National?Cyber?Olympiad?MENTAL?ABILITY?
1.?The?value?of?tan5°?tan25°?tan30°?tan65°?tan85°?is?
1?2?(A)?3?(B)?(C)?
3?3?5?3?(D)?
2.?A?bag?contains?5?red?balls?and?some?blue?balls.?If?the?probability?of?drawing?a?blue?ball?is?double?that?of?
a?red?ball?then?the?number?of?blue?balls?in?the?bag?is?(A)?10?(B)?5?(C)?8?(D)?7?3.?A?cylinder?open?at?both?ends?has?radius?5/pcm?and?height?12?cm.?If?AandBare?diametrically?opposite?points?lying?on?the?top?and?bottom?rims.?The?shortest?distance?between?Aand?Bis?(A)?13?cm?(B)?17?cm?
(C) 12?10?cm?
p
(D)
12?+ 10?cm?
p 2?( ) 2?4.?Which?of?the?following?equations?have?the?same?graph??
2?x?- 9?
I.?y?=?x?+?3?II. y?= III.?
x?- 3?
(A)?I?and?II?only?(B)?I?and?III?only?(C)?II?and?III?only?(D)?All?of?these.?
(x-3)y=x 2?- 9?
?x?1??
+÷ = 1?is?5.?The?value?of?the?real?number?x?satisfying log9x?-log9??
è109??
(A)?3?(B)?4?(C)?9?(D)?10?
6.?Two?numbers?are?in?the?ratio?of?3:?5.?If?8?is?added?to?each?number,?the?ratio?becomes?2?:?3.?What?are?the?numbers??(A)?24?and?40?(B)?20?and?30?(C)?32?and?42?(D)?35?and?45?7.?The?sum?of?first?24?terms?of?the?sequence?whose?nth?term?isa?n?=?3?+?
(A)?275?
(B)?272?
(C)?280?
(D)?270.?
2?
n,?is?3?
8.?The?ratio?of?the?volume?of?a?cube?to?that?of?a?sphere?which?exactly?fits?inside?the?cube?is?
(A)?6?: p (B) p :?6?(C) p :?12?(D)?12?: p
LOGICAL?&?ANALYTICAL?REASONING?
9.?In?a?group?of?five?people,?K,?L?and?M?are?ambitious,?M,?N?and?R?are?honest,?L,?M?and?N?are?intelligent?and?K,?M?and?R?are?industrious.?Among?these,?neither?industrious?nor?ambitious?person(s)?would?include?(A)?K?alone?(B)?L?and?R?(C)?M?and?N?(D)?N?alone?10.?On?another?planet,?the?local?terminology?for?earth,?water,?light,?air?and?sky?are?‘sky’,?‘light’,?‘air’,?‘water’?and?‘earth’?respectively.?If?someone?is?thirsty?there,?what?would?he?drink??(A)?Sky?(B)?Water?(C)?Air?(D)?Light.?11.?The?yield?versus?fertilizer?input?is?shown?in?the?given?graph:?
Yield?Consider?the?following?statements?based?on?this?graph:?50?1.?Yield?rate?is?zero?at?B?and?C.?
20?2.?There?is?no?yield?with?no?fertilizer?input.?
A?3.?The?yield?is?minimum?at?D.?8?0?4.?The?yield?is?neither?minimum?nor?maximum?at?C.?1?Which?of?the?above?statements?are?correct??(A)?1,?2?and?4?(B)?3?and?4?(C)?2?and?3?(D)?1,?3?and?4?
2?Class?10?
B?(Maximum?Point)?C?(Saddle?Point)?5?10?15D?12.?Step?1?:Multiply?by?2?
Step?2?:?Subtract?1?
Step?3?:?If?less?than?10,?jump?to?step?1?and?continue?from?there??otherwise?proceed?to?step?4?Step?4?:Add?7?
Step?5?:Divide?by?2?Step?6?:?Add?2?
Step?7?:Multiply?by?2?
If?you?start?with?a?value?of?6?then?calculate?how?many?timesyou?had?to?jump?to?step?1.?(A)?4?(B)?5?(C)?3?(D)?0?
13.?A,?B,?C,?D,?E,?F?and?G?are?members?of?a?family?consisting?of?four?adults?and?three?children,?two?of?whom,?F?and?G?are?girls.?A?and?D?are?brothers?and?A?is?a?doctor.?E?is?an?engineer?married?to?one?of?the?brothers?and?has?two?children.?B?is?married?to?D?and?G?is?their?child.?Who?is?C??(A)?G’s?brother?(B)?F’s?father?(C)?E’s?daughter?(D)?A’s?son?
COMPUTERS??&??INFORMATION?TECHNOLOGY?
14.?Which?of?the?following?high?level?language?isNOTsuitable?for?generating?or?developing?a?data?file??(A)?BASIC?(B)?FORTRAN?(C)?COBOL?(D)?PASCAL?15.?The?processing?speed?of?a?computer?is?measured?in?(A)?Mega?byte?(B)?16?bit?(C)?Mega?hertz?(D)?Milli?seconds?
16.?Which?of?the?following?features?distinguishes?a?database?file?from?a?mere?collection?of?data?(A)?Database?enables?data?to?be?organised?for?effective?use?much?faster?(B)?It?organises?data?in?rows?and?columns?
(C)?It?gives?reference?name?to?each?file?created?(D)?It?provides?search?facility?
17.?Each?command?is?followed?by?a?meaning,?match?them.?
Command?Meaning?1.?STEP?A.?To?branch?unconditionally?out?of?the?normal?program?sequence?to?a?specified?line?
number.?
2.?SWAP?B.?To?terminate?program?execution?and?return?to?command?level.?3.?STOP?C.?To?exchange?the?values?of?two?variables.?4.?GOTO?D.?To?specify?the?counter?increment?for?each?loop?in?FOR-NEXT?statement.?(A)?1B,?2C,?3D,?4A?(B)?1A,?2B,?3C,?4D?(C)?1D,?2A,?3B,?4C?(D)?None?of?these.?18.?If?X?represents?“Shweta?can?read”?and?Y?represents?“Shweta?can?write”,?then?write?in?terms?of?X,?X ￠,?Y?andY ￠the?following?statements:?
(i)?Shweta?can?read?but?cannot?write?(ii)?Shweta?cannot?read?or?write?(A)?X × Y ￠,X ￠× Y ￠ (B)?X ￠×Y,X×Y ￠ (C)?X ￠×Y,X ￠×Y ￠ (D)?None?of?these.?19.?Name?the?smallest?addressable?set?of?bits?of?the?computer?memory.?(A)?Byte?(B)?Word?(C)?Pixel?(D)?Digit?20.?Which?of?the?following?is?not?a?hardware?component??(A)?Mouse?(B)?LAN?(C)?Chip?(D)?Semiconductor?memory.
3?
Class?10?
National?Science?Olympiad?MENTAL?ABILITY?
1.?In?an?office?with?21?staff?members,?1/3?are?men?and?2/3?are?women.?To?obtain?a?staff?in?which?1/4?are?
men,?how?many?women?should?be?hired??(A)?7?(B)?5?(C)?3?(D)?2?2.?A?jogger?desires?to?run?a?certain?course?in?1/4?less?time?than?she?usually?takes??by?what?percent?must?she?increase?her?average?running?speed?to?accomplish?this?goal??
1?
(A)?20%?(B)?25%?(C)?33%?(D)?50%.?
3?3.?A?salesman?makes?a?commission?of?x?percent?on?the?first?Rs.?2,000?worth?of?sale?in?any?given?month?and?
y?percent?on?all?further?sales?during?that?month.?If?he?makes?Rs.?700?from?Rs.?4,000?of?sales?in?October?and?he?makes?Rs.?900?from?Rs.?5,000?of?sales?in?November,?what?is?the?value?of?x???(A)?2%?(B)?5%?(C)?10%?(D)?15%.?4.?A?magician?wants?to?ship?a?magic?wand?to?the?location?of?his?next?show.?The?rectangular?box?he?has?available?for?this?purpose?measures?6?inches?wide?by?8?inches?long?by?10?inches?high.?What?is?the?longest?cylindrical?wand?of?negligible?diameter?that?can?be?shipped?in?this?box??(A)?10?inches?(B)?82?inches?(C)?83?inches?(D)?102?inches?5.?The?price?of?sugar?increased?20?percent?in?2000?and?10?percent?in?2001.?By?approximately?what?percent?would?the?price?at?the?end?of?2001?have?to?be?decreased?to?restore?the?price?of?the?sugar?to?its?pre-2000?price??
(A)?40%?
(B)?35%?
(C)?30%?
SCIENCE?
6.?If?the?Moon?were?twice?as?massive?as?it?is?now,?and?it?has?stayed?in?the?same?orbital?radius?about?the?
Earth?as?it?has?now,?its?new?orbital?period?(in?terms?of?its?current?orbital?period?T?)?would?be,?
T?T?
(A)?T?(B)?(C)?(D)?2?T?
2?4?7.?A?virtual?image?is?formed?by?a?concave?mirror?when?object?is?placed?
(A)?Between?focus?and?centre?of?curvature?(B)?Beyond?C?
(C)?At?infinity?
(D)?Behind?the?mirror?
(D)?24%.?
8.?No?heat?loss?occurs?during?flow?of?charge?in?super?conductors?because?
(A)?Speed?of?charge?is?slow?in?it?(C)?It?offers?zero?resistance?
(B)?It?is?bad?conductor?of?heat?(D)?It?generates?very?small?voltage?
9.?How?do?we?know?that?fission?isn't?responsible?for?the?sun’s?energy???
(A)?Fission?doesn't?produce?enough?energy?per?gram?of?fuel?(B)?If?fission?were?going?on?in?the?sun,?the?sun?would?explode?(C)?If?fission?were?going?on?in?the?sun,?the?sun's?mass?would?increase?(D)?There?isn't?very?much?fissionable?material?in?the?sun.?
10.?Which?of?the?following?groups?of?instruments?is?required?to?have?communication?line?between?two?television?
relay?centres??
(A)?Microwave?link,?booster?relay,?satellite?
(B)?Radio?telescope,?microwave?link,?booster?relay,?telephone?(C)?Microwave?link,?telephone,?booster?relay,?satellite?(D)?All?of?these
4?Class?10?
11.?In?a?circular?coil?of?wire?if?the?current?is?flowing?in?the?anticlockwise?direction,?
the?face?will?be?north?pole.?When?there?is?no?current?in?the?coil,?if?the?north-?pole?is?brought?near?the?coil,?during?that?time,?the?current?induced?in?the?coil?will?be?
(A)?Clockwise?(B)?Anticlockwise?
(C)?The?current?will?be?in?the?same?direction?whether?the?north?pole?is?brought?
near?or?taken?away?(D)?(A)?and?(C)?are?correct?12.?During?calcination?of?the?ore?
(A)?The?lower?oxides?are?converted?into?higher?oxides?(B)?The?metal?gets?oxidised?to?its?highest?oxide?(C)?Volatile?impurities?are?expelled?
(D)?Sulphur?present?in?the?ore?is?converted?into?SO?2?
13.?Which?of?the?following?statements?is?NOT?true?regarding?iron??(A)?It?is?hard?and?brittle.?(B)?It?can?be?tempered.?(C)?It?cannot?be?welded.?(D)?It?contains?4?-?5%?of?carbon?14.?Heating?of?rubber?with?sulphur?is?known?as?(A)?Galvanisation?(B)?Sulphonation?(C)?Vulcanisation?(D)?Bessemerisation?15.?The?gas?evolved?in?Bhopal?tragedy?was?(A)?CO?(B)?CO?(C)?Methyl?isocyanate?2?
N???S?G(D)?N?2?
16.?Which?of?the??following?gases?forms?a?stable?complex?compound?(leading?to?death)?with?haemoglobin?of?the?human?blood???(A)?Oxygen?(B)?Carbon?dioxide?(C)?Carbon?monoxide?(D)?Nitrogen?17.?When?copper?is?heated?with?concentrated?H?2SO??4?the?products?obtained?are?(A)?CuSO?(B)?CuSO?4?+?H?2?4?+?SO?2?+H?2?(C)?CuSO?(D)?CuO?+?SO?4?+?SO?2?+?H?2O??3?+?H?2?18.?Lathyrism?due?to?consumption?of?khesari?dal?is?characterised?by?(A)?Skeletal?deformation?and?thinning?of?collagen?fibres?
(B)?Skeletal?deformities,?diabetes?mellitus?and?reproductive?failure?(C)?Retarded?growth,?precocious?puberty?and?renal?dysfunction?
(D)?Cardiovascular?abnormalities,?mental?retardation?and?delayed?puberty.?19.?Which?one?yields?more?energy??
(A)?Direct?burning?of?cowdung?
(B)?Burning?of?biogas?derived?from?cowdung?(C)?Burning?of?manure?derived?from?cowdung?(D)?Burning?of?semidecayed?cowdung?20.?Mark?the?incorrect?match.?
Nutrient?Deficiency?(A)?Iron?Anaemia?(B)?Vitamin?B?Beri?beri?1?(C)?Vitamin?B?Pellagra?4?(D)?Vitamin?C?Scurvy?
Symptom?
Deficiency?of?haemoglobin?in?R.B.C.?Water?logging?of?the?tissue,?paralysis?Pigeon?chest,?loss?of?teeth?
Loosening?of?teeth,?swelling?and?bleeding?of?gums?
5?
Class?10?
LOGICAL?REASONING?
1.?There?are?6?short?pieces?of?link?chain,?each?having?4?links.?It?takes?
10?seconds?to?cut?a?link?and?25?seconds?to?weld?it?back?together.?What?is?the?shortest?possible?time?to?make?the?longest?chain??(A)?175?seconds?(B)?210?seconds?(C)?150?seconds?(D)?60?seconds?2.?What?should?come?at?the?place?of?‘?’?so?that?every?column?or?diagonal?has?the?same?sum??(A)?19?(B)?12?(C)?13?(D)?15?
19?2?4?13?3?7?5?8?15?17?1?6?14?16???10?18?11?9?Magic?Hexagon?3.?Points?A?and?B?on?a?map?are?12?km?apart?if?you?follow?the?path.?A?troop?of?boy?scouts?leaves?point?A?at?11:00?a.m.?They?are?all?carrying?packs?and?travel?3?km/hr?until?they?reach?point?C?at?12:45.?If?they?want?to?reach?point?B?by?2:00,?how?fast?will?they?have?to?go??
A?(A)?5.4?km/hr?(B)?6.75?km/hr?(C)?5.25?km/hr?(D)?1.75?km/hr?
B?C?4.?A?child?was?looking?for?his?father.?He?went?90?metres?in?the?East?before?turning?to?his?right.?He?went?20?metres?before?turning?to?his?right?again?to?look?for?his?father?at?his?uncle’s?place?30?metres?from?this?point.?His?father?was?not?there.?From?here?he?went?100?metres?to?the?North?before?meeting?his?father?in?a?street.?How?far?did?the?son?meet?his?father?from?the?starting?point??(A)?80?metres?(B)?100?metres?(C)?140?metres?(D)?260?metres?5.?If?DELHI?is?coded?as?73541?and?CALCUTTA?as?82589662,?how?can?CALICUT?be?coded??(A)?5279431?(B)?5978213?(C)?8251896?(D)?8543691?6.?If?1st?October?is?Sunday,?then?1st?November?will?be?(A)?Monday?(B)?Tuesday?(C)?Wednesday?
(D)?Thursday?
7.?If?+?stands?for?‘division’,?×?stands?for?‘addition’,?–?stands?for?‘multiplication’?and?stands?for?‘subtraction’,?then?which?of?the?following?equations?is?correct??(A)?36?×?6?+?7 ? 2?–?6?=?20?(B)?36 ? 6?+?3?×?5?–?3?=?45?(C)?36?+?6?–?3?×?5 ? 3?=?24?(D)?36?–?6?+?3?×?5 ? 3?=?74?
MATHEMATICALREASONING?8.?If?O?is?the?centre?of?the?circle,?find?the?value?of?x?in?the?following?figure.?
(A)?75°?(C)?65°?
(B)?40°?(D)?90°?
A?B?D?40°?O?65°?x?C?9.?Parallelogram?ABCD?is?shown?in?the?adjoining?figure.?Which?pair?of?triangles?
can?be?established?to?be?congruent?to?prove?that D DAB @ D BCD??(A) D ADCandD BCD?(B) D AEDandD BEC?(C) D DABandD BCD?(D) D DECandD BEA?
D?A?B?E?C?10.?What?is?the?complete?solution?to?the?equation?|3?–?6x|?=?15??(A)?x?=?2??x?=?3?(B)?x?=?–?2??x=?3?(C)?x?=?2??x=?–?3?(D)?x?=?–?2??x=?–?3
6?Class?10?
11.?In?the?figure?given?here,?AB?>?BC.?
If?we?assume?that?mDA?=?mDC,?it?follows?that?AB?=?BC.?This?contradicts?the?given?statement?that?AB?>?BC.?What?conclusion?can?be?drawn?from?this?contradiction??(A)?mDA?=?mDB?(B)?mDA1mDB?(C)?mDA?=?mDC?(D)?mDA1mDC?12.?Which?polynomial?represents?(3x2??+?x–?4)(2x–?5)??(A)?6x3??–?13x2??–?13x?–?20?(B)?6x3??–?13x2??–?13x?+?20?(C)?6x3??+?13x2??+?3x?–?20?(D)?6x3??+?13x2??+?3x+?20?13. 2x+72x4+21x3+35x2?–37x?+ 46?=?
4?(A)?x3+7x2?–7x?+6–?2x?+7?4?
(C)?x3–7x2?+7x?–6+?2x?+7?
A?C?B?(B)?2x3+14x2?–14x?+12–?4?2x?+7?
4?
(D)?x3+7x2?–7x?+6+?2x?+7?
14.?There?are?two?numbers?with?the?following?properties.?
1)?The?second?number?is?3?more?than?the?first?number.?
2)?The?product?of?the?two?numbers?is?9?more?than?their?sum.?
Which?of?the?following?represents?possible?values?of?these?two?numbers??(A)?–?6,?–?3?
(B)?–?4,?–?1?
(C)?–?1,?4?
(D)?–?3,?6?
15.?If?i = –1,?what?is?the?value?of?i?4???
(A)?i?(B)?–?i?
(C)?1?(D)?–?1?
16.?A?copper?sphere?of?diameter?18?cm?is?drawn?into?a?wire?of?diameter?4?mm.?Find?the?length?of?the?wire.?(A)?240?m?(B)?242?m?(C)?243?m?(D)?245?m?17.?What?is?thenth?term?in?the?arithmetic?series?given?below??
(A)?4n?
3?+?7?+?11?+?15?+?19?...?
(B)?3?+?4n?(C)?2n?+?1?
EVERYDAYMATHEMATICS?18.?Three?ducks?and?two?ducklings?weigh?32?kg.?Four?ducks?and?three?ducklings?weigh?44?kg.?All?ducks?
weigh?the?same?and?all?ducklings?weigh?the?same.?What?is?the?weight?of?two?ducks?and?one?duckling??
(A)?20?kg.?(B)?40?kg.?(C)?60?kg.?
(D)?64?kg.?
A3?(D)?4n?–?1?
19.?A?rectangular?sheet?of?wood?has?four?small?squares?removed?from?the?
corners.?It?is?then?cut?to?make?a?box?that?is?5?cm?by?4?cm?with?a?volume?of?
3?60?cm?.?(Four?pieces?of?size?A4?are?removed.)?Find?the?original?area?of?the?sheet?of?wood.?(A)?200?cm?sq.?(C)?96?cm?sq.?
5?cm?A1?A2?(B)?110?cm?sq.?(D)?100?cm?sq.?
4?cm?A4?20.?A?cereal?company?decided?to?increase?the?height?of?its?boxes?by?30?percent?and?reduce?the?width?in?order?to?maintain?the?same?volume.?Initially,?length?=?20?cm,?height?=?40?cm,?width?=?30?cm?What?will?the?new?width?be?if?the?length?stays?the?same??(A)?52?cm?(B)?20?cm?(C)?23.08?cm?(D)?23?cm?
l?hw?7?
Class?10?
印度国家科学-数学-网络奥林匹克竞赛高一年级样题
