CBSE Class 10 Mathematics 2025 — Set 2

Questions in this 2025 Mathematics paper (Set 2)

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 7 cos² θ + 3 sin² θ = 4, then the value of θ is:

   • (a) 30°
   • (b) 45°
   • (c) 60°
   • (d) 90°
2. 2.
   The probability of drawing an even prime number out of numbers from 1 to 30 is:

   • (a) 1/30
   • (b) 4/15
   • (c) 7/30
   • (d) 0
3. 3.
   The quadratic equation whose roots are 7 and 1/7 is:

   • (a) 7x² − 50x + 7 = 0
   • (b) 7x² − 50x + 1 = 0
   • (c) 7x² + 50x − 7 = 0
   • (d) 7x² + 50x − 1 = 0
4. 4.
   The least number which is a perfect square and is divisible by each of 16, 20 and 50, is:

   • (a) 1200
   • (b) 100
   • (c) 3600
   • (d) 2400
5. 5.
   The coordinates of the end points of a diameter of a circle are (5, −2) and (5, 2). The length of the radius of the circle is:

   • (a) ± 2
   • (b) ± 4
   • (c) 4
   • (d) 2
6. 6.
   The points (−5, 0), (5, 0) and (0, 4) are the vertices of a triangle which is a/an:

   • (a) right-angled triangle
   • (b) isosceles triangle
   • (c) equilateral triangle
   • (d) scalene triangle
7. 7.
   In the given figure, RS is the tangent to the circle at the point L and MN is the diameter. If ∠NML = 30°, then ∠RLM is:

   • (a) 30°
   • (b) 60°
   • (c) 90°
   • (d) 120°
8. 8.
   In the given figure, PQ ∥ BC. If AP/PB = 4/13 and AC = 20.4 cm, then the length of AQ is:

   • (a) 2.8 cm
   • (b) 5.8 cm
   • (c) 3.8 cm
   • (d) 4.8 cm
9. 9.
   Which of the following statements is incorrect?

   • (a) Two congruent figures are always similar.
   • (b) A square and a rhombus of the same area are always similar.
   • (c) Two equilateral triangles are always similar.
   • (d) Two similar triangles need not be congruent.
10. 10.
    The sum of the exponents of prime factors in the prime factorisation of 4004 is:

    • (a) 5
    • (b) 4
    • (c) 3
    • (d) 2
11. 11.
    In a cricket match, a batsman hits the boundary 7 times out of the 42 balls he plays. The probability of his not hitting a boundary is:

    • (a) 1/7
    • (b) 2/7
    • (c) 5/6
    • (d) 1/6
12. 12.
    If a large circular pizza is divided into 5 equal sectors, then the central angle of each sector will be:

    • (a) 60°
    • (b) 90°
    • (c) 45°
    • (d) 72°
13. 13.
    If sin 30° tan 45° = sec 60°/k, then the value of k is:

    • (a) 4
    • (b) 3
    • (c) 2
    • (d) 1
14. 14.
    The line represented by the equation x − y = 0 is:

    • (a) parallel to x-axis
    • (b) parallel to y-axis
    • (c) passing through the origin
    • (d) passing through the point (3, 2)
15. 15.
    The 10th term of the AP 5, 19/4, 9/2, 17/4, ... is:

    • (a) 11/4
    • (b) 4/11
    • (c) 13/4
    • (d) 4/13
16. 16.
    If −4 is a zero of the polynomial p(x) = x² − x − (2 + 2k), then the value of k is:

    • (a) 3
    • (b) 9
    • (c) 6
    • (d) −9
17. 17.
    The equation of a line parallel to the x-axis and at a distance of 3 units below x-axis is:

    • (a) x = 3
    • (b) x = −3
    • (c) y = −3
    • (d) y = 3
18. 18.
    The HCF of 40, 110 and 360 is:

    • (a) 40
    • (b) 110
    • (c) 360
    • (d) 10
19. 19.
    Assertion (A): Common difference of the AP: 5, 1, −3, −7, ... is 4. Reason (R): Common difference of the AP: a₁, a₂, a₃, ..., aₙ is obtained by d = aₙ − aₙ₋₁. Select the correct option:

    • (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…
20. 20.
    Assertion (A): The pair of linear equations px + 3y + 59 = 0 and 2x + 6y + 118 = 0 will have infinitely many solutions if p = 1. Reason (R): If the pair of linear equations px + 3y + 19 = 0 and 2x + 6y + 157 = 0 has a unique solution, then p ≠ 1. Select the correct option:

    • (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
    • (b) Both…
21. 21.
    If p and q are zeroes of the polynomial p(y) = 21y² − y − 2, then find the value of (1 − p) · (1 − q).
22. 22.
    In the given figure, the shape of the top of a table is that of a sector of a circle with centre O and ∠AOB = 90°. If AO = OB = 42 cm, then find the perimeter of the top of the table.
23. 23.
    If tan A = √3, where A is an acute angle, then find the value of sin²A / (1 + cos²A).
24. 24.
    In the given figure, D is a point on the side BC of ΔABC such that ∠ADC = ∠BAC. Show that CA² = CD · CB.
25. 25.
    At point A on the diameter AB of a circle of radius 10 cm, tangent XAY is drawn to the circle. Find the length of the chord CD parallel to XY at a distance of 16 cm from A.
26. 26.
    Prove that the parallelogram circumscribing a circle is a rhombus.
27. 27.
    Prove that: (1 + 1/tan²θ)(1 + 1/cot²θ) = 1/(sin²θ − sin⁴θ).
28. 28.
    If the mid-point of the line segment joining the points A(3, 4) and B(k, 6) is P(x, y) and x + y − 10 = 0, then find the value of k.
29. 29.
    The length of the hour hand of a clock is 10 cm. Find the area of the minor sector swept by the hour hand of the clock between 5 a.m. to 8 a.m. Also, find the area of the major sector.
30. 30.
    Prove that √3 is an irrational number.
31. 31.
    A sum of ₹2,000 is invested at 7% per annum simple interest. Calculate the interests at the end of 1st, 2nd and 3rd year. Do these interests form an AP? If so, find the interest at the end of the 27th year.
32. 32.
    Two ships are sailing in the sea on either side of a lighthouse. The angles of depression to the two ships as observed from the top of the lighthouse are 60° and 45°, respectively. If the distance between the ships is 100[(1 + √3)/√3] m, then find the height of the lighthouse.
33. 33.
    The sum of the areas of two squares is 52 cm² and the difference of their perimeters is 8 cm. Find the lengths of the sides of the two squares.
34. 34.
    Prove that a line drawn parallel to one side of a triangle to intersect the other two sides in distinct points divides the other two sides in the same ratio. Hence, in the figure given below, prove that AM/MB = AN/ND where LM ∥ CB and LN ∥ CD.
35. 35.
    Find the Mean and Mode of the following frequency distribution: Class: 0–10, 10–20, 20–30, 30–40, 40–50, 50–60, 60–70 Frequency: 8, 7, 15, 20, 12, 8, 10
36. 36 (a).
    Case Study 1: A school is organizing a grand cultural event to show the talent of its students. To accommodate the guests, the school plans to rent chairs and tables from a local supplier. It finds that rent for each chair is ₹50 and for each table is ₹200. The school spends ₹30,000 for renting the chairs and tables. Also, the total number of items (chairs and tables) rented are 300. (i) If the…
37. 36 (b).
    Case Study 1 (contd.): A school rents 'x' chairs at ₹50 each and 'y' tables at ₹200 each. Total items = 300, total cost = ₹30,000. (ii)(a) Find the number of chairs and number of tables rented by the school.
38. 36 (c).
    Case Study 1 (contd.): A school rents chairs at ₹50 each and tables at ₹200 each. Total budget = ₹30,000. (iii) What is the maximum number of tables that can be rented in ₹30,000 if no chairs are rented?
39. 37 (a).
    Case Study 2: Rahul is a lucky charm for his cricket team. He has a jar of cards with numbers from 10 to 74. Before each match, he draws a card from the jar. If the card bears an even number, the team wins. If the number is even and divisible by 5, they win by a big margin. If the number is an odd number less than 30, they win by a small margin. And if the number is a prime number between 50 and…
40. 37 (b).
    Case Study 2 (contd.): Rahul has cards numbered 10 to 74. (ii) What is the probability that Rahul draws a card with an odd number less than 30?
41. 37 (c).
    Case Study 2 (contd.): Rahul has cards numbered 10 to 74. (iii)(a) What is the probability that Rahul draws a card with a prime number between 50 and 74?
42. 38 (a).
    Case Study 3: A skilled carpenter decided to craft a special rolling pin for the local baker. He carefully joined three cylindrical pieces of wood — two small ones on the ends and one larger in the centre to create a perfect tool. The length of the bigger cylindrical part is 12 cm and diameter is 7 cm. The length of each smaller cylindrical part is 5 cm and diameter is 2.1 cm. (i) Find the…
43. 38 (b).
    Case Study 3 (contd.): Rolling pin with bigger cylinder (length 12 cm, diameter 7 cm) and two smaller cylinders (length 5 cm each, diameter 2.1 cm each). (ii) Find the curved surface area of the bigger cylindrical part.
44. 38 (c).
    Case Study 3 (contd.): Rolling pin with bigger cylinder (length 12 cm, diameter 7 cm) and two identical smaller cylinders (length 5 cm each, diameter 2.1 cm each). (iii)(a) Find the ratio of the volume of the bigger cylindrical part to the total volume of the two smaller (identical) cylindrical parts.

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