Goa Board Class 10 Question Paper 2024 Mathematics Basic Level 2

2025

GOA BOARD
QUESTION
PAPERS
2024
Question Papers

Prepare yourself for upcoming Goa
Board Exams

2024 IV 22 0930 Seat No.

Time : 3 Hours MATHEMATICS BASIC LEVEL 2 (E)

Subject Code
S 2 0 2 4
Total No. of Questions : 42 (Printed Pages : 15) Maximum Marks : 80

INSTRUCTIONS : Read the following instructions very carefully and strictly follow
them :
(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, Questions 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 28 are short answer
type I (SA-I) questions carrying 2 marks each.
(v) In Section C, Question Nos. 29 to 40 are short answer
type II (SA-II) questions carrying 3 marks each.
(vi) In Section D, Question Nos. 41 and 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 question on constructions, the drawing should be clear
and exactly as per the given measurements. The
construction lines and arcs should also be maintained.
(ix) Graph page is provided on the answer booklet.
(x) Use of calculator and mathematical tables is not
permitted.

S-2024 1 P.T.O.

SECTION-A

Select and write the correct alternative from those given below each

statement :

1. Which of the following is a rational number ? 1

3 2

49

7
2

2. The quadratic polynomial whose zeroes are 7 and – 7 is : 1

x2 + 7

x2 – 7

x2 – 7

x2 – 49

3. The pair of linear equations which represent two parallel lines has : 1

no solution

one solution

two solutions

infinitely many solutions

S-2024 2

4. If 12x + 11y = 57 and 11x + 12y = 58, then x – y is : 1

– 1

0

1

3

5. If one root of the quadratic equation 2x2 + kx – 6 = 0 is 2, then the value

of k is : 1

– 2

– 1

1

2

6. The 16th term of an Arithmetic Progression is 79. If the common difference

is 5, then the first term is : 1

1

4

9

14

S-2024 3 P.T.O.

7. ABC ~ PQR, if 25 ar( ABC) = ar( PQR) and QR = 15 cm, then BC

is : 1

3

10

15

75

8. If sin2 2p + cos2 60° = 1, then the value of p is : 1

0

30

60

90

9. If sin (B – 15)° = 0, then the value of B is : 1

0

15

75

90

S-2024 4

10. If sec 4A = cosec (A + 40°), where 4A is an acute angle, then the value of

A is : 1

10°

30°

50°

90°

11. In the given figure, B is the centre of the circle, DA and DC are tangent

segments. If ADB = 35°, then ABC is : 1

70°

90°

110°

180°

12. A circle is inscribed in a square whose side is 12 cm. therefore the radius

of the circle is : 1

3 cm

6 cm

12 cm

24 cm

S-2024 5 P.T.O.

13. The curved surface area of a hemisphere whose radius is 5 cm is : 1

5 cm2

10 cm2

25 cm2

50 cm2

14. The curved surface area of a cone is 176 cm2. If the radius of the base

of cone is 4 cm, then the slant height of the cone is : 1

22
7

8 cm

14 cm

44 cm

56 cm

15. The class-size of class interval 80 – 100 is : 1

10

20

80

90

S-2024 6

16. The probability of a sure event is : 1

0

0.5

1

1.5

17. Find the polynomial p(x) which when divided by the polynomial

g(x) = (x – 1) gives 4x as quotient and 9 as remainder. 1

18. The pair of linear equations 4x + ky = 6 and 2x + y = – 1 has a unique

solution. Find the value of k. 1

19. Find the area of a semicircle whose radius is 12 cm. (Do not substitute

for ). 1

20. Five cards of diamond are lost from a pack of 52 playing cards. From the

remaining cards, one card is drawn at random. Find the probability that the

card drawn is of red colour. 1

S-2024 7 P.T.O.

SECTION-B

17
21. Without actually performing long division show that has a terminating
250

decimal expansion and hence find its decimal expansion. 2

Or

Assuming that 5 is an irrational number, prove that 3 5 is an irrational

number.

22. Using Euclid's division algorithm, find the HCF of 102 and 150. 2

Or

Find LCM of 24 and 180 by prime factorisation method.

23. The following table shows the ages of 45 members of a Village

Library : 2

Ages in Years Number of Members

0–20 11

20–40 6

40–60 18

60–80 10

Find the mode of the given data.

S-2024 8

12
24. In right PQR, Q = 90°. If sin R , then find QR and the value of
13
tan P : 2

25. Evaluate the following expression by substituting the known values of

trigonometric ratios 2

3 tan2 30° – sin2 60°

26. The shorter side of a rectangular plot ABCD is 10 m. If its diagonal is 26 m,

calculate the perimeter of the rectangular plot. 2

27. Find the distance between the points A (3, 0) and B (6, 4). 2

28. Find the value of p for which the points A (– 2, 2), B (5, 3) and

C (3p, 4) are collinear. 2

SECTION-C

29. Divide the polynomial 2x3 + 9x2 – 3x – 20 by x + 3 and write the quotient

and the remainder. 3

Hence express the result in the form,

Dividend = Divisor × Quotient + Remainder.

S-2024 9 P.T.O.

30. Find the solution of the pair of linear equation 5x – 3y = 1 and

2x + 5y = 19 by Elimination Method. 3

Or

Find the solution of the pair of linear equations 4x – y = 6 and x + y = 9

by substitution method.

31. Find the roots of the quadratic equation 6x2 + 13x + 5 = 0 by factorisation

method. 3

32. Find the roots of quadratic equation 2x2 + 3x – 2 = 0 by using Quadratic

Formula. 3

33. Given an Arithmetic Progression 4, 9, 14, 19 ....... 3

find the 25th term and the sum of first 25 terms.

34. Draw a circle with centre A and radius 3 cm. Take a point P at a distance

of 7.5 cm from the centre of the circle. Using a pair of compasses and ruler,

construct two tangents PM and PN from the point P to the circle.

Measure and state the length of the tangent segments. 3

35. Construct APR, such that PR = 8 cm, P = 60°, AP = 6.5 cm., then using
4
a pair of compasses and ruler construct A'PR' whose sides are of the
5
corresponding sides of APR. 3

S-2024 10

36. Given : In PQR, PQR = 90° and QS PR where P – S – R : 3

Prove that : PR2 = PQ2 + QR2

(Write only the proof with reasons)

Or

In DEF, PQ || EF where points P and Q lie on DE and DF respectively.

QM DE and PN DF

N

E

DP DQ
Prove that : =
PE QF

(Write only the proof with reasons)

S-2024 11 P.T.O.

37. The angle of depression of the Car C standing on the ground from the top

of a 75 m high building AB is 60°. Find the distance of the Car from the

foot of the building ( 3 1.73) 3

38. Given : Point O is the centre of a circle. RA and RB are two tangent

segments drawn from an external point R to the circle at A and B

respectively. 3

Prove that RA = RB

(Write only the proof with reasons)

S-2024 12

39. The figure given below shows a kite in which ABCD is a square and CPQ

is an isosceles right-angled triangle whose equal sides are 8 cm. If sector C

– BD is in the shape of a quadrant of a circle of radius 28 cm., then find

22
the area of the shaded region. use 3
7

40. A cuboidal container of internal dimensions 16 cm × 10 cm × 8 cm, contains

7 solid spherical balls each of radius 3 cm packed in it. 3

Find the volume of the water required to fill the container upto the brim.

22
use .
7

S-2024 13 P.T.O.

SECTION-D

41. The following table shows the number of plants grown in 40 houses in a

locality. Rewrite and complete the table and find the mean number of plants

grown per house by using Direct Mean Method. 4

Number of Plants Number of Houses Class Mark

fi × xi
(CI) (fi) (xi)

3–5 5 ........ ........

5–7 10 ........ ........

7–9 8 ........ ........

9–11 9 ........ ........

11–13 5 ........ ........

13–15 3 ........ ........

fi = 40 fixi = .....

S-2024 14

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

x + y = 5 and 2x – y = 4

Rewrite and complete the following tables :

x + y = 5 2x – y = 4

x x

y y

(Plot at least three points for each line using a graph paper.)

S-2024 15 P.T.O.

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