CBSE Class 10 Mathematics 2025 — Set 3

Questions in this 2025 Mathematics paper (Set 3)

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 tan 3θ = √3, then θ/2 equals:

   • (a) 60°
   • (b) 30°
   • (c) 20°
   • (d) 10°
2. 2.
   If x is the LCM of 4, 6, 8 and y is the LCM of 3, 5, 7 and p is the LCM of x and y, then which of the following is true?

   • (a) p = 35x
   • (b) p = 4y
   • (c) p = 8x
   • (d) p = 16y
3. 3.
   The value of 'k' for which the system of linear equations 6x + y = 3k and 36x + 6y = 3 have infinitely many solutions is:

   • (a) 6
   • (b) 1/6
   • (c) 1/2
   • (d) 1/3
4. 4.
   If α and β are the zeroes of the polynomial p(x) = x² – ax – b, then the value of (α + β + αβ) is equal to:

   • (a) a + b
   • (b) –a – b
   • (c) a – b
   • (d) –a + b
5. 5.
   If x/12 – 3/x = 0, then the values of x are:

   • (a) ±6
   • (b) ±4
   • (c) ±12
   • (d) ±3
6. 6.
   The line represented by x/4 + y/6 = 1, intersects x-axis and y-axis respectively at P and Q. The coordinates of the mid-point of line segment PQ are:

   • (a) (2, 3)
   • (b) (3, 2)
   • (c) (2, 0)
   • (d) (0, 3)
7. 7.
   Two of the vertices of ΔPQR are P(–1, 5) and Q(5, 2). The coordinates of a point which divides PQ in the ratio 2 : 1 are:

   • (a) (3, –3)
   • (b) (5, 5)
   • (c) (3, 3)
   • (d) (5, 1)
8. 8.
   If tangents PA and PB drawn from an external point P to the circle with centre O are inclined to each other at an angle of 80° as shown in the given figure, then the measure of ∠POA is:

   • (a) 40°
   • (b) 50°
   • (c) 60°
   • (d) 80°
9. 9.
   (cot θ + tan θ) equals:

   • (a) cosec θ sec θ
   • (b) sin θ sec θ
   • (c) cos θ tan θ
   • (d) sin θ cos θ
10. 10.
    If in two triangles ΔDEF and ΔPQR, ∠D = ∠Q and ∠R = ∠E, then which of the following is NOT true?

    • (a) DE/QR = DF/PQ
    • (b) EF/PR = DF/PQ
    • (c) EF/RP = DE/QR
    • (d) DE/PQ = EF/RP
11. 11.
    The measurements of ΔLMN and ΔABC are shown in the figure given below. The length of side AC is: [Figure: ΔLMN has LM = 45 cm, MN = 63 cm, ∠M = 130°, ∠N = 28°. ΔABC has AB = 5 cm, ∠B = 130°. LN = 72 cm.]

    • (a) 16 cm
    • (b) 7 cm
    • (c) 8 cm
    • (d) 4 cm
12. 12.
    If the volumes of two cubes are in the ratio 8 : 125, then the ratio of their surface areas is:

    • (a) 8 : 125
    • (b) 4 : 25
    • (c) 2 : 5
    • (d) 16 : 25
13. 13.
    If the area of a sector of circle of radius 36 cm is 54π cm², then the length of the corresponding arc of the sector is:

    • (a) 8π cm
    • (b) 6π cm
    • (c) 4π cm
    • (d) 3π cm
14. 14.
    A die is thrown once. The probability of getting a number which is NOT a factor of 36, is:

    • (a) 1/2
    • (b) 2/3
    • (c) 1/6
    • (d) 5/6
15. 15.
    If the mean of 2, 9, x+6, 2x+3, 5, 10, 5 is 7, then the value of x is:

    • (a) 9
    • (b) 6
    • (c) 5
    • (d) 3
16. 16.
    AOBC is a rectangle whose three vertices are A(0, 2), O(0, 0) and B(4, 0). The square of the length of its diagonal is equal to:

    • (a) 36
    • (b) 20
    • (c) 16
    • (d) 4
17. 17.
    Zeroes of the polynomial p(x) = x² – 3√2 x + 4 are:

    • (a) 2, √2
    • (b) 2√2, √2
    • (c) 4√2, –√2
    • (d) √2, 2
18. 18.
    In the given figure, in ΔABC, AD ⊥ BC and ∠BAC = 90°. If BC = 16 cm and DC = 4 cm, then the value of x is: [Figure shows triangle ABC with AD perpendicular to BC, BC = 16 cm, DC = 4 cm, AC = x]

    • (a) 4 cm
    • (b) 5 cm
    • (c) 8 cm
    • (d) 3 cm
19. 19.
    Assertion (A): A ladder leaning against a wall, stands at a horizontal distance of 6 m from the wall. If the height of the wall up to which the ladder reaches is 8 m, then the length of the ladder is 10 m. Reason (R): The ladder makes an angle of 60° with the ground.

    • (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
    • (b) Both Assertion…
20. 20.
    Assertion (A): If two tangents are drawn to a circle from an external point, then they subtend equal angles at the centre of the circle. Reason (R): A parallelogram circumscribing a circle is a rhombus.

    • (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…
21. 21.
    If 4k = tan² 60° – 2 cosec² 30° – 2 tan² 30°, then find the value of k.
22. 22.
    The probability of guessing the correct answer of a certain test question is x/12. If the probability of not guessing the correct answer is 5/6, then find the value of x.
23. 23.
    Find the smallest number which is divisible by both 644 and 462.
24. 24.
    Find the value(s) of 'k' so that the quadratic equation 4x² + kx + 1 = 0 has real and equal roots.
25. 25.
    Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
26. 26.
    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, find the value of k.
27. 27.
    Prove that (5√3 + 2/3) is an irrational number given that √3 is an irrational number.
28. 28.
    Prove that: √((sec A – 1)/(sec A + 1)) + √((sec A + 1)/(sec A – 1)) = 2 cosec A
29. 29.
    A chord of a circle of radius 10 cm subtends a right angle at the centre of the circle. Find the area of the corresponding minor segment. [Use π = 3.14]
30. 30.
    Three unbiased coins are tossed simultaneously. Find the probability of getting:

    • (a) exactly two tails
    • (b) at least one head
    • (c) at most two heads
31. 31.
    In the given figure, PC is a tangent to the circle at C. AOB is the diameter which when extended meets the tangent at P. If ∠PCA = 110°, find ∠CBA and ∠BCO. [Figure shows circle with centre O, diameter AOB extended to P, PC tangent at C]
32. 32.
    The perimeter of an isosceles triangle is 32 cm. If each equal side is 5/6 th of the base, find the area of the triangle.
33. 33.
    The sum of the third and the seventh term of an AP is 6 and their product is 8. Find the sum of the first sixteen terms of the AP.
34. 34.
    In the given figure, PA, QB and RC are perpendicular to AC. If PA = x units, QB = y units and RC = z units, prove that 1/x + 1/z = 1/y. [Figure shows points A, B, C on a line with perpendiculars PA, QB, RC]
35. 35.
    A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm, are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
36. 36 (a).
    [Case Study 1 - Garden Lawn] A garden designer is planning a rectangular lawn that is to be surrounded by a uniform walkway. The total area of the lawn and the walkway is 360 square metres. The width of the walkway is same on all sides. The dimensions of the lawn itself are 12 metres × 10 metres. (i) Formulate the quadratic equation representing the total area of the lawn and the walkway, taking…
37. 36 (b).
    [Case Study 1 - Garden Lawn] (ii)(a) Solve the quadratic equation to find the width of the walkway 'x'.
38. 36 (c).
    [Case Study 1 - Garden Lawn] (iii) Find the perimeter of the lawn.
39. 37 (a).
    [Case Study 2 - Lighthouse] A lighthouse stands tall on a cliff by the sea, watching over ships that pass by. One day a ship is seen approaching the shore and from the top of the lighthouse, the angles of depression of the ship are observed to be 30° and 45° as it moves from point P to point Q. The height of the lighthouse is 50 metres. (i) Find the distance of the ship from the base of the…
40. 37 (b).
    [Case Study 2 - Lighthouse] (ii) Find the measures of ∠PBA and ∠QBA.
41. 37 (c).
    [Case Study 2 - Lighthouse] (iii)(a) Find the distance travelled by the ship between points P and Q.
42. 38 (a).
    [Case Study 3 - Rainfall Data] The India Meteorological Department observes seasonal and annual rainfall every year in different sub-divisions of our country. It helps them to compare and analyse the results. The table below shows sub-divisions wise seasonal (monsoon) rainfall (in mm) in 2023: | Rainfall (mm) | No. of Sub-divisions | |---|---| | 200 – 400 | 3 | | 400 – 600 | 4 | | 600 – 800 | 7…
43. 38 (b).
    [Case Study 3 - Rainfall Data] (ii)(a) Find the median of the given data.
44. 38 (c).
    [Case Study 3 - Rainfall Data] (iii) If a sub-division having at least 800 mm rainfall during monsoon season is considered a good rainfall sub-division, then how many sub-divisions had good rainfall?

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