Mathematics Sa1 04

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SUMMATIVE ASSESSMENTI (2011)

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MATHEMATICS /xf.kr

Class

X / X

Time allowed : 3 hours Maximum Marks : 80

fu/kkZfjr le; % 3 ?k.Vs : 80

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 10 questions of 1 mark each, section B comprises of 8

questions of 2 marks each, section C comprises of 10 questions of 3 marks each and

section D comprises 6 questions of 4 marks each.

(iii) Question numbers 1 to 10 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; funk

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(ii) bl izu i= esa34 izu gSa,ftUgsapkj [k.Mksav,c,l rFkk n esackaVk x;k gSA [k.M & v esa10 izu gSa

ftuesaizR;sd 1 vad dk gS,[k.M & c esa 8 izu gSa ftuesaizR;sd ds2 vad gSa,[k.M &l esa10 izu gSaftuesaizR;sd ds3 vad gS rFkk [k.M & n esa 6 izu gSa ftuesaizR;sd ds4 vad gSaA

(iii)

[k.M v esaizu la[;k 1 ls10 rd cgqfodYih; izu gSatgkavkidkspkj fodYiksaesals ,d lgh fodYipquuk gSA

(iv) bl izu i= esadksbZ Hkh loksZifj fodYi ugha gS,ysfdu vkarfjd fodYi 2 vadksads,d izu esa,3 vadksads3

izuksaesavkSj 4 vadksads2 izuksaesafn, x, gSaA izR;sd izu esa,d fodYi dk p;u djsaA

(v) dSydqysVj dk iz;ksx oftZr gSA

Section-A

Question numbers 1 to 10 carry one mark each. For each questions, four alternativechoices have been provided of which only one is correct. You have to select thecorrect choice.

560020


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1.Given that HCF (2520, 6600) 40, LCM (2520, 6600) 252k, then the value of kis :

(A) 1650 (B) 1600 (C) 165 (D) 1625

HCF (2520, 6600) 40, LCM (2520, 6600) 252k, k

(A) 1650 (B) 1600 (C) 165 (D) 16252. If , are the zeroes off(x)px22x3p and , then the value of p is :

(A)1

3 (B)

1

3 (C)

2

3 (D)

2

3

f(x)px22x3p , p

(A)1

3 (B)

1

3 (C)

2

3 (D)

2

3

3.In the given figure YXZXPZ, then

ZX

ZYis equal to :

(A) ZYZP (B) XZ2 (C)PZ

XZ (D) PZ2

YXZXPZZX

ZY

(A) ZYZP (B) XZ2 (C)PZ

XZ (D) PZ2

4.If cot

7

8, then tan2equals to :

(A)8

7 (B)

49

64 (C)

64

49 (D)

7

8

cot

7

8 tan2


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(A)8

7 (B)

49

64 (C)

64

49 (D)

7

8

5.

In figure given below,

tan A cot C is equal to :

(A) 713

(B) 713

(C) 512

(D) 0

tan A cot C

(A)7

13 (B)

7

13

(C)

5

12 (D)

6. If cosec2 (1 cos ) (1 cos ) , then the value of is :

(A) 0 (B) cos2 (C) 1 (D) 1

cosec2 (1cos ) (1cos )

(A) 0 (B) cos2 (C) 1 (D) 1

7.From the following, the rational number whose decimal expansion is terminating is :


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(A)2

15 (B)

11

160 (C)

17

60 (D)

6

35

8. If the pair of linear equations a1xb1yc10 and a2xb2yc20 has infinite number of

solutions, then the relation among the coefficients is :

(A) 1 1 1

2 2 2

a b c

a b c (B) 1 1 1

2 2 2

a b c

a b c

(C) 1 1 1

2 2 2

a b c

a b c (D) 1 1 1

2 2 2

a b c

a b c

a1xb1yc10 a2xb2yc20

(A) 1 1 1

2 2 2

a b c

a b c (B) 1 1 1

2 2 2

a b c

a b c

(C) 1 1 1

2 2 2

a b c

a b c (D) 1 1 1

2 2 2

a b c

a b c

9.In fig., if PS14 cm, the value of tan a is equal to :

PS14 tan a

(A)4

3 (B)

14

3 (C)

5

3 (D)

13

3

10.The class mark of the class 29.530.5 is :

(A) 30 (B) 30.5 (C) 31.5 (D) 31

29.530.5

(A) 30 (B) 30.5 (C) 31.5 (D) 31

Section-B

Questions numbers 11 to 18 carry two marks each.

11.Check whether 6n can end with the digit 0 for any natural number n ?


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n 6n

12. What must be added to the polynomial x42x32x2x1 so that the resulting polynomial is

divisible by x22x3 exactly ?

x42x32x2x1 x22x3

13. Solve the following system of linear equations by substitution method :

2xy2

x3y15

2xy2

x3y15

14.If tan

1

7, find the value of

2 2

2 2

cosec sec

cosec sec

.

tan1

7

2 2

2 2

cosec sec

cosec sec

.

OR /

Without using the trigonometric tables, prove that :

tan 9tan 23tan 60tan 67tan 81 3

tan 9tan 23tan 60tan 67tan 81 3

15. In given figure, in ABC ; D, E and F are points on AB, BC and AC respectively such that

ADEF is a parallelogram, then prove that

CF AD

FA BD .

D, E F ABC AB, BC AC ADEF


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CF AD

FA BD .

16.In the given figure ABC is an isosceles triangle with ABAC. D is mid point of BC. If

DE AB, DF AC, prove that DEDF.

ABC ABAC D BC

DE AB DF AC DEDF.

17. Find the mean of the following data :

Classes 06 612 1218 1824 2430 Total

Frequency 6 8 10 9 7 40

0 6 6 12 12 18 18 24 24 30

6 8 10 9 7 40

18. Find the mode of the following data :

Classes 0 25 25 50 50 75 75 - 100 100 - 125 125 150

Frequency 10 30 40 25 20 15


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0 25 25 50 50 75 75 - 100 100 - 125 125 150

10 30 40 25 20 15

Section-C

Questions numbers 19 to 28 carry three marks each.

19.Prove that

7 5

3is an irrational number

7 5

3

20. Show that 4ncan never end with the digit zero for any natural number n.

n 4n

OR /

If d is the HCF of 45 and 27, find x, ysatisfying d27x45y

45 27 HCF, d x y d27x45y

21.Solve :

5 12

x y

6 31 ; 0, 0x y

x y

5 1

2x y

6 31 ; 0, 0x y

x y

OR /

Two women and 5 men can together finish a piece of work in 4 days, while 3 women and 6 men

can finish it in 3 days. Find the time taken by 1 woman alone to finish the work and also time

taken by 1 man alone to finish it.


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4 28 15 20 17 16

OR /

200 surnames were randomly picked up from a local telephone directory and the frequency

distribution of the number of letters in English alphabets in the surnames was obtained as

follows.

No. of letters 15 510 1015 1520 2025

No. of surnames 20 60 80 32 8

Find the median.

200

15 510 1015 1520 2025

20 60 80 32 8

28. Mean of the following data is 21.5. Find the missing value k.

21.5 k

Section-D

Questions numbers 29 to 34 carry four marks each.

29. Find all the zeroes of 2x43x33x26x2, if two of its zeroes are 2 and 2 .

2x43x33x26x2, 2 2

30. Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of

the other two sides.


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OR /

Prove that, if a line is drawn parallel to one side of a triangle to intersect the other two sides in

distinct points, the other two sides are divided in the same ratio.

31.Prove that : sec2

2 4

4 2

sin 2sin

2cos cos

1.

sec22 4

4 2

sin 2sin

2cos cos

1

OR /

If cosecx1

4x

, prove that

coseccot2xor1

2 x

cosecx1

4 xcoseccot2x

1

2 x

32.

Without using trigonometric tables, evaluate the following :

2 22

2 2

cos 20 cos 70 2cosec 58 2cot58 tan32 4tan13 tan37 tan45 tan53 tan77

sec 50 cot 40

2 22

2 2

cos 20 cos 70 2cosec 58 2cot58 tan32 4tan13 tan37 tan45 tan53 tan77

sec 50 cot 40

33. Solve 2xy1 and 3x2y12 graphically. Also find the area of the region bounded by theselines and xaxis.

2xy1 3x2y12 x

34. Change the following frequency distribution to less than type distribution and draw its ogive.

Hence obtain the median value.

Classes 1020 2030 3040 4050 5060 6070 7080


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Frequeny

f

5 15 18 25 11 9 8

1020 2030 3040 4050 5060 6070 7080

f 5 15 18 25 11 9 8

Mathematics Sa1 04

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