Goa Board Class 10 Question Paper 2024 Mathematics Regular Level 1

2025

GOA BOARD
QUESTION
PAPERS
2024
Question Papers

Prepare yourself for upcoming Goa
Board Exams

2024 IV 12 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 : 11) 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 questions (VSA) of 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 exactly as per given measurements. The
construction lines and arcs should also be maintained.

(ix) Graph page is provided on the answer booklet.

(x) Use of calculators and mathematical tables is not
permitted.
S-2021 1 P.T.O.

Section–A

Select and write the correct alternative from those given below each statement :

1. The HCF and LCM of two numbers is 3 and 216 respectively. If one of the
number is 36, then the other number is : 1

• 3 • 18

• 36 • 648

2. The sum of the zeroes of the quadratic polynomial 2x2 – 8x – 6 is : 1

• –4 • –3

• 3 • 4

3. The zeroes of the quadratic polynomial 3x2 – 15 are : 1

• 5, 5 • 5, –5

• 15, 15 • 15, –15

4. If a pair of linear equations in two unknowns is consistent, then the lines
representing the system will be : 1

• parallel • always coincident

• always intersecting • intersecting or coincident

5. The sum of the ages of two brothers 10 years back was x + y – 10. Therefore
the sum of their present ages is : 1

• x + y • x + y + 10

• x + y + 20 • x + y + 30
S-2021 2

6. The thirteenth term of the Arithmetic Progression –104, –91, –78 is : 1

• –260 • –52

• 52 • 260

7. In ABC, M and N are points on the sides AB and AC respectively such that
MN BC . If AM = 6 cm, MB = 8 cm and AN = 9 cm, then AC is equal to : 1

• 9 cm • 12 cm

• 14 cm • 21 cm

8. The value of cosec2 27º – tan2 63º is equal to : 1

• –1 • 0

• 1 • 90

1
9. cos (x + 30)º = , then x is equal to : 1
2

• 0 • 15

• 30 • 60

10. If cosec 3A = sec (A + 30)º where 3A is an acute angle, then the value of
cos 2A is : 1

2 3
• •
3 2

1 1
• •
2 2

11. Point P is 15 cm away from the centre of the circle of radius 5 cm. The length
of the tangent segment drawn to the circle from point P is : 1

• 10 2 • 20

• 250 • 200

S-2021 3 P.T.O.

12. Area of a sector of a circle of radius R and subtending an angle of 30º at
the centre of the circle is : 1

R R2
• •
6 12

R2 R2
• •
6 3

13. The radii of the two bases of a frustum of a cone are 7 cm and 1 cm respectively
and its perpendicular height is 8 cm. Therefore its slant height is : 1

• 6 cm • 8 cm

• 10 cm • 16 cm

14. The lateral surface area of a cube is 100 cm2, then the volume of the cube
is : 1

• 125 cm3 • 400 cm3

• 600 cm3 • 1000 cm3

15. The X coordinate of the point of intersection of the more than Ogive and less
than Ogive gives the : 1

• Mean • Median

• Mode • Range

16. If the probability that it will rain on a particular day is 0.03, then the probability
that it will not rain on that day is : 1

• 0.01 • 0.03

• 0.07 • 0.97
S-2021 4

17. A piggy bank collection consisted of coins of Rs. 2 and Rs. 5. In all there
were 77 coins totalling Rs. 220. Write a pair of linear equations in two variables
x and y to represent the above information. 1

18. If tangents PA and PB from a point P to a circle with centre O are inclined

to each other at an angle of 70º, then find m POA. 1

22
19. Find the perimeter of a quadrant of a circle of radius 7 cms. Take .
7
1

20. A bag contains 8 black balls and some red balls. If the probability of drawing
1
a red ball is , then find the number of red balls. 1
3

Section–B

27
21. Without performing actual division state whether the rational number
480
has a terminating decimal or a non-terminating decimal expansion. If it is
a terminating decimal, then write its decimal expansion. 2

22. Two friends met together at a club. After how many days will they meet

again if one of them visits the club after every 64 days and the other visits

the club after every 72 days. 2

23. A vertically held stick 20 cm long casts a shadow 5 cm long on the ground.

At the same time a tower casts a shadow of 7.5 meters on the ground. Draw

an appropriate figure and find the height of the tower in meters. 2

S-2021 5 P.T.O.

24. A point R (–1, 2) divides the line segment joining the points P (2, 5) and

Q(a, b) in the ratio 3 : 4. Find a and b. 2

25. The coordinates of the vertices of ABC are A (4, 1); B (–3, 2) and

C (0, K). Given that the area of ABC is 12 sq units, find the value of ‘K’. 2

Or

If E (5, 2); F (4, 7) and G (7, –4) are the vertices of EFG, find area of

EFG.

17
26. In PAN A = 90º. If sec P = , then find : 2
8
(i) length of AN
(ii) tan N.

Or

Evaluate the following expression using known numerical values of

trignometrical ratios :

2 cosec2 60 – 3 sin2 45

S-2021 6

27. Prove the following identity : 2

sec 1 sec 1
2 cosec
sec 1 sec 1

28. In the following figure point O is the centre of two concentric circles of radii
25 and 7 units. AB is a chord of the outer circle which touches the inner

circle at point P. Find the length of chord AB : 2

29. The following grouped distribution table shows the distribution of marks of
60 students in a mathematics test : 2

Marks obtained Number of students

0 – 20 6

20 – 40 22

40 – 60 18

60 – 80 12

80 – 100 2

Find the mode of the data given above.
S-2021 7 P.T.O.

Section–C

30. If two zeroes of a polynomial 2x4 – 3x3 – 5x2 + 9x – 3 are 3 and 3,
find the other remaining zeroes. 3

31. Find the solution of the following pair of linear equations :

3x + 2y = 32 and 11x – 5y = 31 (by elimination method). 3

Or

8x + 5y = 9 and 3x + 2y = 4 (by cross multiplication method).

32. Find the roots of the following :

2x2 + 3x – 27 = 0 (by Factorisation method). 3

Or

5x2 + 7x – 6 = 0 (by completing the square method).

33. A farmer undertakes to pay off a debt of Rs. 6,240 by monthly instalments.
He pays Rs. 300 as the first instalment and increases every instalment by
Rs. 40 over the immediate previous instalment. Calculate the number of
months he will take to clear his debt. 3

34. In the following figure ABC is right-angled at B. Points E and D trisect
BC.

Prove that 8AE2 = 3AC2 + 5AD2 3

S-2021 8

35. Two pillars of equal height stand on either side of the road BC which is

80 meters wide. The angles of elevation of the top of the pillars from a

point M on the road between the pillars is 60º and 30º. Find the height of

the pillars and the distance of the point M from both the pillars AB and

CD. (Take 3 = 1.73) 3

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

distance of 7.5 cm from the centre of the circle. Using a pair of compass and

ruler construct two tangent segments QA and QB touching the circle at

points A and B respectively. Measure and state the length of the tangent

segments. 3

37. Using a pair of compass and ruler construct XYZ with XY = 5 cm,

5
XZ = 7 cm and m X = 60º. Then construct XY'Z' whose sides are of
3

the corresponding sides of XYZ. 3

S-2021 9 P.T.O.

38. In the following figure, semicircles are drawn using AB, AC and BC

as diameters. Find the area of the shaded region if AB = 3 cm and

AC = 4 cm. 3

39. A solid metallic sphere of diameter 18 cm is melted to make solid right

circular cones of base diameter 9 cm and height 4 cm. Find the number of

cones that can be made. 3

Section–D

40. Find the solution of the following pair of linear equations graphically : 4

2x – y = 4 and

x – 3y = – 3

Rewrite and complete the following tables :

2x y 4 x 3y 3

S-2021 10

41. If the length of a rectangle is increased by 1 unit and the breadth is

decreased by 2 units, its area becomes 30 square units. If the length of the

same rectangle is decreased by 1 unit and the breadth is increased by 2

units its area becomes 56 square units. Find the length and breadth of the

original rectangle. 4

42. The following table gives the distribution of total household expenditure

(in Rs.) of 200 farmers in a village : 4

Expenditure Number of Class

xi a
in Rs. Farmers Mark ui f iui
h
(CI) ( fi ) ( xi )

2000 – 3000 34

3000 – 4000 38

4000 – 5000 31

5000 – 6000 43

6000 – 7000 32

7000 – 8000 22

fi 200

Take the class mark denoted as ‘a’ of the class interval 5000 to 6000 as the

assumed mean and ‘h’ as the class size. Rewrite and complete the table and

also find the mean expenditure by the step deviation method.

S-2021 11 P.T.O.

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