National?Cyber?OlympiadMENTAL?ABILITY?
1.?The?pointsz1?,?,?,?on?the?complex?plane?are?the?vertices?of?an?equilateral?triangle?if?and?only?if?:??z2?z3?
? (z
(C) ?z
(A)?2.
1
-z2)(z2-z3? )= 0?
= 4??? z1z2?
(B)?
?z1
2
= 2? ?z1z2?
21
(D)?(z1+z2+z3)2?= 3?? z1z 2?
? C
nr?= 0?
n?- 1?n?
r
C?r?
= n?
+ C?r?+ 1?
n + 1?
(B)?
2?
n?
(C)?(n+ 1)?2?
n(n?- 1)?(D)?2(n + 1)?
n?(A)?
2?
3.?A?student?is?allowed?to?select?atmost?n?books?from?a?collection?of?(2n?+?1)?books.?If?the?total?number?of?
ways?in?which?he?can?select?atleast?1?book?is?63,?find?the?value?of?n.?(A)?6?(B)?3?(C)?5?(D)?4?4.?The?number?of?ways?in?which?5X’s?can?be?placed?in?the?squares?of?the?figure?so?that?no?row?remains?empty?is?(A)?97?(B)?98?(C)?100?(D)?126?
5.?c?1?is?a?fixed?circle?andc?2?is?a?variable?circle?with?fixed?radius.?The?common?transverse?tangents?toc?1?and?c?2?are?perpendicular?to?each?other.The?locus?of?the?centre?of?variable?circle?is?(A)?Circle?(B)?Ellipse?(C)?Hyperbola?(D)?Parabola?6.?
x-x1y- y?1?
== r ,?represents?cosqsin?q
(A)?Equation?of?a?straight?line,?if q is?constant?&?r?is?variable?(B)?Equation?of?a?circle,?if?r?is?constant?& q is?a?variable?
(C)?A?straight?line?passing?through?a?fixed?point?&?having?a?known?slope?(D)?All?of?these?
7.?The?value?of?log2?[cos2(a+b)+cos2?(a-b)-cos2a×cos2b ]
(A)?Depends?on a & b both?(B)?Depends?on a but?not?on b (C)?Depends?on b but?not?on a (D)?Is?Independent?of?both a & b
LOGICAL&ANALYTICALREASONING?
8.?Which?alternative?is?sufficient?for?answering?the?following?question?based?on?the?information?given?in?the?two?statements??
QUESTION?:?Does?drinking?coffee?lead?to?headache??STATEMENTS?:?
I.?Overstimulation?of?pancreas?leads?to?headache??
II.?Coffee?contains?caffeine?which?when?excessive,?stimulates?pancreas.?(A)?Statement?I?alone?is?sufficient?to?answer?the?question?(B)?Statement?II?alone?provides?answer?to?the?question?(C)?Both?statements?I?and?II?provide?answer?to?the?question?
(D)?Neither?statement?I?nor?statement?II?provide?answer?to?the?question?9.?‘P?+?Q’?means?‘P?is?brother?of?Q’??‘P?–?Q’?means?‘P?is?mother?of?Q’?and?‘P?×?Q’?means?‘P?is?sister?of?Q’.?
Which?of?the?following?means?‘M?is?maternal?uncle?of?R’??(A)?M?–?R?+?K?(B)?M?+?K?–?R?(C)?M?+?K?×?Q?(D)?There?is?no?such?symbol?
2?Class?11?
10.?If?1?is?coded?as?Y,?2?is?coded?as?M,?3?as?D,?4?as?H,?5?as?T,?6?as?L,?7?as?P,?8?as?V?and?9?as?N,?which?of?the?
following?is?the?coded?form?of?3972465??(A)?DNPMHLP?(B)?DNPMHNT?(C)?DNPMHLT?(D)?DNPMNLT?11.?Which?alternative?applies?to?the?assumptions?of?the?statement??STATEMENT?:?Most?people?who?stop?smoking?gain?weight.?ASSUMPTIONS?:?I.?If?one?stops?smoking?one?will?gain?weight?
II.?If?one?does?not?stop?smoking?one?will?not?gain?weight.?
(A)?Only?assumption?I?is?implicit?(B)?Only?assumption?II?is?implicit?(C)?Both?assumptions?I?and?II?are?implicit?(D)?Neither?assumption?I?nor?II?is?implicit?
12.?Which?letter?will?be?the?sixth?to?the?left?of?the?nineteenth?letter?from?the?right?end?of?the?following?alphabets??A?B?C?D?E?F?G?H?I?J?K?L?M?N?O?P?Q?R?S?T?U?V?W?X?Y?Z?(A)?N?(B)?M?(C)?Y?(D)?F?13.?Bablu?ranked?sixteenth?from?the?top?and?twenty-ninth?from?the?bottom?among?those?who?passed?an?examination.?Six?boys?did?not?participate?in?the?competition?and?five?failed?in?the?examination.?How?many?boys?were?there?in?that?class??(A)?44?(B)?50?(C)?55?(D)?40?
COMPUTERS?&?INFORMATION?TECHNOLOGY?
14.?Which?of?the?following?is?not?correct?
(A)?E-commerce?includes?all?business?activities?involved?in?thedevelopment,?facilitationandimplementation?of?business?communications?and?transaction?through?electronic?media?
(B)?The?Intranet?is?a?restricted?version?of?the?Internet?within?a?group?of?users?
(C)?The?Extranet?is?a?closed?online?network?connecting?two?or?more?organisations?(D)?None?of?the?above.?15.?A?debugging?tool?is?a?program?which?
(A)?Removes?bugs?from?a?user?program?(B)?Removes?viruses?from?the?computer?(C)?Helps?the?user?find?bugs?in?his/her?program?(D)?Displays?errors?in?a?user?program?16.?Computers?can?be?protected?from?virus?by?using?
(A)?Software?(B)?Hardware?(C)?Software?and?hardware?(D)?Cannot?be?protected?at?all?17.?Y2K?problem?mainly?arose?in?computer?programmes?written?in?(A)?COBOL?(B)?BASIC?(C)?FORTRAN?
(D)?PASCAL?
18.?In?the?context?of?information?technology,?the?term?security?refers?to?(A)?Confidentiality?only?(B)?Authentication?only?(C)?Integrity?only?(D)?All?of?these?
19.?Which?of?the?following?are?super?computers?developed?by?Indian?Scientists??1.?PARAM?2.?ANURAG?3.?GIST?4.?CDAC?Answer?choices?(A)?1?&?2?only?(B)?1?only?(C)?All?except?3?(D)?1?and?4?
20.?Which?of?the?following?statements?about?DOS?are?true??1.?DOS?is?an?acronym?for?Disk?Operating?System?
2.?Loading?of?DOS?into?the?main?memory?is?known?as?booting?
3.?Storage?areas?on?a?disk?are?known?as?directories.?A?directory?may?contain?files?and/or?subdirectories?
inside?it.?
4.?Wildcards?are?special?characters?carrying?special?meaning.?Two?MS-DOS?wild?cards?are???and?*?5.?A?filter?is?a?command?that?recieves?its?input?from?the?standard?input?device?and?sends?its?
output?to?standard?output?device.?FIND,?MORE?and?SORT?are?MS-DOS?filters.?(A)?1?and?2?only?(B)?1,?2?and?3?(C)?All?excepts?3?(D)?All?of?these
3?Class?11?
National?Science?OlympiadMATHEMATICS?
1.?A?man?moving?on?a?parabolic?path?finds?the?angle?of?elevation?of?a?pole,?standing?on?the?focus?of?path,?
to?be?75°.?If?the?directrix?of?path?is?at?a?distance?of?7?meters?from?him?then?height?of?pole?is?
(2+ 3) (2- 3) mtr. mtr. (A) (14+ 73)mtr. (B) (C) (14- 73)mtr. (D) 7 7 2.?Three?ladies?have?each?brought?a?child?for?admission?to?a?school.?The?head?of?the?school?wishes?to?
interview?the?six?people?one?by?one,?taking?care?that?no?child?is?interviewed?before?its?mother.?The?number?of?ways?of?doing?this?is?(A)?6?(B)?36?(C)?72?(D)?90?3.?Arefrigerator?is?offered?for?sale?at?Rs.?250.00?with?successive?discounts?of?20%?and?15%.The?sale?price?of?the?refrigerator?is?
(A)?35%?less?than?Rs.?250.00?(B)?65%?of?Rs.?250.00?(C)?77%?of?Rs.?250.00?(D)?68%?of?Rs.?250.00?4.?The?number?of?revolutions?of?a?wheel,?with?fixed?center?and?with?an?outside?diameter?of?6?m,?required?to?cause?a?point?on?the?rim?to?go?one?km?is?(A)?880?(B)?440/p (C)?500/3p (D)?440 p
OR?BIOLOGY?
1.?Which?of?the?following?statements?are?true?for?photosynthetic?bacteria?(PB)?and?chemosynthetic?bacteria?(CB)??
(a)?obtain?energy?from?the?oxidation?of?inorganic?molecule?such?as?ammonium?salt?(b)?obtain?energy?from?sunlight?(c)?contain?photosynthetic?pigments?(d)?are?autotrophs.?
(A)?PB?-?b,?c,?d???CB?-?a,?d?(B)?PB?-?a,?c???CB?-?b,?d?(C)?PB?-?b,?d???CB?-?a,?b?(D)?PB?-?a,?b,?c???CB?-?b,?c,?d?2.?Anaerobic?respiration?releases?less?energy?than?aerobic?respiration?because?
(A)?Energy?from?oxygen?is?not?made?available?(B)?Ethyl?alcohol?is?a?source?of?energy?(C)?Carbon?dioxide?is?released?
(D)?Less?energy?is?required?by?fermenting?organisms?
3.?Three?bean?seedlings?were?grown?in?three?culture?solutions.?After?six?weeks,?X?had?yellow?leaves?and?
short?internodes,?Yhas?red?patches?on?the?stem?and?Z?had?green?leaves?and?stem.?It?can?be?deduced?that?
(A)?Xlacked?magnesium,Ylacked?calcium?andZlacked?molybdenum?(B)?X?lacked?calcium,Ylacked?nitrogen?andZlacks?chlorine?(C)?X?lacked?calcium,Ylacked?nitrogen?andZhad?all?nutrients?(D)?Xlacked?magnesium,Ylacked?nitrogen?andZhad?all?nutrients?4.?In?the?life?cycle?of?a?fern?the?meiosis?occurs?during?the?
(A)?Formation?of?spores?(B)?Formation?of?gametes?(C)?Germination?of?a?spore?(D)?Development?of?a?zygote?
PHYSICS?&?CHEMISTRY?
5.?Hydrogen?sulphide?(H?2S)?contains?94.11%?sulphur,?water?(H??2O)?contains?11.11%?hydrogen?and?sulphur??dioxide?(SO?2)?contains?50%?oxygen.?Find?the?ratio?of?all?given?elements.?After?your?calculations?which??
law?has?been?verified??
(A)?Law?of?multiple?proportion?(B)?Law?of?reciprocal?proportion?(C)?Law?of?constant?components?(D)?Law?of?combining?volumes?6.?An?astronaut?in?the?space?shuttle?orbiting?the?earth?performs?a?trick?for?a?television?audience.?She?inflates?a?helium?filled?balloon?within?the?shuttle's?controlled?atmosphere?and?lets?go?of?it.?To?the?aston-?ishment?of?all?watching,?the?balloon?
(A)?Hovers?in?place?where?it?was?released.?(B)?Rises?noticeably?away?from?the?earth.?(C)?Falls?noticeably?towards?the?earth.?
(D)?Drifts?backwards?opposite?to?the?direction?of?the?shuttle's?velocity.?
4?Class?11?
7.?A?boy?throws?a?table?tennis?ball?of?mass?20?g?upwards?with?a?velocity?of?u?0?=?10?m/s?at?an?angle q 0?with?
the?vertical.?The?wind?imparts?a?horizontal?force?of?0.08?N,?so?that?the?ball?returns?to?the?starting?point.?Then,?the?angle q 0?must?be?such?that,?tan q 0?is?(A)?0.2?(B)?0.4?(C)?2.5?(D)?1.2?8.?A?weight?is?attached?to?the?free?end?of?a?sonometer?wire.?It?gives?resonance?at?a?length?40?cm?when?it?is?resonanced?with?a?tuning?fork?of?frequency?512.?The?weight?is?then?immersed?wholly?in?water,?the?resonant?length?is?reduced?to?30?cm.?The?relative?density?in?which?weight?suspended?is?(A)?16/9?(B)?16/7?(C)?16/5?(D)?16/3?9.?A?tank?of?water?has?a?pinhole?leak?in?the?side,?1?m?below?the?water?line.?If?the?tank?is?open?to?the?
5?pa),?how?fast?is?the?water?leaving?the?pinhole???atmosphere?(air?pressure?=?1.013?×10?
(A) g?/4 (B) g?/0.1 (C) 2g?(D) g?10.?Find?the?correct?statement?from?the?following.?
(A)?In?planetary?motion,?total?energy?remains?constant?but?total?angular?momentum?may?vary?
(B)?Both?total?energy?and?total?angular?momentum?are?constant?in?planetary?motion?and?the?total?energy?is?negative?
(C)?Motion?of?a?planet?about?the?Sun?and?motion?of?an?electron?about?an?attracting?nuclear?centre?are?governed?by?identical?relations?and?the?total?energy?is?always?positive?in?both?cases?
(D)?Both?total?energy?and?total?angular?momentum?are?constant?in?planetary?motion?and?the?total?energy?is?positive?11.?One?mole?of?an?ideal?monatomic?gas?expands?till?its?temperature?doubles?under?the?process?V2??T?=?
constant.?If?the?initial?temperature?is??400?K,?the?work?done?by?the?gas?is?(A)?400?R?(B)?200?R?(C)?–?200?R?(D)?Indeterminate?12.?A?projectile?is?thrown?such?that?its?range?should?be?1000?metres,?but?at?highest?point?it?breaks?into?two?equal?masses,?one?of?whom?falls?vertically?downwards.?The?other?mass?will?fall?at?a?distance?(A)?1500?metres?from?launching?point?(B)?2000?metres?from?launching?point?(C)?3000?metres?from?launching?point?(D)?2500?metres?from?launching?point?13.?A?spirit?level?containing?a?bubble?in?a?liquid?is?jerked?forward.?Relative?to?the?level?and?liquid?the?bubble?moves?
(A)?Backwards,?due?to?its?inertia??(B)?Backwards,?due?to?a?pressure?gradient?in?the?liquid??(C)?Forwards,?due?to?its?inertia??(D)?Forwards,?due?to?a?pressure?gradient?in?the?liquid??14.?The?fourth?state?of?matter?is?(A)?Super?fluid?(C)?Liquid?crystals?
(B)?Plasma?
(D)?Small?particles?suspended?in?the?gas?
15.?The?use?of?12?C?scale?has?suspended?the?older?scale?at?atomic?mass?based?on?16?O?isotope,?one?important?
advantage?of?the?former?being?
(A)?The?atomic?masses?on?12?C?scale?became?whole?number?(B)?12?C?is?more?abundant?in?earth?crust?than?16?O?
(C)?The?difference?between?the?physical?and?chemical?atomic?masses?got?narrowed?down?significantly?(D)?12?C?is?situated?midway?between?metals?and?non-metals?in?the?periodic?table.?16.?Electric?cookers?have?a?coating?that?protects?them?against?fire.?The?coating?is?made?of?
(A)?Magnesium?oxide?(B)?Heavy?lead?(C)?Chromium?oxide?(D)?Nickel?17.?
is?
(A)?Aromatic?compound?(C)?Heterocyclic?compound?
(B)?Annulene?
(D)?Polycyclic?compound?
18.?Atom?may?be?regarded?as?comprising?of?protons,?neutrons?and?electrons.?If?the?mass?attributed?to?a?
12?would?neutron?were?halved?and?that?attributed?to?the?electron?were?doubled,?the?atomic?mass?of?6?C?
(A)?Remain?approximately?the?same?(B)?Be?approximately?doubled?(C)?Be?approximately?halved?(D)?Be?reduced?approximately?by?25%?19.?The?chemistry?of?lithium?is?very?much?similar?to?that?of?magnesium?even?though?they?are?placed?in?different?groups.?The?reason?is?
(A)?Both?have?nearly?the?same?size?(B)?The?ratio?of?their?charge?to?size?is?nearly?the?same?(C)?Both?have?similar?electronic?configuration?(D)?Both?are?found?together?in?nature?20.?A?bottle?of?dry?ammonia?and?a?bottle?of?dry?hydrogen?chloride?connected?through?a?long?tube?are?opened?
simultaneously?at?both?ends,?the?white?ammonium?chloride?ring?first?formed?will?be?(A)?At?the?centre?of?the?tube?(B)?Near?the?hydrogen?chloride?bottle?(C)?Near?the?ammonium?bottle?(D)?Throughout?the?length?of?the?tube
5?Class?11?
LOGICAL?REASONING?
1.?Tony?and?Sunil?are?participating?in?a?jog-a-thon?to?raise?money?for?charity.Tony?will?raise?Rs.20,?plus?Rs.2?for?
each?lap?he?jogs.?Sunil?will?raise?Rs.?30,?plus?Rs.1.50?for?each?lap?he?jogs.?The?total?amount?of?money?each?will?raise?can?be?calculated?using?the?follwing?expressions?wherenrepresents?the?number?of?laps?run:?
Tony?:?20?+?2n????Sunil?:?30?+?1.50n?
After?how?many?laps?will?they?have?raised?the?same?amount?of?money??(A)?3?(B)?6.5?(C)?14.5?(D)?20?2.?There?is?a?proportional?relationship?between?the?size?of?a?projected?image?on?a?screen?and?the?distance?of?the?screen?from?the?projector.?
An?image?that?is?projected?onto?a?screen?10?feet?away?is?a?rectangle?with?dimensions?of?2?feet?by?3?feet.?If?the?screen?is?moved?to?a?distance?of?15?feet?from?the?projector,?what?will?be?the?dimensions?of?the?larger?image?projected?onto?the?screen??(A)?3?feet?by?4.5?feet?(B)?4?feet?by?6?feet?(C)?4.5?feet?by?6.75?feet?(D)?7?feet?by?8?feet?3.?A?formula?for?computing?a?value?r?is?r?=
mx+ my?
,?where?m,?x,?y,?w?and?z?are?positive?integers.?An?wz
increase?in?which?variable?would?result?in?a?corresponding?decrease?in?r??(A)?m?(B)?x?(C)?y?(D)?z?
4.?Matt’s?mathematics?class?is?playing?“Guess?My?Rule.”?The?teacher?writes?this?table?of?values?on?the?chalkboard,?and?the?class?finds?an?equation?that?fits?the?values?in?the?table.?Which?of?these?equations?describes?the?relationship?between?the?values?in?the?table??
(A)?y?=?2x?–?2?(B)?y?=?–?2x?–?2?(C)?y?=?–?3x?–?2?(D)?y?=?3x?–?2?5.?The?Venn?diagram?below?shows?the?types?of?novels?the?literature?club?members?read?during?their?summer?break.?
Which?of?the?following?is?NOT?supported?by?the?information?in?the?Ven?diagram??
(A)?21?members?read?both?an?adventure?novel?and?a?romance?novel?(B)?64?members?read?only?an?adventure?novel?or?a?mystery?novel?(C)?26?members?read?all?three?types?of?novels?(D)?67?members?read?a?romance?novel?
Table?of?Values?x?–3?0?2?5?y?–11?–2?4?13?Literature?Club?Summer?Reading?Adventure?Romance?36?14?43?7?2?3?28?Mystery?Hours?Total?Number?of?(h?)?Guitars?Made?(g)?2?4?8?16?18?42?90?186?6.?A?guitar?manufacturer?uses?a?computer-controlled?machine?to?make?electric?
guitars.?The?table?below?shows?the?total?number?of?guitars?made?after?2,?4,?8?and?16?hours.?If?g?represents?the?total?number?of?guitars?made?after?h?hours,?which?equation?represents?the?pattern?shown?in?the?table??(A)?g?=?12h?–?6?(B)?g?=?12h?(C)?g?=?3h2??–?6?(D)?g?=?3h2??+?6?
7.?Look?at?this?container.?
Water?flows?into?this?container?at?a?constant?rate.?Which?graph?could?represent?the?height?of?the?water?in?the?container?over?time??
Height?of?Water?Height?of?Water?(A)?(B)?
Time?(C)?
Time?(D)?
Time?Height?of?Water?Heightof?Water?Time?MATHEMATICALREASONING?8.?In?an?examination?of?9?papers,?a?candidate?has?to?pass?in?more?papers?than?the?number?of?papers?in?
which?he?fails?in?order?to?get?the?success.?The?number?of?ways?in?which?he?can?fail?(A)?128?(B)?256?(C)?255?(D)?9?×?8!
6?Class?11?
9.?What?is?the?solution?to?the?system?of?equations?shown?below??
2x-y+3z?= 8?ì ?
í x-6y-z?= 0?? -6x+3y-9z = 24??
(A)?(0,?4,?4)?
(B)??1,4,?
?
è10?? ÷ 3 ?
(C)?No?solution?(D)?Infinitely?many?solutions?
10.?What?is?thenth?term?in?the?arithmetic?series?below??
3?+?7?+?11?+?15?+?19?.....?
(A)?4n?(B)?3?+?4n?(C)?2n?+?1?
(D)?4n?–?1?
11.?A?train?is?made?up?of?a?locomotive,?7?different?cars,?and?a?caboose.?If?the?locomotive?must?be?first,?and?the?caboose?must?be?last,?how?many?different?ways?can?the?train?be?ordered??(A)?5040?(B)?181,440?(C)?362,880?(D)?823,543?12.?If?A+B=?
(A)?1?
p
then?value?of?(1?+?tanA)?(1?+?tanB)?equals?4
(B)?2?(C)?–2?
(D)?–1?
13.?What?are?the?coordinates?of?the?image?of?pointP(–3,?–7)?after?a?reflection?about?the?liney=?2??
(A)?(–?3,?9)?(B)?(–?3,?11)?(C)?(5,?–?7)?(D)?(7,?–?7)?14.?Look?at?this?function?As?the?value?of?xincreases,?they-values?form?a?repeating?pattern.?If?this?pattern?continues,?what?is?the?y-value?when?x=?26??(A)?–?2?(B)?–?1?(C)?1?(D)?2?y?3?2?1–1?–1?1?2?3?4?5?6?7?8?x?–2?–3?15.?What?is?the?range?of?the?function?f(x)?=?x2??+?3?if?the?domain?is?{–?3,?0,?3}??
(A)?{3,?12}?(B)?{–?6,?3,?12}?(C)?All?real?numbers?(D)?All?real?numbers?greater?than?or?equal?to?3?16.?The?sum?of?three?consecutive?odd?integers?is?21.?If?x?is?the?least?of?these?odd?integers,?which?equation?must?be?true??(A)?3x?=?21?(B)?3x?+?3?=?21?(C)?3x?+?4?=?21?(D)?3x?+?6?=?21?17.?The?harmonic?mean?of?the?roots?of?the?equation 2+3x2?-3+5x?+6+25= 0?is?
(A)?2?
(B)?7?
(C)?8?
EVERYDAYMATHEMATICS?18.?Julie?works?at?the?amusement?park?with?the?maintenance?crew.?She?needs?to?replace?a?string?of?burned-out?lights?along?the?arc?shown?between?seat?1?and?seat?6.?The?arc?makes?up?1/4?of?the?Gaint?Wheel.?
The?20?seats?of?the?wheel?are?equally?spaced,?and?the?supports?from?the?center?of?the?wheel?to?each?seat?are?15?feet?in?length.?How?long,?to?the?nearest?foot,?does?the?string?of?replacement?lights?need?to?be??(A)?24?feet?(B)?30?feet?(C)?47?feet?(D)?90?feet?
Gaint?Wheel?( ) ( ) ( ) (D)?4?
Seat?6?15?feet?Seat?1?19.?The?typical?wingspan?of?the?little?blue?heron?is?4?inches?more?than?half?the?typical?wingspan?of?the?great?
blue?heron.?Ifgrepresents?the?typical?wingspan?of?the?great?blue?heron,?which?expression?represents?the?typical?wingspan?of?the?little?blue?heron??
1?1??1??
g?÷ g?+ 4?(g?+ 4)?(A) 4??(B) (C)?2g?+?4?(D) è2?? 2?2?20.?This?diagram?shows?the?angle?of?inclination?of?the?triangular?faces?of?the?Great?
Pyramid?in?Egypt.?
When?it?was?built,?the?length?of?each?side?of?the?square?base?was?230?meters.?Which?equation?represents?the?height,h,?of?the?Great?Pyramid?when?it?was?built??(A)?h?=?115?sin?52°?(B)?h?=?115?tan?52°?
(C) h?=
115?
sin52?°
h?52°?(D) h=
115?
tan52?°
230?m?7?Class?11?
印度国家科学-数学-网络奥林匹克竞赛高二年级样题
