Mathematics Grade X SA II Papers (22)

7/30/2019 Mathematics Grade X SA II Papers (22)

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1

041/X/SA2/32/A1

Class - X

MATHEMATICS

Time : 3 to 3 hours Maximum Marks : 80

: 3

3

U : 80

Total No. of Pages : 11

c U : 11

General Instructions :

1. All questions are compulsory.

2. The question paper consists of 34 questions divided into four sections A, B, C and D.Section - A comprises of 10 questions of 1 mark each, Section - B comprises of 8 questions of2 marks each, Section - C comprises of 10 questions of 3 marks each and Section - D comprisesof 6 questions of 4 marks each.

3 . Question numbers 1 to 10 in Section - A are multiple choice questions where you are to selectone correct option out of the given four.

4. There is no overall choice. However, internal choice has been provided in 1 question of twomarks, 3 questions of three marks each and 2 questions of four marks each. You have toattempt only one of the alternatives in all such questions.

5. Use of calculator is not permitted.

6. An additional 15 minutes time has been allotted to read this question paper only.

1.

2. -

34 ,

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10 U

1

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8

2

, -

10

3 , - 6 U 4

3. - 1

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4. U , U

1

2 ,

3

3 U

2

4 U

5. U

6. -

15 U U U

- U- S U


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SECTION - A

Question numbers 1 to 10 carry 1 mark each. For each of these questions 4alternatives are given, out of which only one is correct. Choose the correct one.

1. If x53is one root of the quadratic equation x222kx2650, then value of k is

(A) 1 (B) 2 (C)1

2

(D)1

3

2. If a11, 2a11, 4a21 are in A.P., then value of a is :

(A) 1 (B) 2 (C) 3 (D) 4

3. The area of sector of central angle x8 of a circle with radius 4r is

(A)4

360

xp

(B)2

2 r

45

xp(C)

2r

360

xp(D)

2 r

360

xp

4. A garden roller has a circumference of 4 m. The no. of revolutions it makes in moving40 metres are :

(A) 12 (B) 16 (C) 8 (D) 10

5. Two concentric circles are of radii 5 cm and 4 cm. The length of the chord of biggercircle which touches the smaller circle is :

(A) 8 cm (B) 10 cm (C) 4 cm (D) 6 cm

6. In Fig. 1, O is centre of a circle, MN is chord and the tangent ML at M makes an angle

of 708 with MN then MON is equal to :

(A) 1208 (B) 908 (C) 1408 (D) 708

7. The distance between two parallel tangents of a circle of radius 5 cm is :

(A) 5 cm (B) 10 cm (C) 15 cm (D) 2.5 cm

8. A quadrilateral ABCD is drawn to circumscribe a circle. If AB512 cm, BC515 cmand CD514 cm, then AD is :

(A) 10 cm (B) 11 cm (C) 12 cm (D) 14 cm


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9. A pole 6 metre high casts a shadow 2 3 mt. on the ground, then the suns elevation

is :

(A) 608 (B) 458 (C) 308 (D) 908

10. A bag contains cards which are numbered from 2 to 90. A card is drawn at random

from the bag. The probability that it bears a two digit number is :

(A)88

92(B)

88

90(C)

81

89(D)

89

90

SECTION - B

Question numbers 11 to 18 carry 2 marks each.

11. Determine the 2nd term of an A.P. whose 6th term is 12 and 8th term is 22.

OR

Find the sum of first 10 terms of the sequence { an

} where an5526n, where n is a natural

number.

12. For what values of k does (k212)x212(k212)x1250 have equal roots ?

13. In Fig.2, a circle touches the side BC of DABC at P and touches AB and AC producedat Q and R respectively. If AQ55 cm. Find the perimeter of DABC.

14. In Fig.3, sectors of two concentric circles of radii 7 cm and 3.5 cm are given. Find the

area of shaded region.22

use7

p5

15. A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. Thediameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the

inner surface area of the vessel.

22Take

7

p5


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16. If points A(22, 21), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogramABCD, find the values of a and b.

17. Find the value of x such that PQ5QR where the coordinates of P, Q and R are (6, 21),(1, 3) and (x, 8) respectively.

18. Two dice are thrown simultaneously. Find the probability that the sum of the twonumbers appearing on their tops is less than or equal to 10.

SECTION - C


19. If the sum of first m terms of an A.P. is n and the sum of first n terms is m, then showthat the sum of its first (m1n) terms is 2(m1n).

20. Solve for x :

4 3 2 1 1 310 3,

2 1 4 3 2 4

x xx ,

x x

2 12 5 2

1 2

OR

find the value of x for the following :

1 1 114, 7

4 7 30, x

x x

2 5 21 2

21. Prove that the angle between the two tangents to a circle drawn from an external

point, is supplementary to the angle subtended by the line segment joining the pointsof contact at the centre.

22. Draw a DABC with side BC56 cm, AB55 cm and ABC5608. Construct a DA'BC'

similar to DABC such that sides of DA'BC' are3

4of the corresponding sides of DABC.

23. Find the area of the shaded region in Fig.4, if PR524 cm, PQ57 cm and O is the centre

of the circle.22

use 7

p5

OR


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Find the area of the shaded region in Fig.5, where ABCD is a square of side 14 cm andfour circles are each of same radius.

24. Solid spheres of diameter 6 cm are dropped into a cylindrical beaker containing somewater and are fully submerged. If the diameter of the beaker is 18 cm and the waterrises by 40 cm, find the number of solid spheres dropped in the water.

25. Find the value of k for which the points A(21, 3), B(2, k) and C(5, 21) are collinear.

26. Find the lengths of the medians AD and BE of the triangle ABC whose vertices areA(1, 21), B(0, 4) and C(25, 3).

OR

Find the coordinates of the points of trisection of the line segment joining (1, 22) and(23, 4).

27. The angle of elevation of the top of a tower from two points distant a and b from the

base and in the same straight line with it are complementary. Prove that the height of

tower is ab .

28. A bag contains 5 white balls, 7 red balls, 4 black balls and 2 blue balls. One ball isdrawn at random from the bag. What is the probability that the ball drawn is :

(I) white or blue

(II) not white

(III) neither white nor black

SECTION - D


29. A motor boat whose speed is 18 km/hr in still water takes 1 hr. more to go 24 kmupstream than to return downstream to the same spot. Find the speed of stream.

30. A contractor on construction job specifies a penalty for delay of completion beyond acertain date as follows : Rs 200 for the first day, Rs. 250 for the second day, Rs. 300 forthe third day etc., the penalty for each succeding day being Rs. 50 more than for thepreceeding day. How much money the contractor has to pay as penalty if he has

delayed the work by 30 days ?


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31. Prove that the lengths of tangents drawn from an external points to a circle are equal.

OR

In Fig. 6, XY and X'Y' are two parallel tangents to a circle with centre O and anothertangents AB with point of contact C intersecting XY at A and X'Y' at B. Prove that

AOB5908.

32. In Fig.7, ABC is a quadrant of a circle of radius 14 cm and a semi circle is drawn withBC as diameter. Find the area of shaded region.

33. A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindricaltank in her field, which is 10 m in diameter and 2 m deep. If water flows through thepipe at the rate of 3 km/hr, in how much time will the tank be filled ?

34. The angle of elevation of an aeroplane from a point A on the ground is 608. After aflight of 30 seconds, the angle of elevation changes to 308. If the plane is flying at a

constant height of 3600 3 mt., find the speed of the plane in km/hour.

OR

The angle of elevation of the top of a building from the foot of tower is 30 8 and theangle of elevation of the top of the tower from the foot of the building is 608. If thetower is 50 m high, find the height of the building.

- o O o -


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-

1

10

1

1. x53 m U x222kx2650 ,

k

(A) 1 (B) 2 (C)

1

2 (D)

1

3

2. a11, 2a11, 4a21 ,

a

(A) 1 (B) 2 (C) 3 (D) 4

3. 4r

x8

(A)4

360

xp

(B)2

2 r

45

xp(C)

2r

360

xp(D)

2 r

360

xp

4. l U U

4

40 U U R ,

(A) 12 (B) 16 (C) 8 (D) 10

5.

5

4 , U U S U ,

(A) 8

(B) 10

(C) 4

(D) 6

6.

1 ,

O ,

MN

M S U

ML

MN

708

MON U

1

(A) 1208 (B) 908 (C) 1408 (D) 708

7. 5 U S U U U

(A) 5 (B) 10 (C) 15 (D) 2.5

8. U

ABCD

AB512 ,

BC515 CD514

AD

U

(A) 10 (B) 11 (C) 12 (D) 14


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9. 6 2 3 U ,

(A) 608 (B) 458 (C) 308 (D) 908

10. U U

2

90 U U

U U

(A)88

92(B)

88

90(C)

81

89(D)

89

90

-

11 18 2

11. U U U

12 U

22

{ an

} an5526n

n

, 10

12. k (k212)x212(k212)x1250 ?

13.

2

ABC

BC

P S U

AB

AC

R Q R S U AQ55 DABC U

2

14.

3 ,

7

3.5 U

22

7

p5

3

15. U U U

14

13

U c

22

7

p5


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16.

A(22, 21), B(a, 0), C(4, b)

D(1, 2)

ABCD

a

b

17. x

PQ5QR ,

P, Q

R R

(6, 21), (1, 3)

(x, 8)

18. U U

10

-

19 28 3

19.

m

n

n

m ,

(m1n) 2(m1n)

20. x

4 3 2 1 1 3

10 3,2 1 4 3 2 4

x xx ,

x x

2 12 5 2

1 2

x

1 1 114, 7

4 7 30, x

x x2 5 2

1 2

21. h S U , S

U U m U U U U

22.

DABC

BC56 ,

AB55 ABC5608

DA'BC'

U DABC

M DABC

3

4

23. 4 U , PR524 , PQ57 O

22

7

p5

4


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5

U ABCD

14

U

5

24. 6 U U , U ,

U U U U 18 40 h , U

25. k

A(21, 3), B(2, k) C(5, 21) U

26.

DABC

AD

BE

A(1, 21),

B(0, 4) C(25, 3)

(1, 22) (23, 4)

U U U

27. U U

a b U S U U

U h U

ab

28.

5 ,

7 ,

4

2 U

(I) (II)

(III)

-

29 34 4

29. U U, S

18 U ,

24 U , U

U 1

U U

30. U , U U ,

200

L , U 250

L , U

300

L . , U U 50

L .

U U M U U , 30

?


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31. h s U S U ?

6

,XY

X'Y', O

S U S C

S

U AB , XY

A

X'Y'

B

U U

h AOB5908

6

32. 7 , ABC 14 Z BC U

U

7

33 . 10 2 U U 20 U

m U 3

U U ,

U U ?

34.

A

608

30

308

3600 3

S U U U

- 308

- U

608 50 ,

- o O o -

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Mathematics Grade X SA II Papers (22)