paper - i (quantitative abilities) iz'u i=k & .888 888 888 888 888 888 ... if f(x)= 4x3 – 2x2 +

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1. Ram borrows ` 6800 at 121

2% per annum

compound interest. He agrees to pay in twoequal instalments. Find his eachinstallemnt.

(A) ` 4000 (B) ` 4500(C) ` 4050 (D) ` 3890

2. Find the value of cos20cos40cos60cos80

(A)1

16(B)

3

16(C) 1 (D) 0

3. If 2 4 8x y z , and 1 1 1

72 4 8x y z

; then

find the value of x.

(A) 4 (B)1

4

(C)7

16(D)

16

7

4. The diameters of two cylinders, whosevolumes are equal, are in the ratio 3 : 2Their heights will be in the ratio(A) 4 : 9 (B) 5 : 6(C) 5 : 8 (D) 8 : 9

5. Average of 11 numbers is 36, whereasaverage of 9 of them is 34. If the remainingtwo numbers are in the ratio 2 : 3, thenfind the smaller number (betweenremaining two numbers).(A) 36 (B) 35(C) 48 (D) 54

6- The average weekly salary of A, B and Cis ` 4,000 and that of B, C and D is `5,000. If the weekly salary of A is ` 2,750then the weekly salary of D is(A) ` 5, 750 (B) ` 4, 750(C) ` 5, 280 (D) ` 3, 800

7. Find the minimum value of sincos

(A)1

8(B)

1

8

(C)1

4 (D)

1

4

8- If x = 19 and y = 18, then the value of

33

22

yx

xyyx

is

(A) 1 (B) 37(C) 324 (D) 361

PAPER - I (QUANTITATIVE ABILITIES)

iz'u i=k & I (ifjek.kkRed vfHk#fp)

1. jke 121

2% okf"kZd pof C;kt dh nj ij ` 6800

.k ysrk gSA og bls nks leku okf"kZd fdLrksa esa ykSVkus ijlger gksrk gSA mldk izR;sd fdLr crk,A(A) ` 4000 (B) ` 4500

(C) ` 4050 (D) ` 3890

2. cos20 cos40 cos60 cos80 dk eku Kkr djsaA

(A)1

16(B)

3

16

(C) 1 (D) 0

3. ;fn 2 4 8x y z vkSj 1 1 1

72 4 8x y z

gks] rks x

dk eku Kkr dhft,A

(A) 4 (B)1

4

(C)7

16(D)

16

7

4- nks leku vk;ru okys csyu dk O;kl 3 % 2 osQ vuqikresa gSA mudh pkb;ksa esa vuqikr gksxk&(A) 4 : 9 (B) 5 : 6(C) 5 : 8 (D) 8 : 9

5. 11 la[;kvksa dk vkSlr 36 gS, tcfd muesa ls 9 dk vkSlr34 gSA ;fn 'ks"k nks la[;kvksa dk vuqikr 2 : 3 gks rks NksVhla[;k ('ks"k nks la[;kvksas esa) fudkysaA(A) 36 (B) 35(C) 48 (D) 54

6- A, B rFkk C dk lkIrkfgd vkSlr osru ` 4]000 rFkkB, C vkSj D dk ` 5]000 gSA ;fn A dk lkIrkfgdosru ` 2750 gS] rks D dk lkIrkfgd osru gksxk&(A) ` 5, 750 (B) 4, 750(C) ` 5, 280 (D) 3, 800

7. sincosdk U;wure eku crk;sA

(A)1

8(B)

1

8

(C)1

4 (D)

1

4

8- ;fn x = 19 rFkk y = 18 gks rks 3322

yx

xyyx

dk eku gksxk &

(A) 1 (B) 37

(C) 324 (D) 361

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2007, OUTRAM LINES, 1ST FLOOR, OPPOSITE MUKHERJEE NAGAR POLICE STATION, DELHI-110009

9. Let K be a positive integer such that k + 4is divisible by 7. Then the smallest positiveinteger n, greater than 2, such that k +2nis divisible by 7 is -

(A) 9 (B) 7(C) 5 (D) 3

10. If 31

2

xx , then the value of

(x72 + x66 + x54 +x36 + x24 +x6 + 1)(A) 1 (B) 2(C) 3 (D 4

11. In ABC, A = 80, B = 60. AD is meadianand AE is perpendicular on side BC. FindDAE.

(A) 20 (B) 28(C) 10 (D) 23

12. If P = x

x

sin1

sin1

, Q =

x

x

cos

sin1and R =

x

x

sin1

cos

then which of the following is correct ?

(A) RQP (B) PRQ

(C) QPR (D) RQP

13. A merchant bought 200 eggs, of which 38got broken. He sold the remaining eggs atthe rate of 4.80 per dozen and thus gained8%. The total investment (in `) is :

(A) `120 (B) `80(C) `60 (D) `45

14. The expression 53cot33tan

37cot57tan

is equal to

(A) tan 33cot57 (B) tan 57 cot 57(C) tan 33 cot 53 (D) tan 57 cot 37

15. The simplified form of

1 2 3 4 5 6888 888 888 888 888 888

7 7 7 7 7 7

(A) 5997 (B) 5331(C) 5994 (D) 5328

16. Two poles are 'A' meter apart and the heightof one is double than that of the other. Iffrom the middle point of line joining theirfeet, an observer finds the angular elevationof their tops to be complementary, then theheight of shorter pole is

(A) 4

Ameter (B)

2

Ameter

(C) 2A meter (D) 22

Ameter

17. Base of a right pyramid is a square of area324 m2. If the volume of the pyramid is 1296cu.m., then the area (in m2) of the slantsurface is :(A) 360 (B) 432(C) 540 (D) 1080

9. ekuk fd K ,d /ukRed iw.kkZad la[;k bl izdkj gS fdk + 4, 7 ls foHkkftr gksrk gS] rks 2 ls cM+h U;wure/ukRed iw.kkZad la[;k n, (tks bl izdkj gS fd k +2n, 7ls foHkkftr gks) fudkysa(A) 9 (B) 7(C) 5 (D) 3

10. ;fn 31

2

xx gks] rks (x72 + x66 + x54 +x36 + x24

+ x6 + 1) dk eku gS &(A) 1 (B) 2(C) 3 (D) 4

11. ABC esa A = 80, B = 60, AD ekf;dk gS rFkkAE Hkqtk BC ij yEc gSA DAE dk eku Kkr djsaA(A) 20 (B) 28(C) 10 (D) 23

12. ;fn P = x

x

sin1

sin1

, Q =

x

x

cos

sin1 ,oa R =

x

x

sin1

cos

gS] rks fuEufyf[kr esa ls dkSu lk dFku lR; gS\

(A) RQP (B) PRQ

(C) QPR (D) RQP

13. ,d O;kikjh us 200 vaMs [kjhns ftlesa ls 38 VwV x,A 'ks"kvaMs mlus `4.80 izfr ntZu dh nj ls csp fn, vkSj blizdkj mls 8% dk ykHk gqvkA dqy fuos'k (` esa) gSA(A) `120 (B) `80(C) `60 (D) `45

14. O;tad 53cot33tan

37cot57tan

dk eku gS &

(A) tan 33cot57 (B) tan 57 cot 57(C) tan 33 cot 53 (D) tan 57 cot 37

15.1 2 3 4 5 6

888 888 888 888 888 8887 7 7 7 7 7

dk

ljyhr :i gS&(A) 5997 (B) 5331(C) 5994 (D) 5328

16. nks [kEHks ,d nwljs ls A* ehVj dh nwjh ij gSa vkSj muesa ls,d dh mQpkbZ nwljh ls nqxquh gSA ;fn mu nksuksa ds vk/kj dksfeykus okyh js[kk ds chp ls] mu nksuksa [kaHkks ds 'kh"kksZa ds mUu;udks.k ,d nwljs ds vuqiwjd gSa rks NksVs [kaHks dh mQpkbZ gS &

(A) 4

AehVj (B)

2

AehVj

(C) 2A ehVj (D) 22A

ehVj

17. ,d yEc fijkfeM dk vk/kj oxkZdkj gS ftldk {ks=kiQy324 oxZ ehVj gSA ;fn fijkfeM dk vk;ru 1296 ?ku ehVjgS] rks frjNh lrg dk {ks=kiQy (oxZ ehVj esa) gS :(A) 360 (B) 432(C) 540 (D) 1080

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2007, OUTRAM LINES, 1ST FLOOR, OPPOSITE MUKHERJEE NAGAR POLICE STATION, DELHI-110009

18. I is the incentre of a triangle ABC. If

65ABC and 55ACB , then the

value of BIC is

(A) 130 (B) 120

(C) 140 (D) 110

19. The simplified value of 3.36 1.33 2.05 is:

(A) 2.6 (B) 2.61

(C) 3.41 (D) 2.64

20. The ratio between the number of sides oftwo regular polygons is 1 : 2 and the ratiobetween their interior angles is 2 : 3. Thenumber of sides of these polygons arerespectively.(A) 6, 12 (B) 5, 10

(C) 4, 8 (D) 7, 1421. From any point inside an equilateral

triangle, the lengths of perpendiculars onthe sides are a cm, b cm and c cm. Itsarea (in cm2) is :

(A) 2

3

a b c (B) 2

3a b c

(C) 23

3a b c (D)

3

3a b c

22. If f(x)= 4x3 2x2 + 5x 8 is divided by (x 2)then the remainder is(A) 26 (B) 16

(C) 42 (D) 1823. A bag contains ` 1,50-paise and 25-paise

coins in the ratio of 5 : 8 : 16. If the totalamount is ` 520, the number of 25-paisecoins is:

(A) 48 (B) 120

(C) 640 (D) 19224. The product of two expressions is (x 7)

(x2 + 8x + 12). If HCF of these expressions is(x + 6) then their LCM is(A) x2 5x + 14 (B) x2 + 5x 14

(C) x2 5x 14 (D) x2 + 5x + 14

25. If a b c b c a c a b

a b b c c a

and a + b +

c = 0, then

(A) a b c (B) a b c

(C) a b c (D) a b c

26. A batsman scores some runs in his 51stcompletes inning so that his averageincreases from 59.6 to 60. The runs scoredby the batsman in his 51st inning is(A) 75 (B) 70

(C) 100 (D) 80

18. I] f=kHkqt ABC dk var%dsUnz gSA ;fn 65ABC vkSj

55ACB gS] rks dk BIC eku gS &(A) 1300 (B) 1200

(C) 1400 (D) 1100

19. 3.36 1.33 2.05 dk ljyhr eku gS&(A) 2.6 (B) 2.61

(C) 3.41 (D) 2.64

20. nks lecgqHkqt ds Hkqtkvksa dh la[;kvksa dk vuqikr 1% 2 gS,oa muds izR;sd var%dks.k ds eku dk vuqikr 2 % 3 gS]rks mu lecgqHkqt dh Hkqtkvksa dh la[;k ozQe'k% gS&(A) 6] 12 (B) 5] 10(C) 4] 8 (D) 7] 14

21. fdlh leckgq f=kHkqt ds Hkhrj fdlh Hkh fcUnq ls Hkqtkvksa ijMkys x;s yEcksa dh yEckbZ a lseh, b lseh rFkk c lseh gSAmldk {ks=kiQy (oxZ lseh esa) gS :

(A) 2

3

a b c (B) 2

3a b c

(C) 23

3a b c (D)

3

3a b c

22. f(x)= 4x3 2x2 + 5x 8 esa (x 2) ls Hkkx nsus ij'ks"kiQy gS(A) 26 (B) 16

(C) 42 (D) 18

23. ,d FkSyk esa 1,50-iSls vkSj 25-iSls ds flDds 5 : 8 : 16ds vuqikr esa gSaA ;fn dqy jkf'k ` 520 gS] rks 25-iSls dsflDdksa dh la[;k gS&(A) 48 (B) 120

(C) 640 (D) 192

24. nks O;atdsksa dk xq.kuiQy (x 7) (x2 + 8x + 12) gSA ;fnbu O;atdksa dk el (x + 6) gks] rks budk yl gS(A) x2 5x + 14 (B) x2 + 5x 14

(C) x2 5x 14 (D) x2 + 5x + 14

25. ;fn a b c b c a c a b

a b b c c a

rFkk a + b +

c = 0 gks, rks(A) a b c (B) a b c

(C) a b c (D) a b c

26. ,d cYysckt viuh 51oha iw.kZ ikjh esa dqN ju cukrk gS]ftlls mldk vkSlr 59-6 ls c

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27. A sum of money amounts to 500 in 2 yearsand 600 in 3 years at compound interestrate, then the rate percent per annum is :(A) 6% (B) 20%(C) 8% (D) 10%

28. If (b + c), (c + a), (a + b) are in A.P. then

(A) b = a + c (B) 2

cba

(C) 2

bac

(D)

2

cab

29. If sec cos= 3

2, where is a positive

acute angle, then the value of secis:

(A) 0 (B)1