CBSE Class 10 Mathematics 2025 — Set 1

Questions in this 2025 Mathematics paper (Set 1)

All 38 questions from this set, exactly as asked. Try each one, then open the question-paper PDF above for the complete paper.

1. 1.
   If α and β are the zeroes of the polynomial 3x² + 6x + k such that α + β + αβ = −2/3, then the value of k is:

   • (a) −8
   • (b) 8
   • (c) −4
   • (d) 4
2. 2.
   If x = 1 and y = 2 is a solution of the pair of linear equations 2x − 3y + a = 0 and 2x + 3y − b = 0, then:

   • (a) a = 2b
   • (b) 2a = b
   • (c) a + 2b = 0
   • (d) 2a + b = 0
3. 3.
   The mid-point of the line segment joining the points P(−4, 5) and Q(4, 6) lies on:

   • (a) x-axis
   • (b) y-axis
   • (c) origin
   • (d) neither x-axis nor y-axis
4. 4.
   If θ is an acute angle and 7 + 4 sin θ = 9, then the value of θ is:

   • (a) 90°
   • (b) 30°
   • (c) 45°
   • (d) 60°
5. 5.
   The value of tan²θ − (1/cos θ) × sec θ is:

   • (a) 1
   • (b) 0
   • (c) −1
   • (d) 2
6. 6.
   If HCF(98, 28) = m and LCM(98, 28) = n, then the value of n − 7m is:

   • (a) 0
   • (b) 28
   • (c) 98
   • (d) 198
7. 7.
   The tangents drawn at the extremities of the diameter of a circle are always:

   • (a) parallel
   • (b) perpendicular
   • (c) equal
   • (d) intersecting
8. 8.
   In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3DE. Then, the two triangles are:

   • (a) congruent but not similar
   • (b) congruent as well as similar
   • (c) neither congruent nor similar
   • (d) similar but not congruent
9. 9.
   If (−1)ⁿ + (−1)⁸ = 0, then n is:

   • (a) any positive integer
   • (b) any negative integer
   • (c) any odd number
   • (d) any even number
10. 10.
    Two polynomials are shown in the graph below. The number of distinct zeroes of both the polynomials is:

    • (a) 3
    • (b) 5
    • (c) 2
    • (d) 4
11. 11.
    If the sum of first m terms of an AP is 2m² + 3m, then its second term is:

    • (a) 10
    • (b) 9
    • (c) 12
    • (d) 4
12. 12.
    Mode and Mean of a data are 15x and 18x, respectively. Then the median of the data is:

    • (a) x
    • (b) 11x
    • (c) 17x
    • (d) 34x
13. 13.
    A card is selected at random from a deck of 52 playing cards. The probability of it being a red face card is:

    • (a) 3/13
    • (b) 2/13
    • (c) 1/2
    • (d) 3/26
14. 14.
    Which of the following is a rational number between √3 and √5?

    • (a) 1.4142387954012....
    • (b) 2.326̄
    • (c) π
    • (d) 1.857142
15. 15.
    If a sector of a circle has an area of 40π sq. units and a central angle of 72°, the radius of the circle is:

    • (a) 200 units
    • (b) 100 units
    • (c) 20 units
    • (d) 10√2 units
16. 16.
    In the given figure, PA is a tangent from an external point P to a circle with centre O. If ∠POB = 115°, then ∠APO is equal to:

    • (a) 25°
    • (b) 65°
    • (c) 90°
    • (d) 35°
17. 17.
    A kite is flying at a height of 150 m from the ground. It is attached to a string inclined at an angle of 30° to the horizontal. The length of the string is:

    • (a) 100√3 m
    • (b) 300 m
    • (c) 150√2 m
    • (d) 150√3 m
18. 18.
    A piece of wire 20 cm long is bent into the form of an arc of a circle of radius 60/π cm. The angle subtended by the arc at the centre of the circle is:

    • (a) 30°
    • (b) 60°
    • (c) 90°
    • (d) 50°
19. 19.
    Assertion (A): The probability of selecting a number at random from the numbers 1 to 20 is 1. Reason (R): For any event E, if P(E) = 1, then E is called a sure event.

    • (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
    • (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). (c)…
20. 20.
    Assertion (A): If we join two hemispheres of same radius along their bases, then we get a sphere. Reason (R): Total Surface Area of a sphere of radius r is 3πr².

    • (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
    • (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). (c)…
21. 21.
    If x cos 60° + y cos 0° + sin 30° − cot 45° = 5, then find the value of x + 2y.
22. 22.
    Find the zeroes of the polynomial p(x) = x² + (4/3)x − 4/3.
23. 23.
    The coordinates of the centre of a circle are (2a, a − 7). If the circle passes through the point (11, −9) and has diameter 10√2 units, find the value(s) of 'a'.
24. 24.
    If △ABC ~ △PQR in which AB = 6 cm, BC = 4 cm, AC = 8 cm and PR = 6 cm, then find the length of (PQ + QR).
25. 25.
    A person is standing at P outside a circular ground at a distance of 26 m from the centre of the ground. He found that his distances from the points A and B on the ground are 10 m (PA and PB are tangents to the circle). Find the radius of the circular ground.
26. 26.
    In the given figure, O is the centre of the circle and BCD is tangent to it at C. Prove that ∠BAC + ∠ACD = 90°.
27. 27.
    Prove that: tan θ/(1 − cot θ) + cot θ/(1 − tan θ) = 1 + sec θ cosec θ.
28. 28.
    Find the ratio in which the y-axis divides the line segment joining the points (5, −6) and (−1, −4). Also find the point of intersection.
29. 29.
    Prove that 1/√5 is an irrational number.
30. 30.
    A room is in the form of a cylinder surmounted by a hemispherical dome. The base radius of the hemisphere is half of the height of the cylindrical part. If the room contains 1408/21 m³ of air, find the height of the cylindrical part. (Use π = 22/7).
31. 31.
    Two dice are thrown at the same time. Determine the probability that the difference of the numbers on the two dice is 2.
32. 32.
    Vijay invested certain amounts of money in two schemes A and B, which offer interest at the rate of 8% per annum and 9% per annum, respectively. He received ₹1,860 as the total annual interest. However, had he interchanged the amounts of investments in the two schemes, he would have received ₹20 more as annual interest. How much money did he invest in each scheme?
33. 33.
    The diagonal BD of a parallelogram ABCD intersects the line segment AE at the point F, where E is any point on the side BC. Prove that DF × EF = FB × FA.
34. 34.
    The perimeter of a right triangle is 60 cm and its hypotenuse is 25 cm. Find the lengths of the other two sides of the triangle.
35. 35.
    Find the missing frequency 'f' in the following table, if the mean of the given data is 18. Hence find the mode of the data. Daily Allowance | Number of Children 11–13 | 7 13–15 | 6 15–17 | 9 17–19 | 13 19–21 | f 21–23 | 5 23–25 | 4
36. 36 (a).
    A school is organizing a charity run to raise funds for a local hospital. The run is planned as a series of rounds around a track, with each round being 300 metres. To make the event more challenging and engaging, the organizers decide to increase the distance of each subsequent round by 50 metres. For example, the second round will be 350 metres, the third round will be 400 metres and so on…
37. 36 (b).
    Determine the distance of the 8th round.
38. 36 (c).
    Find the total distance run after completing all 10 rounds.
39. 37 (a).
    A brooch is a decorative piece often worn on clothing like jackets, blouses or dresses to add elegance. Made from precious metals and decorated with gemstones, brooches come in many shapes and designs. One such brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in the…
40. 37 (b).
    Find the length of the arc ACB.
41. 37 (c).
    Find the area of each sector of the brooch.
42. 38 (a).
    Amrita stood near the base of a lighthouse, gazing up at its towering height. She measured the angle of elevation to the top and found it to be 60°. Then, she climbed a nearby observation deck, 40 metres higher than her original position and noticed the angle of elevation to the top of lighthouse to be 45°. If CD is h metres, find the distance BD in terms of 'h'.
43. 38 (b).
    Find distance BC in terms of 'h'.
44. 38 (c).
    Find the height CE of the lighthouse. [Use √3 = 1.73]

Class 10 Mathematics exam pattern (80 marks)

The theory paper carries 80 marks over 3 hours (38 questions, with internal choice in some). Section-wise structure:

Structure per the CBSE 2023-24 sample-paper design; question wording varies by set.

Prepare with

How to use these papers

1. 1Start chapter-wise early in the year — solve only the Mathematics questions from a chapter you have just finished.
2. 2Switch to full timed papers 2–3 months before the exam: one complete set in the real time limit, no notes.
3. 3Self-mark against the marking scheme, then fix every mistake with our free NCERT solutions.
4. 4Re-attempt your weakest chapters until the recurring question types feel routine.

CBSE Class 10 Mathematics 2025 paper — FAQ