10th Maths - Theni District Quarterly Exam 2025 Question Paper

Reg. No. _________________

COMMON QUARTERLY EXAMINATION - 2025 (Theni District)

Time: 3.00 hrs

Standard X | MATHEMATICS

Marks: 100

Part-I

14 × 1 = 14

1. Choose the correct answer:

1. If n(A × B) = 6 and A = {1,3} then n(B) is:
   a) 1

   b) 2

   c) 3

   d) 6
2. The range of the relation R = {(x, x²) / x is a prime number less than 13} is:
   a) {2,3,5,7}

   b) {2,3,5,7,11}

   c) {4,9,25,49,121}

   d) {1,4,9,25,49,121}
3. If f: A → B is a bijective function and if n(B) = 7, then n(A) is equal to:
   a) 7

   b) 49

   c) 1

   d) 14
4. Euclid's division lemma states that for positive integers a and b, there exist unique integers q and r such that a = bq + r where r must satisfy:
   a) 1 < r < b

   b) 0 < r < b

   c) 0 ≤ r < b

   d) 0 < r ≤ b
5. If 6 times of 6^th term of an A.P. is equal to 7 times the 7^th term, then the 13^th term of the A.P. is:
   a) 0

   b) 6

   c) 7

   d) 13
6. 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
7. If (x - 6) is the HCF of x² - 2x - 24 and x² - kx - 6 then the value of k is:
   a) 3

   b) 5

   c) 6

   d) 8
8. The values of a and b if 4x⁴ - 24x³ + 76x² + ax + b is a perfect square are:
   a) 100, 120

   b) 10, 12

   c) -120, 100

   d) 12, 10
9. In ΔLMN, ∠L = 60°, ∠M = 50°. If ΔLMN ~ ΔPQR then the value of ∠R is:
   a) 40°

   b) 70°

   c) 30°

   d) 110°
10. 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) 4:25
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 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
13. tanθ cosec²θ - tanθ is equal to:
    a) secθ

    b) cot²θ

    c) sinθ

    d) cotθ
14. If f is the identity function, then the value of f(1) - 2f(2) + f(3) is:
    a) 1

    b) 0

    c) -1

    d) -3

Part-II

10 × 2 = 20

II. Answer any 10 questions. (Q.No.28 is compulsory)

15. Find A × B and B × A if A = {2,-2,3} and B = {1,-4}.
16. Let f = {(x, y) | x, y ∈ &mathbb{N} and y = 2x} be a relation on &mathbb{N}. Find the domain, co-domain and range. Is this relation a function?
17. If f(x) = 3x - 2, g(x) = 2x + k and if fog = gof, then find the value of k.
18. Find the number of terms in the A.P. 3, 6, 9, 12, ..., 111.
19. If 3 + k, 18 - k, 5k + 1 are in A.P, then find k.
20. Find the sum of 1 + 3 + 5 + ...... + to 40 terms.
21. Find the sum: 3 + 1 + 13 + ...... + ∞
22. Find the sum and product of the roots for x² + 3x - 28 = 0.
23. Determine the nature of the roots for 2x² - 2x + 9 = 0.
24. If the difference between a number and its reciprocal is 245, find the number.
25. If ΔABC is similar to ΔDEF such that BC = 3 cm, EF = 4 cm and area of ΔABC = 54 cm². Find the area of ΔDEF.
26. Find the slope of a line joining the points (14,10) and (14,-6).
27. Prove that tan²θ - sin²θ = tan²θ sin²θ.
28. Show that the given points are collinear: (1,2), (2,3) and (3,4).

Part-III

10 × 5 = 50

III. Answer any 10 questions. (Q.No.42 is compulsory)

29. A relation f: A → B is defined by f(x) = x2 - 1, where A = {2, 4, 6, 10, 12} and B = {0, 1, 2, 4, 5, 9}. Represent f by:
    (i) an arrow diagram, (ii) a table, (iii) a set of ordered pairs, (iv) a graph.
30. Let f: &mathbb{R} → &mathbb{R} be defined as:
    f(x) = 2x + 7x < -2
    f(x) = x² - 2-2 ≤ x < 3
    f(x) = 3x - 2x ≥ 3
    Find: (i) f(4)    (ii) f(-2)    (iii) f(4) + 2f(1)    (iv) [f(1) + 3f(4)] / f(-3).
31. Find the sum to n terms of the series: 3 + 33 + 333 + ... to n terms.
32. Find the square root of the expression: 64x⁴ - 16x³ + 17x² - 2x + 1.
33. Simplify: 1x²-5x+6 + 1x²-3x+2 - 1x²-8x+15
34. Find the GCD of the following polynomial sequences:
    2x⁴ + 13x³ + 27x² + 23x + 7,   x³ + 3x² + 3x + 1,   x² + 2x + 1
35. State and prove Thales theorem.
36. Find the area of the quadrilateral whose vertices are at (-9,0), (-8,6), (-1,-2) and (-6,-3).
37. Without using Pythagoras theorem, show that the points (1,-4), (2,-3) and (4,-7) form a right angled triangle.
38. Find the equation of a straight line passing through (1,-4) and has intercepts which are in the ratio 2:5.
39. Prove the following identity: √(1+sinθ1-sinθ) + √(1-sinθ1+sinθ) = 2 secθ
40. Let A = The set of all natural numbers less than 8, B = The set of all prime numbers less than 8, C = The set of even prime number. Verify that (A ∩ B) × C = (A × C) ∩ (B × C).

Part-IV

2 × 8 = 16

IV. Answer all the questions.

43. a) Construct a triangle similar to a given triangle PQR with its sides equal to 73 of the corresponding sides of the triangle PQR (scale factor 7/3 > 1).
    (OR)
    b) Draw a triangle ABC of base BC = 8 cm, ∠A = 60° and the bisector of ∠A meets BC at D such that BD = 6 cm.
44. a) Varshika drew six 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.

    Diameter (x) cm	1	2	3	4	5
    Circumference (y) cm	3.1	6.2	9.3	12.4	15.5

    (OR)
    b) Draw the graph of xy = 24, x, y > 0. Using the graph find (i) y when x = 3 and (ii) x when y = 6.

Frequently Asked Questions

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

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

Why should I refer to Theni District quarterly exam papers?

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Where can I find the Theni 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.