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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 gSa 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 es a ,d fodYi dk p;u djsaA

(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.

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1. A rational number equivalent to a rational number

7

19is :

(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. Zeroes of the polynomial x2

4x21 are :

(A) 3 and 7 (B) 3 and 7 (C) 3 and 7 (D) 3 and 7

x24x21

(A) 3 7 (B) 3 7 (C) 3 7 (D) 3 7

3. The value of p for which (x2) is a factor of polynomial x4x32x2px4 is :

(A) 10 (B) 9 (C) 4 (D) 10

(x2) x4x32x2px4 p

(A) 10 (B) 9 (C) 4 (D) 10

4. If the polynomial x3x2x1 is divided by x1, then the quotient is :

(A) x21 (B) x21 (C) x2x1 (D) x2x1

x3x2x1 x1

(A) x21 (B) x21 (C) x2x1 (D) x2x1

5. The things which coincide with one another are :

(A) equal to another (B) unequal

(C) double of same thing (D) Triple of same things

(A) (B)

(C) (D)

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6. In ABC, A100, B30 and C50 then

(A) AB > AC (B) AB < AC

(C) BC < AC (D) none of these

ABC A100, B30 C50

(A) AB > AC (B) AB < AC

(C) BC < AC (D)

7. The perimeter of an equilateral triangle is 60 m then its area is :

(A) 10 3 m2 (B) 15 3 m2

(C) 20 3 m2 (D) 100 3 m2

60

(A) 10 3 2 (B) 15 3 2

(C) 20 3 2 (D) 100 3 2

8. Area of a triangle having base 6 cm and altitude 8 cm is :

(A) 48 cm2 (B) 24 cm2 (C) 64 cm2 (D) 36 cm2

6 8

(A) 48 2 (B) 24 2 (C) 64 2 (D) 36 2

Section-B

Question numbers 9 to 14 carry two marks each.

9. Represent 2 by a point on the real line ?

2

10. If x2 is a factor of ax22x4a9 find a.

ax22x4a9 x2 a

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11. Find the remainder when p (x)x36x22x4 is divided by q (x)12x

p (x)x36x22x4 q (x)12x

12. In figure, it is given that 14 and 32. By which Euclid’s axiom, it can be shown

that if 24 and 13.

14 32

24 13.

13. In the figure below, AXBY and AXBY prove that APX BPY.

AXBY AXBY APX BPY.

OR

In the given figure, ABC is a triangle in which altitudes BE and CF to sides AC and AB

respectively are equal. Show that ABE ACF.

ABC AC AB BE CF

ABE ACF

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14. Plot the points P (1, 1), Q (2, 3) and R (8, 11). Show that they are collinear.

P (1, 1), Q (2, 3) R (8, 11)

Section-C

Question numbers 15 to 24 carry three marks each.

15.

If 3 2

3 2

p

and 3 2

3 2

q

, find p2q2.

3 2

3 2p

3 2

3 2q

p2q2

OR

Simplify : .

.

16.

Represent on the number line.

17. Factorize : (pq)3(qr) 3(rp)3

(pq)3(qr) 3(rp)3

OR

13 41 1

3 35 8 27

13 41 1

3 35 8 27

17

17

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Find the value of ‘k’ for which (x1) is factor of p(x)(kx23xk)

‘k’ (x1) p(x)(kx23xk)

18. Find the value of x3y3

15xy125 when xy5.

x3y3

15xy125 xy5.

19. In the given figure, ABCD. Find the value of x.

ABCD. x

OR In the figure given below, ABCDEF and ABC 60 , CEF 140 , find the value of BCE .

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ABCDEF, ABC 60 , CEF 140 BCE

20. In the figure given below, if ABCD, then find

.

ABCD,

21. ABC and DBC are two isosceles triangles on the same base BC. Show that ABDACD.

ABC DBC BC ABDACD.

FAE 90 and AFE 40 ECD

FAE 90 and AFE 40 ECD

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22.

In figure, ABAD, ACAE and BAD EAC. Prove that BCDE

ABAD, ACAE BAD EAC . BCDE

23. In the given Figure, ABCD and CDEF. Also, EAAB. If BEF55, find the values of x,

y and z.

ABCD CDEF EAAB BEF55 x, y z

24. The sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540 cm.

Find its area.

12 : 17 : 25 540 cm

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Section-D

Question numbers 25 to 34 carry four marks each.

25. Prove that :

1 1 1 1 1

3 7 7 5 5 3 3 1

1 1 1 1 1

3 7 7 5 5 3 3 1

OR

Show that :

26. If ‘x’ is a positive real number and exponents are rational numbers, simplify :

b c a c a b (a b c)b c a

c a b

x x x

x x x

‘x’

b c a c a b (a b c)b c a

c a b

x x x

x x x

27. If the polynomial (2x3ax23x5) and (x3 x22x a) leave the same remainder when

divided by (x2), find the value of a. Also, find the remainder in each case.

(2x3ax23x5) (x3 x22x a) (x2)

‘a’

28. Factorize : 2x2

5

6x

1

12

2x2 5

6x

1

12

1 1 1 1 1 5

3 8 8 7 7 6 6 5 5 2

1 1 1 1 1 5

3 8 8 7 7 6 6 5 5 2

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29. If the polynomials f (x) px34x23x4 and g (x)x34xp are divided by (x3), then the

remainder in each case is the same. Find the value of p.

f (x) px34x23x4 g (x)x34xp x3

p

OR

If 2x3y12 and xy6 find the value of 8x327y3.

2x3y12 xy6 8x327y3

30. (a) Plot the following points in the coordinate plane

A (4, 4) B (6, 0) C (4, 4) D (2, 0)

(b) Name the figure formed by joining the points A, B, C and D and also find its area.

(a)

A (4, 4) B (6, 0) C (4, 4) D (2, 0)

(b) A, B, C, D

31. In the given figure lm , show that 1 2 3180

lm , 1 2 3180

32. In the figure below, PQQR and x y. Prove that ARPB.

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PQQR x y ARPB.

33. In right ABC in given figure, right angled at C, M is the 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 is a right angle

ABC C M

AB C M D

DMCM D B

(i) AMC BMD

(ii) DBC

34. In an isosceles triangle ABC with ABAC the bisector of B and C intersect

each other at O. Join A to O. Show that :

(i) OBOC (ii) AO bisects A

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ABC ABAC B C O A

O

(i) OBOC (ii) AO, A