Goa Board Class 10 Question Paper 2025 Mathematics Level 1

2025 III 11 0930 Seat No.

Time : 3 Hours MATHEMATICS REGULAR LEVEL 1 (E)
Subject Code

S 2 0 2 1
Total No. of Questions : 42 (Printed Pages : 19) Maximum Marks : 80

INSTRUCTIONS : (i) This question paper consists of 42 questions. All
questions are compulsory.
(ii) This question paper is divided into four sections-A, B,
C and D.
(iii) In Section A–Question Nos. 1 to 16 are multiple choice
questions (MCQs) and Question Nos. 17 to 20 are very
short answer type (VSA) questions carrying 1 mark each.
(iv) In Section B–Question Nos. 21 to 29 are short answer
type-I (SA-I) questions carrying 2 marks each.
(v) In Section C–Question Nos. 30 to 39 are short answer
type-II (SA-II) questions carrying 3 marks each.
(vi) In Section D–Question Nos. 40 to 42 are long answer
(LA) questions carrying 4 marks each.
(vii) There is no overall choice. However an internal choice
has been provided in two questions of 2 marks each
in Section B and two questions of 3 marks each in
Section C.
(viii) In questions on constructions, the drawing should be
clear and exact as per given measurements. The
construction lines and arcs should also be maintained.
(ix) Graph paper is provided on the answer booklet.
(x) Logarithm and Antilogarithm tables are printed on the
last pages of the question paper.
(xi) Use of calculator is not permitted.

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Section A (1 mark each)

Select and write the correct alternative from those given below each

statement for questions 1 to 16 :

1. The sum of the zeroes of the quadratic polynomial 6x2 – 7x – 3 is :

7
•
6

3
•
6

6
•
7

7
•
6

2. The zeroes of the polynomial 6x2 – 3 are :

1
• 0,
2

1 1
• ,
2 2

1 1
• ,
2 2

1 1
• ,
2 2

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3. The pair of linear equations x + 3y = 6 and 2x – 3y = 12 have :

• no solution

• unique solution

• exactly two solutions

• infinitely many solutions

4. The ages of father and his son 3 years ago was x and y years respectively.

Therefore the sum of their ages five years from now will be :

• (x y 3) years

• (x y 6) years

• (x y 10) years

• (x y 16) years

5. The common difference of the arithmetic progression –10, –6, –2, 2, ......

is :

• –16

• –4

• 4

• 16

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6. In ABC, points D and E are on side AB and AC respectively. DE BC

AD 3
and . If AC = 5.6 cm, then the length of AE is :
DB 5

• 2.1 cm

• 16.8 cm

• 15 cm

• 3 cm

7. The value of sin 90º cos 90º is :

• 1

3
•
2

1
•
2

• 0

8. The value of sin 56º – cos 34º is :

• 0º

• 22º

• 34º

• 56º

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9. If tan cot 2 , then the value of tan 2 cot2 is :

• 1

• 2

• 4

• 10

10. If an angle between radii of a circle is 130º, then the angle between the tangents

at the ends of the radii is :

• 90º

• 70º

• 50º

• 40º

11. The area of a circle that can be inscribed in a square with a side length

of 6 cm is :

• 36 cm2

• 18 cm2

• 12 cm2

• 9 cm2

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12. If the sum of the areas of two circles with radii R1 and R2 is equal to the

area of a circle with radius R, then :

• R1 + R2 = R

• R12 R 22 R2

• R1 + R2 < R

• R12 R 22 R2

13. If the length of each edge of a cubical box is 1.5 m, then its lateral surface

area is :

• 2.25 m2

• 6 m2

• 9 m2

• 13.5 m2

14. The total surface area of a hemispherical solid with a diameter of 14 cm,

22
using , is :
7

• 308 cm2

• 462 cm2

• 616 cm2

• 1848 cm2

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15. Playing cards numbered from 2 to 101 are placed in a bag and mixed

thoroughly. If one card is randomly drawn from the bag, then the probability

that the number on the card is a perfect square is :

• 0.1

• 0.3

• 0.9

• 0.09

16. The value of log 102 is :

• 100

• 10

• 20

• 2

17. If the system of linear equations 2x + ky = 1 and 3x – 5y = 7 has no solution,

then find the value of k.

18. A chord AB of a circle subtends a right angle at the centre of the circle. If

the radius is 10 cm, then find the length of the chord AB.

19. The diameter of a circle is 7 cm. Find the area of the quadrant of the circle.

(Do not substitute for )

20. Two dice are rolled simultaneously. Find the probability of getting the same

number on both dice.

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Section B (2 marks each)

21. Find the HCF of 112 and 84 by prime factorisation method.

22. In the given figure, O-ABC is a quadrant of a circle with centre O. If

BP OA , BOA = 45º and BP = 6 cm, then find the area of the shaded

region.

(Take = 3.14)

23. In ABC, points D and E are an side AB and AC respectively such

that DE BC . If AD = (x – 2) cm, AB = x cm, DE = (x – 1) cm and

BC = (x + 2) cm, then find the value of x.

24. Find the coordinates of a point M which lies on the y-axis and is equidistant

from the points A(5, –2) and (–3, 2).

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25. The coordinates of the vertices of a triangle are P(1, –3), Q(4, k) and

R(–9, 7). If its area is 15 cm2, then find the value of k.

Or

The coordinate A(3, 0), B(4, 5), C(–1, 4) and D(–2, –1) are the vertices of a

rhombus ABCD. Find the ar(ABCD).

5
26. In KLM, KLM = 90º and sin M . Find the length of LM and the
3
value of cot K.

Or

Evaluate the following trigonometric expression using known numerical

values of trigonometrical ratios :

1 5
sec 2 30º sin 2 45º .
3 6

27. Prove the following identity :

tan cot
sec 2 cosec2 .
sin cos

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28. In the given figure O is the centre of the circle with radius 5 cm. A tangent

XAY is parallel to the chord CD of the circle. The diameter AB intersects

chord CD at point M. If the length of AM = 8 cm, then find the length of

chord CD.

29. The following table shows the grouped frequency distribution of the daily

income of 50 workers of a factory :

Daily Income No. of Workers

(in `)

100—120 12

120—140 14

140—160 8

160—180 6

180—200 10

Find the mode of the above data.

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Section C (3 marks each)

30. If 3 and 3 are two zeroes of the polynomial x4 – 3x3 – 7x2 + 9x + 12,

then find the other two zeroes.

31. Find the solution of the given pair of linear equations by elimination

method :

3x + 4y = 24 and 20x – 11y = 47

Or

Find the solution of the given pair of linear equations by cross multiplication

method :

2x + y = 11 and 3x + 4y = 9

32. Find the roots of the quadratic equation 4x 2 – 5x – 21 = 0 by the

factorisation method.

Or

Find the roots of the quadratic equation 2x2 – 9x + 10 = 0 by completing

the square method.

33. If the sum of first 14 terms of an arithmetic progression is 1505 and its first

term is 10, then find the 25th term of the arithmetic progression.

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34. Given : Points E and C are on segment BF such that BE = 5 EC,
1
CF = 2EC. DE CA and DE = CA
2

Prove that : ar ( AMB) 4 ar ( DNF) .

35. A helicopter is flying at an altitude of 1200 m above sea level. A man seated

inside the helicopter observes two ships, C and D, positioned directly behind

one another on the same side of the helicopter. The angles of depression to

the ships, as observed from the helicopter, are 60º and 45º respectively as

shown in the figure. Find the distance between the two ships.

(Take 3 1 732 )

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36. Using a pair of compasses and ruler, construct ABC with AB = 5 cm,

BC = 6 cm and AC = 7 cm. Then construct A'BC' similar to ABC whose
5
sides are of the corresponding sides of ABC.
4

37. Draw a circle with centre P and radius 3.5 cm. Then take a point Q at a

distance of 8 cm from the centre of the circle. Using a pair of compasses and

ruler construct two tangents QA and QB touching the circle at A and B

respectively. Measure and state the length of the tangent segments.

38. A wooden block is in shape of a cylinder. Its height is 10 cm and the

diameter of its base is 8 cm. If two equal cones of diameter 6 cm and height

5 cm is hollowed out from both its end, then find the volume of the

remaining solid.

22
(Take )
7

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39. Evaluate the following by using the logarithm method :

(5.96)2 29
.
21.56

Section–D (4 marks each)

40. A particular engineering college has two classrooms A and B, for first-

year mechanical students. If 5 students are moved from classroom A to

classroom B, the number of student in each room becomes equal.

However, if 10 students are moved from classroom B to classroom A, the

number of students in classroom A becomes twice that of classroom B.

Using linear equations in two variables, solve for the initial number of

students in each classroom.

41. A man bought some pens, each costing the same amount as the total

number of pens purchased. The shopkeeper, who enjoys applying discounts

in a mathematical way, offers a special deal if the quantity of pens is

doubled. The discount on each pen is calculated as ` 3 less than one fourth

of the original price. As a result of doubling the number of pens, the total

cost increases by ` 432. Find the original cost of each pen.

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42. The following table represents the frequency distribution of rainfall (in cm)

recorded in a city over 66 days.

Rainfall Number of Days Cumulative

(in cm) ( f) frequency

(C.I.)

0—10 22 .........................

10—20 10 .........................

20—30 8 .........................

30—40 15 .........................

40—50 5 .........................

50—60 6 .........................

Rewrite and complete the table by adding the cumulative frequency in the

third column and then draw a ‘less than’ type ogive based on the data

provided.

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Space for rough work

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Space for rough work

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