2012 10 Lyp Mathematics Sa2 02

7/27/2019 2012 10 Lyp Mathematics Sa2 02

1/11

1

041/X/SA2/03/C1

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 ,

U , ,

-

10 U

1

, -

8

2

, -

10

3

, - 6 U 4

3. - 1

10 U

4. U , U

1

2 ,

3

3 U

2

4 U

5. U

6. -

15 U U U

- U- S U


2/11

2041/X/SA2/03/C1

SECTION - A

Question numbers 1 to 10 carry 1 mark each. Each of these questions has beenprovided with four alternative choices of which only one is correct. You have toselect the correct choice.

1. If 8 is a root of the equation x2210x1k50, then the value of k is.

(A) 2 (B) 8 (C) 28 (D) 16

2. Which term of the A.P. 1, 4, 7, ..... is 88 ?

(A) 26 (B) 27 (C) 30 (D) 35

3. In fig. 1, PT and PT are tangents to the circle with centre O. If TRT 70 5 8 , then xequals.

(A) 308 (B) 358 (C) 408 (D) 508

4. In fig. 2, two concentric circles of radii a and b (a > b) are given. The chord AB of largercircle touches the smaller circle at C. The length of AB is

(A) 2 2a b2 (B) 2 2a b1 (C) 2 22 a b1 (D) 2 22 a b2

5. The length of tangent drawn from an external point P to a circle with centre O, is 8 cm.If the radius of the circle is 6 cm, then the length of OP (in cm) is :

(A) 2 7 (B) 4 7 (C) 10 (D) 10.5

6. The sides of a triangle (in cm) are given below : In which case, the construction of D isnot possible ?

(A) 8, 7, 3 (B) 8, 6, 4 (C) 8, 4, 4 (D) 7, 6, 5


3/11

3041/X/SA2/03/C1

7. In fig. 3, area of shaded region is :

(A) p (r11r

2) (B) p (r

121r

22) (C) p (r

12r

2) (D) p (r

222r

12)

8. If the radius of base of a cylinder is doubled and the height remains unchanged, itscurved surface area becomes.

(A) double (B) three times (C) half (D) no change

9. A pole 6 m high casts a shadow 2 3 m long on the ground, then the suns elevation is.

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

10. Two coins are tossed together. The probability of getting Head on both is :

(A) 0 (B)1

4(C)

1

2(D)

3

4

SECTION - B

Question numbers 11 to 18 carry 2 marks each.

11. Find the values of k for which roots of the equation x228 kx12k50 are equal.

12. The 8th term of an A.P. is 37 and its 12th term is 57. Find the A.P.

13. Prove that tangents drawn at the end-points of a diameter of a circle are parallel.

14. If the area and circumference of a circle are numerically equal, then find the radius ofthe circle.

15. The radius of the base and the height of a right circular cylinder are in the ratio of 2 : 3and its volume is 1617 cu.cm. Find the curved surface area of the cylinder.

(Use p522

7).

16. If A and B are the points (22, 22) and (2,24) respectively find the coordinates of P on

the line segment AB such that AP5

3

7 AB.


4/11

4041/X/SA2/03/C1

17. Show that the points (1, 21), (5, 2) and (9, 5) are collinear.

OR

Find those points on the x-axis which are at a distance of 5 units from the point(5, 23).

18. A bag contains 2 green, 3 red and 4 black balls. A ball is taken out of the bag atrandom. Find the probability that the selected ball is (i) not green (ii) not black.

SECTION - C


19. Solve for x : 7 x226x213 7 50.

OR

Solve for x :1 1 1

; 3, 53 5 6

x

x x

2 5 22 1

20. Find three numbers in A.P. whose sum is 15 and the product is 80.

21. In fig. 4, from an external point P, PA and PB are tangents to the circle with centre O.If CD is another tangent at point E to the circle and PA512 cm. Find the perimeter ofD PCD.

OR

In fig. 5, tangent segments PS and PT are drawn to a circle with centre O such that

SPT 120 . 5 8 Prove that OP52 PS.

22. Construct a D ABC in which BC55 cm, CAB 120 5 8 and ABC 30 5 8 . Then

construct another triangle whose sides are4

5times the corresponding sides of D ABC.

P


5/11

5041/X/SA2/03/C1

23. In fig. 6, ABCD is a square of side 8 cm CBED and ADFB are quadrants of circle. Findthe area of the shaded region. (Use p53.14).

OR

The length of a rope by which a cow is tethered is increased from 16 m to 23 m. How

much additional area can the cow graze now ? [ Use p522

7].

24. A toy is in the form of a cone mounted on a hemisphere of base radius 3.5 cm. The total

height of toy is 15.5 cm. Find the total surface area of the toy. (Use p522

7)

OR

Find the volume of the largest right circular cone that can be cut out of a cube of side

4.2 cm. (Take p522

7)

25. If the shadow of a tower is 30 m long, when the suns elevation is 30 8. What is the

length of the shadow, when suns elevation is 608 ?

26. Find the area of a rhombus if its vertices are (3, 0), (4, 5), (21, 4) and (22, 21) takenin order.

27. Find the area of the triangle formed by joining the mid-points of the sides of the trianglewhose vertices are (0, 21), (2, 1) and (0, 3).

28. A bag contains 19 cards, bearing numbers 1, 2, 3, ....... , 19. A card is drawn at randomfrom the bag. Find the probability that number on the drawn card is.

(i) prime (ii) Divisible by 3

SECTION - D


29. Three consecutive positive integers are taken such that the sum of the square of the firstand the product of the other two is 154. Find the integers.

30. The 4th term of an A.P. is equal to 3 times the first term and the 7th term exceeds twicethe 3rd term by 1. Find the A.P.

OR

Find the sum of all multiples of 9 lying between 300 and 700.


6/11

6041/X/SA2/03/C1

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

32. In fig. 7, OPQR is a rhombus whose three vertices P, Q, R lie on a circle of radius 8 cm.Find the area of the shaded region.

OR

In fig. 8, AC524 cm, BC510 cm and O is the centre of the circle. Find the area of theshaded region. (Use p53.14)

33. A well of diameter 3 m is dug 14 m deep. The earth taken out of it is spread evenly allaround it to a width of 4 m, to form an embankment. Find the height of the embankment.

(Use p522

7).

34. Two men on either side of a cliff, 60 m high, observe the angles of elevation of the topof the cliff to be 458 and 608 respectively. Find the distance between two men.

- o O o -


7/11

7041/X/SA2/03/C1

-

1

10

1

U

1. U x2210x1k50 8 , k

(A) 2 (B) 8 (C) 28 (D) 16

2. 1, 4, 7, ____ 88 ?

(A) 26 (B) 27 (C) 30 (D) 35

3. PT PT, O S U TRT 70 5 8 , x

1

(A) 308 (B) 358 (C) 408 (D) 508

4.

2 ,

a

b (a > b)

AB, U U

C

U S U ,

2

(A) 2 2a b2 (B) 2 2a b1 (C) 2 22 a b1 (D) 2 22 a b2

5. O s P S U 8 6

, OP ( )

(A) 2 7 (B) 4 7 (C) 10 (D) 10.5

6. ( )

D U ?

(A) 8, 7, 3 (B) 8, 6, 4 (C) 8, 4, 4 (D) 7, 6, 5


8/11

8041/X/SA2/03/C1

7.

3 , U

3

(A) p (r11r

2) (B) p (r

121r

22) (C) p (r

12r

2) (D) p (r

222r

12)

8. U , U , D

(A) (B) (C) (D) U

9.

6 . U U

2 3 .

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

10. P U U

(A) 0 (B)1

4(C)

1

2(D)

3

4

-

11 18 2

11. U x228 kx12k50

k

12. 8 37 12 57 U

13. h U S U

14. U M ,

15.

2 : 3

1617

D (p5

22

7

)

16.

A

B

(22,22) (2,24) , U U

AB S

P

AP5

3

7 AB


9/11

9041/X/SA2/03/C1

17.

(1, 21), (5, 2) (9, 5) U

x- U

(5, 23)

5 U U

18.

2 U ,

3

4 U

(i)

U (ii)

-

19 28 3

19. x : 7 x226x213 7 50.

x

:1 1 1

; 3, 53 5 6

x

x x

2 5 22 1

20.

15

80

21.

4 ,

O U s

P

PA

PB S U

E U

CD

S U PA512 , DPCD U

4

5

,O

PS

PT

S U SPT 120 5 8 h

OP52 PS

5

22.

DABC U

BC55

, CAB 120 5 8 ABC 30 5 8 U

U DABC

45

P


10/11

10041/X/SA2/03/C1

23.

6

ABCD,

8

CB EDC

ADF BA Z U

(p53.14

)

6

US , , 16

23

?

[p5

22

7

]

24. U U 3.5

15.5

D (p5

22

7

)

4.2 U

(p522

7 )

25.

308 U U U

30

608

, U U U ?

26.

(3, 0), (4, 5), (21, 4) (22,21) ,

27. ,

(0, 21), (2, 1)

(0, 3) ,

28. U 1, 2, 3, _____, 19 U U

U

(i) (ii) 3


11/11

11041/X/SA2/03/C1

-

29 34 4

29. Z

154 Z

30. U

300 700 9

31. h s S U

32.

7 ,

OPQR

P, Q

R ,

8 ,

S U

7

8 ,

AC524

BC510

O U

(p53.14

)

8

33. 3

14 U ^

4 U U

U U (p522

7 )

34. 60 U U U

458

608 U

- o O o -

Date post:	02-Apr-2018
Category:	Documents
Upload:	govind-sai
View:	216 times
Download:	0 times

2012 10 Lyp Mathematics Sa2 02

Documents