10th Maths Second Revision Test Question Paper 2 with Answers

Advance your board exam practice to the next level with the 10th Maths Second Revision Test Question Paper 2. Moving a step ahead of standard mock tests, this second model paper in our revision series challenges your problem-solving depth across the entire full syllabus. It features a curated mix of tricky compulsory questions, high-yielding algebraic proofs, coordinate geometry derivations, and essential 8-mark graph and practical geometry constructions. Treat this blueprint-aligned question paper as a final rehearsal to master your time management, refine your step-by-step presentation, and secure a perfect centum!

CLASS: X EXAM NO: ______________ TIME: 3 hr

SECOND REVISION EXAMINATION 2025-26

MATHEMATICS MARKS: 100

PART - I: Choose the correct answer: 14 × 1 = 14

1. A = {a, b, p}, B = {2, 3}, C = {p, q, r, s} then n((A ∪ C) × B) is
a) 8 b) 20 c) 12 d) 16

2. Let f(x) = √(1 + x²) then
a) f(xy) = f(x) · f(y) b) f(xy) ≥ f(x) · f(y) c) f(xy) ≤ f(x) · f(y) d) None of these

3. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is
a) 2025 b) 5220 c) 5025 d) 2520

4. The value of (1³ + 2³ + 3³ + ... + 15³) - (1 + 2 + 3 + ... + 15) is
a) 14400 b) 14200 c) 14280 d) 14520

5. The solution of (2x - 1)² = 9 is equal to
a) -1 b) 2 c) -1, 2 d) None of these

6. Find the matrix X if 2X +

1	3
5	7

5	7
9	5

-2	-2
2	-1

2	2
2	-1

1	2
2	2

2	1
2	2

7. In ΔLMN, ∠L = 60°, ∠M = 50°. If ΔLMN ~ ΔPQR then the value of ∠R is
a) 40° b) 70° c) 30° d) 110°

8. The point of intersection of 3x - y = 4 and x + y = 8 is
a) (5, 3) b) (2, 4) c) (3, 5) d) (4, 4)

9. The slope of the line which is perpendicular to a line joining the points (0, 0) and (-8, 8) is
a) -1 b) 1 c) ¹/₃ d) -8

10. (1 + tan θ + sec θ)(1 + cot θ - cosec θ) is equal to
a) 0 b) 1 c) 2 d) -1

11. The height of a right circular cone whose radius is 5 cm and slant height is 13 cm will be
a) 12 cm b) 10 cm c) 13 cm d) 5 cm

12. The ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height is
a) 1:2:3 b) 2:1:3 c) 1:3:2 d) 3:1:2

13. The standard deviation of a data is 3. If each value is multiplied by 5 then the new variance is
a) 3 b) 15 c) 5 d) 225

14. The probability of getting a job for a person is ^x/₃, if the probability of not getting the job is ²/₃, then the value of x is
a) 2 b) 1 c) 3 d) 1.5

PART - II: Answer any 10 questions (Question No. 28 is compulsory) (10 × 2 = 20)

15. If A = B = {p, q}, find A × B and A × A.

16. If f(x) = 3 + x, g(x) = x - 4, check whether f ∘ g = g ∘ f.

17. Compute x, such that 10⁴ ≡ x (mod 19).

18. Which term of an A.P. 16, 11, 6, 1, ... is -54?

19. Determine the quadratic equation, whose sum and product of roots are -9 and 20.

20. Construct a 3 × 3 matrix whose elements are given by a_ij = |i - 2j|.

21. In the figure, AD is the bisector of ∠A. If BD = 4 cm, DC = 3 cm and AB = 6 cm, find AC.

22. Show that the points P(-1.5, 3), Q(6, -2) and R(-3, 4) are collinear.

23. Find the equation of a straight line which is parallel to the line 3x - 4y = 12 and passing through the point (6, 4).

24. Prove that √[^{(1 + cos θ)}/_{(1 - cos θ)}] = cosec θ + cot θ.

25. Find the diameter of a sphere whose surface area is 154 m².

26. Find the range and coefficient of range of the following data: 25, 67, 48, 53, 18, 39, 44.

27. Write the sample space for tossing three coins using a tree diagram.

28. Solve: 2x² - 3x - 3 = 0. (Compulsory)

PART - III: Answer any 10 questions (Question No. 42 is compulsory) (10 × 5 = 50)

29. Let A = {x ∈ W | x < 2}, B = {x ∈ ℕ | 1 < x ≤ 4} and C = {3, 5}. Verify that A × (B ∩ C) = (A × B) ∩ (A × C).

30. Let f: A → B be a function defined by f(x) = ^x/₂ - 1, where A = {2, 4, 6, 10, 12}, B = {0, 1, 2, 4, 5, 9}. Represent f by:
i) Set of ordered pairs
ii) Table
iii) Arrow diagram
iv) Graph

31. Find the HCF of 396, 504, 636.

32. Find the sum of 5³ + 10³ + 15³ + ... + 105³.

33. Find the values of a and b if the following polynomial is a perfect square: 4x⁴ - 12x³ + 37x² + bx + a.

34. State and prove "Baudhayana Theorem" (Pythagoras Theorem).

35. Find the area of the quadrilateral formed by the points (8, 6), (5, 11), (-5, 12) and (-4, 3).

36. Find the equation of the median and altitude of ΔABC through A where the vertices are A(6, 2), B(-5, -1), C(1, 9).

37. Two ships are sailing in the sea on either side of a lighthouse. The angles of elevation of the top of the lighthouse as observed from the ships are 30° and 45° respectively. If the lighthouse is 200 m high, find the distance between the two ships.

38. If the radii of the circular ends of a frustum which is 45 cm high are 28 cm and 7 cm, find the volume of the frustum.

39. A right circular cylindrical container of base radius 6 cm and height 15 cm is full of ice cream. The ice cream is to be filled in cones of height 9 cm and base radius 3 cm, having a hemispherical cap. Find the number of cones needed to empty the container.

40. The number of televisions sold on each day of a week are 13, 8, 4, 9, 7, 12, 10. Find its standard deviation.

41. Two dice are rolled together; find the probability of getting a doublet or sum of faces as 4.

42. If A =

1	2	1
2	-1	1

, B =

2	-1
1	4
0	2

, show that (AB)^T = B^TA^T. (Compulsory)

PART - IV: Answer all the questions (2 × 8 = 16)

43. a) Construct a triangle ΔPQR such that QR = 5 cm, ∠P = 30° and the altitude from P to QR is of length 4.2 cm.

(OR)

b) Draw the two tangents from a point which is 10 cm away from the centre of the circle of radius 5 cm. Also measure the lengths of the tangents.

44. a) A bus is travelling at a uniform speed 50 km/hr. Draw the distance-time graph and hence find:
i) Constant of variation
ii) How far will it travel in 1¹/₂ hr
iii) The time required to cover a distance of 300 km from the graph.

(OR)

b) Draw the graph of y = x² - 5x - 6 and hence solve x² - 5x - 14 = 0.