 red, 7 white balls. Probability of drawing white?
35. If CSA of a hemisphere = 50π cm², find radius.
36. If mean of 5,7,9,4,3,(x+2) = 6, find x.

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SECTION – B (Short Answer Type)

37. Find HCF and LCM of 12, 15, 21 using prime factorisation.
38. If α and β are zeros of 3x² – 5x + 9, find (α + β) and αβ.
39. Solve using elimination:
    3x + 5y = 7
    6x + y = -4
40. Find number of terms in A.P.: 7, 13, 19, …, 205.
41. In figure, DE ∥ BC. Find x.
42. Ratio in which x-axis divides line joining (5, 3) and (-3, -2).
43. Find value: 4cot245° – sec260° + sin260°.
44. A 12 m ladder makes 60° with wall. Find height of wall.
45. Prove: For quadrilateral ABCD circumscribing a circle, AB + CD = AD + BC.
46. Arc subtends 50° at centre, arc length = 5π cm. Find radius.

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SECTION – C (Long Answer Type)

47. Find sum of first 15 terms of A.P. with nth term = 3 + 2n.
    OR There are 60 terms in an A.P. First term = 7, last term = 125. Find 32nd term.
48. Find coordinates of points dividing line (4,0)–(0,-8) into 4 equal parts.
    OR If AB is diameter of circle with centre (2, -3) and B(1,4), find A.
49. Prove: In two concentric circles, chord of larger circle touching smaller circle is bisected.
    OR Prove: Tangents drawn from an external point to a circle are equal.
50. Find mean of following frequency distribution:

    x	3	5	7	9	11
    f	1	2	3	2	2

    
    OR If mean of given distribution is 7, find value of P.

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SECTION – D (Essay Type)

51. Difference of squares of two numbers = 180. Square of smaller number = 8 × larger. Find both.
    OR Find two consecutive positive integers whose sum of squares = 365.
52. Prove trigonometric identity (given in paper).
    OR Prove: sin2A cosA + cos3A + tanA sinA = secA.
53. Find median:

    Class	7–17	17–27	27–37	37–47
    Frequency	22	18	20	12

    
    OR Find mode:

    Class	2–11	11–20	20–29	29–38	38–47
    Frequency	15	16	17	12	11