10th Maths - Thoothukudi District Quarterly Exam 2025 Question Paper

Reg. No.: _________________

COMMON QUARTERLY EXAMINATION - 2025

Time : 3.00 Hrs

Std - X | Mathematics

Marks: 100

Part-I

14 × 1 = 14

Note: i) Answer all the questions. ii) Choose the most suitable answer from the given four alternatives and write the option code with the corresponding answer. iii) Each questions carries 1 mark.

1. If A = {1,2} B = {1,2,3,4}, C = {5,6} and D = {5,6,7,8} then state which of the following statement is true.
   a) (A × C) ⊆ (B × D)

   b) (B × D) ⊆ (A × C)

   c) (A × B) ⊆ (A × D)

   d) (D × A) ⊆ (B × A)
2. If g = {(1,1), (2,3), (3,5), (4,7)} is a function given by g(x) = αx + β then the values of α and β are:
   a) (-1, 2)

   b) (2, -1)

   c) (-1, -2)

   d) (1, 2)
3. Using Euclid's division lemma, if the cube of any positive integer is divided by 9 then the possible remainders are:
   a) 0, 1, 8

   b) 1, 4, 8

   c) 0, 1, 3

   d) 1, 3, 5
4. The next term of the sequence 316, 18, 112, 118 is:
   a) 124

   b) 127

   c) 181

   d) none of these
5. The solution of (2x - 1)² = 9 is equal to:
   a) -1

   b) 2

   c) -1, 2

   d) none of these
6. If the constant term of ax² + bx + c = 0 is zero, then the sum and product of roots are:
   a) -ba and -ca

   b) -ba and ca

   c) -ba and -ac

   d) none of these
7. The square root of 256x⁸y⁴z¹⁰25x⁶y⁶z⁶ is equal to:
   a) 165 [ x²z⁴y² ]

   b) 16 [ y²x²z⁴ ]

   c) 165 [ yxz² ]

   d) 165 [ xz²y ]
8. In ΔLMN, ∠L = 60°, ∠M = 50°. If ΔLMN ~ ΔPQR then the value of ∠R is:
   a) 40°

   b) 70°

   c) 30°

   d) 110°
9. In a given figure ST || QR, PS = 2 cm and SQ = 3 cm. Then the ratio of the area of ΔPQR to the area of ΔPST is:
   a) 25:4

   b) 25:7

   c) 25:11

   d) 25:13
10. A man walks near a wall, such that the distance between him and the wall is 10 units. Consider the wall to be the Y axis. The path travelled by the man is:
    a) x = 10

    b) y = 10

    c) x = 0

    d) y = 0
11. If (5,7), (3,p) and (6, 6) are collinear, then the value of p is:
    a) 3

    b) 6

    c) 9

    d) 12
12. The value of sin²θ + 11+tan²θ is equal to:
    a) tan²θ

    b) 1

    c) cot²θ

    d) 0
13. (1 + tanθ + secθ) (1 + cotθ - cosecθ) is equal to:
    a) 0

    b) 1

    c) 2

    d) -1
14. The remainder when 7 × 13 × 19 × 23 × 29 × 31 is divided by 6 is:
    a) 4

    b) 5

    c) 1

    d) 3

Part-II

10 × 2 = 20

Answer any 10 questions. Question No. 28 compulsory. Each question carries 2 marks.

15. Let A = {1,2,3,4...45} and R be the relation defined as "square is of a number" in A. Write R as a subset of A × A. Also, find the domain and range of R.
16. If X = {-5,1,3,4} and Y = {a,b,c} then which of the following relations are functions from X to Y?
    i) R₁ = {(-5,a), (1, a), (3, b)}    ii) R₂ = {(-5, b), (1, b), (3, a), (4, c)}
17. If 13824 = 2^a × 3^b then find a and b.
18. Compute x, such that 10⁴ ≡ x (mod 19).
19. Find the 19th term of an A.P. -11, -15, -19, .....
20. Find: x²+20x+36x²-3x-28 - x²+12x+4x²-3x-28
21. Determine the quadratic equation, whose sum and product of roots are -32 and -1.
22. Solve the quadratic equation by using formula: x² + 3x - 10 = 0.
23. If one root of the equation 3x² + kx + 81 = 0 (having real roots) is the square of the other, then find k.
24. If ΔABC ~ ΔDEF such that area of ΔABC is 9cm² and the area of ΔDEF is 16cm² and BC = 2.1 cm. Find the length of EF.
25. Check whether AD is bisector of ∠A of ΔABC if AB = 5cm, AC = 10cm, BD = 1.5 cm and CD = 3.5 cm.
26. Find the slope of line joining the points (sinθ, -cosθ) and (-sinθ, cosθ).
27. Show that the straight lines x - 2y + 3 = 0 and 6x + 3y + 8 = 0 are perpendicular.
28. Prove that √(1+sinθ1-sinθ) = secθ + tanθ.

Part-III

10 × 5 = 50

Answer any 10 questions. Questions No. 42 is compulsory. Each question carries 5 marks.

29. Given A = {1,2,3}, B = {2,3,5}, C = {3,4} and D = {1,3,5} check if (A ∩ C) × (B ∩ D) = (A × B) ∩ (C × D) is true?
30. Let f be a function f: N → N be defined by f(x) = 3x + 2, x ∈ N.
    i) Find the images of 1, 2, 3    ii) Find the pre-images of 29, 53    iii) Identify the types of function.
31. If f(x) = x², g(x) = 3x and h(x) = x - 2 prove that (fog) ∁ h = f ∁ (goh).
32. Find the sum of all natural numbers between 300 and 600 which are divisible by 7.
33. Find the sum to n terms of the series 3 + 33 + 333 + ...
34. In a G.P. the 9th term is 32805 and 6th term is 1215. Find the 12th term.
35. If 4x⁴ - 12x³ + 37x² + bx + a is a perfect square, find the values of a and b.
36. A flock of swans contained x² members. As the clouds gathered, 10x went to a lake and one-eighth of the members flew away to a garden. The remaining three pairs played about in the water. How many swans were there in total?
37. If the roots of the equation (c² - ab)x² - 2(a² - bc)x + b² - ac = 0 are real and equal, prove that either a = 0 (or) a³ + b³ + c³ = 3abc.
38. State and prove basic proportionality theorem.
39. Find the equation of the median of ΔABC through A where the vertices are A (6,2), B (-5, -1) and C (1,9).
40. Find the area of the quadrilateral formed by the points (-9, 0), (-8,6), (-1, -2) and (-6, -3).
41. If √3 sinθ - cosθ = 0, then show that tan 3θ = 3 tanθ - tan³θ1 - 3 tan²θ.
42. Find the area of a triangle formed by the lines 3x + y - 2 = 0, 5x + 2y - 3 = 0 and 2x - y - 3 = 0.

Part-IV

2 × 8 = 16

Answer both questions. Each question carries 8 marks.

43. a) Construct a triangle similar to a given triangle PQR with its sides equal to 74 of the corresponding sides of the triangle PQR (scale factor 7/4 > 1).
    (OR)
    b) Construct a ΔPQR in which the base PQ = 4.5 cm, ∠R = 35° and the median RG from R to PQ is 6 cm.
44. a) A garment shop announces a flat 50% discount on every purchase of items for their customers. Draw the graph for the relationship between the Marked Price and the discount. Hence find:
    i) the marked price when a customer gets a discount of 3250 (from graph)
    ii) the discount when the marked price is 2500.
    (OR)
    b) A company initially started with 40 workers to complete the work by 150 days. Later, it decided to fasten up the work increasing the number of workers as shown below.
    
    

    Number of workers (x)	40	50	60	75
    Number of days (y)	150	120	100	80

    
    i) Graph the above data and identify the type of variation.
    ii) From the graph, find the number of days required to complete the work if the company decides to opt for 120 workers?
    iii) If the work has to be completed by 200 days, how many workers are required?

Frequently Asked Questions

Can students still use the Thoothukudi District 10th Maths Quarterly Exam 2025 paper for study?

Yes, past district-level papers are valuable for practice and exam preparation, even though the exam is over.

Why should I refer to Thoothukudi District quarterly exam papers?

District papers highlight local question trends and help students understand how topics are emphasized regionally.

Where can I find the Thoothukudi District 10th Maths Quarterly Exam 2025 answer key?

The answer key is available on Kalvi Seithi and other Tamil Nadu education portals for reference.

How do district-level past papers help in SSLC preparation?

They provide additional practice, improve accuracy, and build confidence for the final SSLC board exam.