10th Maths - Ramanathapuram District Quarterly Exam 2025 Question Paper

Reg. No.: _________________

QUARTERLY EXAMINATION 2025 (Ramanathapuram District)

Time: 3.00 Hrs

MATHEMATICS

MARKS: 100

Part-A

14 × 1 = 14

1. Choose the best answer.

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

   b) 2

   c) 3

   d) 6
2. If A = {a,b,c} and f = {(a,a), (b,b), (c,c)} then, which of the following is not a function of f?
   a) 1-1 function

   b) onto function

   c) Identity function

   d) constant function
3. 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)
4. 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
5. An A.P consists of 31 terms. If its 16th term is m, then the sum of all the terms of this A.P is:
   a) 16m

   b) 62m

   c) 31m

   d) 312m
6. y² + 1y² is not equal to:
   a) y⁴+1y²

   b) (y + 1y)²

   c) (y + 1y)² + 2

   d) (y + 1y)² - 2
7. Which of the following should be added to make x⁴ + 64 a perfect square?
   a) 4x²

   b) 16x²

   c) 8x²

   d) -8x²
8. If ΔABC is an isosceles triangle with ∠C = 90° and AC = 5 cm, then AB is:
   a) 2.5 cm

   b) 5 cm

   c) 10 cm

   d) 5√2 cm
9. If (5,7), (3,p) and (6,6) are collinear, then the value of p is:
   a) 3

   b) 6

   c) 9

   d) 12
10. (1 + tanθ + secθ)(1 + cotθ - cosecθ) is equal to:
    a) 0

    b) 1

    c) 2

    d) -1
11. When proving that a quadrilateral is a trapezium, it is necessary to show:
    a) Two sides are parallel

    b) Two parallel and two non-parallel sides

    c) Opposite sides are parallel

    d) All sides are of equal length.
12. The number of excluded values of x²+3x+2x²-1 is:
    a) 0

    b) 1

    c) 2

    d) 4
13. In ΔABC, AD is the bisector of ∠BAC. If AB = 8 cm, BD = 6 cm and DC = 3 cm. The length of the side AC is:
    a) 6cm

    b) 4cm

    c) 3cm

    d) 8cm
14. The inclination whose slope is 1√3 is:
    a) 30°

    b) 45°

    c) 60°

    d) 90°

PART-B

10 × 2 = 20

II. Answer any 10 questions. Question No. 28 is compulsory.

15. If B × A = {(-2,3), (-2,4), (0,3), (0,4), (3,3), (3,4)} find A × B.
16. Let A = {1,2,3,4} and B = N. Let f: A → B defined by f(x) = x³ then:
    (i) find the range of f    (ii) Identify the type of function.
17. Find k if f ∁ f(k) = 5 where f(k) = 2k - 1.
18. 'a' and 'b' are two positive integers such that a^b × b^a = 800. Find 'a' and 'b'.
19. How many consecutive odd integers beginning with 5 will sum up to 480?
20. Simplify: x+24y ÷ x²-x-612y²
21. Find the excluded values of the expressions: 7p+28p²+13p+5
22. If the discriminant of 3x² - 4x - k = 0 is 64, then find the value of k.
23. If AB = 5cm, AC = 10cm, BD = 1.5cm and CD = 3.5cm of ΔABC, check whether AD is bisector of ∠A.
24. A boy of height 90cm is walking away from the base of a lamp post at a speed of 1.2 m/sec. If the lamp post is 3.6m above the ground, find the length of his shadow cast after 4 seconds.
25. If the three points (3,-1), (a,3) and (1,-3) are collinear, find the value of a.
26. Find the intercepts made by the line 4x - 3y + 36 = 0 on the coordinate axes.
27. Prove that: sin A1+cos A = 1-cos Asin A
28. If a^x, a^y, a^z are in G.P then show that x, y, z are in A.P.

PART-C

10 × 5 = 50

III. Answer any 10 questions. Question No. 42 is compulsory.

29. 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).
30. If f(x) = 2x+3, g(x) = 1-2x and h(x) = 3x, prove that f ∁ (g ∁ h) = (f ∁ g) ∁ h.
31. The function 't' which maps temperature in Celsius (C) into temperature in Fahrenheit (F) is defined by t(C) = F where F = 95C + 32. Find:
    i) t(0)    ii) t(28)    iii) t(-10)    iv) the value of C when t(C) = 212
    v) the temperature when the Celsius value is equal to the Fahrenheit value.
32. In a winter season let us take the temperature of Ooty from Monday to Friday to be in A.P. The sum of temperatures from Monday to Wednesday is 0°C and the sum of the temperatures from Wednesday to Friday is 18°C. Find the temperature on each of the five days.
33. Find the sum to n terms of the series 5 + 55 + 555 + &dots;
34. Rekha has 15 square colour papers of sizes 10cm, 11cm, 12cm, &dots; 24cm. How much area can be decorated with these colour papers?
35. The sum of three numbers is 24. Among them one number is equal to half of the sum of other two numbers but four times the difference of them. Find the three numbers.
36. If 9x⁴ + 12x³ + 28x² + ax + b is a perfect square, find the values of a and b.
37. The hypotenuse of a right angled triangle is 25cm and its perimeter 56cm. Find the length of the smallest side.
38. State and prove the Basic proportionality theorem.
39. Find the area of a quadrilateral formed by the points (8,6), (5,11), (-5,12) and (-4,3).
40. Find the equation of the straight line through the point (4,-5) and having x and y intercepts in the ratio 3:5.
41. Find the equation of a straight line parallel to Y axis and passing through the point of intersection of the lines 4x + 5y = 13 and x - 8y + 9 = 0.
42. 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 aba+b metres.

PART-D

2 × 8 = 16

Answer all the Questions.

43. (A) Construct a triangle similar to a given triangle PQR with its sides equal to 35 of the corresponding sides of the triangle PQR (scale factor 3/5 < 1).
    [OR]
    (B) Construct a triangle ▵PQR such that QR = 5cm, ∠P = 30° and the altitude from P to QR is of length 4.2cm.
44. (A) Graph the following linear function y = 12x. Identify the constant of variation and verify it with the graph. Also (i) Find y, when x = 9 (ii) Find x, when y = 7.5.
    [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

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