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SUMMATIVE ASSESSMENT –I (2011)

Lakdfyr ijh{kk &I MATHEMATICS / xf.kr

Class – IX / & IX

Time allowed: 3 hours Maximum Marks: 90 fu/kkZfjr le; % 3 ?k.Vs vf/kdre vad % 90

General Instructions:

(i) All questions are compulsory.

(ii) The question paper consists of 34 questions divided into four sections A,B,C and D. Section

A comprises of 8 questions of 1 mark each, section B comprises of 6 questions of 2 marks

each, section C comprises of 10 questions of 3 marks each and section D comprises 10

questions of 4 marks each.

(iii) Question numbers 1 to 8 in section-A are multiple choice questions where you are to select

one correct option out of the given four.

(iv) There is no overall choice. However, internal choice have been provided in 1 question of

two marks, 3 questions of three marks each and 2 questions of four marks each. You have

to attempt only one of the alternatives in all such questions.

(v) Use of calculator is not permitted.

lkekU; funsZ”k %

(i) lHkh iz”u vfuok;Z gSaA

(ii) bl iz”u i= esa 34 iz”u gSa, ftUgsa pkj [k.Mksa v, c, l rFkk n esa ckaVk x;k gSA [k.M & v esa 8 iz”u gSa ftuesa

izR;sd 1 vad dk gS, [k.M & c esa 6 iz”u gSa ftuesa izR;sd ds 2 vad gSa, [k.M & l esa 10 iz”u gSa ftuesa

izR;sd ds 3 vad gS rFkk [k.M & n esa 10 iz”u gSa ftuesa izR;sd ds 4 vad gSaA

(iii) [k.M v esa iz”u la[;k 1 ls 8 rd cgqfodYih; iz”u g S a tgka vkidks pkj fodYiksa esa ls ,d lgh fodYi pquuk

gSA

(iv) bl iz”u i= esa dksbZ Hkh loksZifj fodYi ugha gS, ysfdu vkarfjd fodYi 2 vadksa ds ,d iz”u esa, 3 vadksa ds 3

iz”uksa esa vkSj 4 vadksa ds 2 iz”uksa esa fn, x, gSaA izR;sd iz”u esa ,d fodYi dk p;u djs aA

(v) dSydqysVj dk iz;ksx oftZr gSA

Section-A

Question numbers 1 to 8 carry one mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice.

1. A rational number equivalent to a rational number

7

19 is :

460044

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(A) 17

119 (B)

14

57 (C)

21

38 (D)

21

57

7

19

(A) 17

119 (B)

14

57 (C)

21

38 (D)

21

57

2. The value of k for which (x1) is a factor of the polynomial 4x3

3x24xk is :

(A) 3 (B) 0 (C) 1 (D) 3

4x33x2

4xk (x1) k

(A) 3 (B) 0 (C) 1 (D) 3

3.

The degree of the polynomial p(x)(x7)3x3 is :

(A) 3 (B) 2 (C) 1 (D) 0

p(x)(x7)3x3

(A) 3 (B) 2 (C) 1 (D) 0

4.

If , then which one of the following expression is

correct :

(A) x3y3

z30 (B)

(C) xyz 3xyz (D) x3y3

z3 3xyz

,

(A) x3y3

z30 (B)

(C) xyz 3xyz (D) x3y3

z3 3xyz

5. The number of lines that can pass through a given point is :

(A) Two (B) None

(C) Only one (D) Infinitely many

1 1 1

3 3 3 0x y z

1 1 1

3 3 3 3 . .x y z x y z

1 1 1

3 3 3 0x y z

1 1 1

3 3 3 3 . .x y z x y z

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(A) (B)

(C) (D)

6.

If ABC, is right angled at B, then :

(A) ABAC (B) AC < AB (C) ABBC (D) AC > AB

ABC B

(A) ABAC (B) AC < AB (C) ABBC (D) AC > AB

7.

The sides of a are 7 cm, 24 cm and 25 cm. Its area is :

(A) 168 cm2 (B) 84 cm2

(C) 87.5 cm2 (D) 300 cm2

7 24 25

(A) 168 2 (B) 84 2

(C) 87.5 2 (D) 300 2

8.

The sides of a triangular plot are in the ratio 4 : 5 : 6 and its perimeter is 150 cm. Then the

sides are

(A) 4 cm, 5 cm, 6 cm (B) 40 cm, 50 cm, 60 cm

(C) 8 cm, 10 cm, 12 cm (D) 120 cm, 150 cm, 180 cm

4 : 5 : 6 150

(A) 4 , 5 , 6 (B) 40 , 50 , 60

(C) 8 , 10 , 12 (D) 120 , 150 , 180

Section-B Question numbers 9 to 14 carry two marks each.

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9. Simplify

3264

25

.

3264

25

.

10. For what value of k is the polynomial (2x4

3x32kx2

3x6)

exactly divisible by (x2) ?

k (2x43x3

2kx23x6), (x2)

11. Find the coefficient of x in the expansion of (x3)3.

(x3)3 x

12.

In the figure given below, if PSRQ, then prove that PRSQ.

PSRQ PRSQ.

13.

In the given figure, OA, OB are opposite rays and AOC BOD90. Find COD.

OA OB AOC BOD90 COD

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OR In the given figure, ABC is a triangle in which ABAC and AD is an altitude on BC. Prove

that AD bisects .

ABC ABAC AD BC AD,

14. In which Quadrant, can a point have :

(i) abscissa equal to its ordinate

(ii) ordinate equal in magnitude to abscissa

(iii) ordinate equal and opposite of abscissa

(iv) abscissa twice that of the ordinate

(i)

A

A

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(ii)

(iii)

(iv)

Section-C Question numbers 15 to 24 carry three marks each.

15. Represent 5 on the number line.

5

OR

Simplify :

16.

If ab then find the values of a and b.

ab a b

17.

Expand .

OR

If ab8 and a2b2

40 find the value of a3b3.

ab8 a2b2

40 a3b3

18. If x2y6 then find the value of x3

8y336xy216.

p q r p

r q

2 .2

2

p q r p

r q

2 .2

2

5 2 3

7 4 3

3

5 2 3

7 4 3

3

314

3x

314

3x

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x2y6 x38y3

36xy216

19. In given figure QPML. Find the value of x.

QPML ‘x’

OR Show that the bisectors of the base angles of a triangle can never enclose a right angle.

90

20. In the given figure, PQR PRQ, then prove that PQS PRT.

PQR PRQ PQS PRT.

21. In right triangle ABC, C90, M is midpoint of hypotenuse AB. C is joined to M and

produced to a point D such that DMCM. Point D is joined to point B. Show that

(i) AMC BMD (ii) DBC ACB

ABC C90 AB M C M D

DMCM D B

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(i) AMC BMD (ii) DBC ACB

22. ABC is an isosceles triangle in which ABAC. Side BA is produced to D such that

ADAB. Show that BCD is a right angle.

ABC ABAC BA D ADAB.

BCD

23. In Fig. given below, ABCDEF and AEEF. If DEF50 then find the values of x, y and z.

ABCDEF AEEF . DEF50 , x, y z

24. A rhombus shape field has green grass for 18 cows to graze. If each side of the rhombus is

30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting ?

18 30

48

Section-D Question numbers 25 to 34 carry four marks each.

25. Simplify :

6 3 4 3

2 3 6 3 6 2

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6 3 4 3

2 3 6 3 6 2

OR Express as a fraction in simplest form.

26.

Insert five rational numbers between

5

7 and

4

9 .

5

7

4

9

27. Verify :

x3y3

z33xyz (xyz) [ (xy)2(yz)2(zx)2] and then

factorise : 64x3125 y3

64z3240xyz.

x3y3

z33xyz (xyz) [ (xy)2(yz)2(zx)2]

64x3125 y3

64z3240xyz.

28.

Simplify by factorization :

29. If abc6, find the value of : (2a)3(2b)3(2c)33(2a)(2b)(2c).

abc6, (2a)3(2b)3(2c)33(2a)(2b)(2c)

OR

Factorize : .

2 36 0.23.

2 36 0.23.

1

2

1

2

2

2

9 2 3

3

x x

x

2

2

9 2 3

3

x x

x

23

3 2

1 27a 9a27a

4b64b 16b

23

3 2

1 27a 9a27a

4b64b 16b

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30. Prove that the difference of any two sides of a triangle is less than the third side.

31.

m and n are plane mirrors perpendicular to each other. Prove that incident ray CA (to mirror

n) is parallel to reflected ray (to mirror m) BD.

m n CA ( n )

BD ( m )

32.

In figure below, two isosceles triangles ABC and DBC have a common base BC. Prove that the

line joining their vertices is the perpendicular bisector of the base.

BC ABC DBC

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33.

In the given figure, PQRS is a square and SRT is an equilateral triangle. Prove that :

(i) PST QRT

(ii) PTQT

(iii) QTR15

PQRS SRT

(i) PST QRT

(ii) PTQT

(iii) QTR15

34. Prove that two triangles are congruent if any two angles and the included side of one triangle

is equal to any two angles and the included side of the other triangle.

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