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01. ` 720 dks A, B, C, D, E ds chp esa ckaVk t kuk gSA mudsn~okjk çkIr èkujkf' k vkjksgh Øe esa vkSj l ekarj Js<+h esa FkhA Edks A l s ` 40 v fèkd çkIr gq, A B dks fdruh èkujkf' k çkIrgqbZ\(1) `134 (2) `144(3) `154 (4) `124

02. fn, x, ] i kbZ pkVZ esa Hkkjr dh eksckby i Qksu fofuekZ.kdai fu; ksa ds ckjs esa t kudkjh çnf' kZr gSA fufeZr eksckby i Qksudh dqy l a[ ; k 12,40,000 gSA

30%

ABC

LMN

DEF

PQR

XYZ28%

12%

25%

5%

dai uh 'LMN' n~okjk dqy fdrus eksckby i Qksu fufeZr fd,x, \(1) 12,40,000 (2) 6,12,000(3) 6,20,000 (4) 3,72,000

03. The area of the triangle whose vertices are givenby (1, 2), (–4, –3) and (4, 1) is:(1) 7 sq. units (2) 10 sq. units(3) 14 sq. units (4) 20 sq. units

04. nks buysV i kbi ] A vkSj B , d [ kkyh Vdh dks Øe' k% 22vkSj 33 ?kaVs esa Hkj l drs gSaA mUgsa , d l kFk [ kksyk x; k ysfduVadh Hkjus l s 3 ?kaVs i gys i kbi A dks can dj fn; k x; kA Vadhdks Hkjus es nksuksa i kbi ksa n~okjk dqy fdrus ?kaVs yxsaxs\(1) 16.2 (2) 15(3) 14.2 (4) 16

05. fn, x, ç' u dks i <sa vkSj fu.kZ; ysa fd fuEufyf[ kr esa l s dkSul h l wpuk ç' u dk mÙkj nsus ds fy, i ; kZIr gSA

ACB dk eku D; k gS\l wpuk%1)

A B

C D

x

2) D 60 (1) ; k rks 1 vFkok 2 i ; kZIr gS(2) 1 vkSj 2 nksuksa gh i ; kZIr gSa(3) dsoy 2 i ; kZIr gS(4) dsoy 1 i ; kZIr gS

06. fuEufyf[ kr esa l s dkSu l k l gh gS\

(1) 9 1316 24

(2) 9 1316 24

(3) 9 1316 24

(4) 9 1316 24

07.

3 3 3a b b c c a?

3 a b b c c a

mi jksDr O; at d dk eku D; k gS\(1) 1 (2) 4(3) 0 (4) 2

08. , d i su dks ` 144 esa cspus i j vuqjkx dks Ø; ewY; i j 1/7 dh gkfu gksrh gSA ; fn i su ` 189 esa cspk t krk] rks ykHkçfr ' kr D; k gksrk\(1) 11% (2) 12.5%(3) 11.5% (4) 14%

09. The HCF of 2 8 10 32, , ,3 9 27 81 is:

(1) 1603 (2) 160

81

(3) 23 (4) 2

8110. vki dks , d ç' u vkSj nks dFku fn, x, gSA ç' u dk mÙkj nsus

ds fy, dkSu l k@l s dFku vko' ; d@i ; kZIr gS@gSa\ç' u%l fCt ; ksa ds 20 fMCcksa dk dqy Hkkj D; k gS\ muesa l s çR; sdcjkcj Hkkj dk gSAdFku%1. i gys 10 fMCck es- çR; sd fMCcs ds , d frgkbZ dk Hkkj10kg gS2. 6 fMCcksa dk dqy Hkkj 4 fMCcksa ds dqy Hkkj l s 40kgv fèkd gS(1) dFku 1 vkSj 2 nksuksa i ; kZIr ugha gSaA(2) dFku 1 vkSj 2 , dl kFK i ; kZIr gSaA(3) dFku 1 vdsyk i ; kZIr gSA

Railway Group D Exam 2018Maths Solved Paper

Visit www.KVClasses.com Date: 17/09/2018By: Vivek Sir

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(4) dFku 2 vdsyk i ; kZIr gSA11. A, B vkSj C , d VSad l s t qMs+ rhu okYo gSaA A vkSj B

feydj VSad dks 6 ?kaVs es Hkj l drs gSaA B vkSj C feydj VSad

dks 10 ?kVsa esa Hkj l drs gSaA A vkSj C feydj VSad dks 172

?kaVs esa Hkj l drs gSaA A vdsyk VSad dks Hkjus esa dqy fdrukl e; ysxk\(1) 10 ?kaVs (2) 12 ?kaVs(3) 11 ?kaVs (4) 13 ?kaVs

12. fuEufyf[ kr esa l s dkSu l k i w.kZ ?ku gS\(1) 9261 (2) 9999(3) 8000 (4) 9000

13. ; fn , d Mªkboj dkj dks 15 m/sec. dh pky l s pykrk gS]rks ml ds n~okjk 3 ?kaVs 20 feuV esa r; dh x; h dqy nwjh Kkrdhft , A(1) 150 km (2) 180 km(3) 200 km (4) 165 km

14.sin A sin B cos A cos B ?cos A cos B sin A sin B

(1) sin A cos B (2) 0(3) tan A tan B (4) cos A cos B

15. 5 nksLrksa ds chp , d dsd ckaVk t krk gSA 4 dks dsd dk

Øe' k% 1 1 5 1, , ,8 6 12 12 fgLl k feyrk gSA dsd dk fdruk

fgLl k i kapos nksLr dks feysxk\

(1) 16 (2) 5

24

(3) 14

(4) 38

16. fuEu esa l s vHkkT; l a[ ; kvksa dk ; qXe dkSu&l k gS\(1) (37, 41) (2) (43, 47)(3) (3, 7) (4) (71, 73)

17. ; fn 22

1cos 17 xcos ec

gS] rks 2x dk eku D; k

gksxk\(1) 16 (2) 256(3) 324 (4) 18

18. jksgu vkSj jksfgr , dl kFk fdl h dke dks 10 fnuksa esa l ekIrdj l drs gS] t cfd jksgu ml h dke dks vdsyk 15 fnuksa esdj l drk gSaA jksfgr vdsyk ml h dke dks fdrus fnuksa esdjsxk\(1) 32 fnu (2) 30 fnu(3) 25 fnu (4) 35 fnu

19. 156 15 12 9 6 5 7 ?3

(1) 9 (2) 8(3) 12 (4) 7

20. fnYyh esa , d Vhoh ` X es cspk t krk gSaA , d O; ki kjh paMhx<+t krk gS vkSj fnYyh dh dher l s 20% de ewY; i j Vhoh

[ kjhn ykrk gSA og ` 600 i fjogu i j [ kpZ djrk gSA ml dsckn og fnYyh esa Vhoh ` X ewY; i j csp nsrk gS vkSj (100/7)% ykHk v ft Zr djrk gS] X dk eku t kr dhft , \(1) ` 96000 (2) ` 8000(3) ` 8800 (4) ` 7200

21. ; fn 4 2sec sec 3 gS] rks 4 2tan tan dk ekugksxk%(1) 8 (2) 3(3) 6 (4) 4

22. If the number x4461 is divisible by 11, what isthe face value of x ?(1) 2 (2) 4(3) 3 (4) 5

23. ` 1,60,000 dh , d èkujkf' k i j 2 o"kZ ds fy, 10% okf"kZdnj i j pØof¼ C; kt fdruk gksxk] ; fn C; kt dh x.kukvèkZ&okf"kZd rkSj i j gksrh gks\(1) ` 34, 481 (2) ` 30,000(3) ` 34,400 (4) ` 34, 480

24. foi jhr fn' kkvksa l s vk jgh 152.5 m vkSj 157.5 m yach nksxkfM+; k¡ 9.3 l sadM esa , d&nwl js dks i kj dj t krh gSaA rks nksuksaxkfM+; ks dh l a; ksft r xfr çfr ?kaVk fdruh gksxh\(1) 120 km (2) 125 km(3) 130 km (4) 115 km

25. uhps nh xbZ vkÑfr ds vkèkkj i j fn, x, ç' u dk mÙkj nsaAA

B C

E

D

; fn AB, EC ds l ekarj gks vkSj BCD 70 gks] rksBAC dk eku D; k gksxh\

(1) 75° (2) 72°(3) 73° (4) 67°

26. vP; qR; ` 25,000 dk fuos' k dj , d pk; dh nqdku [ kksyrkgSA og bl jkf' k dk 30% nqdku dh i QfuZf' kax i j vkSj 20%nqdku ds fy, vU; vko' ; d l kexzh [ kjhnus esa djrk gSAv i uh nqdku ds fy, ckdh ds l eku [ kjhnus ds fy, vcml ds i kl fdrus #i , cps\(1) ` 12,500 (2) ` 5,000(3) ` 20,000 (4) ` 12,000

27. The HCF of two co-prime numbers is :(1) the product of the co-primes(2) 2(3) 0(4) 1(4) 1 : 2

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01. (1) ekuk A, B,C, D rFkk E dks i zkIr jkf' k = x, x + 10, x+ 20, x + 30, x + 40vr% x + x + 10 + x + 20 + x + 30 + x + 40 = 7205x + 100 = 7205x = 620x = 124vr% B dks i zkIr jkf' k = x + 10 = 124 + 10 = 134

02. (4) oqQy fufeZr eksckby i Qksu dh l a[ ; k= 12]40]000v r % LMN d Ei uh } kj k eksckby d k

mRi knu 3012,40,000100

= 3,72,000

03. (2) f=kHkqt ds rhuksa funsZ' kkad

2 21 2

x yx y1,2 4, 3 vkSj

3 3x y4,1 gSA

vr% f=kHkqt dk {ks=ki Qy 1 2 3 2 3 1 3 1 2

1 x y y x y y x y y2

1 1 3 1 4 1 2 4 2 32

1 4 4 202

202

= 10 oxZ bdkbZ

04. (2) ekuk nksuksa i kbi ksa }kjk Vadh dks Hkjus esa yxk l e; x ?kaVs gSAx 3 x 122 33

3x 9 2x 166

5x – 9 = 665x = 75x = 15vr% nksuksa i kbi ksa }kjk Vadh dks Hkjus esa 15 ?kaVs yxrs gSA

05. (2)

A B

C D

60°

vr% nksuksa l wpukvksa dh vko' ; drk i M+sxh]

ABC dk eku Kkr djus osQ fy, gesa l wpuk &1dhvko' ; d gksxh fi Qj Hkh ge ABC Kkr ugha dj l drs t crd l wpuk &2 dk ç; ksx u djsaAvr% l wpuk &2 l s D = 600 vkSj l wpuk &1 osQ fp=k l sLi ‘ gS fd ABC = ADB = 600

06. (2) fodYi l s]

9 131. 0.56 .5416 24

xyr

9 132. 0.56 0.5416 24

l gh

9 133. 0.56 0.5416 24

xyr

9 134. 0.56 0.5416 24

xyr

vr% fodYi (2) l gh gSA

07. (1)

3 3a b b c c a?

3 a b b c c a

ekuk a – b = Ab – c = Bc – a = Cvr% A + B + C = a – b + b – c + c – a = 0 A3 + B3 + C3 = 3ABCvFkkZrl w=k% (a – b)3 + (b – c)3 + (c – a)3 = 3(a – b)(b – c)(c– a)

vr%

3 a b b c c a3 a b b c c a

= 1

08. (2) fn; k gS&

gkfu CP7

Ø; ewY;

foØ; ewY; (SP) = 144vr% gkfu = Ø; ewY; – foØ; ewY; (SP)CP CP 1447

CPCP 1447

6CP 1447

CP = 24 × 7CP = 168u; k foØ; ewY; = 189

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SP-CP%= 100CP

ykHk

189 168 100168

21 100168

= 12.49= 12.50%

09. () feUuksa dk e-l - v'ak dk eúl úgjkas dk yúl ú

2 8 10 32, . .3 9 27 81

281

10. (2) dFku 1 l s i gys 10 fMCcksa dk Hkkj çR; sd fMCcs dk Hkkj1 103

çR; sd fMCcs dk Hkkj = 30 kgvr% 10 fMCcksa dk oqQy Hkkj = 30 × 10 = 300 kgdFku 2 l s6 fMCcs dk Hkkj = 4 fMCcs dk Hkkj + 402 fMCcs dk Hkkj = 401 fMCcs dk Hkkj = 20v fUre 10 fMCcs dk oqQy Hkkj = 20 × 10 = 200 kgvr% oqQy 20 fMCcs dk Hkkj = 300 + 200 = 500kggksxkAvr% mÙkj osQ fy, nksuksa dFkuksa dh vko' ; drk gksxhA

11. (1) A + B }kjk 1 ?kaVs esa Hkjk x; k Hkkx 16

B + C }kjk 1 ?kaVs esa Hkjk x; k Hkkx 110

C + A }kjk 1 ?kaVs esa Hkjk x; k Hkkx 215

vr% rhuksa }kjkA + B + B + C + C + A }kjk 1 ?kaVs esa Hkjk x; k Hkkx

1 1 26 10 15

2(A + B + C) }kjk 1 ?kaVs esa Hkjk x; k Hkkx 1230

A + (B + C) }kjk 1 ?kaVs esa Hkjk x; k Hkkx 12 160 5

A }kjk 1 ?kaVs esa Hkjk x; k Hkkx 1 15 10

A }kjk 1 ?kaVs esa Hkjk x; k Hkkx2 1 110 10

A }kjk Vadh dks 10 ?kaVs esa Hkjk t krk gSA12. (*) fodYi l s]

39261 9261 21 39999 9999 21.54 38000 8000 20 39000 9000 20.80

vr% fodYi 1 rFkk 3 nksuksa l gh gSAbl ç' u dks jsyos fjØwVesaV cksMZ }kjk fujLr dj fn; k x; k gSA

13. (2) pky = 15m/sec18155

= 54km/hl e; = 3 ?kaVk 20 feuV

20 1 103 360 3 3

?kaVk

nwjh = pky × l e;10543

= 180 km

14. (2) sin A sinB cos A cosBcos A cosB sin A sinB

sin A sinB sin A sinB cosA cosB cosA cosB

cosA cosB sin A sinB

2 2 2 2sin A sin B cos A cos B

cosA cosB sin A sinB

l w=k%

2 2 2 22 2

sin A cos B sin A cos Ba b

cos A cosB sin A sinB

1 1

cos A cosB sin A sinB

= 015. (2) pkjksa nksLrksa dks i zkIr dsd dk Hkkx

1 1 5 1 198 6 12 12 24

5 osa nksLr dks i zzkIr dsd dk Hkkx19124

524

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16. (4) vHkkT; l a[ ; k & t ks l a[ ; k, ¡ Lo; a l s rFkk 1 l s foHkkft rgksrh gS ml s vHkkT; l a[ ; k dgrs gSA t Sl s& 2] 3] 5] 7vr% fodYi esa l Hkh vHkkT; l a[ ; k, ¡ gS v r% vHkkT; l a[ ; kvksachp esa vUrj fodYi (1)] (2) rFkk (3) osQ l eku gS rFkkfodYi (4) esa vHkkT; l a[ ; kvksa dk vUrj 2 gS v r% fodYi(4) gh fo"ke ; qXe gSA

17. (3) 22

1cos 17 xcos ec

2 2cos sin 17 x

22

1 sincosec

1 + 17 = x18 = xnksuksa i {kksa esa oxZ djus i j324 = x2

18. (2) jksgu vkSj jksfgr }kjk 1 fnu esa dke dk fd; k x; k Hkkx1

10

jksgu }kjk 1 fnu eas dke dk fd; k x; k Hkkx 115

jksfgr }kjk 1 fnu eas dke fd; k x; k Hkkx 1 110 15

3 230

130

vr% jksfgr ml dke dks 30 fnuksa esa l ekIr dj nsxkA

19. (4) 156 15 12 9 6 5 73

156 15 12 15 123

156 15 12 33

156 243

156 243

= 56 ÷ 8568

= 7

20. (2) fnYyh esa Vhoh dk foØ; ewY; = ` xpaMhx<+ esa Vh-oh- dk Ø; ewY;

80 4xx100 5

vr% Vh-oh- dk dqy ykxr ewY;4x 6005

i z' ukuql kj]4x 800600 x5 700

3200x 480000 700x5

3200x480000 700x5

300x4800005

480000 5x300

x = ` 8000

21. (2) 4 2sec sec 3

2 2sec sec 1 3

2 2sec tan 1 4 2tan tan 3

22. (4) 11 dk foHkkT; rk dk fu; e& ; fn fdl h l a[ ; k osQ l eLFkkuksa i j vk, vadksa osQ ; ksx vkSj fo"ke LFkkuks i j vk, vadksadk ; ksx dk vUrj 0 gks ; k 11 l s foHkkft r gksrk gks rks ogl a[ ; k Hkh 11 l s foHkkft r gksxhAl a[ ; k & x 4 4 6 1x + 4 + 1 – (4 + 6) = 0x + 5 – 10 = 0x = 5

23. (1) / ujkf' k = ` 1,60,000nj = 10% = v¼Zokf"kZd = 5%v¼Z&o"kZ = 4

TRA P 1100

45A 1,60,000 1100

105 105 105 105A 1,60,000100 100 100 100

A = 194481pØof¼ C; kt = feJ/ u (A) ewy/ u (P)

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= 194481 – 1,60,000= ` 34,481

24. (1) nksuksa jsyxkfM+; kssa dh yEckbZ = 152.5 + 157.5 = 310ml e; = 9.3 sec

nwjhpky l e;

310=9.3

pky

100 m / sec3

km/h esa cnyus i j100 18 120km / h

3 5

25. (2)

BCD = 72°BAC = ?; fn oÙk dh t hok osQ , d v fUre fcUnq l s gksrh gq, js• k vkSjt hok osQ chp dk dks.k] , dkUrj • .M esa t hok }kjk varfjrdks.k osQ cjkcj gks rks ; g js• k oÙk dh Li ' kZ js• k gksrh gSAekuk oÙk dk osQUæ O gS rFkk AC bl oÙk dh t hok gSA fcUnqC l s t krh gqbZ , d l jyjs• k DE bl çdkj • haph xbZ gS fdBCD = BAC t gk¡ BAC , dkUrj oÙk• .M esa fLFkrgSAvr% BAC = 72°

26. (1) vP; qR; ds i kl jkf' k = ` 25,000nqdku dh i QfuZf' kax rFkk vU; l kexzh [ kjhnus esa [ kpZ jkf' k =30% + 20%= 50%%

vr% ' ks"k jkf' k 5025000100

= ` 12,50027. (4) egÙke l eki orZd & nks ; k nks l s v fèkd l a[ ; k dk egÙke

l eki orZd og cM+h l s cM+h l a[ ; k gksrh gS] t ks çR; sd nh xbZl a[ ; kvksa dks i wjk&i wjk foHkkft r dj l osQAvHkkT; l a[ ; k& os 1 l s cM+h çkÑfrd l a[ ; k, ¡ t ks Lo; a vkSj1 osQ v frfjDr vkSj fdl h çkÑfrd l a[ ; k l s foHkkft r ughagksrh gS mUgsa vHkkT; l a[ ; k dgrs gS t Sl s& 2] 3] 5] 7

nks l g&vHkkT; l a[ ; kvksa dk e-l - l nSo 1 gksrk gSA t Sl s&(37] 41) (71] 73) vkfn dk e-l - gSA

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