~..,

1. Pa'"T

.c

.Part:t / ~ IAptitude 'lest / ~ -qif~

Directions: (For Q. 1 to 3).:~: (fl.l ~3 -q; ~)I

Find the oUdfig'ure out in the problem figures ~iven below:;;ft'# ~ "IT{ ~ 31/rpf&<l '# ~ .Fcffrq 3WjiFrr ~ I

1. * * * *(1) ft) : (3) (4)

W :-;'& W &' ;

2.

(1) (2) (3) J4)

3.~

I@] [Q] [E](1) (2) ( (3) .,;(4)

Direction~ : (For Q. 4 and 5). One of the answer figures given below is hidden in the problemfigure,in the same size and direction. Select, which one is correct.

RW : (rr. 4 3i1r 5 -q; ffflJ:) I -;ft:;t ~ "IT{ dfff3wpf(pjf '# il1!!fi ~ rrTTf atk ~ '# 'frI1F1 (F;;T1 "i1~~'#ft9r:ft~1 ~-m7~ ~I

Problem Figure / rrFf 3WfiRr Answer Figures / "3"fIr 3f1rpRt47'"

4. D.,j3)

(J(1)

(J(2)

5.

(2) (3)

L:J(1)

<\(4)

(4)

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Directions: (For Q. 6 to 12).

f.rW : (rr. 6 "« 12 "If; fffl!: ) I

Problem Figure / ~ ~

6.

7.

8.

••-~--~~-.

rJ ())t/;J[;;~•

The 3-D pre{1le1?'lfigure shows an object. Identify, the correct view, tttM'from amongst th,ea,nswer figures, looking in the direction of the arrow.}' ~ .

-. ~/3-D >I'f'f ~ 71 ~ cn:g q;1 ~ Tj?:ff tI rik C1ft ~ "# ~ ~wi/> ~ ~ ;;;T 3'ffl" 311$Ift<if >f"«. ,"T#H~' V ~

Answer Figures / '3tf( ~ ~.~

. ',.c-?l\(v~

(1) (2) is) (4)

(1) , (2) (4)(3)

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Problem. F.igure / JWf 3Wfi(tT \. '

9.

/

10.

11.

12.

..•

Answer Figures / 3TR" ~

O/Page 4

(1) (2) (3) (4)

(1) (2) (3) (4)

(1) (2) (3) (4)

(1) (2) (3) (4)

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•~, \'

Directions : (For Q. 13). How many total number of rectangles are there in the problem figUte givenbB10w r

~: ('R'.13 ~ ft;ru:)1

...\ ~~':LProblem Figure / JPR~..t I:> ~ ~ 0

13. I . J ; ;1-~ ..\:~.-\ "t°n.t..?-\-"\J..(1) 19 (2) 20 (3) 17 .)41" 18~

Directions: (For Q. 14 and 15). How many total number of triangles are there, in the problf'l"i§fgmt5given below ?

Problem FigJ!E_j_ rwf 31FfiFrr ". ~v

~>\~~.

14'~

(1) 18 (2) 20 y) 16 (4) 17

15.

(1) 17 'f2) 19 (4) 18(3) 20

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. ! ... .c

••Directions: (For Q. 16 and 17).,,'

The problem figure shows the top view o.{~n object. Identify tl 'correct front view, from amongst the answer figures.~ ~ -q fc1;ift Cf@?fiT m~ ~jp;ff ~I ~ ~

"# PlCfiT "ffit ."fl1J]}§" ~ q(j#JHI.!, I

~ : (.11.16 .3Iir 17 cJ;'fffi!:) I

Problem Figure / >rR ~

17. ~

! II II •I .I

Answer Figures / '3'U( ~

.aillruJBI I

[ThrnoI

. rills1B .I i

(1) (2) (3) (4)

DrS]I

(1) (2) (3)

The 3 - D problem figure shows an object. Identify, its correct toiview, from amongst the answer figures.3 - D !ffrf 3WfiFrr "# 7!,Cfi eng CfiT ~ 7fllT t/ PlCfiT mit mm~ ~"# "# qfj#}HI.!, I

Answer Figures /_~ ~

, Directions: (For Q. 18 and 19).

~: (11.18 ath'19 ~ ~)I

/Problem Figure / >rR ~

18.

19.

(1) (2) "(3) (4)

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•Directions: (For Q. 20 to 23).

'I.'

~: (rr,20 #23 tfi ~)I ..' .

.c

•Which one of the answer figures is the correE~mirrorimage of theproblem figure with respect to X - X ?drfr~.q#~~·G1·7f{·~~-q;rx-x w~~31f&f¥4 ~?

Answer Figures / ~. ~Problem Figure / JIR 31fCFfrr .

20.

21.

22.

23.

x

x (1)

x

(2)

i (2)

(2)

(3)

{3) (4)

(4)

,?J (4)

O/Page 7

x

x

(1) \

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x

x

(1)x

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. .. ..Directions': '.(For Q. 24 to 27): Which one of the answer figures, will complete the sequence of the, •

\,, three problem figures ? \.'

~ : (J1. 24 'R' 27 ~ fR1l: ) I dffl" .51/r;rn4t -q t1, CFft;rr.it ~ cnT rit:r JWf 317r;rn4f "# ~ #3ffl1i1r (sequence) "l!' -m: \fflT!!IT ?

Problem Figures / r;w-r 3fliflfdqj Answer Figures / ~ 3fliflrnqt

?•

J?Y (2)

B@E]

(3) (4)

27.••• •••• •••

••• •• ••• • •

••• ••• • •• •• ••.:••• •

••• •••• •••(1) (2)

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•••• •••••

•• ••••••'. ._.

(4)

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...•

Directions: (For Q. 28 to 32).•

~": (Jl'28 ~ 32 ~ fffi[)1Problem Figure / '!lR ~

,,'Find out the total number of surfaces of the object given, bekno, in the ....problem figure. . •/ .. .:rm~ -q Hl#fI'Phff CRfJ·~ ~ ~ Ji<7 if&n "ifRf ~ I

28. (1) 17 ~ 18

29.(2) 22(1) 20

30. (1) 16

31.(2) 12(1) 13

32.

(3) 16 (4) 15

(3) 19 (4) 18

(3)----W- (4) 18

(4) 15

~_ (3) 15 (4) 14

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"

j

!

, II,

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•Which one of the answer figures shows the correct view of the 3 - Dproblem figure, 'RJterthe figure is opened up ]

3-D·>rR·~!fiT7Sk#w. '~~##, ~~' ..~~?. .

Directions f(For Q. 33 to 35)..

RW : (J1. 33 ~ 35 ~ fFrr!: ) I

Problem Figure /J1R~

33. [t?

34. ~

35 e • LjJ

Answer Figures / ~ ~ .

(1)

(1)

(1)

(2)

(2)

(3)

(3)

(4)

(4)

(2) (3) (4)

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39. Which one of the following cities in India 39. - 'qffiJ ~, f~101f<'1P~Hl~ -q ~,.~ <:rn- am:lie in Cold and Dry region ? ~~#~t:(1) Leh (1) ~(2) Gangtok (2) ~(3) Simla m fimm(4) Datjeeling (4) t;lf-lffdll

40. Which one is not a sound absorbing 40; ~ 'IGT~ ~ ~Cj~ni!4Cfl ~ t?material? il

11(1) ~"CflT ~ ilGlass wool (1) I,i(2) Ground glass (2) tmrr~J(3) , Jute bags (3) ~~ .~

Ii(4) ~. :l ,Thetmocol (4) 1)

if

Ie

•3~. Which one of the following consumes least\.

amount of electricity ?•

• (1) Fluorescent Tube .

(2) Light Emitting Diodes (LED)

(3) Tungsten Bulb

(4) Compact Fluorescent Lamp (CFL)

37. Qutab Minar is largely cladded with :

(1) Marble

(2) Brick

(3) Granite

(4) Red sand stone

38. In which place in India can we find cavetemples of three faiths ?

(1) Ellora

(2) Agra

(3) Madurai

(4). Delhi

.c

•36. f1lO1f<'1fujd-q ~ ~, ~ qft ~ ~

m Cf;lt .cmm t?.(1) S1rn~lN ~~ 'SfCfirn' dffi 4Cfl ~ (LED)

(3) ~.~

(4) ~ (Compact) Slrni!.lN m (CFL)

37. ~ -rff.m: 1R ~ a:rf~ "tRf ~ ~ t?(1) ~f~jl:WH~

(2) #f~!~~.~

(4) ~, ~3TI "tf"cm: ~

38. 'qffiJ#~~1R~~ wn~~~~~?p( ~.-q(2) awro-q~) ~-q(4) ~#

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I ·-t . - ..~-,,-~.--'--.--- -,

'1.1, 'i

.G!.I

.c

LIi.ii •,-j

~~~w.rnt?I, 41~ . Palace of\.\Vinds (Hawa MahaI) is located 41. ..i

in: \.'

i· (1) Jammu 'and Kashmir (1) ~am~-q, , (2) Andhra Pradesh (2) 31T'1 mr-q, I

I (3) Madhya Pradesh (3) lJ~m-q(4) Rajasthan ~~-q

42. Hori~ontal sun shades are required to 42. ~~, 1JCA ~ ~ am. ~ ~ 'q11J i

protect windows on which facades of a r~~rCfl4lq;l~ Cfft ~ ~ ~ f?building?

(1) West .' .

~~(2) North (2) ~

(3) South (3) GfPdUT(4) East (4) ~

43. .Name the city where canals are used as 43. ~mq;r~~, ~~, ~~ .transportation channels : -qwWT -qa:rnft f ?(1) Venice (1) ~

(2) Tokyo (2) ~

(3) Canberra (3) ~

._______{4) Manhattan (4) ~

44. Which type of roof will keep the room 44. m~ctt~~~~~?cooler?

(1) Concrete slab with mud, brick tiles (1) ~ qft ~, lltt, #{ Cfft G$ffand covered with. potted plants m~'qhff~~~

(2) Asbestos sheet roofing (lL Q;~ RTft ~ ctt 'ffif

(3) Concrete slab with cement plaster 41) ~qft-mr, ~~~m~(4) Concrete slab with mud and brick (4) ~ qft~, lltt ~ 'ffl·Cfft ~

tiles ~~

45. Which city is based on sector planning? 45. ~ ~ '~~' 1R 3W-lTfuf t?i :

Cfl'j(1Cfildl(1) Kolkata (1)(2) Pune (2) ~.

(3) Patna (3) -qc;rr

(4) Chandigarh (4) ~

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• •46. Which one of the following is an 46. Ri01fc,?1f~d-q ~ Cfit.r ~ CfI«lCf)R,~?~, ~,

Architect ?

(1) Christopher- Benninger

(2) Salman Rushdie

(3) Arnrita Sher-Gill

(4) M.F. Hussain

47. The summer sun in Northern Hemisphererises from:

(1) North East

(2) East

(3) North

(4) South East

48. Point out the incorrect combination :

(1) Eiffel Tower and Congo

(2) Agora and Greece

(3) Pagoda and Burma

(4) Vat and Combodia

49. Which one of the following is a horizontalmember in a building that carries load ?

(1) Vault

(2) Beam

·(3) Arch

(4) Column

50. Natural shadowless light is available fromwhich direction in India?

(1) East

(2) North'

(3) South

(4) North-West

(1) f!ih'Elil4'1{ Gtf.f.,15H

(2) m1l!R~

(3) ~ m-ftre"(4) ~.1!;fi. ~

(1) ~~~

~ ~~

(3) ~~

)4) Gf~~~

48. ~~CiiT~:(1) ~ ifcn: 3Th:~(2) 3llTm 3Th: "tim(3) ~ 3Th: GflTI(4) ~ am Cflkllfs41

49. f1i01f<'iP3d~ ~ ~ .~ tfiT ~ ~'EI\q.,Ic-'iCf) 'qTlf t ~ fcf; 'W CWJ q;urr t?(1) ~mf(~)

(2) ~ ,

(3) ~,(awf)

(4) , ~'q (~)

50. 'qffif -q, ~ f.W:rr 'CflT $I1~l(jCfl ~ ~ fum~~~?

(1) ~~

(2) '3m: ~

(3) Gf~~(4) ~-~~

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•

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Part II / ~ IIMathematics /1'fftmf

chord is: i~\.\:J ')._

~>V

't"(1) 16.J3 ........ \.. ' (1) 16.J3 , 'lo"'l'{4

(2) 32.fi (2) 32.fi

(3) 32 (3) 32

(4) ie-Ii ~16.fi

51 .• Let y2 = 16x be a given parabola and L bean extremity of its latus rectum in the firstquadrant. If a chord is drawn through Lwith slope -I, then the length of this

52. If the quadratic equation

3x2+ 2(a2 + l)x + (a2-3a + 2) =0

possesses roots of opposite signs, thenI, , th . ' al xt/( t''jies In e mterv: ~ ')--

t ~><'} )(.¥ )(v0 ~ ~C-)

(1) (I, 2) ~ IV ~ oX

~~ \J'~ (\.e,><--"':,'» >-.. ..J:./ ::>

(3) ( - 00,-:-1) ~ ~ '/~ . t<- L--

IV'<~r:,i--'

,?~r

(2) (2, 3)

(4) (-1, 1)

53. If P is any logical statement, then:

(1) pAp=p

(2) pv(~p) = p

(3) pA(~p) is a tautology

(4) pv(~p) is a contradiction

•

51. l:fRl y2=16x ~ ~.l"'RfI ~ ~ (f~ L

~ '1If~ CfiT "5l~ ~~. ~ ~ W ~ I. ~L~~\lfRqwft~\iIlqyt ~~

-1 t m~\iIlqyCfft~~:

52. ~ ~ tp'fl Cfi {OJ

3x2+ 2(a2 + l)x + (a2- 3a + 2) =0

~ lFl fcfqfffi ~ ~~! m a flm ~ -q t~~:

(1) (I, 2)

(2) _ (2, 3)

(3) (-00,-1)

(4) (-1,1)

53. ~ p~~Wre~t m:(1) pAp=p

(2) pv(~p)=p

J3} pA(~p)"BGl ~ ~ I

(4) pv(~p) ~ fcro~ ~ I

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..•

54. From a window x meter high above the. ground, in a street, the angles of elevation. .

and aepression of the top and the foot ofanother house exactly opposite to thewindow in the same street are 0: and 13respectively. Then the height (in meters)of the house on the opposite side is :

(1) x(l + coto tanl3)(2) x(l + cote cosp)(3) x(l + tano cotp)

(4) x(l+tano: cosl3)

55. The least positive integral value of x whichsatisfies the inequality lOCx -1 > 2 x 10Cx

is:

(1) 9(2) 6

(3) 5(4) 8

______5_6. The rate of change of the volume of asphere with respect to its surface area,when the radius is 2 units, is :

(1) 2(2) 1

(3) 4

(4) 3

57. If m is the slope of a tangent to the curveeY =1+ x2, at the point (x, y) on the curve,then all possible values of m lie in theinterval:

(1) ( -'-00, -:1)(2) '. [ -1, 1](3) [a, 1](4) (1, 00)

.... '-_". '_-"''''-'-''-''''_'_

..•

54. ~ lfffi -q, ~ ~ x 1#. ctT ~ TRWrn ~~ ~ ~ lfffi ~ 00 ctT aW Wrn cqq.:r

~. ~ a2TT lfIG ~ ~ a~T ~ q;)ur~: a a2TT.13 ~ I aT 00 ~ 'qCR ctT ~(~-q)~: L_.~x(l +coto tanl3)

(2) x(l +cote cosl3)y(3) x(l + tan« cotp)(4) x(l+tana co's(3)'"

55. x CflT ~ ~-::rn+T ~ erol fctl4 l:IFI, m·~ lOCx_1 > 2x10Cx qi) ~ ~ t~:

(1)

(2)

(3)(4)

96

58

56. ~ lTffi t" _~___:b!_ ~~ t" ~~ ~m t" qf<cHf'i Cfil ~, ~ ~ ~2~t~: 0n) 2 ,. L(2) 1(3) 4

(4) 3

57. 7:lft:: ~ eY== 1 + x2, ~ ~.~ (x, y) -q-{ ~Cfl

~OO Cfft ~ m taT m~ W1{t ~'qq l1Rflm~-qWm~, ~~:

(- 00, -1)[-1, 1]to, 1](1, 00)

(1)(2)

(3)(4)

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(1) ~ (a3

+ b3) )1) % (a3 + b3

)

(2) ~ (a3_ b3) (2) % (a3

- b3)

(3) ~ (I b 13

- 1 a 13

) (3) ~ (I b 13

- 1 a 13

), ,

:::['; I'!:

.!_ 1 b3 - a3 I .!_ 1 b3 - a3 1(4) (4)3 3

i

IIi

..•

5~. A common tangent to x2 - 2y2= 18 and" x2+y2=9 is :

•(1) y= 2x+3.j7

(7) y=.fi x+3./5

'(3) y=2x+3./5

(4) y=.fi x+3../3

.59. The coefficient of t24 in(1+ t2)12 (1 + t12) (1 + t24) is :(1) 12C6 +1(2) 12C6(3) 12C6+ 13(4) 12C6 +2

60. If the system of linear ,equations,

x + 2ay + az = 0, x + 3by + bz = ° andx + 4cy + ez = ° has a non - zero solution,then a, b, e satisfy :(1) 2ae = ab + be(2) 2ab = ae + be(3) 2b=a+c(4) b2=ac

61. Iif (x)= x I x I, then for any real numbersa and b with a<b, the value of

bJ f(x)dx equals:a

••

. .58. x2-2y2=18 q~ x;+y2~9 Cfll ~"3'IflI

-mnm%: ",.' '.(1) y=2x+3.j7-

(2) y= J2 x+3J5

(3) y=2x +3 J5

(4) . y=.fi x+3../3

59. (1+ t2)12 (1+ t12) (1+ t24) ~ ~ ~ t2.

~~: ~ASY(1)' 12C6 + 1 'V~ >(2) 12C6 d I ~, .(3). 12C6+13 .~ i) '.¥ ~."(4) 12C6+2 r ~"b"

/ / ~

6,Q. ~ ~ '81flefHOI f.r<tr:TX + 2ay+ az = 0, x + 3by + bz = °x+4cy+ez=0 q)1 ~ ~~~ re ta,b,c~~~:(1) 2ac = ab + be(2) 2ab=ae+be(3) ~a+c(4) b2=ac

61. Gffu:f(x)=X 1 x I t (f) qlWfqCf) ~aTI a q

b~ffilt ~a<bt Jf(x)dxGRm~:

a

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·_..4 __ .•. _ ...L.L . __1 J.

•c

•f 7X13 + 5X15 J' 7X13 + 5X15 .....62. .' . . 3 dx equals: 62. 3dx~~: .(x7+ x2+ 1) .' ' . ~7 + OX2+ 1)

(1) x7+C (1) x7

+C(x·7+ x2+ 1/ 2

(x7 + x2+ 1)

x7 7(2) +C (2) x

+C2(x7 + x2+ It .. , ,. 2

- 2(x7 + x2+ 1)

(3)x14

+C (3)x14

+C(x7 + x2+ It (x7 + x2+ 1)2

(4)x14

+C (4)x14

+C2(x7 + x2+ ]t 2

2(x7+ x2+ 1)

-t A A A -t A A -t /\ A A -t A /\

63. Let v = 2 i + j -- k and w = i + 3k. 63. lWJT v = 2 i + j - k (f2fl w = i + 3k-t

If u is a unit vector, then the maximum

value of the scalar triple product

1°1141<1 [~.-; ~] CfiT m~ ~ % :~

,.-'-1 f"\ '1 --t ~ ... ,... \-\J ;1..·L ) ~.

(1) J59 \J e- j' ~~, .

ft"i if) ~)J

[-t -t -'uvw is:

(1) J59

(2) $a (2)

yr/ 16 "(3) 16

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>.._ ;

•64.'-' If atV~riaple line, passing through the point

• of intersection of the lines x + 2y-1 = 0and 2x - y -1= 0, meets the coordinateaxes in A and B, then the 10,<;;9;8 of themid-point of AB is :

64. 7:ffu: l1!fi T.R ~, m311·x+ 2y -1 = 0 d'?lT

2x-y-l==Ot" S1rd~G ~ ~ m ~ \ifRfttam r1a:~liCfl &Ian. ~ A.d'?TT B 1:J\. ~ ~, aTAB ~ ll~-~ cor ~?1 ~ :

(1) x+3y=10 xy (1) x+3y=10 xy

(2) x+3y+10xy=0(2) x +3y+l0xy=O·" _-t', ..

(3)5: 83' 1 .- r·~!t.15:;' ,~ F18'\:1;;::

x+3y=O x+3y=O(3)

(4) x+3y=10 (4)

65. Statement 1 : The line 2x + y + 6 = 0 is 65. Cfi?Rl: ~ 2x+y+6=O U9T x-2y+5=0perpendicular to the line x - 2y +5 = 0 and. 1:J\ ~ ~ a~ ~ U9T (1,3)~ m ~.~second line passes through (1, 3). ~I

Statement 2 : Product of the slopes of any Cfi?R 2 : Gl w:rRR ~aTI CfiT ~ CJil !!OI14"it'i

two parallel Iines is equal to -1. -1rr-

(1) Statement - 1 is true; Statement - 2 ~:q;~ -1~t q;-~ - 2~~1

is false.I.,."

(2) Statement - 1 is false; Statement - 2~.

Cfi?R -1 ~ t q;-~ - 2 ~ ~Iis true.

(3) Statement - 1 is true; Statement - 2 (3) q;-~ - 1 ~ ~ ; q;-~ - 2 ~ tis true; Statement - 2 is a correct .i" ~ - 2, ~ -1CfIl-mft~~1

explanation for Statement - 1.

(4) Statement - 1 is true; Statement - 2 (4) q;-~ - 1 ~ t q;~ - 2 ~ ~ ;

is true; Statement - 2 is not a correct 'Cfi?R ~2, ~ - 1 CfiT ~ ~ ~explanation for Statement - 1. ~I

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·. . .66. Let A and B be two events such that

,,' P(AuB)~3/4 and 1/8 -s P(AnB)s 3/8.

_ Statement 1 : P(A) +P(B) ~ 7/8

Statement 2 : P(A) +P(B)S 1i/8

(1) Statement - 1 is true ; Statement - 2is false.

(2) Statement - 1 is false; Statement - 2is true.

(3) Statement - 1 is true ; Statement > 2is true; Statement - 2 is a correctexplanation for Statement - 1.

(4) Statement - 1 is true ; Statement - 2is true; Statement - 2 is not it correctexplanation for Statement - 1.

67. Consider

L1: 3x+y+a-2=O ;L2 : 3x+y - a +3 =0, where a is a positivereal number, and

c: x2+y2-2x+4y-4=0.Statement 1 : If line Ll is a chord of thecircle C, then the line L2 is not always adiameter of the circle C.

Statement 2 : If line Lt is a diameter of thecircle C, then the line L2 is not a chord ofthe circle C.

Then,

(1) Statement - 1. IS true andstatement - 2 is false.

(2) Statement - 2 is true andStatement - 1is false.

(3) both the statements are true.

(4) both the statements are false.

...

66. l=fRTA"ij?ITB~G)~t~P(AvB)~3/4 ~(l'9"ij?ITi./8 S P(AnB)s"3/8 t I'" . f{j ~ 1/1C6?Frl: P(A)+P(R)~ 7'/8 ~~~t~~ 2: P(A)+P(B)" 11/8 No!- ~(1) ~-1~t~'-2~tl (f'

~-1~t ~ -2~tIJ ~.1JV>

(3) ~~ - 1 ~ t ;q;~ 2 ~ t~~-2~-1qft~~tl

", .. (';,I ..:;..;- \( r"

(2)

,( '1"1'1 ~ 1 l«'I t "''l'I ~2 l«'I t ;~-2,~-1Cfft~~~tl ~r~~

'1-t-k1 d.._ k ":> '": .

67. ~::::{a~;!~;.~.L2: 3x+y.-a+3=Ot ~ a ~~~, ,~:cli'("(1fClCfi ~t"ij?IT c>-)3V k\ _____c: x2+y2_2x+4y-4=0.

C6¥Rl~~ ~Ccn1'Q(-li·~t mL2~~ C CfiT 0lfR1 -::rID t I

C6?Fr2 : ~ Lt ~ c CfiT "&I'R1 t m ~ ~ CCfft~ -::rID t I

(1) ~-1~t,q;2R-2~tl

(2) - q;~ - 2 ~ t q;~ - 1 ~ t-I

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......_____.,._.....--~-.,~-.---.'-'----.< .

69.Let fbe a differentiable function such that

69."tfR1 f ~ .q_~l 31~~ "ql~ ~ I fcti

8f(X)+6f(~ J-x==5, (x:;t:O) and

8f(X)+6f(~ J-x=5, (x:;t:O)t-a~

, dyt dy

y==x2 f(x), then ~ at x= -1 is :y ==x2 f(x) I it x = -1 -.n: dx CfillWl~;.(

I'l-

l

1 ~~ .0

(1) --(1) -- ' r

14

14 ~v y1

1 ~l ·(2) -

(2) 14-L 0

14'/ ;>

1515

'~\Y j

(3)(3)

~ V

1414 .>{I \; I

(4)15 (4)

15 ~\ :1-'-.0 y 15

1414 ~ ~X \.;._/

I "

70.If z == i (i + .J2), then the value of 70.

~ z==i (i + .J2)t it z4+4z3+6z2+4z

\

z4+4z3+6z2+4z is :CfiT t:lR t : \

~

(1) 6(1) 6 \

N

(~) -9(2)

\

-9

i

(3) -5(3) -5

(4) 3(4) 3

.c

• 1 •68. "tWfl f am g, f(x) == -;+q" xER, xi:- -1 -am

g(x) == x2 +1, x€R "IDU -qft~. ~ f '({G{

gof:(1) ~ -a~ 3i1'i%§I~Cfi -zyu t I

(2) '1 it ~ t alR "1 m 311'i%§IGCfi ~ I

(3) ~ ~ ~ an:ama:iti" -;@ t I

(4) 311'C®IGcti t~ ~ :;@ ~ I

;8. L~tif a.nd g be functions defined by

1f(x) = x + 1' XER, xi:- -1, and

g(x) == x2 +1, xeR. Then gof is :

(1) both one - one and onto.

(2) neither one - one nor onto.

(3) one - one but not onto. ,

(4) onto but not one - one.

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•71. If for some real number a,\'

lim, sin 2x + a sin x . t th th li it3 exis s, en e nrux ~O xis equal to:

(1) 1I

(2)

(3)

(4)

2

-2

-1

.iI

72. 2 cot -1(7)+ cos -1 (~lin principal value, 72. 2 cot-1(7) +'C:6s'--1(~) Cfil' ~ llR· ~'

~:!

, is equal to : r-. ':1

(1) -1( 41 J (1) 1( 41 ) , I

tan 117 t_an- 117 \,ii

)2) . -1(117) (2) cosec -1 ( .!!.~)cosec 125 125

(3) cos-1( 1~5 ) -1( 44 J(3) __50S 125

(4) 1( 44 ) (4) 1( 44 ) V"- 'cos- 117' cos- 117

73. A tree, in each year, grows 5 em less thanit grew in the previous year. If it grewhalf a metre in the first year, then theheight of the tree (in metres), when it ceasesto grow, is:

(1) 2.50

(2) 2.00

(3) 3.00

(4) 2.75f

O/Page 21

(2)

(3)

(4)

2

-2

-1, ~" . ';,..;;0 j"?,)n' iUiJ i

(1) 2.50

(2) 2.00

(3) 3.00

(4) 2.75

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!.~,.~.,_.,_J..,,,... .~

•\,'

74. LetS be the set of all real matrices, 74.' llAT s~,:ft cm:~fqCfl ~ q)f ~~ t

A= [: :]SUCh that a+d=2

AT =A2_2A. Then S :

(1) has exactly. two elements.

(2) has exactly four elements.

(3) is an empty set.

(4) has exactly one element.

and

M xcosx2dx <>75. The integral ~ cos(1n35 _ x~~1os x2

is equal to :

(3)

(4)

76. If a variable plane passes through a fixedpoint (I, - 2,3) and meets the coordinateaxes at points A, B, C, then the point ofintersection of the planes through A, B, Cparallel to the coordinate planes lies on :

(1) xy .-.2yz +3zx = 3xyz

. 1 1(2) xy+ -yz- - zx=6

2 3

1 1xy- 2Yz+ '3 zx=6(3)

(4) yz - 2zx + 3xy= xyz

A = ~ ~1~m t f\t;

AT=A2-2AtmS:

(1) 'ij~~~fl

(2) ii~~~~1(3) 'Q,Cfi ~ ~ t I

(4) ii~~~tl

a+d=2 Q~T

75.

~~:

X~ 1 7(1) - In-

4 5

(2)1 7-In -2 5

(3) .!. In 24 7

.! In 22 7(4)

76. ~ 'Q,Cfi ":q{ ~ 1J;Cfl' .~ ~ (I, - 2, 3) ~~ ~ t o~ f1~~liiti 31an"Cfll~aTI A, B,C 'fR ~ t eft A, s. C ~ ~ "\if'R ~,f1e:~liiti:.alan t" ~ ~ CfiT T1"F.:I~=

~,~1R~t~~:

(1) xy - 2yz + 3zx = 3xyz

. (2)

d xy - .!.yz +.!.zx = 62 3

(4) yz - 2zx + 3xy = xyz

O/Page 22 SPACE FOR ROUGH WORK / ~ Cfi1'4 ~ ftwro: ~

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77. Suppose a population A has 100observations 101, 102, ..., 200 and anotherpopulation B has 100 observations 151,152, ..., 250. If VA and VB represent thevariances of two populations respectively,then the ratio VA: VB is:

(1) 1: 2

(2) 3: 2

(3) 1: 1

(4) 2: 3

78. Statement 1: If three positive numbers inG.P. represent the sides of a triangle, thenthe common ratio of the G.P. must lie

b Fs-1 d J5+1etween an .2 2

Statement 2 : Three positive numbersform sides of a triangle if sum of any twonumbers is greater than the third number.

(1) Statement - 1 is true; Statement - 2is false.

(2) Statement - 1 is false; Statement - 2is true.

(3) Statement - 1 is true ; Statement - 2is true; Statement ..,2 is a correctexplanation for Statement - 1.

(4) Statement - 1 is true; Statement - 2is true; Statement - 2 is not a correctexplanation for Statement - 1.

..

(3) 1: 1

(4) 2: 3

lI) , .f'78. Cfi~ 1 : ~ 1011c"14Cfl ~ C!ft <fR ~

~.~ ~ f5f'lJ,\jf efT 'lJ,\5fT31T' eft f.;~(1

ef~m ~, m lJ,1TTTm .I))~TefT -met 31'1.<mr

J5 -1 J5 + 1 -+- ~ ~"..-r ~ u.....\.tID--- G~ q, ~I-q 1~C1 'Q I ~ )_

2 2 V

cn~2:~aFr ~~,mll~~Cfil'lllrr cmm ~ ~ m, m ~ ~~ ~ f3r:prqft :rman q;) ~. CR ~ ~ : ~ s- j_.

(1) C'fi~ -1~ t 'q1~ - 2 ~ ~I

(3) Cfl~1' - 1 ~0f t ;ef~1' 2 'B;::~ tCfl~ - 2, Cfl~ - 1 en1 ~ 'O'J.'T&rT % I

Cfl2fo1 - 1 ~ t ef~ - 2 ~ t ;Cfl~ - 2, Cfl~ 1 en1-mn ~ ~ t I

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.c

• •79. The general solution of the differential

equation79. ~ fp:fl Cfl <01

\.

~ T sin '( x ; Y) == sin (x ; Y)~~~:

dy . (x + 1/) ,. (x - y)dx'+sm 2 =sm -2-, is:

(1) log (cotf) + 2sinx = C (1) log (cotf) + 2sinx - C

(2) log (cot~) + 2sin~ = C (2) log (cot~) + 2sin~ = C

,(3) log (tanf) + 2sinx = C (3) log (tanf) + 2sinx = C

(4) log (tan~) + 2Sin~ = C (4) log (tan~) + 2sin~ = C

80. The angle between the lines 2x = 3y = - zand -6x=y=4z is :

80. ~3if 2x=3y= -z"ij~ -6x=y=4z~ ~Cfi1 CfiTur ~ :

(1) 90° (1) 90° 0/t(2) 0° (2) 0° <~:bq~<V"

"V ~q(3) 30° (3) 30° "'7

(4) 45° ,YY' 45°

-000- ,

O/Page 24 SPACE FOR ROUGH WORK / ~ ~ ~ ~ ~

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Ie

. lfeadt'hi! f6.1~ing instructions carefully:

1. Part'I lias 50 objective type questions of (Aptitude 1. ~ ~ ~ I if (~ -qUaJUT) ~ 50 ~ ~ t'Test) consisting of FOUR (4) marks each for each c~rrect f-;rwr ~ ~ ~. mT ~ ~. ~ 1iIR (.4)aicf; f.f.response. Part II Mathematics has 30 objecti~ type I\''l~

questions consisting of FOUR· (4) marks for each ... ~ ~ ~ I 'I1Jl1 II TffUrn if 30 ~ ~ ~ f;Rif ~correct response. Part III consists of 2 quessions ]' . ~~~ffirl:;;rrr(4)3:tcf;fl ~~~rrrTIIlif2mcarrying 70 marks which are to be attempted on a ~ 'f>I~ ~ 70 a:fc!; f.:Imftf f I ~ m ~ we_n~separate Drawing Sheet which is also placed inside "*.~ \00 "'i!Ti!TT.;. me: 'R ~ ~ I~ m~ f.:Imf«rthis Test Booklet. Marks allotted to each question are 'i"~-' Q {!~

written against each question. For each incorrect afcl:i "I1v-:r ~ ~ affifm ~ I . \Wf I 31'1r 'I1Jl1 II if ~response in Part I and Part II, onti-fourth (1/4) of the 71fflf:m'f ~ furo: ~ ~ ~ ~ f.:It:ITfu:r~ 3T<f,l if ~total marks allotted to the question would be deducted ~.....J (11)' ~ if ~ B=.rr ~ ~from the total score. No deduction from the total score, l{CI'-<il'Cf'-l> /4 a:rq:; ~ <.fI'1 ~ q;g 1,1'<, "11'<,'1 I "11~

however, will be made if no response is indicated for an ~ -.:r:i if ~ m 'fiT ~ "3Tff -:rtf ~ 1]GIl.t, m liBitem in the Answer Sheet. <WT if ~ ~ afq; -::r(f q;rt ~ I

2. Handle the Test Booklet,. AnsWer Sheet and Drawing 2. -wan~, OU{ ~ ~ ~ me: 'fiT ~~ mSheet with cal'e?as\tHi~I'!Fiq c:drqm,sfimues (except for ~, ~ ~ '1ft ~.mr if (~ wan ~ ~discrepancy rn' 'Fest'·,'~1*l~fC06a.artd Answer Sheet 6W ~ ~ <irs if f'llmIT Cf>1 ~ -A-~ z r )..-:r:r.ft 11U!llTCode), another set;\\d1l'lJe ptovidelf. "1">1'<91,':>"1">\ ~""" ""

3. The candidates are not allowed.to-dn any rough work ~ ~ -.® q:;zy.ft ~ Ior writing work on the Answer Sheet. All calculations / 3. 11Uanf*if c@ OU{ .q-;r "tIT <iiW '1ft 'tCfi <FiJ7.f <IT fffig'r~ 'fiT Cf;ll1

writing work are to be done on the spaee provided for q:;f.t Cf>1 ~ -:nIT % I ~'Ift 1J11RT v:ci ~ ~ CfiTlT, "tJU1l:lTthis purpose in the Test Booklet itself, marked 'Space ~ if. ~ fcf; ~ 4-for Rough Work'. This space is given at the bottom of J""'"f" f.:I ~ ''tCfi ~I<i ~ ~ ~t 1iRTeach page and in 3 pages (pages 25 - 27)at the end of the ~ t "tIT mM~ I ~~~~"T01:R'lN ~booklet, 3fR<ll!U ~ ~ a:ioif3~ (~25 - 27) 'R-ey~tl

4. M'th candidate must show on demand his/her Admit 4. ~ ~ 'R ~ wanm f.Rt~ ~ 3l'RT m CfiTtCard to the Invigilator. ~ I

5 No candidate, without special permission of the .A -P-.-A -A ~ 4- ..,,+.I. Superintendent or Invigilator, should leave his/her 5. 3'l"l1a.:r<fi <IT 1'1('Ia.f1l1 "1">1 Iq~I'l ar:p1fu Ct> f<iA1 "I">I~ wanm

seat. 311RT~ ., ~ I

6. On completion of the test, the candidates should not 6. 1il:TltTT "Bl1TIfm~ 1il:, 1il:hTT~'f f.HTltTCfil 'Cfi"T 3TI8leave the examination hall without handing over their 31f~ W!lJUT- 'I1flT I ~ 11firrq - 'l1JlT II 'fiT OU{ -q;f ~Answer Sheet of Aptitude Test and Mathematics-Part I ~~~ 11U em' ~ ~ ~.......--'='-'""'-& II and Drawing Shed of Aptitude Test-PartIIIto the ~1'l1'Q1'q ~-'l1JlT III. ~ ·we. G'1 ~I(' ~"lI~!O ~

Invigilator on duty and sign the Attendance Sheet at 'R a:rf.t ~a;R $mT q;f.r ~ ~ m 11Uanm'f ~ Ithe time of handing .over the same. Cases where a ~ ';{~ "tIT ~ lfAl ~ fcf; ~ ~ v.ci~ We-.®candidate has not signed the Attendance Sheet the ~ TfQ; ~ ~ ~ tn'I:R m CfiT A itl:fFlT ~ Isecond time will be deemed not have handed over ......A-n......;;~~';!'TQI'~~~=-r~~ ..........-:.:these documents and dealt with as an unfair means "1'I~I~1 {!, .... ~ ·"'·!,V 'fJI ''10711'1 ~'1'~'O '1"1 '"I

case. The candidates are also required to put their left ft{Q: ~ ~ "Q"t ~ ~ I ql!Ufil, wanm 31'Rthand THUMB impression in the space provided in the 31f~"tJ'U!lJUT -q:ci 1JiUm - 'l1JlT I v.ci II Cf>1 wan ~ c@Attendance Sheet. However, the candidates are ~ 'm ~ ~ Iallowed to take away with them the Test Booklet ofAptitude Test and Mathematics - Part I & II.

7. Use of Electronic/Manual Calculator or drawinginstruments (such as scale, compass etc.) is not allowed.

8. The candidates are governed by all Rules andRegulations of the JAB/Board with regard to theirconduct in the Examination Hall. All cases of unfairmeans will be dealt with as per Rules and Regulationsof the JAB/Board.

9. No part of the Test Booklet, Answer Sheet and DrawingSheet shall be lietached/ folded or defaced under anycircumstances.

10. The candidates will write the Test Booklet Number asiiven in the Test Booklet, Answer Sheet and DrawingSheet in the Attendance Sheet also.

11. Candidates are not allowed to carry any textualmaterial, printed or written, bits of papers, pager,mobile phone, electronic device or any other materialexcept the Admit Card inside the examinationhall/room.

,7. ~(.'Jq;:lf~Cf>/~«1"i!1lf<.1a qf(Cfi(YjCfi7.!T ~ ~ (~ fcf;

~, cf;tm:r~) 'fiT m~ % I

8. 'litan mif ~ if, ftrrv: 11Uanm~.v::~. /ont ~ f.:I<n:ITv.ci ~ &m f.rqfi:rn ~ I ~ m'I:R ~ ~ ~'Ift~"Cf>T ~~.v:.q./~~f.!<.n:i'fv.ci f~~ ~~I

9. f~ '1ft ~ if we.n~, <fiR ~ ~ ~ me: 'fiT~ 'I:ft 'l1JlT" ill 3lWT ~~ W';{ m ~ ~:31~~~1

10. 11U!W~. OU{ 1i3! ~ 9Wr -me: if ~ ~ w!w ~~~11Uanm-m1~~~~if'lft~1

11. -.rtt~m mu -.rtta,.tT ~/r.n8,f if ~ m ~ftrcmifuim1JC.'filrCfit~~, ~lIT Ml'1f(YIRsld,~rtf~, ~" ~ liiR, $~q{if"t&i ~ lIT~ 3RTw.m-cnTm-mitCfiT·-R~ lIT~ ~ Cfit3~Rpm~1

O/Page 28

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