10th Maths Revision Exam 10 Question Paper with Answers

Complete your final board preparation with the high-stakes 10th Maths Revision Exam 10 Question Paper. Serving as one of the final full-syllabus mock tests before the actual SSLC public examinations, this paper is designed to challenge your conceptual limits and fine-tune your problem-solving speed. It features top-predicted 2-mark and 5-mark compulsory questions, advanced algebraic simplifications, and full 8-mark graph and practical geometry constructions. Treat this question paper as a real-time exam trial to perfect your paperwork presentation, minimize silly mistakes, and lock in your path toward a perfect centum!

Time: 2.30 hrs REVISION TEST - 10 Reg no: ______________

Standard - X MATHEMATICS Marks: 100

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

1. The given diagram represents:

↗

→

↘

→

(A) an onto function (B) a constant function (C) an one-one function (D) not a function

2. If A = {5, 6, 7}, B = {1, 2, 3, 4, 5} and f: A → B is defined by f(x) = x - 2, then the range of f is
(A) {1, 4, 5} (B) {1, 2, 3, 4, 5} (C) {2, 3, 4} (D) {3, 4, 5}

3. The sum of the exponents of the prime factors in the prime factorization of 1729 is
a) 1 b) 2 c) 3 d) 4

4. If the sequence t₁, t₂, t₃, ... are in A.P., then the sequence t₆, t₁₂, t₁₈, ... is
a) a Geometric progression b) An arithmetic progression
c) Neither an A.P. nor a G.P. d) A constant sequence

5. y² + ¹/_y² is not equal to
a) ^{(y⁴ + 1)}/_y² b) (y + ¹/_y)² c) (y - ¹/_y)² + 2 d) (y + ¹/_y)² - 2

6. If the range of a function is a singleton set, then it is
(A) a constant function (B) an identity function (C) a bijective function (D) an one-one function

7. In the figure, if PR is tangent to the circle at P and O is the centre of the circle, ∠POQ with ∠OPR = 90° and ∠QPR = 60°, then ∠POQ is
a) 120° b) 100° c) 110° d) 90°

8. If the sequence a₁, a₂, a₃, ... is in A.P., then the sequence a₅, a₁₀, a₁₅, ... is
(A) a G.P. (B) an A.P. (C) neither A.P nor G.P. (D) a constant sequence

9. (2, 1) is the point of intersection of two lines:
a) x - y - 3 = 0, 3x - y - 7 = 0 b) x + y = 3, 3x + y = 7
c) 3x + y = 3, x + y = 7 d) x + 3y - 3 = 0, x - y - 7 = 0

10. a cot θ + b cosec θ = p and b cot θ + a cosec θ = q then p² - q² is equal to
a) a² - b² b) b² - a² c) a² + b² d) b - a

11. 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

12. When Karuna divided surface area of a sphere by the sphere's volume, he got the answer as ¹/₃. What is the radius of the sphere?
a) 24 cm b) 9 cm c) 54 cm d) 4.5 cm

13. The mean of 100 observations is 40 and their standard deviation is 3. The sum of squares of all observations is
a) 40000 b) 160900 c) 160000 d) 30000

14. If x ≠ 0 then 1 + sec x + sec²x + sec³x + sec⁴x + sec⁵x is equal to
(A) (1 + sec x)(sec²x + sec³x + sec⁴x)
(B) (1 + sec x)(1 + sec²x + sec⁴x)
(C) (1 - sec x)(sec x + sec³x + sec⁵x)
(D) (1 + sec x)(1 + sec³x + sec⁴x)

Part - II: Answer the following questions (Q.No 28 is compulsory) 10 × 2 = 20

15. If A = {1, 3, 5} and B = {2, 3}, (i) Find A × B (ii) Find B × A.

16. If f(x) = x² - 1, g(x) = x - 2, find a, if g ∘ f(a) = 1.

17. Find the number of terms in the A.P. 3, 6, 9, 12, ..., 111.

18. If the first term of an infinite G.P. is 8 and its sum to infinity is ³²/₃, then find the common ratio.

19. Find the square root of ^{(144a⁸b¹²c¹⁶)}/_{(81f¹²g⁴h¹⁴)}.

20. Verify that A² = I when A =

5	-4
6	-5

21. State Menelaus's Theorem.

22. Show that the straight lines x - 2y + 3 = 0 and 6x + 3y + 8 = 0 are perpendicular.

23. Find the angle of elevation of the top of a tower from a point on the ground, which is 20 m away from the foot of a tower of height 10√3 m.

24. If the total surface area of a cone of radius 7 cm is 704 cm², then find its slant height.

25. If the ratio of radii of two spheres is 4: 7, find the ratio of their volumes.

26. Three chairs and two tables cost ₹700 and five chairs and three tables cost ₹1100. What is the total cost of 2 chairs and 3 tables?

27. What is the probability that a leap year selected at random will contain 53 Saturdays?

28. (i) Prove that sin²θ + ¹/_{(1 + tan²θ)} = 1. (ii) State Ceva's Theorem. (Compulsory)

Part - III: Answer the following questions (Q.No 42 is compulsory) 10 × 5 = 50

29. Find the square root of the following:
(i) ^{[64(a + b)⁴(x - y)⁸(b - c)⁶]}/_{[25(x + y)⁴(a - b)⁶(b + c)¹⁰]}
(ii) ^{(81x⁴y⁶z⁸)}/_{(64w¹²s¹⁴)}
(iii) (2x + 3y)² - 24xy

30. Find the square root of x⁴ - 6x³ + 19x² - 30x + 25.

31. The product of three consecutive terms of a geometric progression is 343 and their sum is ⁹¹/₃. Find the three terms.

32. Find the sum of 6² + 7² + 8² + ... + 21².

33. (i) The sum of a number and its reciprocal is 5¹/₅. Find the number.
(ii) The base of a triangle is 4 cm longer than its altitude. If the area of the triangle is 48 sq. cm, then find its base and altitude.

34. A passenger train takes 1 hour more than an express train to travel a distance of 240 km from Chennai to Virudhachalam. The speed of the passenger train is 20 km/h less than that of the express train. Find the average speed of both trains.

35. Find the equation of the straight lines passing through the point (2, 2) and the sum of the intercepts is 9.

36. State and prove Angle Bisector Theorem.

37. A boy spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground level. The distance of his eye level from the ground is 1.2 m. The angle of elevation of the balloon from his eyes at an instant is 60°. After some time, from the same point of observation, the angle of elevation of the balloon reduces to 30°. Find the distance covered by the balloon during the interval.

38. Find the equation of the perpendicular bisector of the line joining the points A(-4, 2) and B(6, -4).

39. From the top of a 12 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 30°. Determine the height of the cable tower.

40. A metallic sphere of radius 16 cm is melted and recast into small spheres each of radius 2 cm. How many small spheres can be obtained?

41. Water is flowing at the rate of 15 km/hr through a cylindrical pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. In how many hours will the water level in the tank raise by 21 cm?

42. Find the probability that: (Compulsory)
(i) a leap year selected at random will have 53 Fridays
(ii) a leap year selected at random will have only 52 Fridays
(iii) a non-leap year selected at random will have 53 Fridays.

Part - IV: Answer all the questions 2 × 8 = 16

43. (A) Construct a triangle similar to a given triangle PQR with its sides equal to ³/₅ of the corresponding sides of triangle PQR (scale factor ³/₅ < 1).

(OR)

(B) Construct a ΔPQR with the base PQ = 4.5 cm, ∠R = 35° and the median RG from R to PQ is 6 cm.

44. (A) Draw the graph of y = x² - x - 6 and hence solve x² - x - 6 = 0.

(OR)

(B) Draw the graph of y = 2x² and hence solve 2x² + x - 6 = 0.