MAA SARASWATI PUBLIC SR. SEC.

SCHOOL

PRE BOARD EXAMINATIONS- 2- STANDARD (041) - SET B

Class 10 - Mathematics
Time Allowed: 3 hours Maximum Marks: 80

General Instructions:

1. This question paper contains 38 questions.

2. This Question Paper is divided into 5 Sections A, B, C, D and E.

3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are Assertion

Reason based questions of 1 mark each.

4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02 marks each.

5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each.

6. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05 marks each.

7. In Section E, Questions no. 36-38 are case study based questions carrying 4 marks each with sub parts.

Section A
1. The total number of factors of a prime number is: [1]

a) 2 b) 1

c) 3 d) 0

2. The zeroes of the quadratic polynomial x2 + kx + k, k ≠ 0, [1]

a) cannot be both negative b) cannot be both positive

c) are always equal d) are always unequal

3. The pair of linear equations 4x + 6y = 9 and 2x + 3y = 6 has [1]

a) no solution b) two solutions

c) one solution d) many solutions

4. Which of the following quadratic equations has -1 as a root? [1]

a) x2 - 4x - 5 = 0 b) -x2 - 4x + 5 = 0

c) x2 + 3x + 4 = 0 d) x2 - 5x + 6 = 0

5. Which term of the AP: 21, 42, 63, 84,... is 210? [1]

a) 10th b) 12th

c) 11th d) 9th

6. If ΔABC ∼ ΔPQR with ∠ A = 32o and ∠ R = 65o, then the measure of ∠ B is: [1]

a) 32o b) 83o

c) d)

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 97o 65o
7. If in △ABC and △PQR, we have AB

QR
=
BC

PR
=
CA

PQ
then [1]

a) △BC A ∼ △P QR b) △P QR ∼ △ABC

c) △QRP ∼ △ABC d) △C BA ∼ △P QR

8. If the endpoints of a diameter of a circle are (-4, -3) and (2, 7), then the coordinates of the centre are [1]

a) (1, -2) b) (0, 0)

c) (2, -1) d) (-1, 2)

9. The point on x-axis which divides the line segment joining (2, 3) and (6, -9) in the ratio 1 : 3 is [1]

a) (6, 0) b) (0, 3)

c) (3, 0) d) (4, -3)

10. If sin θ = 1

2
then cotθ = ? [1]

a) 1
b) 1
√3

–
c) √3
d) √3
2

11. In a circle of radius 21 cm, an arc subtends an angle of 60o at the centre. The area of the sector formed by the arc [1]
is:

a) 231 cm2 b) 250 cm2

c) 220 cm2 d) 200 cm2

12. A cube whose volume is 1/8 cubic centimeter is placed on top of a cube whose volume is 1 cm3. The two cubes [1]

are then placed on top of a third cube whose volume is 8 cm3. The height of the stacked cubes is

a) 3.5 cm b) 3 cm

c) 6 cm d) 7 cm
13. How many bricks each measuring (25 cm × 11.25 cm × 6 cm) will be required to construct a wall (8 m × 6 m [1]
× 22.5 cm)?

a) 7200 b) 4800

c) 8000 d) 6400
14. The relation between mean, mode and median is [1]

a) mode = (3 × mean) - (2 × median) b) mode = (3 × median) - (2 × mean)

c) mean = (3 × median) - (2 × mode) d) median = (3 × mean) - (2 × mode)

15. The wickets taken by a bowler in 10 cricket matches are 2, 6, 4, 5, 0, 2, 1, 3, 2, 3. The mode of the data is [1]

a) 4 b) 1

c) 2 d) 3
16. A die is rolled once. The probability that a prime number comes up, is: [1]

a) 1

3
b) 0

c) 1

2
d) 2

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17. If PA and PB are tangents to the circle with centre O such that ∠ APB = 50°, then ∠ OAB is equal to [1]

a) 50o b) 40o

c) 25o d) 30o
–
18. A ladder 12 m long rests against a wall. If it reaches the wall at a height of 6√3 m, then the angle of elevation is [1]

a) 60 ∘
b) 30
∘

c) 75 ∘
d) 45
∘

19. Assertion (A): The sum of series with the nth term tn = (9 - 5n) is 220 when no. of terms n = 6. [1]

Reason (R): Sum of first n terms in an A.P. is given by the formula: Sn = 2 n × [2a + (n - 1)d]

a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A. correct explanation of A.

c) A is true but R is false. d) A is false but R is true.

20. Assertion (A): If the probability of an event is P then the probability of its complimentary event will be 1 - P. [1]
Reason (R): When E and E
¯
are complimentary events, then P(E) + P (E
¯
) = 1.

a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A. correct explanation of A.

c) A is true but R is false. d) A is false but R is true.

Section B
21. Explain why (7× 9× 13× 15+15× 14) is a composite number. [2]
22. Determine whether the given points are vertices of a right triangle: (–2, 1), (2 –2), and (5, 2) [2]
23. If tan θ = 4

5
, find the value of cos θ−sin θ

cos θ+sin θ
[2]
24. The inner and outer radii of a hollow cylinder surmounted on a hollow hemisphere of same radii are 3 cm and 4 [2]
cm respectively. If height of the cylinder is 14 cm, then find its total surface area (inner and outer).
OR
The radii of the bases of a cylinder and a cone are in the ratio 3 : 4 and their heights are in the ratio 2 : 3. What is the
ratio of their volumes?
25. The probability of selecting a blue marble at random from a jar that contains only blue, black and green marbles [2]
is 1

5
. The probability of selecting a black marble at random from the same jar is 1

4
. If the jar contains 11 green
marbles, find the total number of marbles in the jar.
Section C
26. On morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. [3]
What is the minimum distance each should walk so that each can cover the same distance in complete steps?

27. ​If α and β are the zeros of the quadratic polynomial f(x) = x2 - 2x + 3, find a polynomial whose roots are [3]
α + 2, β + 2

28. At t minutes past 2 pm the time needed by the minutes hand of a clock to show 3 pm was found to be 3 minutes [3]
2

less than minutes. Find t.

t

OR
A piece of cloth costs ₹ 35. If the piece were 4 m longer and each metre costs ₹ one less, the cost would remain
unchanged. How long is the piece?

29. If the mth term of an A.P. is 1

and nth term be 1
, then show that its (mn)th term is 1. [3]
n m

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30. Prove that: tan A
−
tan A
= 2cosecA [3]
1+sec A 1−sec A

31. A chord PQ of length 12 cm subtends an angle 120o at the center of a circle. Find the area of the minor segment [3]
cut off by the chord PQ.
Section D
32. Vijay had some bananas, and he divided them into two lots A and B. He sold first lot at the rate of ₹ 2 for 3 [5]
bananas and the second lot at the rate of ₹ 1 per banana and got a total of ₹ 400. If he had sold the first lot at the
rate of ₹ 1 per banana and the second lot at the rate of ₹ 4 per five bananas, his total collection would have been
₹ 460. Find the total number of bananas he had.
33. In the given figure PA, QB and RC are each perpendicular to AC. If AP = x, BQ = y and CR = z, then prove that [5]
1 1 1
+ =
x z y

OR
In the figure, if PQRS is a parallelogram and AB || PS, then prove that OC || SR.

34. Find the median wage from the following data: [5]

Wages(in Rs) 800 - 820 820 - 840 840 - 860 860 - 880 880 - 900 900 - 920 920 - 940

Number of workers 7 14 19 25 20 10 5

35. In figure AB and CD are two parallel tangents to a circle with centre O. ST is tangent segment between the two [5]

parallel tangents touching the circle at Q. Show that ∠ SOT = 90o

Section E
36. The students of a school decided to beautify the school on an annual day by fixing colourful flags on the straight [4]
passage of the school. They have 27 flags to be fixed at intervals of every 2 metre. The flags are stored at the
position of the middlemost flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books
where the flags were stored. She could carry only one flag at a time.

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 i. How much distance did she cover in completing this job and returning to collect her books?
ii. What is the maximum distance she travelled carrying a flag?
37. A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the [4]
figure.

If the height of the cylinder is 12 cm and its base is of radius 4.2 cm,
i. find the total surface area of the article.
ii. Also, find the volume of the wood left in the article.
38. Read the following text carefully and answer the questions that follow: [4]
A TV tower stands vertically on a bank of a canal. From a point on the other bank of a canal. From a point on

the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60o from a point 20 m
away from this point on the same bank the angle of elevation of the top of the tower is 30o.

i. Find the width of the canal. (1)

ii. Find the height of tower. (1)
iii. Find the distance between top of the tower and point D. (2)
OR
Find the distance between top of tower and point C. (2)

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