2008 aieee b arch
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8/6/2019 2008 Aieee B Arch
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AIEEE (Architecture) 2008
Part I j ~ J
M.athew.atie;s I ' I r l u r n
(u r is nne-one and .O'nto
(2) f is o ne -o ne bu t not onto
(3) f is n~t one-one.tnt: Qilto
(4) f is neithsrene-one nor onto
2. Let A", I( l):,jy) :x ;> 0, y : : > 0, &2+~':=: 11 a .nd
le t n '"Hx, :y ) :~ . > o, s> o; xlJ + y~s fl.Then An~."
(1) A
{2i B
(1~.} q . t W l il empty set)
~4) l C O , n , (1, O)~
iI. Lc. t Z be ~ICO"i(Tlph~?t number such that ~·z I= 2,
Then . the maxim&m pOS$ibl~ vahle of 3.;.
' Z 4 - · . · ~ . · 1 . j 8zi :
(1) 1
~2) 2
(3) : : I
(4) 4
4. The number of sQlutionl,: .~!fib~quation
,;2:_ 4 . 1 x 1-2 ;;;;; is
(1) 1
(2.)2
(3) S
(4) 4
1.. 'ijRl'f: (1, oo)~. [1,=) ~ ~ ' l 1 I ! f ¥ m f f ir ~ . ~. t! / .. , x+:2' ~.L\l'J - -- rll
- ",-1··
(1) r , t t < l ; q ; l ~ 3Il'6f§l~ .~
(2\ f. ~ .:tl2 ~ ..~ ~ ~
{3} f. ~~~g·~·~t
(4) ' f , : : r m ~ ' ~ . . - m $11~I~<ti t
2. 1 W f l A "" U 'x ,·}" ~ )( > - 0, v > O~ lC .2...-y'l>.= II' WM
".. . ,. , B ' f( , .. a ",,;6· + yfi ~ Ij .•-,nt .. ~ 1X, y .1 ; : :( .. . .. . ' . Y ' ; l o u. .d> •
ffiAnB~
fl) A
(2) B
(3) i j l ( ~ ~~'!'it;l)
[4) Wll,1 ), u, O)}
l'lffi Z 1 lJ ! i ' ~ ~ ~ .ww; 1 i t f ' 1% .1 z I ee 2. ti l
\ z i'~ I 'iiI ~ ~. ' lFT ti Z .
(1) 1
\2) 2
l : ? l } :: I
(4J 4 -
· 0 1 . , 6 4 1 ? f 1 , ( U I Jl;2-4Ixl-2:Q ~~~'~~
(1) 1
{2) :2
'(3) .3
(4). 4 :
. A/Page 2 :
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5 .
(2) A-I
(3) I-A
G . L et A = [a1} he a 3, x 3 ma.trix: w'flM,e
det'ermi:r'l_1IDtis {i. Tb, e: n th e .det.~rminan.t of the 6.
matrix B '= (2~- j. . a ; j J is:
u~ 5
(2) 10
( 3 ) 20
'(4) 40
7. A I$ ciIoQl aw~d-e-d 38m;e;dals in football., 15 ' in
beskeeball and 2G i . t 1 J ! cricket. SupPQ5e tileS'll: '1 .
medals went ' 0 0 ' a wtal of 58 students and. onlythree students got, ~eda.!& in. all tmree SP!uts. If
only 5 students got medals in football and
ba,skfitbaU,th",n th~ number of m eflalsreeei .. . .·Q _
i :p ex , :u; , t!y two of the three. sports is
(1) 1
(4) 13
I J i A T A = [ :o
0 ]o .' ~mBA l- .1 . :3 > ::3 "ffil
]
1
1
{U A+I
(:2) A-I
(3) I-A
(4) , A
:qFfT A""la,,] ~ 3 ..:3-~~ ~~.5 Q '," .Il _ ~ " - , , - o . t < ;:
: ff l ~ . B = [21.-J l\j~q)f~Hj]i~bt
(1) 5·
(,3) 20
(4), 40
~ - ~ ~ ' ~ .~ .- ~ a sm. i ;( i' W i l 1 ii li ~ ~ 'W I l!
15 Wi[ ~ t~o ~ f .m f t . : f f ~ I ~ ~1 } 8 ~ ttI~· ~.~ ~ m~ P r u l m ~" q i l ( f i - & i ~ ~glrl ~ , ~ ~ 5 felQI~ ~
1\lW " & l l T ~ [~e:41d ;i f ~~~r ! m - , ~ : ; r - r f i j ? J J ~ ; ; t 1 < i f
~ ~ - w . r if ~ ~ ~ -~ if . ~~~ : t "m~
(1) 7
(2) " 9
(3) 11
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s , Let /11~ea' ) ,se~'Containing.teil" e~menlts. TheEiThe 8.
num bel' orsubs,ets o f A oontaining'at least four
elemeutsis
(2-) 3
(3) 7
(4) 9
1013-~-,.-
.9 0
1023
'90
( 4) 103390
" + rT m ~ A ,~ ~ ,~ ~ : I. m ~ . ~ - ~ "'R
~ 9 1 ~ ' A · ~ ;l " n j ! ! f o ' l ( 4 1 · 9 f tmr~;
(1) 845
(2) 84~
(3) &50
( 4 , S G 4
(1) 1
(2) 3
, 8 ( . 8.
J
, . , ' ) .~L ~(j~+-]- ' )~-;-U-+-2-)j..
1 . ' 0 • .
IU]{I(l3
90
1 Q 1 3
90
1 0 2 . ' : 3
'9 0
103:3
, : ~ ,O
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Let r: [0• ..,) "'"",0, ...) b e g iv en by I l U . .~o' f
f(~) = ~ _ , ' ~ ' . If -f'(.) donotes t ho d c inva. :t ~1 /e(IfL.irti .1 .
(1)3 0 5
( ,2) 4 0 0
(3) · 4 1 5
(4) 55
0> m - o( 2) 1 0 5
(3) IH.l
( 4) ns
' c m : n f ~~O....}~ [0, -} '{fT ~ '~ w . m " ~ f . f i
10 ~
: J ! x } " " , L . ! . - . *n .J.£(.) < i F ~ R , ti r'. I1...l
en3 5 <
( 2 ) t o
( a l ·1,5
( 4 ) 55 ,
'2(1
~ " .. c " • [ 1 . 1 1 1 ] 1J : . . . J I T + i:~-l+ i - t o ! : ! + - ' " + 20 isi-I
t(J) 1 00
t'l) 1 ( 1 5
(8) !lIO
(4) us
ill. T he cq,uat io: l l 4:-:\5, O : l l : ' ! 1 - 1 t'b ;~ - i 2@x +4tl "". 0
has :UJi" .~ ,!jxi, - + 5i4 - ll)~ -00.1: i'.4I(lt= 1 0 t
( 1 ,) Hi;) r ea l ' "lHl't
(2) t!!!liIi.dJy oM .roolm~~
(3,) ox;Qaq' t~;ttl!ereal room
( - 4 . ) [l1!@If'W] RO'ts
!l4,. Let f: ( ~ o . o ! " "J , "" -, ).(-I","! ....),bEl ncon.linuolls and
di i 'er -ont i i3h lre f~l 'iIcti{~1l a lild l~ Q t ,[~ (•.) d e ~ o~ th~ 1L4 .
d m c Y ' s ;t f fi v e c elf 1 1 l . ) , I T ilC ll ~ - 2, 9mdlf'(x):S S, f~!1"
' E 1 i ! ' l . ~ h i! l ~ to, 2 ], 'tbcn tholatgest; possibleva]ue of
I T & ) i8
c n 1
(2) 2
~3:):3
r4} .~
fl) ~'~'~~~
(2) '~~~h'\Bi
an :~~d i : i f.1~<f~ ' ' ' ! , ' f f ' ifIt) .~.~?#
liAr f : (- «!!, Q<»4 (- '~ . ( j q - l '~ l[ffi1' .~.
3N i& 1 ofiQ ~ i~I l ' R f n·). iI-) < jjJ ~ . 'I ' I~ f% , f l : ) I ] , } . . . . -.2 ' i j I l f I . x r ' o , 2J .~ ·frm(f"(:d s3,
il t 1 1 ' 2 ) 't1 ~ .~ ~ . ~ .~
OJ I
(~),p _
'(3) 3 :
(4) .4 ,
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" 1 1 ( ; 1 : '1 t h u maximum: po~s1li 'bl~ ' " " a I U l , ! o f IN e m
1-1.21 is
U) 1
(3)
( 4)
11.1
..16•l.el rc ( -" " ', -l _J}<f- . . , . «I) be R l v , e r n by
flxl ....1 :1 )li 1 1 - !"-] 1- J x -2 i2",_I :1-3 i3.n A d el l a Ce s Un : ~j" 0]' p o i r J I t . , .s w hew :r{.) is 11<11
i ; l i l i ' rnronl1t lhl ,BJ, ille!:l A ::
W 131
(2) mI J J . r o , ]
(11) ~ 2 1
'I'1 . l.eln· )eud g r . ) bil ' d~ffi l l l"! ! !ntitilil~ fWlwons on 1.1'.
( - . .. .,.,. ;) m Id ld f'(,) illnd g'(.) o en nl lr c ll lc l'iVU ti ve S
Yn~. '<~ITd.,r ,,\ res'."l~ctiVl"l", If nfilj'=!. rn'1)':;;c!. ." _, ... . J'. . 'IV ,2,' ,100' ~ s '
N ?)= .n u nd ~ 'a ~ l; : ; ; 2 , t h d l r n , the value or
2fm:x:2 i- : . h . :) - 1lim;-;'Ill 31~)!:)-1
(Ill
15~ m f:1-1,21--+ (- ....,....:) .~. ~ ~ ~ 'f 1 %
, . . . . . . x '" + , : ) : s , 2 1 " " ! 1jl(X).". 2 .,
x : +1
(l~ 1 .
(2) 2 9 1.5
( 3 ): 2 . 1
6
(4)28
Ii
~ :[:(-....,....-1(-.......j ~ ~ h~tlitf{~'cx I x I " ' " I x~ 1 1 - '~: Ii , - 2 ' I Z . , .!,):~SiS.*A ~i~j , ~ <i '~ ' I . ~ ~ . , )<.!t~ ~'
t. ? i t , A . ..(1l) u n(2) III
(3) I G I
(~,) f 2 1
iJIi1l'Il') 'rim ,g{.), t( ~ ""'. "" '), 'qt; $I<!,'I' lIif.ai,:jI\6R'l , > ~m;;u fit.) ~ g'c·) ~fr·) itW m'l it~'
~: I ~ . :r(O}= !,O,),,,,, !.Ol) "" iL ~ ' g'(O} = 2 •2' : 3
m lim ' 2 : f i f 2 x : 2 : + ax) -1 ~.~ t:.! fli ag.{:I~.-1
o n 1
( 2)1
2
, (S )1-a
(4,)1-
"
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18. 'ftteV1ll!hliCQ : F
l-
I , , ; ; 2 'a- )i()® dx
0-
1.
610
1
G S O
1
641
1
660
1'9~ la, Y =Il!:)l be , 9i, ~ ' which ,~. tlmrugh
(3~ I), ad 'U l Islildl "Uliid. \ \ ~ 8 i l at, ~J po:mt .. iit ];9~
poo~~ through (1. 1), The-n y =: fitx) Ile~l.:ffij
(1)' J J 5
Q
(4) 3
1
11 . , " J X!!(1'_ :x)9 ,d «
(j
OJ,m
E I , l O I
(2)1
G I G
( 8 : ) <J l
& t 0 1
(4)];
G S Q
1 1 R ' I ' s =1l~)~ ~ f c i t ' (3. n l I ' ~ ' > m m '~ ' ~ . 'rp:
HIt ~ t,~ '~ '~ ~ I ff" ~ ,'~
(I,1) ~ ~~ '~ ~' I~Y = 'Ix ), ~ <ii«I ' I t
(1) '~~!if~~'~~'~.
t t ! > . ) , " I 'I F . I 1 : " " " ,, ,' ~ifd ' : i i i ' ~,m.,_, ..,~Ij,~ ,;"" ~'!i;ll . _ ' __ I > • • _. qt~~~ ~'K, lI'
( ~ ) " Q ? i ~ ~ " ~ ~ ~ 31tW
(4) 'V!'"OW 'P .~' ~ 4", ~
I !x ..J I 'C U aTIi1~~ , .,. (~ , J) '~'
fJ( :i l: . " .; = 4 ! ' ' 'R 'fmt~
,(I)2 . / 5
1 5
(2) .Ii
(3)Ji5
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:U . l\v(X verti,c:es of a triangle ~ (1, 1 ) ~ d 1(:3,;.) ..ml.d 21.
the third. vertex I]i~,s'on the line- y= x T'l, Ifhe
: ar .e a o f th i i j i triangl~ is 1, .then ,the thi'l ."d veI'te::s 'O f
the triangle is
(1) (3,4)
~ ~ ~ . ;# ~ . (1 1 1) "",",,"'O ) A I) $om. ~~.~ :~ •. '.' • 1G ,l1 ' ~~1~ ".~' '!;f~·I. 'l:Jl:~ ~ ~ ' i ,Q"1 lU OIt1"{1 " u · . . .jj·m y"'x~l " q t m * ~'~'~'~<m~ 1
. m . > ~ ~ <l l I ~m ~(U (3,4)
(:2) (4,JI)
(2) (4 ,5J r ~ : ) . (5• .6 )
.W) (~, 6) (4) (6.,7)
(4), (6,7)
22. Let ~;be th'e ate~ \ ' i t ! ,sq,oa:r~ ein:unu;;criooillby tlu~
ellipse 4xz + y z = 16_ Then ' A"" ' .
Q~ 4:l2+-t_'16 ~~.~1Jtt.~;;;nf
'C f i T~A~n iTA" "
(I}.61
', 5
(1)61
5 62 ,
(2 J -.
.5
(2),6 2~
635 (3) -5
(3 1'6 3
5 , (4)64
,5
{ 4 )64I)
23. Ut.he.'~in,e 4!M:x - 3y:"" 4S'h; a:ta-ngent ~o~the
hYP'etbola U5~- 9 1 ~ .144 p .t .the point (xo ' Y~)
on the hyperbola., thel'! x~ + i~=:
(1)161
16
(2)],,,8'
16
(3)169
16
(4)1 1 0
16
~. ,4Iff lI"I(i lIH~ I'6~!l -.g~ .~1414'~ '~ '~ (Xo,y,o)
i1R~: 4m x-3y=48~~~, ;ffi i~:4' Y~ =
(1)167
16
(2)168
16
( 3 )16'9
16 ,
1.7'0
ifi
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24. The ,sb.Ottestd:istance hetween the circles
~ , ' J '. + ~'= l~nd Ix - ~9)?- 0 " ~.l~ .,,4 is
(1) 9
(3) 12,
(4) 14
25. The illdiiu;sp r thesphe:re
(x~ 1+ ,Ji)o{x - 1- ../2)+
(y~l+ J'3)(y-l-,J'3)+
(z - 1+ /5} (~- 1- .- Ji ) ."0
is
(1) J 2 .
{ 2 } J3
(3) J5
( 4) J W
In. ~l;riang1e ABC, measures 6f Ifmgles A . B and C
.are 3 0··; 1 0.5 .;' 'and 4fi'~;re5~iv,e~y. l I i f o is the
orth,oeenti:re oftrh.lI l,gJ@ ASC, then .~~=
J G2..
JS2
( 3 )J 2
2
(4)'j2
24. .~ x2 + l' = 1 mil {x - 9)2 + (y - 1 2 )2 : "" "i it t f 1 l ' - l '
~q"~ilt
(f) 9
(2} 11
! S ) 1 2
(4) 14
25. ~
(x - 1 J2 H . , ; - 1-J2~)+
(y-l-j,. J3)(y-1~./3) ""
(z-1+ J5)(z-l-J5)=O
0) J2
( :2) J3
(3) . J f i
(4) . f iO
'26. .~ ~ .ABC T f r < i c T s; B'~ C ~ ~fJN~ 30".
i05;" am ,.50 t ~~ , n , ABC~' ~-~ ~ oi}', m 'bA'00""
J 62
(2) -2
Jj(3) ~
2
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> ( 1 ) 2
{ 2 ) 4
(~) 6
(4) S
:28.. The value of
_ 4· 1t, 4 ~ _ ,4 , 5~ . _4 71 t~'8 + cos 800S- S +CQ~8 .
is
OJ
( 2)1
2 .
4
(4)1
4
29." 1 1 : .an . finSID -_ ,. Sm -_ G ,. Iilll~. is
:1;-4 14 14
1
4
1
8
1
2
(4)1
-e-e--
1 6
-10 ,~, 4 . ~ ~;;\;&
2'1. 1W Ifx '. y ~ '::1$ ~ 'mi.: ' I:! r'l\f ~ - ' 1 1 ~'I.p
I - " .' . .. .I ~'I - I i , ,, - - - . 1 2 r e- ~- '2 9x - y +. y- I ' ! , +'1 2 - ~ , ='"
, . : . I " : : . ' . ' _ , _ " " * ""lo 1 2 -4 -t .~r ... -a- y - z - 4.:X · ~ Y ""
fl) '2
, ( . 2 ) 4 -
' (3) ~
(4) '8
...411;: . 4'.&i: , ,,~ ~_ 4 , 7 1 1 : : . \'CO il .' ~ + - cos- ._. +,(!O.S - + 008 - ~ ~ fi'- S --- ,S . 8 . 8
>: I I . . .
{l)3
2
f2)1
2
fS )a '4 :
1
"
29. _ " _ ' : n ; • 3 1 & • &l; ',. ., ... .. .".. : 4 . ;SIn -_ _ •~1D '-, • : ta.J ll --:-- _ . " " ' 1 "
1,4. 14. 14.
(1 ) 1
4 -
(2)1
,8 .
\ '3)1
2
f4 }1-1 ,6
A/Pa,ge 10
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so . EqW\~ urI! ammon ~t,(ifi1-~.) to
x :lr+ y " : . . 2 - I:nd x~'y~D1 is
DfN Clii!l1l.U : Qus:tiams mun:bu ,iU ~ 3 6 , c : a l I t a i n
St_t!c'M'l'It-,IBnd·8tatfJl1rent~2" Of t'M fhurt:hoi!Ms
gilli'n ~ !Jr ' ~ e :i~ArnmdiS.,~, ,~~Qe:,itd Ii¢s~ I
~,th~~lsm~. 31.
11.. Le' f: (- 'D O. - ) -o J (~-t '-l' m e defined b¥
I; 3 ! . - ' . , I."f:!!i > 1 0
a x ) ' " ;1 0 . , if x S 0
and 'let r(.) ,denete ' d t "C d~tive off{,.).
,6t~k:","ert~!
llim r o o , . . . f '~Ol"~~"o
Slat ::C1 lm!n i- .2 ;
f'(x) ms,l$i' fll}, e ac lJ x : i ! ; : , ( ~ M', !!'?l. !ttId f'(x:) ! , s ,
,continuous a i ' 0' .;r
[U ,Stiltemont-l ig t tu e ! S 't o. 'l lome :n : t- :2 :1 8 tme:S tlit em 'D '1 l.- 2:s 'a ~li:t, ~I_a t io l l ! G l r '
StatemCOiilt-l
(2) Sbatemen~l is '~ ,Sta'temen~2 is true';,
Btatelilitlt-2 is n m : a ~ ' exp l ranat ioD of I
Staiem-'Dt-l
(3) Staiemenl:eil mmu" ,Stateme:_rd...2 is falSe
(4) Sta:tement-l is falim ; S tatem ent-2 ~ trae
H. .;, +l;:ijIIJ x ' - I =1 < it 3 1i 4 'P to a ~ ta (~~ ~ f) ~ \'Ifll~(or •
(I.) x+y: J2
t l ! : l ) : s o . " , 2y = 2 :
(8) x+yi : : : :2
(4.) . x . .. .'2y= ,,fi
fiilIr: JW f r i 1 i t i J 3 '1 i'6 ~ " v , ~ rfji'SfR~l a v n </if ' .R~2
, ~ " ''lRTr{ ~':ll{ iIR" fifit;ffi ;fiR1 , f i R ; C : q
PM'iflR f 1 i f it" ~ ,~Jfpf ~ i if i irdl I~
. 1 I I F I J r·,,__ tro~~" (__ "" ~ 7jiiD' ~ , 1 . ~ '_ _ ! I ! , ' - , - ' ,/---;r ., I I~I ,~I''Y ~'1"1!:I1I1~O '~
Ix', ' I R • " 0 ,'(It) =
0, '~lIl, ,~ 0
lfqf:!illtlll tN. iN ;; m , i j i 'H i i l " l ' ! li
:iji tff-J :
11 m f~'(xl= f'(O).,1:'" ~
~-:2;'
Ifit~, x 'Ii! (- -. -) ~ · Im t 'r() ~'~. it R21Tr't:d~ 1 ;1 { tIffit····
(1) <i1R-1,llIfq , ~-2: ~ t; ~"It ~I ;j"
m~tnn~l ~ ,,~2 ~ ~; i'JilHs~ ~·l q,i
'~~~j
(8) 'PR~1~ .:',~:2 ~ ~
'(,4) ~-1 ~ t~-2 ~~
A'P~gel1
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32. L et f: [11, , ~ > - - - ' j ; . . (0 ,0 : .<» 00 glve:t' I by
10 ,
f(x) "" I I ' T _ 1 _ , •, "-l1=1"" .
where, for real numbers, al,,~...a[J,'~
n.
n at denotes the prodJucta'l K3'2;"x... x an"
' 1 " , f
St(l..tc:~t·l z
HI
f R)!} dx"" Ll . . . 1
( 'itl t, I ' 1 '1',-',j' n x -, .,
(l-l)! flO-/)!
33.
10
w h e:re A , :0:: n , ', [ , ' - , _ , J - . , 1 .. t, 2; .. ., s o .(l-J J
~-=; lJ;e.l
(U Statement.l ~ true. State<ment ..2 is true;Statem~t.2 h , i , a ~rnct axplmatton ofStatemell~] .
(2) S'tatement-l is true. Statement·2 is true;S ta :t er rr eo l- 'Z ' i s liot ;it' correct exphrmation of
Statement- J L
(3) Stat~ent-l is true, Statement-2 is false(4) Statemoot-], is .fhls~,State:r.ne:nt.2 is true
The directrix of a parabola is x + y '" 2 and thefocus is ( , . / ? - + 1, ../ 2 + 1).
~tatenuint·'l ,:
L ength of the 11J.tu!Jrectum. IS 6"
beeaus~
·Statenwnt·2 :
The·dist.anm.~· of directrix from focus is3,
(U S t!;llj;em ent-l i~ ~e;. S~.atem.e.nt.Zis,true;
StjlJtement-2 is a ,e-artect eJtp~aoat.ion (if
St. 'loomen't-l
f2) Statement-l is true, Statement.-2 is true;St'atement.,2 is -not .a correct explanation of''$tute.ment-l
.(3) Swwment-l is false, StareroJcnt·2 ig·[al.se
(4j Statement-l is:true, Statemant-2 is false
32. 1fA i I f ~U.~) -+ (0, 00 ) ~ 1Rm ~ lJlIl ~ '1 %
1 0 0
it,.) '" IT x~l •l-l. .
u
~ qlflifi ji±limr::l1T apS'z, ,."• an ~~n al,
1= 1
< F i I %
q ; : 1 1 F 1 . : . 2 :
, s,&.r L 1 Q A .I:X .~
Ill.=)~1.<'1'"
f(x)sa ,,' '. - i
x-lh
1 Q
.~ 4= n J l' " 0-'""I~I &"1 --., "" l, i; ...•Iv.'(i-J)
J=ljI'd
,(1) 'fr~1'~1'~~' ~-2~' f; <li:~-2" ~~1 < $ I '. . . . . . . . . """""""~ .QI<n, ~I,~'II ~
.(2) ~-l ~~, ~-2 ~ ~; ~!?F'1-2,<r.~-l .~
i R f i " ?41~1 ~,~,
{3 j ~-1~t',.~:<2~·~'(4) ~-l·~ ~, q)~-.2; ~ .~.
. ~ ~ . C 1 J . r"'44tjFx. +Y "= 2 t fJ!lij ; : n f t . l
( . . / 2 + 1~J2. + 1) ~ I
~-1:
~~~~6fll
~
~~2:
~ ~~tft(~ ~',3 ~ I
(1) ~-1 ~.~, < 1 l :i i r- f- ~ ~ ·~~.w:r.t-2~~-1·<iIT
.~~.~
(2:) =>'=-1 ~ ~ ~-2 ~ ~. =a-:...f> ~-l < f . : T ''1."1"1, i Q ' J ! ...~.J! "'1!t...,"1 t:#,
~~~~
(oS) ~-131"rn ~, ~-2~' ~
(4)~-1~~,.~~-2~~
AIP'age 1.2
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An urn contains four balls beRrin,! ; numbers 1,2,34.
3 : and li.2S, Tcspecti 'Vely.; A ball isdtawn ..at
random from the urn" Let :E~,i"", 2; $, deJilote
th e e vent J;. ha td ig it i, appearS on 'the baH drawn.
Stqtemerit·l ;
p(E1 n E:? )"" f(E1 n Ea).: P(E2 f1 E3).., t.Slalemen;i.2 :-
P(E1}=P~E2J",.P(E3):; i'( I )
( 2 )
( 3 )
(4)
85. Lel
St< i l t ement . - ) , h, t rue" Stawinent-.:&is true~,'$ta.t.~meT;rt,.:2 is a eOl'1'ecl explanation Q: [
$tatement-l .
,S t ateml .%1l t -" l is, true, Statenl,entr-2: ir s true;,statemeni~2 is, nat a ,oorre<- t 'cl--planation of
Stat.emre!l.-t-l
Statement-I Is ra,]sej Sta'tem(}nl(.2, is true
Statement-I fstrue, Sta,tement~2 is false
COfitinU01!JS &to ,and let
( ~ + Y ) ' :((j;:)+ f(y) , . .f,2.".. Z ,far 'every x, Y ~ . ' , ( - < > ; > , <xl).
State7r:~,etl.t~1:
« . J is continuous at every'point on. (- -, ~),
'because
Slai'(unen.l:2, ;
2 ftX'iI" h-}+ f { . c j) ' " 2 trllj) + fl2hJ.
fvI' every :;:{.h E i (- ••,\ ... . ).
n ) S t 31 Jem~n ' t ,. .1 i s true. S'tatement-2 is t l 'U 'C ;'S'tate-ment..2 is a. correct ~:xpl~natio.n ofStatement~1
(:2) Statement.., 1 is . true, Stateme:ut-2 is true;StateJ;llent;:2 is n(')#·8 cotteCtex:planation of
$tatJemeo:t.-l
(3) Stawm.ent~ 1 lisfalse, Statenwnt-Z is true
(4) Staooment:-l is t-nlIl;'1 Statemen,t~:2'i : : ;k~Sie
~ ~ t j- ~ :m 1,.2" 3'~ 123 ~ ~ ~.~
~ I ~ it ~- i f e : ~~ ' ' ~1Tf I ~ . E,i
i"",,, 2, :3 w-rJ' t ' N > N.ti i.~ n f ~ , ~ a w n ~ II
~-1:
p mln R2')'~ p(E] n Eaj ",pr~ n '&3) '" ~,
~
35.
<1i!tR-2.:
P(E 1 ) = P(E_2) = = F e E " ,) ; ;;!.._ a 2
(1) ~:_'l 'Hf!4t ~-2 ~ t ; ,~-2't ~q:J-l ~
a l< I; .~ ~
(2) ~~l ~ ~~~-2 ~ t ~-2, ~-1 ' < t i r o
m~.rt '
(3 ) ~ ~ ] ~ i. 'HZA -2 . ~ ~(4} ~~l 'llffi t. 'i~<'!~2~.~
~ f: ,(-:-.,..,«.) ~ {-..", oc) ~ l 1 < f iR ~ ~ f i t>}~
'f.(. ~. t fi~ 1iRT f ( . · · X ~ y ). = {(-xl +~9")2 ., .2
~ Xi yeo (-.,." oo}~ . ' f f l : r o ; l
'fiffif-l:
ft·), (_,00, . , 0 ; , ; ) t~~r( .~ f I~
~2:
~ x, h E ( ~ O o O , ~ ) ~ . ~
2 , f \ x + :rd +~O) ;::::.:f(~)'+ ' ff2h).,
(1)~:'1 ~ ~. ~-,2 ~ ~j ~~2;, ~~ 1~
if.f; ~ t(2)1 ~-1 ~ t ~-.2.~ t~~~~-.2;"i~T'1-1~m ~ ; ; r f J ' : t
( a , ) ~"'1~'g,~tR';'2~"~
(4"~-1 ~ t, ~~2~"~
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Pal"t.n I ' I 1 1 T D
.Aptitude Test I ~fa l f t t a ; r u r
D ir ec tic m,. 8 : Wor Q..t16 to 40). . ; : t c l ) prow'tm f l 'gwa · : shpws tlw ~k'w af , an .yobject, litinttfj i f o e : C(. IJ"1vct . t (Jpuie~
: fr om amo n gs t. the· answgr ( tgure tJ ,
~: (1T.:36:it40 ~ f M : V I'$,·n .~.~.f!j ~.~ : € i ~ ti t ~r 'Iff.lf'.~ i~ r l d f t · c;g ft ~ . S ~ 'i f #~./
37.
38. BEaBa·
(l} (3)
.89. P ~ 5(3}1)
40.
·0000(2) (3) (4).
A/Page 14
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, Directi_s :: (F.r»"Q., 41 . t Q 4 \ ? " ) . 3-D problem (l/JU'i'e shiot,ps ~ t i - w w of ~n o~ject~ IdentifY' the C Q r n U : t fr{fn~
U l eW , f i 'O .m·amoRgs t tM -a.n;s'U'cr f ig. l1res~. l(H)kingin t h e . direc t io11:of the Q:rrow.
f i I tW ; f:r~41 W 4 5 if·~ l:l.on J I J R 31 !¢ fri'f ~ i i f f f J ~ ~ qft ~.''lpff ,~ , · f i J r f b l f f : J r f r if 1 ~ , O ! i J J f1[, ~ m i t
~ '~ q J f 3 1 1 r ~ , if "# '1~~q .r
41.
(1) (2) (3) (4)
42.
43.
(1)
(1) ( 2) (4)
(1.} _ ( 2 ) ( 3 ) (oil
A/Page 15 SPA CE · F OR ROllGH WORK I~lFWq * · k i l l t 'iPTi
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lh "r €tl'tlo ns - ; (P(J/' Q .. 46 t,r" (8). Id£1' tJi fy . tl'~(j' INITeet S ·D figur e fnam Irzr:rtfmgs1, t iu ; ~J i . $'We r f i ff l. u :: ( t' f' ,whi"!:h hae
· thje elet .' f1 . tiu l 'l , (l~ i j . ! :oen; in. th e pr(;lolem figlJ,il! o .n th e lrift,.
A iff] : (:g; 4'6N-4S * ~I J mR lifPi,fjp.j{ if '# 3W ' ~ 3·1 ) ~ ~ ·~f.il1fqji ~.?:f'f 4Wif , W i ! 1 9 7 f / JlR'
M i f' ln . i f P . 7 i t I
P r o b le ,m , . [< ' ig u r e . I J{Fl a ~
&\~rn
O'J
48.. B
!i\~.
(2 )
I~.>•.'..~
(2)
~.
~.
(2) ( ,3)
D i re cti .f( jR S, : (For Q.49), ld(!nlify th« 3-D figure f rom th{~cut-swel'f ig ur e. ,> , ~ IJ .Mch ,doo-}; R o . f lmt /e the sarf .e
d eo a li pn ." , a s gi.ven In t h . . e problem. tigun~.nt'he: i e , P , look.i"tC in th« direction I J ! f ~ rn )w .
ffi ihr ; ' (!c, .49 ~ fffil) '.,fflf' ~ if ~ 3tr . J ~ D .~m q i t ~ ~;ritr"iff}' a m : iJg# S 1{ ~~ . ~ ' : B i h : r . i,r ( !Wr' aqFrt , i t - ; Y ' f i1frm it I
£A .~ .~
~ >P --(1) (2) (3:) (4)
Dir.ections r (For - 'Q . . 50). J?roble.n'l. figu.re· shows top v iew" f (tn abjee! . I'deutify the . D o r r - e ' c t e le :u a ti r in , r iyml
(lllwng.st the ,C U i-s we r figure.~.
f.tW : (!l, 5 0 * W ! i o J . J r .Ff J i l P f i h l if F < W t ~ (fiJ ~ I~ iiii!i't'l4t ." Iplr ~ I ~ ~4f it i1 ,*iffiffl ' : ! ! i t W ! j : l J f ~
~'I
5 ,0 .~
~/ I 1
( 2 )
I I '
A!P~ge 16
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Directions: (For Q. 51). Which one of the answer figures will complete the sequence of the problem
figures?
~ : (J1 . 51 if; f f f i V I :m ~ if it q;'f;fflt . 3 W J i F r r c it J/N ~ if; ~ w r F r W 31 jWJ (sequence) 1 f ! T i t " i i f T I 0 T ?
Problem Figures / J fF f ~ Answer Figures / :m ~
(1) (2) (3) (4)
Directions: (For Q. 52 to 54). 3-D problem figure, on opening up will look like which answer figure?. .
~.: (J I '. 52 '" 54 if; ~ J 3·D J/N ~ c it ?itfR w , q f r ; : f f i t , . d " f R 3 1 F ji f f r ~ R ? M t ?
Problem Figure / >fA ~
52. ~
(1)
5 3 . ~
( 1 )
54.
(1)
Answer Figures / TrR ~
( 2)
(2)
(2)
(3)
(3)
(3)
(4)
(4)
(4)
A/Page 17 SPACE FOR ROUGH WORK I ~ q;pf iI; ~ ~
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Directions : (Po'r Q. 56 to 69). Find o(d the toted number of sUr f r :wes of the oqject gWen below, in the
problem figures.
f . rW ' : (Jr. 55 #59 i;~ /'WI ~' i; ' * ' ~ 7ft ~ fj t 1 i f i f e M J i f f W s w : m e r ~ I
.Problem Figure I JFR" ~
55.
(1) 10
(2) 9
(3) 8
(4) 5 ,
56.
U) 20
(2) 21
(8) 22
(4) 23
(1) 20
~
( 2 ) 17
51.(3) 15
(4) 1 9
(1) 20
@(2) 22
58.(3) 24
(4) 18
59.
(1) 13
(2) 14
(3) 15
{4) 16
A/Page 18 SPA CE F OR ROU GH W O'RIC :I ~ a..~iPIf
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Dire'Ctio#$ ; (FpT Q..66 to ,62). OM Q _ f t J w . , .folw,wing· answer ftjUMl hhiddtm in the probl(fln. filpJre, p: . tlw
same si.ze and direr;,t iQn. Sekcl' the' 6a"f 'Tt r .t f zgu, l 'c .
~ : '(J: 6 0 #62 a r ~ I ; ; f t#·i ff 1 1 ( ~ . ' R l f t f f l 4 f if ""ft)r{?fi"~ .~~ f f : :m i f 'W 1 lF f ~ 1 1 JfiR ~ i f . f i 9 r i J fi~ . I ~ 3 # f i I d < i t ~ I
C7(2) ( 3 ) (4)
a
.
v V0i.
U) (2) (3) (4)
62.~.
l 11J
(7
v 1~1 L J
(1) (a)
Directions; (For Q•. (3). Same figfU'ie'S. aP e ,given in the problem fig~. After assembling them, which fi.f1ilj'(>
w ill ~ {].fa nned, tho .r jt amongSt the ,ulwwer f igure .s · ? .
-fWtr: Of. [6 3 ir ~1:rrR ~ . i l J f J · ~ i f f ift I m7!~ 'R ' ~ 3 f J f j i f f r 4 r ' i ( i t ~ i ! f t r < } f f l . ~ ~ l
63.
n C } : J . [ . 1 .<JU [ S C P · . · · · · · · · . ~ · ·
\ ""' -
v
AlPage "9 SPA CE . F OR ROUGH WORK I~ ~ ~ ~ ~.
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Dire.ctions .: (For Q. 64 ,g.n,d ,65). Row many r o ta l n ,t l.mbe 'r · a l t'Fia~ks ate there i~·the pT.:olJknt {iituie girJen~~~ ,
~ ; (JI. 64 ffm· 65 · i;.(f:rro I : : f t i T ; ;f t " if / . .JfR ~ if f!rpfr < tf j>fl r P . i1 J ! ~ t ?Prob- le1i i F igu ., r e im aH1ffl
( 1 ) 1 0
( 2 ) 14
(3) 1 6
( 4 ) 2][
(1) 9
(2) .1 2
(3 ) 1 3
( ,4} 1 5
64.
lJiree:ti'cms .- (Far Q.6:tl). . 'How mClrty tota.' number .of fle(:tunglc.s Qt:il #u~J'e t~ th e probkm; figure. , g i u c . l ' Z ,
~!()W ?
f.I~t : o: fq : j ; . f t . r : V ) I · i f f i l ( [ t . 7f{ !Wf ~if ~ W Ff ~ f . r ; f r ; f t ~ . ?
Pr1JblernFigltl'~ I m - ~ .( 1 ) 1 4
( 2) 16
( 3) 18
.(.4) 20
66.
Direeti()a.~ ; (For Q. ,(7). How numy total number of Seini-circl9$' (ire therein.t.he problem figure gl'IMn
below?'
(1) 1 0
(2) 9
( 3 ) s .(~)7
A/Page· 2:0
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P ro blem _F igur o I )Jfi{·~
x
68.
10..
A Fi (---""~. 1i8wer _-~g.Unl'$· 0rH ....'~"u'f.r
(2)
(i;)
(.3)
(3)
(4)
(4)
A/Page 21 SPA ce fOR ROU GH W ORIK1~ ~ l lq ' ii~i P I f _
C o l le c te d b y w w w . a r c h i t e c t u r e n t r a n c e . b l o g s p o t . c o m
(1)
( l Jx
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W'me:h 'Q 'r :t ~e f al ll .o " ring : l T t I , ! ! I I ! > l I : ! J S n . S 'i '6, fmm all 'I.
Uirdtitec~ l'iackgro~d '?
III Heme Fel'.l1lU'IO,€'S
(2) Bah~.d
j 3 1 Bhll: pp i _ L~M r '~
1.1) ApadilCl ' Indian
11J Crunn
( Z } M i l ! l: z y ~ i ; '!
nn Sa1utl~ Afr iCa
14) lndin
Which . [ : Ie1:"S(; In i~ fu.mo\1.9" fur tb{! c.:- {wif l .~; ive
b ric k1 l'll0 :I "k I n X u .ra Jla ?
(3:} C!:n:urIM lCerraa
(tH AclmYIl~Ksn\l ',iPld~~
75.
(2) e r n a",~lga:rh1.3) K o'ikatOJ
(41 Pune
N" "tu rn l: !lh adow~M ! I; I~ghli:sa,vail;<l:.Me fri1;lmwWcb I
d i i r< l > e tk J tI 1
(2) Norl :.!1' i-West
(3,~ East
f~tdmi'l 1l. : i t ~ lPiIdiia "'ltt~IFN~ ~'
twm' ?
(1), ~~
(2).Q ij~l1t'1
(3:) ~ - a l l ! € !
(r4, ,~~
' 7 : 1 . ~ l~1I1!I '~ _ W « i 'i
OJ ~ij
(-2) ~:if
(~ ),~~' ~-~l ~rj
1 ( 4 ) ~if
~'ii fz~; i1'~' U ~ m·~·.QT~~.~:?
U) '~' i l t f .{
enm'~ ,ill·
(3) ~,,~
(4) ~~
1 " , , , , . ~ 'm <;9;<M('~ ' I R . ~,t ?
(1) ~
o n ~
G i l } ~ ~ ' HO f f l H t ' l i 1
( 4) ' ' P I
'~~'ffi'~m{fb~lt·~" 7 '
rn 1 i 1 l r o 1 . : i f
(2~:arI\-~ ' ¥ ! :
( , : n ~':f t
(4)' "R\ i l l '
A /P ag (!J 2 2
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Energy ~det!.qy in .bu:ildingJ~i ~ot be '76.achieved,' by ;~neof the foU (bw irig :
(l) Insulated roof
(2) Building orientatio.n
(3) Using' glai\!s on tbetli"Estern faee
{4, ) Using loc;aU.1availaW~ materials
Delhi is ~ttiD:g nady t~ 'hU~t which of~he' '17"tol1oWillg'~ents: ! n 2nio'~ .(1) Aal~d -Games
(2) O]y.mpim5
(3) Commonwealth Gam~s
(4.) SAARc Games
77.
Wbi~ fi:ni$h imp .< ; tr l; s , a glossy lnol< ;:'t Q waUs: '1
(1) Plaster
(2) Distemper
(3) Oil ;P.ai~t·
(4) Lbtfe, wash
7:9. Pentagon is .
(1) the o$ci·al Ns:idenceof the Pri'me- M i.niate:rG!fEngland
(2) the ofH.cial residen.ee o'fthe' Pr,e.s.ide;nt O f 79.the'U IIited States~f .&neric·~, -;. ..
(3) the headquarters of'the DapMtm.ent of
Defence of Ja-pi in
(4) the headquarters or" the Departmoot ·of
D e f u l ) O O , 'o f the United- States of Am.eri-e~
80. 'WhiclJ, one of the foUowing is nm a renewabla
~nergysouroe: ?
(1) WindP(lW~r
(3}FGssH Fuels
(4) Tidal W a : V 'e s
~i:f'~-~ H l 4 R > t f f i r n if ~ & ' ID . ~ if ~~'~~:
(1) j~ ~ { U '4 t ~ . - f t
(2) ~al'~~
(3.) mtft: ~. G 1 : ~mit ~ m~
(4) ~~m~'~~'~ , 2 0 1 0 . if M k l M f lJ i fH i % H ~ . ~ ~ ~
. ~ . ' o m ' ~ < f i \ W t . r
q) ~W
(2:); ~~
(3) ~.
(4) ~'~
78.
U)~·
'(2)'- ~
(jJ .~ it;r
(4 ) ;:u ~
~t
(1)" ~'~~¢it<iir~f.;rqm
( 2 ) . ~ " " " " " . .~.:t..~."""~,~,, ,.~I~~~I 'I~~.~~~'~~~~ ~11~g~ ~q ~:~I~ I~q~~
80.
($) ~ % ' ~ . ~ liI:rmII&l lJ;
(4 ) '~~~~~~~':)imf{i'l14
f 1 : k ' fW i Jw ' 6 if '~ ~ ~ l qjir~rq ~ df W 'r
( .1 ) ~fi
(~}~'6
(3 ) .sft '9W 1 t1 6 f . i({)'~m
< •
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(1) London
(2) Rome-
(3) V,enice
(4) Barcelona
,81. ~-m~'~~wm~?(1) ~ . < ' ! i t
(2) im:qij '
(3) ~r'HiiT
r " ~ ~"ff i1 l : r r ·it82. W'hat is 'the Iunction of Victoria Thrminus 82:. 1 4 ! f i t l t : q ~ ~ ~ fc t l ! r ~ ~ }lin,llMif
h u i l t 1 : i l l l : g ' ?
(I) M US < eum
(2) P~~,~ce,
(3) Railw;aySt~l:jou
(4) Airport.
83. Plaster, of Paris is used for
\1) Sku~tirali f ~mE l
(a) False work over w.aUs/CiliHng
(a ) F]Qoring and rOQ·ong
~4} Loa.dbearing walls
VlIhlebi:s. best used as .1 . sOll lnd ab:sO'rbin~
m a w r i . " l in, partition 'V,ans, ? 8 4 . ,
o n , 8w.e l
(2) G lruP.S -w Qo]
(4) GiaS ' s p i ·e~es
{4} : Swn ,a ,ehips
f i5 . W hic h does ,B9t form pari () f lReiruO'rned C~m~n ; t 85 .Csnerete ?
(2) O~ment
( a Y Sand
(4), Lime
(2) ~
{3) ~"i:;!~H
(4) ~~
83. 'R ? I 1 e : - { ,~ ~ i'ir ~' ~' i
(2) ~~ 'IR~~I m ' ij '
( ,3) q,~ffl ' if
(4) ''qR - m F t ~ ~ if
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(1) ~
(2) ~~ ' 6 f
(3',,), • itm. ~ - .
(4 )1WR_ ~ ,~ '
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8/6/2019 2008 Aieee B Arch
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1. ' : r .at" t . Iha::. 8~ ;Dbj~ctiv e t:y p~ . n{! .st ion:s . o fM~them"?tlcs e~U~slstmg: .of 3_ . - f(~ea.chcorrect. r~lii'pon:se. Pm n (ktltu,e,50:objecti\'~ type·qQestJo.tl$ .c _ . _ m< l:tk5 for,f{OlM. ·_'C1,l.l 'f"ept. re~.onse. . ~a...t,~. o~rtlf)t:I~pain$€. ~ : 'a onemarlliw ill be.d G ld uc t;_ ~d e m the 'scere , , i; o' -<f .e : il u, c .t iQ . 'nf'f(~mh~toLal :$cm;e, _j)w,eV~t;.wm be ~aR~;~fn;ore$:pf ) 'US·e is .indicated. fbr a que.stion: 'in.· " t . h . ~A nsw er S hel\:ft.
2',Hancil{le.st-B()oMet. Answer She~t and._ Q i r a wing .. w ito. . .Ga['~, .as.uj],~et . r i O ,
Cil'Cumst,9;rl:ces (except f or · d lf ic reQ_8 il 11 t: y to ' I ' - e . 1 i tBu0k] ,~ t G od .e~ 1;!Iii A l'I~ w@ - l' S!;leet t;ode),¥J.other~e.t-, : il 1 be p:rt ly l ,ued.
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and -a~alt with a§i an nn(''a1r m!lla!llsaa$e, Tl1e cancDd!lt~S! Dealso ~eq~ea. t- Q
t;h€i' i:r left hand m,i[J'Ii]B : iim.p: Jte $ $ :i .on i '11 ,sPac>CPNvided in t.;he '·At:tli!tJ.d~lu,eSheet-.How~v{ :1 r, t !'u ;j· ·c . aru: li d: ate s a re . .al1CJ\fiJ~dto take,<lwa:vwl~b I . t i~ff i th~ Test 13'O"p,k~.etef M at. .h .«mat. lCs . a n akpti:tud.<t;lThs:~'_·Pa.rt I &,U
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C o l le c te d b y w w w . a r c h i t e c t u r e n t r a n c e . b l o g s p o t . c o mClassroom and Online courses for architecture CET and NATA
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