D.A.V.

INSTITUTIONS,CHHATTISGARH
PRACTICEPAPER-1 :2023-24
CLASS—XII
SUBJECT-MATHEMATICS(041)
Time:3Hrs. MaximumMarks: 80

General Instructions:
1. Allquestionsarecompulsory.
2. The question paper has five sections. Section—A, Section-B, Section-C, Section-D and Section—E.
There are 38 questionsinthe questionpaper.
3. Section—Ahas18MCQquestionsand2Assertion-Reasonbasedquestionof1markseach.Section— B has
S Very Short Answer (VSA) type questionsof 2 marks each, Section-C has 6Short Answer
(SA)typequestions of3markseach,Section—D has4LongAnswer (LA)typequestions of5marks each
and Section—E has3case based questions of 4markseach.
4. Thereisnooverallchoice.However internalchoicehavebeen providedinsomequestions.Attempt only
one of the alternatives insuch questions.
o. Wherevernecessary,neatandproperlylabelleddiagramshouldbedrawn.

Section-A(Fromquestionno.1to 20MultipleChoiceQuestion.Eachquestioncarry-1mark)
1) Vector of magnitude12 units in the direction of vector i-2y+2k is
a) 4i-8j+8k b)8i-4j+8k c)4i-8J-8k d)4i+8J+k
2) The solution set of the in equation 2x+y>5is
a) Half plane that contains the origin
(b) Open half plane not containing the origin
c) Whole xy plane except the points lying on the line 2x+y=5
(d)None of these
3) If A is a square matrix of order3,such that A(adjA) =10I,then Iadj AI is equal to
a) 1 b)10 c)100 d)101
4) Adie is thrown twice and the sum of the numbers appearing is observed to be 8.what is the
conditional probability that then umber 5 has appeared atleast once.
a) 4/5 b)2/5 c)3/5 d)1/5
x—1 l ||
5) Evaluatethedeterminant

a) 3 b)0 c)-1 d)1

6) Thetwolines x ay+b,z cy+d,andx n'y+b’,z—— c'y+d'areperpendiculartoeachother,if
a) b) O C
a’ c’ =-1 c)an'+cc'=1 d)an’+cr’=-1
a’ c’
7) IfAisa3x3matrixsuchthatAI=8,thenI 3Ilequals
a) 8 b)24 c)72d)2ld

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29) Out ofagroup of 8 highly qualified doctors in ahospital,6are very kind and
cooperativewith their patientsandsoareverypopular,whiletheothertworemainreserved.
Forahealth camp, threedoctors are selected at random. Find the probability distribution
ofthe number ofvery popular doctors. What valuesareexpectedfromthedoctors?
30)Evaluate:Jgxtan*'xdx
31) SolvethefollowingLinearProgrammingProblemgraphically:
MaximizeZ-400x+30()y,subjecttoz+y<200,x<40,x 0,y>0

Section-D(Fromquestionno.32to35Eachquestioncarry-5mark)

2 1 3
32) iiA—— 4 —1 0,Findfi*1andhencesolvethefollowingsystemofequation:
—7 2 1
2z+y+3z-3,4z—y=3,—7z-I-2y+z=2.

33) Define the relationR in the set Nx Nas follows: For(a, b), (c, d) C Nx N,
(a,b)R(c,d) ifad=be.Provethat Risan equivalence relation inNxN.

OR
ShowthattherelationRinthesetA={1,2,3,4,5}givenbyR=((a,b):a-b|isaneven}isan
equivalence relation.Showthat all the element of(1,3,5)are related to each other
andallthe element of(2,4} are relatedto eachother. But no element of (1,3,5) is related
to any element of‘ 2,4}.

34) Findthelengthandfootoftheperpendiculardrawnfromthepoint(2,-I,5)ontheline
z—11_ytZ_z#8
10 —4 —11’

OR
Findtheshortestdistancebetweenthelineswhosevectorequationar

e r-(l— f)i - (2-t)y+(3-2t)k

r-{s+1)i (2s-1)j- (2s+1)a

35) Findtheareaofthesmallerpartofthecirclez2+y°=n2cut-offbythelinex=2.

SECTION-E-CaseStudyQuestions
(Fromquestionno.36to35Eachquestioncarrr-4mark)
Thissectioncomprisesof3case-study/passap•e-basedquestionsofFirsttwo
casestudyquestions havethreesub-parts (i),(ii),(iii)ofmarksl,1,2respectively.The
thirdcasestudyquestionhastwo sub partsof2markseach

Readthefollowingpassageandanswerthequestionsgivenbelow.

36) Acardislostfromapackof52cards.Fromtheremainingcardstwocardsaredrawnatrandom.

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 Basedontheaboveinformationanswerthefollowinp•question.

(i) Findtheprobabilityotdrawingtwodiamonds,giventhatacardotdiamondismissing.

(ii) Findtheprobabilityofdrawingtwodiamonds,giventhatacardofheartismissing.

den a missingcard isfound and two cardsare drawnat

randomwithoutreplacement, find theprobabilitythat both drawncards arekings.

OR
Ittwocardsaredrawnfromapackof52cards,onebyonewithreplacement,then findthe
probabilityofgettingnotakingin1'and 2"ddraw.

37) .Rohan,a student of class ted his uncle'sflat withhisfather. He observe thatthe
window ofthe house in the lorm ofarectangle surmountedby
asemicircularopeninghavingperimeterl0m

asshowninthefigure
Basedontheaboveinformationanswerthefollowingquestion.
(i) Ifxandyrepresentsthelengthandbreadthofthe rectangularregion,thenfindtherelationbetweenxand y
forrepresentingperimeter of window.
(ii) Findtheareaofthewindowintermsofx.
(iii) Rohanisinterestedin maximizingtheareaofthe whole window,forthis tohappen,whatwill be
the value o1x when area will be maximum.
OR
FindtheMaximumareaofthewindow.

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38) Anopenwatertankaluminumsheetofnegligiblethickness,withsquarebaseandvertical
sides,
istobeconstructedinafarmforirrigation.Itshouldhold32000/ofwater,thatcomesoutfromatube
ell

Basedonaboveinformation,answerthefollowingquestions

Find thedepthof the tankwhen outer surfacearea oftank willbe

minimum. Findtheminimumoutersurfaceareaoftank.

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