CLASS XII MATHEMATICS F.MARKS: 1OO
Qhree hours)
SectionA -AnsweQr uestionI (Compulsoryri)t ndfiveo therq uestions.
SectionB & Se:ctioCn -Answert wo questionfsro m eitherS ectionB or SectionC .
All working, including rough work, should be done on the same sheet as, and
adja centt o, ther esto f the answerThein tendedm arksfo r questiono r paytso f
SECTIONA
Ouestion1
[t ol I-r 0l (i)Ifl l '. "_&l t =1^ " I thenfi ndk sot hatA 2: 8A+k L t3l
L-l 7) L0 lJ
ii)Solvceo: s(sin'r)=,f pl ,9
(O Findt hee quationo fthe parabola,itvse rtexa t (-2,3)a nd"focuast
(1,3).
./\1/
(iv)Emluat:e lim(e. + 4x)/'
. r->0'
.. Jt+co*
(v)Evaluate : J .:------:16 (r - cos .r), ,
D1
(vi)Evalua:t efo e%c
lx
whenY=10.
(ix)Findthesquareroot-o1f- +Jj i
dv
(x)S olvea:= l -x+Y-xY.
dx
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(v0Four porsonsa rec hpsena t randomit om a groupc ontaining3 men,2
womena nd4 chil&enFindt he probabilityth ate xatlyt wo ofthemw ill be
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(viii) Two.li neso fregressioanr eg ivenb y 6x-I5y--21a nd2Ix+14y.56:0.
Findt her egressionlin eX on Y.( i) Meanv aluesX andY .i i)Valueo f X
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This paperc onsistso f 5 printed pages. ThrnO ye5
Ouestion 2
(a) Usrngp ropertieosf deteminanptrso 'rrtch 4t
-2abc(a*b+c)z
[-t 2 1l lzt t l
(b)If l=11 -4 t
I
and ,=l t -l 0
|
showthat
L3 o -31 L2 1 -1.1
A8:61 ,.Utilize this result to solve : )s6*y*z:5,x'y:0 and 2x*y-z: I .
.ouestion3
tt'
(a) VerifyL agrange'Ms eanV alueT heoremfo r theg iVenfl rrtion:
I
f(x)=
^._,
inl
(3,-3a) ndv ertexa t( 4,-3)
Ouestion 4
(a)Proveth at 2tan-1]-* t*-' ) = tan-'* .
5443
(b)Construetht ec ircuitf or theb ooleanfi.nction
F (A+BXB'+ C)+(B+ CXA +C') .U singl awso f Bool eana lgebrato
srnplifi thec ircuita ndc onstuctth en etworkf or thes rnrplifiecsi rcuit. [5]
Ouestion 5
/ -\ . I I q r I t t- (a)If y = loglx +,1x' + a" I prove that (a' + x")y, * xy, =9. t5]
(b) Show that a closed rigtrt circular cylinder of given surface area has
maximumv olume when its height is equalt o the diametero fits base[.5 ]
l{b+c)' d ;
I u' @+a)2 b2
| ,' t (a+b)2
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Ouestion6
(a)EvaluaJte
-f-4"
J x' +x' +l
(b)Findt hea reao f ther egione nclosebdy the cwvey:x(2-x)
and the lines x:0,y:0,x=2.
Ouestion 7
G)Them arkso btainebdy n ines tudentisn Physicasn dC hemistrayr e
CalculateS pearman'cso efficiento frank correlationa ndc ommento n the
result. t5l
(b)F romt hed atag ivenb elowfindth er egressioenq uaioonf X onY .Using
thee quatio4calculathtev alueo f X whe nY= 22
Ouestion 8
(a)Ttreeg roupso fchildrenc ontain3 girlsa nd1 boy;2 girlsa nd2 boys;1
girl and2 boys.O nec hildi s selecteadt randomfr ome achg roup.Findth e
probabiiityo fthet kee selectecdo nsistos f 1 girl and2 boys. t5l
(U;f ne oddsa gainsst olvinga problemb y a studenXt is 8:6a ndt heo dds
in favouro f solvingth es amep roblemb y anothesr tudenYt is 14 : 16 .( i)
Whati st hep rob abilityo f solvingt hep roblemif botho f themt ry
independently.W(ii)h ati st hep robabilityth atn oneo fthemb ea blet o
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*')%, (l'l < t; tsl
solveth ep roblem?
Question 9
G)Solve(:I - x' ) * . x! = x( I -
(b) If z:x+ iy and lt * il' +lz + il', = 4.
in theArgand plane
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I \ I
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Illustrate the locus
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elow:
X 15 20 28 12 4A 60 20 80
Y 40 30 50 30 20 10 30 60
X 4 5 I I 11 12 12
16 10 I 'l
I o 5 4
Oul:stion1 0 SECTIONB
(a) Usirrgv ectorm ethod,p rovet hati n anyt riangleA BC, a=bcosC+ c
cosA,b:c cosA* a cosC, c: a cosB* b cosA. t5]
(b)Showth att hep ointsw hosep ositionv ectorsa re 4i + 5j + i,- j - k,
3i+9i+4kand -4|+aj+k arecoplanar. t5l
Question 11
(a)Findth ee quationo f the planep assingtlr ough thep oint( t ,2,3)a nd
perpendicularttoh es traighlti ne r = !- = t
.
- / ^aa 1 1
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(b)Findth ee quationo fthe linep assingth roughth ep oints( -3,2,0)a nd
paralletlo thelinejoiningthepointsB(-1,0,7)an4d,-C3(, 5). t5l
Ouestion 12
(a)Ane xperimenstu cceedtsw icea so ftena si t fails.Findth ec hanceth at
in the next six trials,therew ill be at leastf our successes. tsl
(b)Tl-reraer et lneeu msh avingth ef ollowingc ompositionosf blacka ndw hite
balls: Urn I 7 white and 3 black balls. Um II : 4 white and 6 black balls. Um
III:3 whitea nd8 blackb alls.O neo ftheseu rnsi s chosena t randomw ith
prob ablii ties 0.2,0 l .6 and0 .2r espectivelFy.r omt hec hosenu rqtwo balls
ared rawna t randomw ithoutr eplacemen. tB oth theb allsh appento be
white.Calculatthee p robabilittyh att heb allsd rawnw eref romu m III. [5]
SECTION C
Ouestion 1,3
(a)A furnitured ealedr ealsin onlyt ablesa ndc hairs.Hec ans aveu ptoR s
50100o0n lya ndh asa storagec apacityo f 100p ieces.Hicso stp riceo f a
tableis R s1 200a ndo f a chairis R s5 00.H e cane arna p rofito f Rs1 80o n
thes aleo fthet ablea ndR s7 5o nt hes aleo fonec hair.Assumitnhga th ec an
sella llt hei temh eb uys,formulataeL .P.p roblema nds olves ot hath ec an
maximizetheprof?it. t-st L" j
(b)Findt hep resenvt alueo f a sequenooef annuapl aymentos fRs 25000
eactr,thfeir stb eingm adea t thee ndo f5th yeara ndt he lastb eingp aida t the
endo f 12 thy ear,ifmoneiys w orth6 %. tsl
Ouestion1 4
(a)A bill of Rs 28050 is drawn on22 Apri.l 1990 at i1 months and is
discounteodn 11J anuar,y1 991F. indt heb ankergsa ini fther ateo f interest
be 10%.[5]
(b)Thefi xedc osto fa newproducits Rs.3000a0n dt hev ariabeclo aspt er
uniti s Rs.800. Ifthe demandfu nctionis p (x)=4500- 100xf,i ndt heb reak
evenpoints. t5l L*t
Ouestion 15.
a) Calculatteh ei ndexn umbefro r they ear1 990w ith 1991a sb asefr otn
the followingd atau singw eighteda verageo fpricer elatives:
Commoditv A B r^ D E
Pricei n 1990
,l00 RN r60 220 40
Pricei n 19 9l 140 120 r80 240 40
b) The averagenumber,inla khs ofworking daysl ost in strikesd uring each
yyeeaarroo fftthhee pp eerriioodd((11998811-9-90ww0) )aa ssdd ssuu nnddeerr:: l5l
I 981 t982 I 983 1984 1 985 I 986 1987 ] 9BB 1989 1990
AE 1.8 1,9 2.2 2,6 3.7 2.2 6.4 3.6 Er',
Caculate3 -yearm ovinga veragea nds howo n a grapha gainsth e origianl
datafromtable.
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11-02-2010
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