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Section - A ([kaM & v)

1. Find the value of ( )2

3216-

( )2

3216-

dk eku Kkr dhft,A

2. Write the degree of the polynomial ( )2 2 31p p p p+ + +

cgqin ( )2 2 31p p p p+ + + dh ?kkr fyf[k,A

General Instructions :1. The question paper consists of four sections : A, B, C and D.

Section A consists of 4 questions of 1 marks each. Section B consists of 6 questions of 2 marks each. Section C consists of 10 questions of 3 marks each. Section D consists of 11 questions of 4 marks each.

2. All questions are compulsory.3. In questions of construction, the drawing should be neat and clean and exactly as per

the given measurements. Use ruler and compass.4. There is no overall choice. However, internal choices have been given in some

questions.

lkekU; funsZ'k %

1- bl iz'u&i=k ds pkj [k.M gSa & v] c] l vkSj nA [kaM v esa 4 iz'u gSa ftuesa ls izR;sd dk 1 vad gSA [kaM c esa 6 iz'u gSa ftuesa ls izR;sd dk 2 vad gSA [kaM l esa 10 iz'u gSa ftuesa ls izR;sd dk 3 vad gSA [kaM n esa 11 iz'u gSa ftuesa ls izR;sd dk 4 vad gSA

2- lHkh iz'u vfuok;Z gSaA

3- jpuk ds iz'uksa esa] jpuk LoPN rFkk Bhd gksuh pkfg,] tks fd fn;s x;s ekiksa ds vuq:i gksA iqQVs rFkk ijdkj dk iz;ksx djsaA

4- ç'u i=k ds dqN iz'uksa esa dsoy vkarfjd fodYi fn;s x;s gSaA

MATHeMATIcS(Summative Assessment - II)

Time : 3 Hrs. Maximum Marks : 90

1

1

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3. In the word 'rECTANGLE' which letter shows rotational symmetry

of order 2?

fn;s x, 'kCn ^RECTANGLE* esa dkSu lk v{kj ?kw.kZu lefefr dk ?kw.kZu Øe

2 n'kkZrk gS\

4. Write the order of rotational

symmetry of the given figure

at the marked point :

nh xbZ vkÑfr esa fpafgzr fcUnq

ij ?kw.kZu lefefr dk Øe fyf[k,A

Section - B ([kaM & c)

5. Find the value of y, if (100)2 × (10)5 = (1000)y

y dk eku Kkr dhft, ;fn (100)2 × (10)5 = (1000)y

6. Find the value of

eku Kkr dhft,A

( ) ( ){ }1 1 14 2 3- - -- ´

7. Divide ( )6 4 3 22 4 2x x x x- + + + by ( )22 2x

( )6 4 3 22 4 2x x x x- + + + dks ( )22 2x ls Hkkx dhft,A

8. Using factor method, divide the polynomial (z2 + 11z + 24) by (z + 3)

xq.ku[kaM fofèk dk iz;ksx djds cgqin (z2 + 11z + 24) dks (z + 3) ls Hkkx dhft,A

9. Solve the following equation :

fuEu lehdj.k dks gy dhft,A

2 71 33 15x x+ = +

10. Write the order and angle of rotational symmetry of parallelogram.

lekarj prqHkqZt dk ?kw.kZu lefefr Øe vkSj ?kw.kZu lefefr dks.k fyf[k,A

1

1

2

2

2

2

2

2

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Section - c ([kaM & l)

11. Simplify and express the result as a rational number.

ljy dhft,A

2 23 38 27

125 64

-æ ö æ ö÷ ÷ç ç´÷ ÷ç ç÷ ÷ç çè ø è ø

12. Prateek borrowed ` 64,000 from a bank to learn a skill. If the rate of

interest is 25 paise per ten rupees per annum compounded annually,

calculate the amount paid by him after 2 years to clears his debt.

izrhd ,d dkS'ky lh[kus ds fy, ,d cSad ls 64000 :i;s m/kj ysrk gSA ;fn C;kt

dh nj 25 iSls izfr 10 :i;s dh nj ls okf"kZd la;ksftr gksrh gks rks] 2 o"kZ i'pkr~

vius ½.k dh jkf'k pqdkus ds fy, nh xbZ jkf'k dh x.kuk dhft,A

13. Using long division method, show that

(1 + 3x) is a factor of 12x3 – 2x2 + x + 1.

yEcs Hkkx fofèk dk iz;ksx djds] n'kkZb;s fd (1 + 3x)]

12x3 – x2 + x + 1 dk xq.ku[k.M gSA

14. Present ages of Seema and Shruti are in the ratio 4 : 5. Eight years

from now, the ratio of their ages will be 5 : 6. Find their present ages.

lhek vkSj Jqrh dh orZeku vk;q dk vuqikr 4 % 5 gSA vc ls 8 lky ckn] mudh

vk;q dk vuqikr 5 % 6 gksxkA mudh orZeku vk;q Kkr dhft,A

OR (vFkok)

One of the two digits of a two digit number is three times the other

digit. If you inerchange the digits of this two-digit number and add the

resulting number to the original number, you get 88. What is the original

number?

nks vadksa dh ,d la[;k esa ,d vad nwljs ls rhu xq.kk gSA vadksa dks iyVus ij izkIr

la[;k dks ;fn ewy la[;k esa tksM+s rks ;ksx 88 izkIr gksrk gSA ewy la[;k D;k gS\

3

3

3

3

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15. A steamer goes downstream from one port to another in 9 hours. It

covers the same distance up stream in 10 hours. If the speed of the

stream be 1 km/ hr, find the speed of the steamer in still water.

,d LVhej ikuh ds cgko ds lkFk ,d canjxkg ls nwljs canjxkg rd 9 ?kaVs esa igq¡prk

gSA ogh nwjh og ikuh ds cgko ds fo:¼ 10 ?kaVs esa r; djrk gSA ;fn ikuh ds cgko

dh xfr 1 fd-eh- izfr ?kaVk gS rks LVhej dh Bgjs ikuh esa xfr Kkr dhft,A

16. In the given figure, PQRS is a

quadrilateral in which PQ = PS

and QR = SR. Diagonal PR and

QS intersect each other at O.

Show that

(i) DPQR @ DPSR

(ii) DPOQ @ DPOS

fn xbZ vkÑfr esa] prqHkqZt PQRS esa

PQ = PS vkSj QR = SR gSA fod.kZ

PR vkSj QS ,d nwljs dks O ij

dkVrs gSaA n'kkZb, fd &

(i) DPQR @ DPSR

(ii) DPOQ @ DPOS

17. In the given figure, the bisectors

of ∠P and ∠Q meet at a point A.

If ∠R = 1100 and ∠S = 500 ,

find the measure of ∠PAQ.

fn xbZ vkÑfr esa] ∠P vkSj ∠Q ds

lef}Hkktd fcUnq A ij feyrs gSaA

;fn ∠R = 1100 vkSj ∠S = 500 gS rks

∠PAQ dk eku Kkr dhft,A

3

3

3

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18. Construct a quadrilateral PQRS where PQ = 5 cm, QR = 3 cm, RS = 4.5 cm,

SP = 6.5 cm and QS = 6 cm.

,d prqHkqZt PQRS dh jpuk dhft, ftlesa PQ = 5 lseh] QR = 3 lseh] RS = 4.5

lseh] SP = 6.5 lseh vkSj QS = 6 lseh gSA

Alternate question for visually challenged students in lieu of Q. No. 18.

ç'u la[;k 18 ds LFkku ij n`f"V ckfèkr fo|kfFkZ;ksa ds fy,

At what rate percent compound interest per annum will ` 3200 amount to

` 3872 in 2 years?

fdl izfr'kr okf"kZd nj ls 2 o"kZ esa ` 3200 dh jkf'k ` 3872 gks tk,xh] tcfd

C;kt izfro"kZ la;ksftr gksrk gS\

19. An unbiased die is thrown once. What is the probability of getting

(i) an even multiple of 3?

(ii) a number between 3 and 6?

(iii) an odd number?

,d 'kq¼ ikalk ,d ckj isaQdk tkrk gSA izkf;drk Kkr dhft, ;fn izkIr la[;k &

(i) 3 dk le xq.kd gksA

(ii) 3 vkSj 6 ds chp dh la[;k gksA

(iii) ,d fo"ke la[;k gksA

20. The following table shows the spending of pocket money of a student

during a weak. represent it by a pie-chart.

Items Food Entertainment Other Expenditure SavingsExpenditure (in `) 70 45 40 25

fuEu rkfydk ,d Nk=k dh ,d lIrkg ds tsc [kpZ dks n'kkZrh gSA bls ,d o`Ùk fp=k

ls n'kkZb,A

oLrq,¡ [kkuk euksjatu vU; [kpZ cpr[kpZ (:i;ksa esa) 70 45 40 25

3

3

3

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Alternate question for visually challenged students in lieu of Q. No. 20.

ç'u la[;k 20 ds LFkku ij n`f"V ckfèkr fo|kfFkZ;ksa ds fy,

Evaluate : (ljy dhft,)

5 5

4 53 10 125

5 6

- -

- -´ ´

´

Section - D ([kaM & n)

21. If 5x+1 – 5x = 500 then find the value of 4x.

;fn 5x+1 – 5x = 500 gks rks] 4x dk eku Kkr dhft,A

22. Find the amount and compound interest on ` 18,000 for 2½ years at

10% per annum compounded annually.

` 18000 dh jkf'k ds fy, 2½ o"kZ dk 10% okf"kZd nj ls feJ/u vkSj pØo`f¼

C;kt Kkr dhft, tcfd C;kt okf"kZd la;ksftr gksuk gksA

23. The population of a town was 1,60,000 three years ago. It increased by

3%, 2.5% and 5% in last three years. Find its present population.

3 o"kZ igys ,d uxj dh tula[;k 1]60]000 FkhA ;fn tula[;k fiNys rhu o"kks± esa

3%] 2-5% vkSj 5% dh nj ls c<+h rks orZeku esa uxj dh tula[;k Kkr djksA

24. The difference between S.I. and C.I. on a certain sum of money for 2 years

at 4% p.a. is ` 20. Find the sum.

fdlh jkf'k dk 4% okf"kZd nj ls 2 o"kZ ds fy, pØo`f¼ C;kt vkSj lk/kj.k C;kt

dk varj 20 :i;s gS] rks jkf'k Kkr djsaA

OR (vFkok)

The simple interect on a certain sum of money for three years at the rate of

5% p.a. is ̀ 600. What will be the compound interest on that sum at the same

rate and for the same time period, if the interest is compounded annually.

fdlh jkf'k ij 3 lky esa 5% izfro"kZ dh nj ls ` 600 lk/kj.k C;kt feyrk gSA

mlh jkf'k ij] mlh nj vkSj mlh le; esa fdruk pØo`f¼ C;kt feysxk] tcfd C;kt

izfro"kZ la;ksftr gksrk gSA

4

4

4

4

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25. Divide 8p3 – 729 – 108p2 + 486p by (2p – 9) and write down the quotient

and remainder. Also check your answer.

8p3 – 729 – 108p2 + 486p dks 2p – 9 ls Hkkx nhft, vkSj HkkxiQy rFkk 'ks"kiQy

fyf[k,A mÙkj dk lR;kiu Hkh dhft,A

26. ramprakash died leaving one-fourth of his property for his son, one fourth

for his daughter and the rest for his wife. His wife gave one-third of her

property and ` 5000 to the organisation which promotes women's skill

development. If the amount she gave to the organisation was ` 15000, find

the total value of the property and the amount each person got? What value

is shown by the wife?

jkeizdk'k us e`R;q mijkUr viuh lEifr dk ,d pkSFkkbZ vius yM+ds rFkk ,d pkSFkkbZ

yM+dh dks fn;k rFkk 'ks"k Hkkx viuh iRuh dks fn;kA jkeizdk'k dh iRuh us vius fgLls

dh lEifr dk frgkbZ Hkkx rFkk 5000 :i;s ml laLFkk dks fn, tks fd fL=k;ksa esa dkS'ky

dks c<+kok nsrh gSA ;fn bl laLFkk dks 15000 :- dh jkf'k izkIr gqbZ gks rks lEifr

dk dqy ewY; Kkr dhft,A izR;sd O;fDr dks fdruh jkf'k feyhA jkeizdk'k dh iRuh

}kjk fdl ewY; dks n'kkZ;k x;kA

27. The diagonals of a rhombus are in the ratio 3 : 4. If its perimeter is

40 cm, find the lengths of the sides and diagonals of the rhombus.

,d leprqHkqZt ds fod.kks± dk vuqikr 3 % 4 gSA ;fn bldk ifjeki 40 ls-eh- gks

rks leprqHkqZt dh Hkqtkvksa dh yEckbZ rFkk fod.kks± dh yEckbZ Kkr dhft,A

28. ABCD is a rhombus whose diagonals intersect at O. If AB = 10 cm, diagonal

BD = 16 cm, find the ratio of AC and BD.

ABCD ,d vk;r gS ftlds fod.kZ O ij dkVrs gSaA ;fn AB ¾ 10 ls-eh- vkSj

fod.kZ BD = 16 ls-eh- gks rks AC vkSj BD dk vuqikr Kkr dhft,A

29. Using ruler and compass, construct a quadrilateral PQRS, where

PQ = 3.5 cm, QR = 6.5 cm, ∠P = ∠R = 1050 and ∠S = 750 .

iqQVs vkSj ijdkj dk iz;ksx djds prqHkq Zt dh PQRS jpuk dhft, ftlesa

PQ¾ 3-5 ls-eh-] QR ¾ 6-5 ls-eh-] ∠P = ∠R = 1050 vkSj ∠S = 750 gSA

4

4

4

4

4

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Alternate question for visually challenged students in lieu of Q. No. 29.

ç'u la[;k 29 ds LFkku ij n`f"V ckfèkr fo|kfFkZ;ksa ds fy,

I have ` 1000 in ten and five rupee notes. If the number of ten rupee

notes that I have is ten more than the number of five rupee notes, how

many notes do I have of each denomination?

esjs ikl 1000 :i;s 10 vkSj 5 :i;s ds uksVksa esa gSA ;fn esjs ikl 10 :i;s ds uksVksa

dh la[;k 5 :i;s ds uksVksa dh la[;k ls 10 vf/d gks] rks izR;sd oxZ ds uksVksa dh

la[;k fdruh gS\

30. A card is drawn at random from a pack of 52 cards. Find the

probability that the card drawn is :

(i) a face card

(ii) a black card

(iii) other than an ace

(iv) a red king

52 iÙkksa dh ,d rk'k dh xîóh esa ls ,d iÙkk ;kn`PN;k fudkyk tkrk gSA izkf;drk

Kkr dhft, ;fn fudkyk x;k iÙkk gS &

(i) ,d fp=k okyk iÙkkA

(ii) ,d dkyk iÙkkA

(iii) bDds ls vyx dksbZ iÙkkA

(iv) ,d yky ckn'kkgA

31. The given pie-chart represents the

amount spent on different sports

by a school administration in a

year. If the total money spent on

football is ` 10,000, answer the

following questions :

(i) What is the amount spent on sports?

(ii) How much more money is spent on cricket than hockey?

4

4

1000

1400300500

400 Hockey

CricketTennis

Football

Basketball

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(iii) How much money is spent on basketball?

fn;k x;k o`Ùk fp=k ,d o"kZ esa ,d fo|ky; izca/u }kjk fofHkUu [ksyksa ij [kpZ dh

xbZ èkujkf'k dk o.kZu djrk gSA ;fn iqQVcky ij [kpZ dh xbZ dqy /ujkf'k 10]000

:i;s gS rks fuEufyf[kr iz'uksa ds mÙkj nhft, &

(i) [ksyksa ij [kpZ dh xbZ /ujkf'k D;k gS\

(ii) fØdsV ij gkWdh ls fdruh /ujkf'k T;knk [kpZ dh xbZ\

(iii) ckLdsV cky ij [kpZ dh xbZ /ujkf'k D;k gS\

OR (vFkok)

The pulse rate (per minute) of 30 persons was recorded as

Construct a frequency table using class intervals 60-65, 65-70 etc.

Draw histogram also.

30 O;fDr;ksa dh ukM+h dh xfr (izfr feuV dh nj ls) bl izdkj fjdkMZ dh

xbZ Fkh

oxZ vUrjky 60&65] bR;kfn 65&70 dk iz;ksx djds ,d ckjEckjrk lkj.kh cukb,

vkSj ,d vk;r fp=k Hkh cukb,A

Alternate question for visually challenged students in lieu of Q. No. 31.

ç'u la[;k 31 ds LFkku ij n`f"V ckfèkr fo|kfFkZ;ksa ds fy,

Divide 4x (2x3 + 3) + 5(2x3 + 3) by (5+ 4x) and check your answer

4x (2x3 + 3) + 5(2x3 + 3) dks (5+ 4x) ls Hkkx dhft, vkSj mÙkj dh tk¡p dhft,A

61 76 72 73 71 66 78 73 68 81

78 63 72 75 80 68 75 62 71 81

73 60 79 72 73 74 71 64 76 71

61 76 72 73 71 66 78 73 68 81

78 63 72 75 80 68 75 62 71 81

73 60 79 72 73 74 71 64 76 71