HSST MATHEMATICS – KHSE

ISIVORP ON LA ANSWER KEY
Que ts i no P pa re Co ed : 36 2/ 10 /6 OL
C ta ge C yro do e: 1 93 / 02 15
Exam: HSST M athem cita s
Medium of uQ oitse n: E gn l si h
D ta e fo T se t 18 0- 3-2016
A pl ah c do e A
Q eu s it on1 W-: h o amo gn t eh fo oll win si g t eh iw nn re of J na an ip ad wa ra d ni 02 15?
A R-: ga v ee r hC a du ra y
B L-: ee al hd M ra dna loi
C .K-: V . Ch ua dary
D R .S-: ama un gam
oC rrect Ans ew r -: O itp o -n A
Q eu s it on2 W-: h si o select de ht sa e ssiM nU ive i esr n 102 5?
A -: A ayir an G eu t ri us
B vilO-: ia G ro dan
C iP-: a Alo sn o
D M-: aria L ia ug na
oC rrect Ans ew r -: O itp o -n C
Q eu s it on3 W-: h o amo gn t eh fo oll win si g t eh iw nn re of Ezhu ht achan a aw i dr n 102 5?
A S-: gu ta ah kumari
B .K-: R. eM re a
C P-: u ht u R yress amacha dn ran
D M-: e ol o r V sa udevan
oC rrect Ans ew r -: O itp o -n C
Q eu s it on4 -: T eh Fre cn h o ep n 02 15 oW men Champio sn h w si pi no b w y h hci of t eh fo ll o iw n g p yal er?
A -: V ne illiW su ams
B S-: e nir a ailliW ms
C iS-: monia aH el p
D M-: aria Sha ar op va
oC rrect Ans ew r -: O itp o -n B
Q eu s it on5 W-: h o amo gn t eh fo oll win si g t eh f i C tsr ah irman of eN w D ve e ol pmen B t na k ( NDB)?
A .K-: V . Kamath
B riN-: bhay hS ra ma
C iD-: n se h uk m ra Sharma
D H-: arsh S ti ua m ti hra
oC rrect Ans ew r -: O itp o -n A
Q eu s it on6 -: T eh cs heme ” P jor ect A orr w ” ler si ate t d o hw ich a mong ht e f oll wo i gn term?
A M-: de i ic ne
B P-: osta D l ape rtment
C -: Te el ohp ne d ape rtment
D -: In rtsarf uctu f er ac tili y
oC rrect Ans ew r -: O itp o -n B
Q eu s it on7 -: I n 20 51 w h hci am no t g h f e o oll w ni g c r po in K re a al eg t t eh ” Baum sa u akihc ” eltit ?
A P-: okka ciR il e
B -: Vazh ka u al m iP an pple
C -: W ya na ad G da ha sak a al Rice
D C-: ah n ag l ki odan
oC rrect Ans ew r -: O itp o -n D
Q eu s it on8 -: I n 20 51 w h hci am no t g h f e o oll w ni g if ml w no ht e t i lt e ”Su rav n ca h ka o ar ”m in K re a al In ret n ita no la Fi ml F e its val?
A S-: ah d wo eb ih dn t eh m oo n
B ttO-: al
C O-: zhivu viD asa ht e K la i
D -: Jala ‘l s s tory
oC rrect Ans ew r -: O itp o -n B
Q eu s it on9 -: T eh mA acire n Spa rcec af t New H o ir zon i s l aunched uts ot d w y hich am no t g h f e oll wo ni g pl na te ?
A M-: oo n
B lP-: uto
C M-: ars
D -: V ne us
oC rrect Ans ew r -: O itp o -n B
Q eu s it on 01 :-W cih h a mong ht e llof o iw gn oC itutitsn ona l Amendmen t A i tc s r e tal de to ht e L dna oB u dn yra Agreeme tn b te we ne Ind ai na d Ba gn al ed hs ?
A 1-: 00
B -: 119
C -: 110
D -: 112
oC rrect Ans ew r -: O itp o -n A
Q eu s it on11 -: T eh b est t ae c eh r o si en w oh ac si ap lb e fo __ __ _ ___ _.
A nivig-: g a g oo r d esult
B -: inspi ir n t g eh ts ud ne ts t o l ae rn
C -: com lp eti gn ht e ot p ci in it me
D h-: e ipl gn t eh st du en st in rp pe ira n g on tes
oC rrect Ans ew r -: O itp o -n B
Q eu s it on 21 : ‘- eL ra n ni g by D io gn ‘ p icnir p si el re tcelf e i d n _ __ _ __ _ __ .
A R-: ae l si m
B -: I aed l si m
C rP-: agmat si m
D N-: a rut a il sm
oC rrect Ans ew r -: O itp o -n C
Q eu s it on 31 :-In ni ud c vit e r ae s no i gn o , en proc ee orf sd m
A p-: a itr cu t ral o g ne re al
B g-: ne re a l to p lucitra ar
C -: ra oit an l to emp ri ical
D n-: no e o f t eh se
oC rrect Ans ew r -: O itp o -n A
Q eu s it on 41 :-W cih h t fo h f e oll wo i gn i s a rp o evitcej a f di or t ae ching?
A llitS-: model
B -: Wo kr i gn m do el
C C-: ah rts
D ilS-: des
oC rrect Ans ew r -: O itp o -n D
Q eu s it on 51 :-Th e m s tso i ng fi ica ys tn stem o ve f a ul a oit n i s __ _ __ _ __ .
A F-: orma it ve evalu ita on
B S-: ummative ve a ul a oit n
C C-: no ti un ou a s dn compreh ne s vi e eval au oit n
D C-: no ti un ou ve s a ul a oit n
oC rrect Ans ew r -: O itp o -n C
Q eu s it on 61 :- hC ra acte ir s scit o d f e cs rip it ve ser ae rch st du ie ra s e
A -: T eh y od on t in vlov e yh p to eh s rof si m lu a oit n a dn te nits g
B -: T eh y u l es o cig al met oh sd of i dn itcu ve-de ud c vit e r ae s no ni g ot arr vi e ta ge en ra itasil ons
C -: T eh y n ve e e r m lp o y me ht do s o f r dna omiza oit n i n samp il ng
D -: T eh vari ba sel and pro ec ud ser are n to d rcse i deb accura a ylet dn comple let y
oC rrect Ans ew r -: O itp o -n B
Q eu s it on 71 :- oC nd oiti n hc ro s a tcar er citsi s t h t ta h e ex ep ir me tn e r m na i up tal es o oc r n ni slort his o h r e tta r emp t to ascertain t eh ir r e ital o sn h t pi o o b vres e d ph ne omena are c a ll e d __ _ __ _ __ .
A -: In ed p ne d ne t vari ba el s
B D-: pe e dn en t va air bles
C C-: no f uo ndin v g ari ba el s
D N-: no e of t eh se
oC rrect Ans ew r -: O itp o -n A
Q eu s it on 81 :-T py e fo s ex ep ir me tn a l va il di ra yt e
A C-: no t ne t dna co rtsn uc ilav t dity
B tS-: ati ilav lacits d ti y
C -: Inter an l va tidil y
D -: Inter an l va tidil y , exte nr a l va il dity tsitats , ica l va a ytidil dn c no s rt uc ilav t d ti y
oC rrect Ans ew r -: O itp o -n D
Q eu s it on 91 :- uQ tila at vi e re es a f hcr ocu ses o n __ _ __ _ __ .
A -: I -n depth inter iv e w o ln y
B O-: b itavres no s o ln y
C D-: o uc men t ana yl s ,si in-dep i ht n eivret w and o bserva oit ns
D D-: o uc men t ana yl s o si nly
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oC rrect Ans ew r -: O itp o -n C
Q eu s it on 02 😛 or bab i b ytil a es d as m ilp gn m e ht do si __ __ _ __ __.
A rtS-: at ifi e s d amp nil g
B P-: u pr o is ve as mpling
C R-: na dom s amp nil g
D -: J du gemen t sam ilp ng
oC rrect Ans ew r -: O itp o -n A
Q eu s it on 12 :-Th c e ase nk wo n as ‘Pri P yv u esr C sa e’ is
A .R-: C. oC o ep r v . U in no o f India
B -: Ash ko Kum ra Yada v v. aH ry na a
C -: We ts eB n ag l v. N pir ne rd a N ath
D M-: ad ah v aR o Sci dn ai v . UoI
oC rrect Ans ew r -: O itp o -n D
Q eu s it on 22 :-In w h hci o f t eh fo ll o iw n c g ase id s d ht e S pu er m e oC d tru e ralc e S alw uJ a ud m as nu oc nst ti u oit an l?
A iK-: h to o H o ll oh na v. aZ ch lli u
B rP-: a at p iS gn h v hJ . a hkr na d
C N-: na id ni uS n ad r v. hC itta s ag rh
D P-: oo r na v. S tat e of U.P
oC rrect Ans ew r -: O itp o -n C
Q eu s it on 32 :- oN l wa m ade by t h e aP r il am ne t na d ah vi gn ex t-art er tir oria o l ep itar o n w li l eb ed emed
A vni-: alid
B -: void
C -: c no s tit uti no al
D -: va il d
oC rrect Ans ew r -: O itp o -n A
Q eu s it on 42 : A- el g evitalsi B li l hw ich c no iat ns no ly p oisivor n d ae nil g tiw h nivig g of a gua ar nte e by t eh G overnm ne t o f Ind i ai s
A iF-: an laicn B li l
B a-: Mo en y Bil
C rO-: di an ry B li l
D -: A t fo ll h e ba vo e
oC rrect Ans ew r -: O itp o -n B
Q eu s it on 52 :-Th t e o lat numb re of M lcni sretsini u id gn t eh irP me iM n si te t ni r h e oC unci l o iM f nisters s hou dl eb n o e t x ec de _ __ _ __ _ __ _ ep rc ne t o ht f e tot al m em eb r s of t eh oH use t fo h e Pe po el .
A 1-: 5
B 2-: 0
C 1-: 0
D N-: no e of t eh oba ve
oC rrect Ans ew r -: O itp o -n A
Q eu s it on 62 :-Th e maximum a moun nif fo t e t h ac ta n b e i m op es d o n t h r e es op n ed tn who v iola a set p tor e tc i no ro ed r si s deu nu de ht r e rP o itcet o n o f Women f ro m oD me ts i c Viol ne ce Ac i t s
A -: T ne T oh su and R pu ees
B ytfiF-: Thou as dn R pu ees
C T-: wen yt T oh su and R epu es
D N-: no e of t eh se
oC rrect Ans ew r -: O itp o -n C
Q eu s it on 72 :- aN ti no la P ra skra e n o it fi de u dn er
A -: Ind ai n F ro est s cA t
B F-: o C tser no itavres no A ct
C E-: nvir no m ne t P tor ecti no Act
D dliW-: L efi P tor ecti no Act
oC rrect Ans ew r -: O itp o -n D
Q eu s it on 82 :-Th e m ini mum age fo a d no ro of uh m na ro gan i s
A 2-: 0 ey ars
B 1-: 8 ey ars
C 2-: 1 y ae rs
D 2-: 5 y ae rs
oC rrect Ans ew r -: O itp o -n B
Q eu s it on 92 :- nU de r t eh iR hg t t o E ud ca oit n cA ,t ‘ le emen e yrat ud itac on’ me na s de cu ati no f ro m srif t lc as t s o
A -: f uo rth salc s
B -: se ev nth lc ass
C -: f tfi h lc ass
D ie-: g th h c lass
oC rrect Ans ew r -: O itp o -n D
Q eu s it on 03 :- nU de r t eh iR hg t t o Info mr ati no A csid ,tc losure of na info mr ati no o n a n i nciden oc t n rec n ni g ht e ec no om ci intere ts o ht f e s tate
A i-: s n to at a e ll xempted
B -: c na made 1 y 5 e ra afte r t eh icni dent
C -: i s n ro m e ylla xempte orf d m di solcs u er ub t c a n eb re el ase d 2 y 0 e tfa sra er t eh in dic ne t
D -: i s n ro m e ylla xempte orf d m di solcs u er ub t c a n eb re el ase d 1 y 5 e tfa sra er t eh in dic ne t
oC rrect Ans ew r -: O itp o -n C
Q eu s it on 13 :-Th e a er a of a t ri na lg e i s qe ua t ot l h ta of a qs au re who dis es e mea rus es 06 m . T eh si ed o ht f e rt i na lg e w oh rroc es e ps no id n g a itl t edu 9 si 0 m is
A 6-: 0 m
B 4-: 0 m
C 8-: 0 m
D 9-: 0 m
oC rrect Ans ew r -: O itp o -n C
Q eu s it on 23 :-Th e eh i hg t o f a n arc of a ic r lc e i s 1 c 0 m na sti d diameter 1 si 2 c 5. .m Th c e h ro d ht fo e ar si c o el f gn th
A 1-: 0 c m
B 1-: 2 c m
C c 8-: m
D -: 1 c 1 m
oC rrect Ans ew r -: O itp o -n A
Q eu s it on 33 : A- ps eh re of r da iu c 4 s m si ca evr d orf m a homog ne e uo s sphere ar fo dius 8 mc and mass 61 0 g . T eh m as s of t h s e m lla er sphere is
A 8-: 0 g
B 6-: 0 g
C 4-: 0 g
D 2-: 0 g
oC rrect Ans ew r -: O itp o -n D
Q eu s it on 43 : A- pe dn lu um s wi gn s t h or gu h na gna le of 03 ° na d ed s birc e a s n ar c 8.8 c m i n l ne tg h . T eh l ne tg h t fo h e ep n ud lum i sU( s e Π = 22
7
·
¹
¸¸
A .8-: 8 cm
B 1-: 6 c 8. m
C 1-: 2 c 4. m
D 1-: 0 c 2 . m
oC rrect Ans ew r -: O itp o -n B
Q eu s it on 53 : A- ilos d c bu si e cu tni t o t ow c bu io ds o e f auq l v o ul m .se The itar o o ht f e tot a l su cafr e ra ae o ht f e vig e c n ube t ot h ta o o f en o ht f e uc ob i sdi s
A : 2-: 1
B : 3-: 2
C : 4-: 1
D : 4-: 3
oC rrect Ans ew r -: O itp o -n B
Q eu s it on 63 :-Wha i t s t eh va ul e of 1
5 + 1
5 + 1
5+ .. .
?
A:-
−5 + √29
2
B:-
−5 − √29
2
C:-
−5 ± √29
2
D -: 7
oC rrect Ans ew r -: O itp o -n A
Q eu s it on 73 :-2 01 0 00 00 m do i 7 s
A -: 5
B -: 3
C -: 2
D -: 4
oC rrect Ans ew r -: O itp o -n C
Q eu s it on 83 :-Wh ne 𝑥5 + 𝑥4 + 5𝑥2 − 3 si di iv ded by 𝑥 + 2, t eh rem ia dn i re s
A -: 0
B -: 1
C -: 2
D -: 3
oC rrect Ans ew r -: O itp o -n B
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Q eu s it on 93 : A- t r ee tiw h secitrev 7 h sa __ __ _ __ _ __ e gd se .
A -: 8
B -: 7
C -: 5
D -: 6
oC rrect Ans ew r -: O itp o -n D
Q eu s it on 04 :-Th e un mb re o tsid f in tc s ap nnin ert g e fo s 𝐾4 i s
A 1-: 6
B 1-: 2
C 3-: 2
D -: 8
oC rrect Ans ew r -: O itp o -n A
Q eu s it on 14 :-I ht f e i den it t y e el ment 𝑒 � 𝑆 exis ni st a es m rgi uo ,S( p �) , t hen ti si a
A rG-: oup
B rG-: ou op id
C M-: onoid
D N-: no e of t eh oba ve
oC rrect Ans ew r -: O itp o -n C
Q eu s it on 24 :-Th e un mb re o g f ne re a fo srot (𝑍24, + ) is
A -: 2
B -: 6
C -: 8
D 1-: 0
oC rrect Ans ew r -: O itp o -n C
Q eu s it on 34 : A- lyS o w 3-s bu rg uo p o a f g or pu o f or ed r 21 h as order
A -: 2
B -: 3
C -: 1
D 1-: 2
oC rrect Ans ew r -: O itp o -n B
Q eu s it on 44 :- oC isn d re 𝑍5 and 𝑍20 a r s i gn s m odulo 5 and 2 0 r es ep c levit y . Th ne t eh n umbe fo r homomo pr h si m φ :𝑍5 → 𝑍20 i s
A -: 1
B -: 4
C -: 5
D -: 2
oC rrect Ans ew r -: O itp o -n D
Q eu s it on 54 :- eL t 𝑄 b t e h if e eld of r a oit an l un m eb r s and 𝑍2 i s a f ield modulo .2 Th ne t eh op ly on mial 𝑓(𝑥) = 𝑥3 − 9𝑥2 + 9𝑥 + 3 i s
A i-: rredu lbic e over 𝑄 b er tu ud cible vo er 𝑍2
B -: i rr edu lbic e ove b r o ht 𝑄 dna 𝑍2
C -: r de icu b el o rev 𝑄 b ri tu r de icu b el o rev 𝑍2
D -: r de icu b el o rev b to h 𝑄 and 𝑍2
oC rrect Ans ew r -: O itp o -n A
Q eu s it on 64 :- eL t 𝐴 = �
3 1 −1
2 2 −1
2 2 0
� . T eh c ah ra tsiretc i c p ylo nomial of 𝐴 i s
A:-𝑥3 + 5𝑥2 + 8𝑥 + 4
B:-𝑥2 + 5𝑥
C:-𝑥3 − 5𝑥2 + 8𝑥 − 4
D:-𝑥3 + 8𝑥 + 4
oC rrect Ans ew r -: O itp o -n C
Q eu s it on 74 :-Th e e gi ne valu se of t h e mat ir x �
4 −2
−2 1
� are
A ,1-: 4
B -: -1 , 2
C ,0-: 5
D C-: na no b t e d etermined
oC rrect Ans ew r -: O itp o -n C
Q eu s it on 84 :- eL t 𝑉 b e a f in ti e dimen ois an l v ecto r s ap ce, 𝐼 eb t eh i ed ytitn tr na sforma oit n o n 𝑉 , t eh t n h e un ll s p ca e fo 𝐼 is
A:-{0}
B:-𝜑
C:-𝑉
D N-: no e of t eh oba ve
oC rrect Ans ew r -: O itp o -n A
Q eu s it on 94 :-If 𝑉 i s a vecto ps r a ec with dim 𝑉 = 𝑛 ht , ne t eh id men ois n t fo h e h py e psr a ec of 𝑉 i s
A:-𝑛
B:-𝑛 − 1
C:-𝑛 + 1
D -: 0
oC rrect Ans ew r -: O itp o -n B
Q eu s it on 05 :- eL t 𝑉 b e a ve ps rotc ace o lla f 2 × 2 ma rt ices o rev 𝑅 . eL t 𝑇 b e ht e nil ae r m apping 𝑇:𝑉 → 𝑉 such t h ta 𝑇(𝐴) = 𝐴𝐵 − 𝐵𝐴 w eh re 𝐵 = �
2 1
0 3
� . T eh t n eh un ll i fo yt 𝑇 is
A -: 1
B -: 2
C -: 3
D -: 4
oC rrect Ans ew r -: O itp o -n A
Q eu s it on 15 :- aB na s hc p ca e i s a
A C-: omple et n ro me tcev d or s p ca e
B N-: orm de vecto r s ap ce
C C-: omplete tcev or s p ca e
D N-: no e of t eh oba ve
oC rrect Ans ew r -: O itp o -n A
Q eu s it on 25 :-W cih h t fo h f e oll wo i gn i s urt e?
A -: A ll n ro med ps a sec are ni en r produ tc s ap ces
B -: A ni ll en r produ tc sp ca es are on rm de s ap ces
C -: A ni ll en r produ tc sp ca es are aB nach sp ca es
D -: A ni ll en r produ tc sp ca es are H bli e tr s ap ces
oC rrect Ans ew r -: O itp o -n B
Q eu s it on 35 :- aB na s hc p ca e i s a liH b tre s ap i ec f
A htyP-: oga r ae t n heorem h lo ds
B rP-: o oitcej n ht oe er m h olds
C P-: a llar e ol gram l a w h lo ds
D N-: no e of t eh oba ve
oC rrect Ans ew r -: O itp o -n C
Q eu s it on 45 :-If 𝑇 a si ob u dn ed nil ae r po re a rot o n a liH b ps tre a ec 𝐻 w , hich of t eh fo oll win si g on t tr eu ?
A:-𝑇 si on rma l fi 𝑇 si se a-fl djoint
B:-𝑇 si on rma l if 𝑇 si u tin ary
C:-𝑇 i s s elf- da ioj nt fi 𝑇 n si ormal
D N-: no e of t eh oba ve
oC rrect Ans ew r -: O itp o -n C
Q eu s it on 55 :-Th e qe ua oit n of t h e on mr al a ht t e p io nt (𝑎 sec Θ , 𝑏 at n Θ ) no t eh yh p re ob al 𝑥2
𝑎2 − 𝑦2
𝑏2 = 1 i s
A:-
𝑥
𝑎 sec Θ − 𝑦
𝑏 at n Θ = 1
B:-
𝑥
𝑎 sec Θ + 𝑦
𝑏 at n Θ = 1
C:- 𝑎𝑥
es c Θ − 𝑏𝑦
at n Θ = 𝑎2 + 𝑏2
D:- 𝑎𝑥
es c Θ + 𝑏𝑦
at n Θ = 𝑎2 + 𝑏2
oC rrect Ans ew r -: O itp o -n D
Q eu s it on 65 :- il m 𝑥→ ∞
log 𝑥
𝑥𝑛 is
A:-∞
B:-− ∞
C -: 1
D -: 0
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oC rrect Ans ew r -: O itp o -n D
Q eu s it on 75 :-(𝑥 �𝑦) + (𝑥′ + 𝑦′) e si uq t la o
A:-𝑥 �𝑦
B:-𝑥′ + 𝑦′
C -: 0
D -: 1
oC rrect Ans ew r -: O itp o -n D
Q eu s it on 85 :- eL t 𝑎 b e na y e el me ni tn a B oo el na la eg rb a 𝐵 . If 𝑎 + 𝑥 = 1 and 𝑎𝑥 = 0 ht , en
A:-𝑥 = 1
B:-𝑥 = 0
C:-𝑥 = 𝑎
D:-𝑥 = 𝑎′
oC rrect Ans ew r -: O itp o -n D
Q eu s it on 95 :-W cih h t fo h f e oll wo i gn i s r eflexive?
A:-𝑙2
B:-𝑙1
C:-𝐿1[𝑎, 𝑏]
D:-𝑙∞
oC rrect Ans ew r -: O itp o -n A
Q eu s it on 06 :-If 1 < 𝑝 < ∞ and 𝑞 si c no uj ag et of 𝑝 ht , en A:-𝑙𝑝′ = 𝑙𝑞 B:-𝑙𝑝′ = 𝑙𝑝 C:-𝑙𝑝′ < 𝑙𝑞 D:-𝑙𝑝′ > 𝑙𝑞
oC rrect Ans ew r -: O itp o -n A
Q eu s it on 16 :-If𝑆 si a on -n em ytp se r fo t e la numb ,sre t eh n
A -: I fn 𝑆 = S pu 𝑆
B -: Inf 𝑆 = S- pu ( − 𝑆)
C -: In f 𝑆 = S pu ( − 𝑆)
D -: Inf 𝑆 = – uS p 𝑆
oC rrect Ans ew r -: O itp o -n B
Q eu s it on 26 :-E ifni yrev nite tes has
A a-: n u cn ounta lb e s bu set
B c a-: oun at ble s bu set
C b-: o c ht ounta lb e a dn u n oc nu at ble su sb ets
D n-: no e o f t eh a ob ve
oC rrect Ans ew r -: O itp o -n B
Q eu s it on 36 : A- er a l valued uf n oitc n 𝑓 ah s d si c no ti un ti y of t eh se oc dn ki dn at 𝑥 = 𝑎 i f
A:-𝑓(𝑎 + ) ex o tsi nly
B:-𝑓(𝑎 − ) ex o tsi nly
C N-: e hti er 𝑓(𝑎 + ) n ro 𝑓(𝑎 − ) exist
D B-: o ht 𝑓(𝑎 + ) a dn 𝑓(𝑎 − ) ex si t
oC rrect Ans ew r -: O itp o -n C
Q eu s it on 46 :- oF r t eh seq neu ce {𝑥𝑛} , where 𝑥𝑛 = ( − 1)𝑛𝑛 t , h e �il�m�� 𝑥𝑛 i s
A -: 1
B -: 0
C:-+ ∞
D:-− ∞
oC rrect Ans ew r -: O itp o -n D
Q eu s it on 56 :-E o yrev ep s n et o er f a n l umbe sr ht si e u in o n of
A -: c uo tn ba le lloc ecti no fo di js o solc tni e i d n lavret s
B u-: n oc nu at ble co oitcell n of disjoint lc os de intervals
C -: c uo tn ba le lloc ecti no o jsid f o tni op ne intervals
D u-: n oc nu at b c el olle oitc n fo disjoint po en tni ervals
oC rrect Ans ew r -: O itp o -n C
Q eu s it on 66 : A- tes 𝐸 n si wo here ed sn e i f
A -: clo rus e fo 𝐸 co tn ains non-empty po en tes s
B -: clo rus e fo 𝐸 c o tn ains n o on -n emp yt epo tes n s
C -: clo rus e fo 𝐸 c o tn a sni emp yt po en es t
D n-: no e o f t eh a ob ve
oC rrect Ans ew r -: O itp o -n B
Q eu s it on 76 :-If 𝑓1 na d 𝑓2 ra e t ow r ae l-va ul de b uo n ed f d u itcn o d sn e if ned o n [𝑎, 𝑏] t eh f n or ever y p oititra n 𝑃 no [𝑎, 𝑏]
A:-𝑈�𝑃, 𝑓1 + 𝑓2� = 𝑈�𝑃, 𝑓1� + 𝑈�𝑃, 𝑓2�
B:-𝑈�𝑃, 𝑓1 + 𝑓2� ≤ 𝑈�𝑃, 𝑓1� + 𝑈�𝑃, 𝑓2�
C:-𝑈�𝑃, 𝑓1 + 𝑓2� ≥ 𝑈�𝑃, 𝑓1� + 𝑈�𝑃, 𝑓2�
D N-: no e of t eh oba ve
oC rrect Ans ew r -: O itp o -n B
Q eu s it on 86 :-If 𝑓:[𝑎, 𝑏] → 𝑅 si c no ti un ou a s dn m onoto uf cin ncti no t eh n
A:-𝑓 iR si em na i n n et gra lb e o n [𝑎, 𝑏]
B:-𝑓 n si o iR t em nna in et gra lb e o n [𝑎, 𝑏]
C:-𝑓 iR si ema nn inte rg a lb e o n 𝑅
D N-: no e of t eh oba ve
oC rrect Ans ew r -: O itp o -n A
Q eu s it on 96 :-W cih h t fo h f e oll wo i gn i s urt e?
A -: T eh set [0, 1] si on t c uo tn ba le
B -: If 𝐸1 na d 𝐸2 a er eL be gs eu me sa u ar ble, t hen 𝐸1 � 𝐸2 si eL besgue m ae sura lb e
C -: T eh fam yli 𝑀 of eL besgue m ae sura lb e se st si a n a gl be ar of sets
D -: A t fo ll h e ba vo e
oC rrect Ans ew r -: O itp o -n D
Q eu s it on 07 :-Giv ne �
0
1 sin �
1
𝑥�
√𝑥 𝑑𝑥 , t eh n
A -: I tn e rg a l i s divergent
B -: Inte rg a l i s a sb o tul ely c o vn e gr ne t
C -: Inte rg a l i s n to a sb o tul ely c o vn e gr ne t
D N-: no e of t eh oba ve
oC rrect Ans ew r -: O itp o -n B
Q eu s it on 17 :-If 𝑓 sa it s if es t eh c no oitid n fo s Lagran eg s’ me na valu t e heorem and fi 𝑓′(𝑥) = 0�𝑥 � [𝑎, 𝑏] , t hen w cih h o ht f e llof o iw gn urt si e?
A:-𝑓 si c no st na t no [𝑎, 𝑏]
B:-𝑓 si s tcirt l rcni y e isa n i g n [𝑎, 𝑏]
C:-𝑓 si s cirt t yl d erce a nis g i n [𝑎, 𝑏]
D N-: no e of t eh oba ve
oC rrect Ans ew r -: O itp o -n A
Q eu s it on 27 :- il m𝑧→0
𝑧
¯
𝑧 is
A -: 0
B -: 1
C:-
1
2
D D-: eo s n to exist
oC rrect Ans ew r -: O itp o -n D
Q eu s it on 37 :-Th r e a id us o oc f n rev eg cn e o ht f e po ew r s erie s �
𝑛= 0
∞ 2𝑛!
(𝑛!)2 (2 − 3𝑖)𝑛 i s
A -: 1
B -: 0
C:-
1
2
D:-
1
4
oC rrect Ans ew r -: O itp o -n D
Q eu s it on 47 : A- uf n tc i no i s s aid ot eb h arm no ic i f
A:-
∂2𝑢
∂𝑥2 + ∂2𝑣
∂𝑥2 = 0
B:-
∂2𝑢
∂𝑥2 + ∂2𝑢
∂𝑦2 = 0
Home Page f li e ///: H /: h ss t maths.html
4 of 6 3/18/20 61 3:10 P M

C
:
–
∂
𝑢
∂
𝑥
+
∂
𝑢
∂
𝑦
=
0

D
:
–
∂
𝑣
∂
𝑥
+
∂
𝑣
∂
𝑦
=
0
oC
r
r
e
c
t
A
n
s ew
r -:
O itp
o -n
B
Q eu
s it
o
n 57
:
–
T
h v e
a
l eu fo
�𝑐
l
o
g
𝑧
𝑑
𝑧 w eh
r
e
𝑐
i t s
h e
u ic tin
r lc
e
i
s

A
:
–
Π
𝑖

B
:
–
2
Π
𝑖

C
:
–
4
Π
𝑖

D -:
0
oC
r
r
e
c
t
A
n
s ew
r -:
O itp
o -n
B
Q eu
s it
o
n 67
:
–
T
h i e
m
a eg ht fo
e
u c tin
i lcr
e
|
𝑧
|
=
1 u dn t re
h art e
n rofs
m ita no
𝑤
=
2
𝑧
+
𝑧
2
i
s

A criC-:
l
e

B rtS-:
a
i hg
t il
n
e

C P-:
a ar ob
l
a

D C-:
a idr
o
i
d
oC
r
r
e
c
t
A
n
s ew
r -:
O itp
o -n
D
Q eu
s it
o
n 77
:
–
I
f
𝑋 i
s na
y s
e
t
,
𝑇
i s
a
c
o oitcell
n
o
f
a ll
s bu
s
e fo st
𝑋 ht ne
(
𝑋
,
𝑇
)
i
s

A csiD-:
r
e
t
e
t po lo go
y

B -:
I dn
i
s rc
e
t
e t
o
p
o ol
g
y

C -:
T ir
v
i
a l
t po lo go
y

D N-: no e
o
f
t eh oba
v
e
oC
r
r
e
c
t
A
n
s ew
r -:
O itp
o -n
A
Q eu
s it
o
n 87
:
– eL
t
𝑋 na
d
𝑌 ra
e ot op
l go
i
c
a ps l
a .sec
T eh
f nu
c it no
𝑓 a si oh
m
e
o
m
o pr
h si
m i
f

A
:
–
𝑓
:
𝑋
→
𝑌 i
s
a jib
e
c
t vi
e
f nu
c
t
i
o
n

B
:
–
𝑓 oc si
n nit ou
u
s

C
:
–
𝑓
−
1
:
𝑌
→
𝑋 si
c no nit ou
u
s

D -:
A t fo ll
h e ba vo
e
oC
r
r
e
c
t
A
n
s ew
r -:
O itp
o -n
D
Q eu
s it
o
n 97
:
–
E yrev
c
o
m
p
a tc
s bu
s
e fo t
a H ua
s od
rff s
p ca
e
i
s

A lC-:
o
s de
s
e
t

B O-: ep es n
t

C N-:
u ll
s
e
t

D N-: no e
o
f
t eh oba
v
e
oC
r
r
e
c
t
A
n
s ew
r -:
O itp
o -n
A
Q eu
s it
o
n 08
:
–
T
h e
o dr
e a r dn d ge
r ee t fo
h e
d
i
f ref ne
t
i
a e l uq ita
o
n
𝑑𝑑𝑥
�
𝑑
2
𝑦
𝑑
𝑥
2
�
4
=
0
i
s

A ,1-:
4

B ,2-:
4

C ,3-:
1

D ,3-:
4
oC
r
r
e
c
t
A
n
s ew
r -:
O itp
o -n
C
Q eu
s it
o
n 18
:
–
T
h v e
a
l eu orW fo
n
s
k
i na
𝑊
�
𝑥
,
𝑥
2
,
𝑥
3
� i
s

A
:
–
2
𝑥
2

B
:
–
2
𝑥
4

C
:
–
2
𝑥
3

D
:
–
𝑥
2
oC
r
r
e
c
t
A
n
s ew
r -:
O itp
o -n
C
Q eu
s it
o
n 28
:
–
T
h e eg
n
e s lar
o
l
u oit
n
o
f
∂
2
𝑢
∂
𝑥
2
+
∂
2
𝑢
∂
𝑦
2
=
0 i
s
o ht f
e rof
m

A
:
–
𝑢
=
𝑓
(
𝑥
+
𝑖
𝑦
)
−
𝑔
(
𝑥
−
𝑖
𝑦
)

B
:
–
𝑢
=
𝑓
(
𝑥
−
𝑖
𝑦
)
−
𝑔
(
𝑥
−
𝑖
𝑦
)

C
:
–
𝑢
=
𝑓
(
𝑥
+
𝑖
𝑦
)
+
𝑔
(
𝑥
−
𝑖
𝑦
)

D
:
–
𝑢
=
𝑓
(
𝑥
−
𝑖
𝑦
)
+
𝑔
(
𝑥
+
𝑖
𝑦
)
oC
r
r
e
c
t
A
n
s ew
r -:
O itp
o -n
C
Q eu
s it
o
n 38
:
–
T
h e ap
r it
a
l
d
i
ff
e er
n lait
e
q au
t
i no rof
m
e
d yb
e
l mi
i
n ita
n t g
h e
a rtibr
a
r f y
u oitcn
n orf
m
𝑧
=
𝑓
�
𝑦𝑥
�
i
s

A
:
–
𝑥
∂
𝑧
∂
𝑥
+
∂
𝑧
∂
𝑦
=
0

B
:
–
∂
𝑧
∂
𝑥
+
∂
𝑧
∂
𝑦
=
0

C
:
–
∂
𝑧
∂
𝑥
+
𝑦
∂
𝑧
∂
𝑦
=
0

D
:
–
𝑥
∂
𝑧
∂
𝑥
+
𝑦
∂
𝑧
∂
𝑦
=
0
oC
r
r
e
c
t
A
n
s ew
r -:
O itp
o -n
D
Q eu
s it
o
n 48
:
–
T
h e
o htr go
o an
l rt
a yrotcej
o
f t
h f e
a
m vruc fo yli
e
s
𝑥
2
−
𝑦
2
=
𝑘 vig si
e n
b
y

A
:
–
𝑥
2
+
𝑦
2
=
𝑐

B
:
–
𝑥
𝑦
=
𝑐

C
:
–
𝑦
=
𝑐

D
:
–
𝑥
=
0
oC
r
r
e
c
t
A
n
s ew
r -:
O itp
o -n
B
Q eu
s it
o
n 58
:
–
T
h e eg
n
e s lar
o
l
u oit
n
o
f
t eh aw
v
e
e
q au
t
i no
∂
2
𝑦
∂
𝑡
2
=
𝑐
2
∂
2
𝑦
∂
𝑥
2
i
s

A
:
–
𝑦
(
𝑥
,
𝑡
)
=
Φ
(
𝑥
+
𝑐
𝑡
)
+
𝜓
(
𝑥
−
𝑐
𝑡
)

B
:
–
𝑦
(
𝑥
,
𝑡
)
=
𝑓
(
𝑥
+
𝑐
𝑡
)

C
:
–
𝑦
(
𝑥
,
𝑡
)
=
𝑓
(
𝑥
−
𝑐
𝑡
)

D N-:
o g ne re
a l
s
o
l
u
t
i no e
x si
t
s
oC
r
r
e
c
t
A
n
s ew
r -:
O itp
o -n
A
Q eu
s it
o
n 68
:
–
S it
r il gn s’ f
o mr
u si al
t eh _ __ _ __ _ __ __
o
f aG ssu ‘
f
o wr
a
r
d na d ab
c
k
w ra
d rof
m lu ea
.

A -:
A htir
m
e
t
i c
m
e
a
n

B G-: oe
m
e
t
r ci
m ae
n

C H-:
a
r
m no
i c
m
e
a
n

D N-: no e
o
f
t eh oba
v
e
oC
r
r
e
c
t
A
n
s ew
r -:
O itp
o -n
A
Q eu
s it
o
n 78
:
–
T
h i e
n ret
p lo
a nit
g
p ylo
n
o
m lai
o
f
t eh ih
g
h
e d ts ge
r ee w
h rroc hci
e
s nop ht sd
e uf
n tc
i ano
l v
a ul
e
s
𝑓
(
−
1
)
=
9
,
𝑓
(
0
)
=
5
,
𝑓
(
2
)
=
3
,
𝑓
(
5
)
=
1
5 i
s

A
:
–
𝑥
3
+
𝑥
2
+
2
𝑥
+
5

B
:
–
𝑥
2
−
3
𝑥
+
5

C
:
–
𝑥
4
+
4
𝑥
3
+
5
𝑥
2
+
5

D
:
–
𝑥
+
5
oC
r
r
e
c
t
A
n
s ew
r -:
O itp
o -n
B
Q eu
s it
o
n 88
:
–
T
h s e
o
l
u it
o n
o
f
t eh
i
n
t
e rg
a
l uqe ita
o
n
Φ
(
𝑥
)
=
𝑥
+
�0
𝑥
(
Ξ
−
𝑥
)
Φ
(
Ξ
)
𝑑
Ξ i
s

A
:
– oc
s
𝑥

B
:
– at
n
𝑥

C
:
–
s
in
𝑥

D
:
– es
c
𝑥
oC
r
r
e
c
t
A
n
s ew
r -:
O itp
o -n
C
Q eu
s it
o
n 98
:
–
T
h e
m ini
m
i
z
i gn
c
u
r
v
e
m
u ts
s
a it
s a yf
d
i
ff
e
r ne
t
i
a l
e
q au
t
i no
c
a ell
d

A L-: ga
r gna
e
‘ e s uq ita
o
n

B E-:
u -rel
L
a
g
r
a
n eg e uq ita
o
n

C G-:
a e ssu auq
t
i
o
n

D N-: no e
o
f
t eh oba
v
e
oC
r
r
e
c
t
A
n
s ew
r -:
O itp
o -n
B
Q eu
s it
o
n 09
: A- ilos
d
f
i ug
r
e
o
f r
e lov
u
t
i no ,
fo a r
g evi
n
s
u cafr
e ra ae
, ah
s
m
a
x
i
m
u
m
v
o
l
u
m
e i
s i
n
t eh
c
a es
o
f

A ric a-:
c
l
e

B s a-:
p
h
e
r
e

C a-:
n ille
p
s
e

D a-:
p ra ba lo
a
oC
r
r
e
c
t
A
n
s ew
r -:
O itp
o -n
B
Q eu
s it
o
n 19
: A- igir
d b do
y
m ivo
n i g
n
s ap
c
e
w
i
t
h
o
n
e p
o
i
n
t if
x
e d
h sa
d
e
g
r
e e
o
f rf
e
e od
m

A -:
3

B -:
1
H
o
me
P
a
g
e
f li
e ///:
H /:
h ss
t
ma
th
s
.
html
5
o
f
6
3
/
1
8
/
2
0 61
3
:
1
0 P
M
C -: 6
D -: 9
oC rrect Ans ew r -: O itp o -n A
Q eu s it on 29 : A- p itra cle of nu i t m i ssa s m ivo n g nu de rg r av ti a oit an l if e ,dl a ol gn t eh c iolcy d 𝑥 = 𝜑 − sin 𝜑, 𝑦 = 1 + oc s 𝜑 . Then t h e Lagrangia f n or m ito no is
A:-𝜑2(1 + cos 𝜑) − 𝑔(1 − oc s 𝜑)
B:-𝜑2(1 − cos 𝜑) + 𝑔(1 + oc s 𝜑)
C:-𝜑2(1 − cos 𝜑) − 𝑔(1 + oc s 𝜑)
D:-2𝜑2(1 − oc s 𝜑) − 𝑔(1 + cos 𝜑)
oC rrect Ans ew r -: O itp o -n C
Q eu s it on 39 :-𝐿 −1� 1
𝑠�𝑠2 + 𝑎2�
� i s
A:-
1
𝑎2 (1 − cos 𝑎𝑡)
B:-
2 sin �𝑡
𝑡
C:-
1
𝑎2 �𝑒𝑎𝑡 − 1�
D:-
1
𝑎2 sin �𝑎𝑡
oC rrect Ans ew r -: O itp o -n A
Q eu s it on 49 :-�
0
∞
𝑒−𝑥2
𝑑𝑥 is
A:-
1
2
B:-
𝜋
2
C:-
√𝜋
2
D:-−�𝜋
oC rrect Ans ew r -: O itp o -n C
Q eu s it on 59 :-U nis g F uo rie ires r es er , pres ne ti gn 𝑥 i n t eh interval [ − 𝜋, 𝜋], t eh sum o f t eh se seir 1 − 1
3 + 1
5 − 1
7 + .. . i s
A -: 0
B -: 1
C:-
𝜋
2
D:-
𝜋
4
oC rrect Ans ew r -: O itp o -n D
Q eu s it on 69 :-Th e no l i y dempote -t tn c no ro m i s
A la-: eg rb aic s um
B rd-: as u cit nion
C -: stan ad f dr uzz u y nion
D b-: uo n ed s d um
oC rrect Ans ew r -: O itp o -n C
Q eu s it on 79 :-U nis g uf zz y a htir m o cite ep itar o sn o i n n ,4[ slavret 01 ] [/ 1 i ]2, s
A -: [4,5]
B -: [2,10]
C -: [2,8]
D -: [4,20]
oC rrect Ans ew r -: O itp o -n B
Q eu s it on 89 :-Th l e an ug a eg g ne re a et d by t h e g ar mm ra 𝐺 = ({𝑆}, {𝑎, 𝑏}, 𝑆, 𝑃) hw re e 𝑃 si g evi n by si 𝑆 → 𝑎𝑆𝑏, 𝑆 → 𝜆 is
A:-{𝑎𝑛𝑏𝑛:𝑛 ≥ 0}
B:-�𝑎𝑛𝑏𝑛+1:𝑛 ≥ 0�
C:-�𝑎𝑛+ 1𝑏𝑛:𝑛 ≥ 0�
D:-�𝑎𝑛+ 2𝑏𝑛:𝑛 ≥ 1�
oC rrect Ans ew r -: O itp o -n A
Q eu s it on 99 :-W cih h t fo h f e oll wo i gn i s n rt to u i e n t eh ed ir va it ve of a s mo to h if rotcev eld 𝑋?
A:-�𝑣 (𝑋 + 𝑌) = �𝑣 𝑋 + �𝑣 𝑌
B:-�𝑣 (𝑓𝑋) = (�𝑣 𝑓)𝑋(𝑝) + 𝑓(𝑝)(�𝑣 𝑋)
C:-�𝑣 (𝑋 �𝑌) = (�𝑣 𝑋) �𝑌(𝑝) + 𝑋(𝑝) �(�𝑣 𝑌)
D:-�𝑣 (𝑓𝑋) = 𝑓(�𝑣 𝑋)
oC rrect Ans ew r -: O itp o -n D
Q eu s it on 01 -:0 L te 𝑋 b e a on -n emp yt compact aH su d ro f ps f a .ec I ve f ery op in t of 𝑋 si a il m ti p io nt o f 𝑋, t eh n
A:-𝑋 si di js o ni t
B -: 𝑋 si c nuo t ba le
C:-𝑋 si u cn ounta lb e
D N-: no e of t eh oba ve
oC rrect Ans ew r -: O itp o -n C
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