CBSE Class 10 Mathematics 2025 — Set 6

Questions in this 2025 Mathematics paper (Set 6)

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.
   √0.4 is a/an

   • (a) natural number
   • (b) integer
   • (c) rational number
   • (d) irrational number
2. 2.
   Which of the following cannot be the unit digit of 8ⁿ, where n is a natural number?

   • (a) 4
   • (b) 2
   • (c) 0
   • (d) 6
3. 3.
   Which of the following quadratic equations has real and equal roots?

   • (a) (x + 1)² = 2x + 1
   • (b) x² + x = 0
   • (c) x² − 4 = 0
   • (d) x² + x + 1 = 0
4. 4.
   If the zeroes of the polynomial ax² + bx + 2a/b are reciprocal of each other, then the value of b is

   • (a) 2
   • (b) 1/2
   • (c) −2
   • (d) −1/2
5. 5.
   The distance of the point A(−3, −4) from x-axis is

   • (a) 3
   • (b) 4
   • (c) 5
   • (d) 7
6. 6.
   In the adjoining figure, PQ ∥ XY ∥ BC, AP = 2 cm, PX = 1.5 cm and BX = 4 cm. If QY = 0.75 cm, then AQ + CY =

   • (a) 6 cm
   • (b) 4.5 cm
   • (c) 3 cm
   • (d) 5.25 cm
7. 7.
   Given ΔABC ~ ΔPQR, ∠A = 30° and ∠Q = 90°. The value of (∠R + ∠B) is

   • (a) 90°
   • (b) 120°
   • (c) 150°
   • (d) 180°
8. 8.
   Two coins are tossed simultaneously. The probability of getting at least one head is

   • (a) 1/4
   • (b) 1/2
   • (c) 3/4
   • (d) 1
9. 9.
   In the adjoining figure, PA and PB are tangents to a circle with centre O such that ∠P = 90°. If AB = 3√2 cm, then the diameter of the circle is

   • (a) 3√2 cm
   • (b) 6√2 cm
   • (c) 3 cm
   • (d) 6 cm
10. 10.
    For a circle with centre O and radius 5 cm, which of the following statements is true? P: Distance between every pair of parallel tangents is 5 cm. Q: Distance between every pair of parallel tangents is 10 cm. R: Distance between every pair of parallel tangents must be between 5 cm and 10 cm. S: There does not exist a point outside the circle from where length of tangent is 5 cm.

    • (a) P
    • (b) Q (c)…
11. 11.
    In the adjoining figure, TS is a tangent to a circle with centre O. The value of 2x° is

    • (a) 22.5
    • (b) 45
    • (c) 67.5
    • (d) 90
12. 12.
    If x√(2 tan 30°/(1 + tan² 30°)) = y√(2 tan 30°/(1 − tan² 30°)), then x : y =

    • (a) 1 : 1
    • (b) 1 : 2
    • (c) 2 : 1
    • (d) 4 : 1
13. 13.
    A peacock sitting on the top of a tree of height 10 m observes a snake moving on the ground. If the snake is 10√3 m away from the base of the tree, then the angle of depression of the snake from the eye of the peacock is

    • (a) 30°
    • (b) 45°
    • (c) 60°
    • (d) 90°
14. 14.
    If a cone of greatest possible volume is hollowed out from a solid wooden cylinder, then the ratio of the volume of remaining wood to the volume of cone hollowed out is

    • (a) 1 : 1
    • (b) 1 : 3
    • (c) 2 : 1
    • (d) 3 : 1
15. 15.
    If the mode of some observations is 10 and sum of mean and median is 25, then the mean and median respectively are

    • (a) 12 and 13
    • (b) 13 and 12
    • (c) 10 and 15
    • (d) 15 and 10
16. 16.
    If the maximum of students has obtained 52 marks out of 80, then

    • (a) 52 is the mean of the data
    • (b) 52 is the median of the data
    • (c) 52 is the mode of the data
    • (d) 52 is the range of the data
17. 17.
    The system of equations 2x + 1 = 0 and 3y − 5 = 0 has

    • (a) unique solution
    • (b) two solutions
    • (c) no solution
    • (d) infinite number of solutions
18. 18.
    In a right triangle ABC, right-angled at A, if sin B = 1/4, then the value of sec B is

    • (a) 4
    • (b) √15/4
    • (c) √15
    • (d) 4/√15
19. 19.
    Assertion (A): For any two prime numbers p and q, their HCF is 1 and LCM is p + q. Reason (R): For any two natural numbers, HCF × LCM = product of numbers.

    • (a) Both Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
    • (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
    • (c) Assertion (A) is true…
20. 20.
    Assertion (A): Event E₁: getting a number less than 3 and Event E₂: getting a number greater than 3 are complementary events in an experiment of throwing a die. Reason (R): If two events E and F are complementary events, then P(E) + P(F) = 1.

    • (a) Both Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
    • (b) Both Assertion (A) and Reason (R) are true, but…
21. 21.
    Solve the following pair of equations algebraically: 101x + 102y = 304 102x + 101y = 305
22. 22.
    If a sec θ + b tan θ = m and b sec θ + a tan θ = n, prove that a² + n² = b² + m².
23. 23.
    Prove that the abscissa of a point P which is equidistant from points with coordinates A(7, 1) and B(3, 5) is 2 more than its ordinate.
24. 24.
    P is a point on the side BC of ΔABC such that ∠APC = ∠BAC. Prove that AC² = BC · CP.
25. 25.
    The number of red balls in a bag is three more than the number of black balls. If the probability of drawing a red ball at random from the given bag is 12/23, find the total number of balls in the given bag.
26. 26.
    Prove that √5 is an irrational number.
27. 27.
    Find the zeroes of the polynomial p(x) = 3x² − 4x − 4. Hence, write a polynomial whose each of the zeroes is 2 more than zeroes of p(x).
28. 28.
    Check whether the following pair of equations is consistent or not. If consistent, solve graphically. x + 3y = 6 3y − 2x = −12
29. 29.
    If the points A(6, 1), B(p, 2), C(9, 4) and D(7, q) are the vertices of a parallelogram ABCD, then find the values of p and q. Hence, check whether ABCD is a rectangle or not.
30. 30.
    Prove that: (cos θ − 2cos³θ)/(sin θ − 2sin³θ) + cot θ = 0.
31. 31.
    In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If ∠OPQ = 15° and ∠PTQ = θ, then find the value of sin 2θ.
32. 32.
    There is a circular park of diameter 65 m as shown in the figure, where AB is a diameter. An entry gate is to be constructed at a point P on the boundary of the park such that distance of P from A is 35 m more than the distance of P from B. Find distance of point P from A and B respectively.
33. 33.
    If a line drawn parallel to one side of a triangle intersecting the other two sides in distinct points divides the two sides in the same ratio, then it is parallel to the third side. State and prove the converse of the above statement.
34. 34.
    From one face of a solid cube of side 14 cm, the largest possible cone is carved out. Find the volume and surface area of the remaining solid. (Use π = 22/7, √5 = 2.2)
35. 35.
    The following distribution shows the marks of 230 students in a particular subject. If the median marks are 46, then find the values of x and y. Marks | Number of Students 10−20 | 12 20−30 | 30 30−40 | x 40−50 | 65 50−60 | y 60−70 | 25 70−80 | 18
36. 36 (a).
    Case Study: Anurag purchased a farmhouse which is in the form of a semicircle of diameter 70 m. He divides it into three parts by taking a point P on the semicircle such that ∠PAB = 30°, where O is the centre of the semicircle. In Part I he planted Mango trees, Part II tomatoes, Part III oranges. (i) What is the measure of ∠POA?
37. 36 (b).
    Case Study (continued): Semicircular farmhouse, diameter 70 m. (ii) Find the length of wire needed to fence the entire piece of land.
38. 36 (c).
    Case Study (continued): Semicircular farmhouse, diameter 70 m, ∠POA = 120°. (iii)(a) Find the area of region in which saplings of Mango tree are planted (Region I, sector with angle ∠POA).
39. 37 (a).
    Case Study: A school prepared an eight-lane running track with an integrated football field. The innermost lane is 400 m and each subsequent lane is 7.6 m longer than the preceding lane. (i) What is the length of the 6th lane?
40. 37 (b).
    Case Study (continued): Running track, a = 400, d = 7.6. (ii) How long is the 8th lane than that of 4th lane?
41. 37 (c).
    Case Study (continued): Running track, a = 400, d = 7.6. (iii)(a) While practicing for a race, a student took one round each in first six lanes. Find the total distance covered by the student.
42. 38 (a).
    Case Study: The Statue of Unity in Gujarat stands over a 58 m high base. A student uses an inclinometer from two places. Situation I: From Place A, 80√3 m from the base, angle of elevation = 60°. Situation II: From Place B, 40 m above ground, angle of elevation = 30°, total height = 240 m. (i) Represent Situation I with the help of a diagram.
43. 38 (b).
    Case Study (continued): Statue of Unity. (ii) Represent Situation II with the help of a diagram.
44. 38 (c).
    Case Study (continued): Statue of Unity. (iii)(a) Calculate the height of Statue excluding the base and also find the height including the base with the help of Situation I.

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