Goa Board Class 10 Question Paper 2025 Mathematics Level 2

2025 III 10 0930 Seat No.

Time : 3 Hours MATHEMATICS REGULAR LEVEL 2 (E)

Subject Code

S 2 0 2 4

Total No. of Questions : 42 (Printed Pages : 19) Maximum Marks : 80

INSTRUCTIONS : Read the following instructions 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, Question Nos. 1 to 16 are multiple choice
questions (MCQs) and Question Nos. 17 to 20 are very short
answer type questions (VSA) carrying 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 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 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 from question 1 to 16 :

1. The maximum number of zeroes that a polynomial of degree 3 can have :

• 0

• 1

• 2

• 3

2. If the graphs of a pair of linear equations in two variables intersect at a

point, then the given pair of equations has :

• no solution

• unique solution

• two solutions

• infinitely many solutions

3. The solution of a pair of linear equations x 2 y 6 and 2 x y 2 is :

• x = 2 and y = –2

• x = –2 and y = –2

• x = 2 and y = 2

• x = –2 and y = 2

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4. The non-zero root of 5 x2 4x 0 is :

4
•
5

5
•
4

5
•
4

4
•
5

5. The 7th term of the A.P. 2, 7, 12, 17, ...... is :

• 22

• 27

• 32

• 37

6. Two poles of heights 7 m and 10 m stand vertically on the ground. If the

distance between their feet is 4 m, then the distance between their tops

is :

• 3 m

• 4 m

• 5 m

• 6 m

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7. The value of cot 45º tan 45º is :

• –1

• 0

• 1

• 2

sin A
8. If 1 where A is an acute angle, then the value of A is :
cos36º

• 18º

• 36º

• 54º

• 72º

9. The value of 10 cosec 2 A 10 cot2 A is :

• 0

• 1

• 10

• 20

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10. In the figure, O is the centre of the circle and PT is a tangent to it at point

T. If TOR 100º , then PTR is equal to :

• 40º

• 50º

• 60º

• 80º

11. The area of a semi-circle of radius 7 cm, is :

• 22 cm2

• 44 cm2

• 77 cm2

• 154 cm2

12. A circle is inscribed in a square of perimeter 20 cm. Hence, the radius of

the circle is :

• 2.0 cm

• 2.5 cm

• 4.5 cm

• 5.0 cm

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13. If a cube of 8 cm has to be painted fully in blue colour, then the painted

area will be :

• 64 cm2

• 88 cm2

• 256 cm2

• 384 cm2

14. The curved surface area of a right cylinder of height 10 cm and radius

3.5 cm is :

• 220 cm2

• 256 cm2

• 385 cm2

• 440 cm2

15. If two coins are thrown once, at the same time, then the probability of

getting exactly two heads is :

1
•
4

1
•
2

3
•
4

• 1

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16. The value of log 2 128 is :

• 2

• 6

• 7

• 8

1
17. Write a quadratic polynomial in ‘x’ if the sum of its zeroes is and the
2
3
product of its zeroes is .
2

18. Find the value of ‘k’ if the given pair of linear equations has infinitely many

solutions :

( k 3) x 3y k

kx 6y 12 .

19. Find the length of the arc of a circle of radius 6 cm and subtending an angle

of 90º at the centre. (Do not substitute for ).

20. The alphabets of the word ‘MATHEMATICS’ are jumbled and put in a

bag. What is the probability of picking a vowel without looking into the

bag ?

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Section B (2 marks each)

21. Find the HCF of 105 and 120 using Euclid’s Division Algorithm.

Or

3
Without actually performing long division, show that has a terminating
160

decimal expansion and hence find its decimal expansion.

22. In the given figure, a circle with centre O and diameter AB is drawn in a

trapezium PQRS of height 14 cm and its parallel sides PQ = 17 cm and

SR = 27 cm touch the circle at points A and B respectively. Find the area

of the shaded region.

22
(Take )
7

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23. Find the mode of the following distribution table :

Class Interval Frequency

(C.I.) (f)

15—25 11

25—35 21

35—45 23

45—55 15

7
24. In DEF, E = 90º. If tan F . Find : sin D.
24

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

trigonometric ratios :

4sin 2 60º tan 2 45º tan 2 60º .

ar( XYZ) 9
26. If XYZ ~ STR, and YZ = 15 cm,
ar( STR) 4

then find the length of TR.

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27. Find the distance between the points A(8, –2) and B(–3, –6).

Or

Find the co-ordinates of the mid-point which divides the line segment joining

the points P(6, 4) and Q(2, –8).

28. Find the area of the triangle formed by joining the points :

L(6, 4), M(–3, 4) and N(6, –2).

Section C (3 marks each)

29. Divide the polynomial 2 x3 13 x 2 29 x 45 by x – 2 and write the

Quotient and Remainder.

Hence express the result in the form,

Dividend = Divisor × Quotient + Remainder.

30. Find the solution of the pair of linear equations :

4x – 3y = 10 and 2x + 5y = 18

by Elimination method.

Or

Find the solution of the pair of linear equations :

4x – y = –1 and 6x – 5y = 9

by Substitution method.

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31. Find the roots of the Quadratic equation :

2 x2 17 x 21 0 by factorization method.

32. Find the roots of the Quadratic equation :

2 x2 3x 44 0 by using Quadratic formula.

33. In an Arithmetic Progression, the 3rd term is 13 and the 10th term is –1.

Find the sum of the first 20 terms.

34. Evaluate the following expression using logarithm method :

(5.96)2 24
.
1.372

35. Draw a circle with centre O and radius 3 cm. Take a point P at a distance

of 8.5 cm from the centre of the circle. Using a pair of compasses and ruler,

construct two tangents PA and PB from the point P to the circle. Measure

and state the length of the tangent segments.

36. Using a pair of compasses and ruler, construct ABC, in which AB = 6.5 cm,

3
B = 60º and BC = 7.5 cm. Then construct A'BC' whose sides are of
5

the corresponding sides of ABC.

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37. Given : In PQR, PR2 = PQ2 + QR2. XYZ is constructed such that :

Y = 90º, XY = PQ and YZ = QR.

Prove that : PQR is a right angled triangle.

Or

Given : In RST, LM RS such that T – L – R and T – M – S. LA TS

and MB TR . MR and LS are joined. Prove that :

TL TM
.
LR MS

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38. A ladder 5.4 m long, touches the top of a wall of a house when its angle

of elevation with the horizontal ground is 45º. Find the height of the wall

of the house.

39. Given : Point O is the centre of a circle. TA and TB are two tangent

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

respectively.

Prove that : TA = TB

(Write only the proof with reasons)

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40. A solid metallic sphere of radius 4.5 cm is melted and recast into the shape

of a solid cylinder of radius 5 cm. Find the height of the cylinder.

Section D (4 marks each)

41. The following table shows the donation collected by 40 students for a needy

old-aged home.

Donation Number of Class Mark

Collection (`) Students (xi) (fi × xi)

(C.I.) (fi)

150—250 2 ............ ............

250—350 4 ............ ............

350—450 7 ............ ............

450—550 9 ............ ............

550—-650 10 ............ ............

650—750 8 ............ ............

fi = fixi =

Find the mean collection of the students using Direct Method.

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

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

Rewrite and complete the following tables :

x + y = 3 x + 2y = 9

x x
y y

(Plot at least 3 points of each line)

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Space for rough work

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Space for rough work

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