10th Maths Full Test Question Paper 1 with Answers

Kickstart your final board exam countdown with the 10th Maths Full Test Question Paper 1. Taking a comprehensive, full-syllabus mock exam is the absolute best way to measure your overall board readiness and sharpen your time-management strategies. This 100-mark question paper strictly mirrors the official SSLC public exam structure, taking you through the initial 14 multiple-choice questions, challenging 2-mark and 5-mark compulsory problems, and the final 8-mark graph and practical geometry constructions. Treat this paper as a real-time trial to refine your step-by-step paperwork presentation, eliminate silly arithmetic mistakes, and track your path toward a perfect centum!

SSLC - 10TH

MATHEMATICS FULL PAPER - 1

TIME: 3 hrs MAXIMUM MARKS: 100

PART - I: CHOOSE THE MOST SUITABLE ANSWER [14 × 1 = 14]

Note: (i) Answer all the questions.
(ii) Choose the most appropriate answer from the given four alternatives and write the option code and the corresponding answer.

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. If n(A) = p, n(B) = q, then the total number of relations that exist from A to B is:
(a) 0 (b) 1 (c) 2^pq - 1 (d) 2^pq

3. Given F₁ = 1, F₂ = 3 and F_n = F_n-1 + F_n-2 then F₅ is:
(a) 3 (b) 5 (c) 8 (d) 11

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 Arithmetic Progression nor a Geometric Progression
(d) a constant sequence

5. ^{(3y - 3)}/_y ÷ ^{(7y - 7)}/_3y² is:
(a) ^9y/₇ (b) ^9y³/_{(21y - 21)} (c) ^{(21y² - 42y + 21)}/_3y³ (d) ^{7(y² - 2y + 1)}/_y²

6. Graph of a Quadratic equation is a:
(a) straight line (b) circle (c) parabola (d) hyperbola

7. If in triangles ABC and EDF, ^AB/_DE = ^BC/_FD then they will be similar, when:
(a) ∠B = ∠E (b) ∠A = ∠D (c) ∠B = ∠D (d) ∠A = ∠F

8. A tangent of a circle is perpendicular to the radius at the:
(a) centre (b) point of contact (c) infinity (d) chord

9. The slope of the straight line perpendicular to x-axis is:
(a) 1 (b) 0 (c) ∞ (d) -1

10. If sin θ = cos θ, then the value of 2 tan²θ + sin²θ - 1 is:
(a) ³/₂ (b) -³/₂ (c) ²/₃ (d) -²/₃

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 volume 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. If the sum and mean of a data are 407 and 11 respectively, then the number of observations in the data are:
(a) 37 (b) 4477 (c) 396 (d) 418

14. If a letter is chosen at random from the English alphabets {a, b, ..., z}, then the probability that the letter chosen precedes x:
(a) ¹²/₁₃ (b) ¹/₁₃ (c) ²³/₂₆ (d) ³/₂₆

PART - II: ANSWER ANY 10 QUESTIONS (Q.NO. 28 IS COMPULSORY) [10 × 2 = 20]

15. If B × A = {(-2, 3), (-2, 4), (0, 3), (0, 4), (3, 3), (3, 4)}, find A and B.

16. Find k if f(f(k)) = 5, where f(k) = 2k - 1.

17. Find x so that x + 6, x + 12 and x + 15 are consecutive terms of a Geometric Progression.

18. Simplify: ^{(x + 2)}/_4y ÷ ^{(x² - x - 6)}/_12y².

19. Determine the nature of roots for the following quadratic equation: 2x² - x - 1 = 0.

20. Find the 19th term of an A.P. -11, -15, -19, ...

21. A cat is located at the point (-6, -4) in xy-plane. A bottle of milk is kept at (5, 11). The cat wishes to consume the milk travelling through shortest possible distance. Find the equation of the path it needs to take to the milk.

22. If the straight lines 12y = -(P + 3)x + 12 and 12x - 7y = 16 are perpendicular, then find P.

23. Prove that: ^{sec θ}/_{sin θ} - ^{sin θ}/_{cos θ} = cot θ.

24. The radius of a conical tent is 7 m and height is 24 m. Calculate the length of the canvas used to make the tent if the width of the rectangular canvas is 4 m.

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

26. Find the range and co-efficient of range of the following data: 63, 89, 98, 125, 79, 108, 117, 68.

27. A and B are two candidates seeking admission to IIT. The probability that A getting selected is 0.5 and the probability that both A and B getting selected is 0.3. Prove that probability of B being selected is at the most 0.8.

28. If p² × q¹ × r⁴ × s³ = 3,15,000, then find p, q, r and s. (Compulsory)

PART - III: ANSWER ANY 10 QUESTIONS (Q.NO. 42 IS COMPULSORY) [10 × 5 = 50]

29. 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) a table
(iii) an arrow diagram
(iv) a graph

30. The houses of a street are numbered from 1 to 49. Senthil's house is numbered such that the sum of numbers of the houses prior to Senthil's house is equal to the sum of numbers of the houses following Senthil's house. Find Senthil's house number.

31. Find the sum to n terms of the series 5 + 55 + 555 + ...

32. Solve the following system of linear equations in three variables: x + 20 = ^3y/₂ + 10 = 2z + 5 = 110 - (y + z).

33. If A =

5	2	9
1	2	8

, B =

1	7
1	2
5	-1

. Verify that (AB)^T = B^TA^T.

34. Two poles of height a metres and b metres are p metres apart. Prove that the height of the point of intersection of the lines joining the top of each pole to the foot of the opposite pole is given by ^ab/_{(a + b)} metres.

35. State and prove the Angle Bisector Theorem.

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

37. Find the equation of a straight line parallel to the X-axis and passing through the point of intersection of the lines 7x - 3y = -12 and 2y = x + 3.

38. From the top of a lighthouse, the angle of depression of two ships on opposite sides of it are observed to be 30° and 60°. If the height of the lighthouse is h metres and the line joining the ships passes through the foot of the lighthouse, show that the distance between the ships is ^4h/_√3 m.

39. The radius and height of a cylinder are in the ratio 5: 7 and its curved surface area is 5500 sq.cm. Find its radius and height.

40. Arul has to make arrangements for the accommodation of 150 persons for his family function. For this purpose, he plans to build a tent which is in the shape of a cylinder surmounted by a cone. Each person requires 4 sq.m of space on ground and 40 cu. metre of air to breathe. Find the height of the conical part of the tent if the height of cylindrical part is 8 m.

41. Two unbiased dice are rolled once. Find the probability of getting:
(i) a doublet
(ii) the product as a prime number
(iii) the sum as a prime number
(iv) the sum as 1

42. Let A = {x ∈ W | x < 3}, B = {x ∈ ℕ | 1 < x ≤ 5}, C = {3, 5, 7}. Verify that A × (B ∪ C) = (A × B) ∪ (A × C). (Compulsory)

PART - IV: ANSWER ALL THE QUESTIONS [2 × 8 = 16]

43. Take a point which is 11 cm away from the centre of a circle of radius 4 cm and draw two tangents to the circle from that point.

44. Varshika drew 6 circles with different sizes. Draw a graph for the relationship between the diameter and circumference (approximately related) of each circle as shown in the table and use it to find the circumference of a circle when its diameter is 6 cm: