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March 14, 2018 20:53
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{ | |
"test": { | |
"title": "S02T03", | |
"slug": "S02T03", | |
"description": "Přípravný test k státní maturitě.", | |
"successfulLimit": 33, | |
"tasks": [ | |
{ | |
"slug": "S02T03U01", | |
"title": "S02T03U01", | |
"question": | |
"Na jakou hodnotu vzroste jistina 10 000 Kč po jednom roce, při roční úrokové sazbě 7%, jestliže banka vybírá daň 15% z úroků ročně?", | |
"maxPoints": 1, | |
"type": "options", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ "name": "opt1", "problem": "##595##Kč" }, | |
{ "name": "opt2", "problem": "##10~595##Kč" }, | |
{ "name": "opt3", "problem": "##10~715##Kč" }, | |
{ "name": "opt4", "problem": "##715##Kč" }, | |
{ "name": "opt5", "problem": "jiná hodnota " } | |
], | |
"correctAnswer": ["opt2"], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S02T03U02", | |
"title": "S02T03U02", | |
"question": | |
"Vypočítejte, v kterém intervalu je výsledek? $${{[(-{1\\over3})+{1\\over6}]:(-{5\\over6})}\\over{-(-{3 \\over 2})^2 - 0.3 \\cdot {30 \\over 12}}}=$$", | |
"maxPoints": 1, | |
"type": "options", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ | |
"name": "opt1", | |
"problem": "##\\lt-{1\\over7};{1\\over7}##" | |
}, | |
{ | |
"name": "opt2", | |
"problem": "##\\lt-{1\\over20};-{1\\over7}##" | |
}, | |
{ | |
"name": "opt3", | |
"problem": "##\\lt{1\\over7};{1\\over20}##" | |
}, | |
{ | |
"name": "opt4", | |
"problem": "##\\lt-\\infty;-{1\\over20}##" | |
}, | |
{ "name": "opt5", "problem": "##\\lt{1\\over20};\\infty##" } | |
], | |
"correctAnswer": ["opt!!"], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S02T03U03", | |
"title": "S02T03U03", | |
"taskText": | |
"Zboží bylo nejprve zlevněno o 15% a později z této nové ceny o dalších 10%. Cena po obou zlevnění je 1 600 Kč.", | |
"question": "Jaká byla původní cena před prvním zlevnění?", | |
"maxPoints": 1, | |
"type": "options", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ "name": "opt1", "problem": "##2~156##" }, | |
{ "name": "opt2", "problem": "##2~232##" }, | |
{ "name": "opt3", "problem": "##2~092##" }, | |
{ "name": "opt4", "problem": "##2~186##" }, | |
{ "name": "opt5", "problem": "##2~065##" } | |
], | |
"correctAnswer": ["opt3"], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S020T03U04", | |
"title": "S02T03U04", | |
"taskText": "Sedm dělníků postaví dům za 330 dní.", | |
"question": | |
"Jaký je nejmenší možný počet dělníků, aby stavba trvala méně než 140 dnů?", | |
"maxPoints": 1, | |
"type": "options", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ "name": "opt1", "problem": "##18##" }, | |
{ "name": "opt2", "problem": "##15##" }, | |
{ "name": "opt3", "problem": "##16##" }, | |
{ "name": "opt4", "problem": "##17##" }, | |
{ "name": "opt5", "problem": "jiný počet" } | |
], | |
"correctAnswer": ["opt4"], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S02T03U05", | |
"title": "S02T03U05", | |
"taskText": | |
"Součet druhých mocnin tří za sebou jdoucích celých je o 25 menší, než trojnásobek druhé mocniny největšího z těchto tří čísel. ", | |
"question": "Které číslo je z této řady nejmenší?", | |
"maxPoints": 2, | |
"type": "options", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ "name": "opt1", "problem": "##8##" }, | |
{ "name": "opt2", "problem": "##9##" }, | |
{ "name": "opt3", "problem": "##4##" }, | |
{ "name": "opt4", "problem": "##2##" }, | |
{ "name": "opt5", "problem": "jiná hodnota " } | |
], | |
"correctAnswer": ["opt3"], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S02T03U06", | |
"title": "S02T03U06", | |
"question": | |
"Vypočítejte velikost úhlu ##\\phi##, jestliže ##\\alpha=84°##a ##\\beta=145°##. &&\\images\\tasks\\S02T03\\S02T03U06.jpg&&", | |
"maxPoints": 2, | |
"type": "options", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ "name": "opt1", "problem": "##56°##" }, | |
{ "name": "opt2", "problem": "##35°##" }, | |
{ "name": "opt3", "problem": "##61°##" }, | |
{ "name": "opt4", "problem": "##53°##" }, | |
{ "name": "opt5", "problem": "jiná hodnota " } | |
], | |
"correctAnswer": ["opt3"], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S02T03U07", | |
"title": "S02T03U07", | |
"taskText": | |
"Ze zápalek máme sestavenou následující řadu obrazců. &&\\images\\tasks\\S02T03\\S02T03U07.jpg&&", | |
"question": | |
"Kolik zápalek budeme potřebovat na sestavení desátého obrazce?", | |
"maxPoints": 1, | |
"type": "options", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ "name": "opt1", "problem": "##39##" }, | |
{ "name": "opt2", "problem": "##35##" }, | |
{ "name": "opt3", "problem": "##42##" }, | |
{ "name": "opt4", "problem": "##33##" }, | |
{ "name": "opt5", "problem": "jiná hodnota" } | |
], | |
"correctAnswer": ["opt4"], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S02T03U08", | |
"title": "S02T03U08", | |
"taskText": | |
"Ve čtvercové síti je nakreslen pětiúhelník. &&\\images\\tasks\\S02T03\\S02T03U08.jpg&&", | |
"question": "Jak dlouhá je tato lomená čára?", | |
"maxPoints": 2, | |
"type": "options", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ | |
"name": "opt1", | |
"problem": "##6+\\sqrt{5}(3\\cdot\\sqrt2+1)##" | |
}, | |
{ "name": "opt2", "problem": "##8+\\sqrt{5}(\\sqrt2+3)##" }, | |
{ "name": "opt3", "problem": "##8+\\sqrt{2}(\\sqrt5+3)##" }, | |
{ | |
"name": "opt4", | |
"problem": "##6+\\sqrt{10}+3\\cdot\\sqrt2##" | |
}, | |
{ "name": "opt5", "problem": "##6+\\sqrt{2}(\\sqrt5+2)##" } | |
], | |
"correctAnswer": ["opt3"], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S02T03U09", | |
"title": "S02T03U09", | |
"question": | |
"##{{2x+1}\\over{x+3}}-{5\\overx}={15\\over{x^2+3x}}{+2}##", | |
"maxPoints": 2, | |
"type": "options", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ "name": "opt1", "problem": "##K=0##" }, | |
{ "name": "opt2", "problem": "##K=-3##" }, | |
{ "name": "opt3", "problem": "##K={1\\over3}##" }, | |
{ "name": "opt4", "problem": "##K=-{1\\over3}##" }, | |
{ "name": "opt5", "problem": "##K=3##" } | |
], | |
"correctAnswer": ["opt1"], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S02T03U10", | |
"title": "S02T03U10", | |
"question": | |
"Určete součet prvních 20-ti členů aritmetické posloupnosti ve které je ##a_8=-2,~a_{10}=0##", | |
"maxPoints": 1, | |
"type": "options", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ "name": "opt1", "problem": "##0##" }, | |
{ "name": "opt2", "problem": "##22##" }, | |
{ "name": "opt3", "problem": "##20##" }, | |
{ "name": "opt4", "problem": "##10##" }, | |
{ "name": "opt5", "problem": "jiná hodnota " } | |
], | |
"correctAnswer": ["opt4"], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S02T03U11", | |
"title": "S02T03U11", | |
"question": | |
"Určete délku strany ##s## &&\\images\\tasks\\S02T03\\S02T03U11.jpg&&", | |
"maxPoints": 2, | |
"type": "options", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ "name": "opt1", "problem": "##4##cm" }, | |
{ "name": "opt2", "problem": "##5##cm" }, | |
{ "name": "opt3", "problem": "##5,5##cm" }, | |
{ "name": "opt4", "problem": "##4,4##cm" }, | |
{ "name": "opt5", "problem": "jiná hodnota " } | |
], | |
"correctAnswer": ["opt1"], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S02T03U12", | |
"title": "S02T03U12", | |
"taskText": | |
"Obdélník má obvod 82m, délka jeho uhlopříčky je 29m.", | |
"question": "O kolik centimetrů je delší strana delší?", | |
"maxPoints": 2, | |
"type": "options", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ "name": "opt1", "problem": "##1##cm" }, | |
{ "name": "opt2", "problem": "##4##cm" }, | |
{ "name": "opt3", "problem": "##21##cm" }, | |
{ "name": "opt4", "problem": "##6##cm" }, | |
{ "name": "opt5", "problem": "jiná hodnota " } | |
], | |
"correctAnswer": ["opt1"], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S02T03U13", | |
"title": "S02T03U13", | |
"question": "##{{{(x-3)!+(x-1)!}}\\over{(x-2)!}}=3##", | |
"maxPoints": 1, | |
"type": "options", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ "name": "opt1", "problem": "##K=-1;3##" }, | |
{ "name": "opt2", "problem": "##K=-1##" }, | |
{ "name": "opt3", "problem": "##K=0##" }, | |
{ "name": "opt4", "problem": "##K=3##" }, | |
{ "name": "opt5", "problem": "jiná hodnota " } | |
], | |
"correctAnswer": ["opt4"], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S02T03U14", | |
"title": "S02T03U14", | |
"taskText": "Na přímce je znázorněno 10 různých bodů.", | |
"question": "Kolik různých přímek tyto body určují?", | |
"maxPoints": 1, | |
"type": "options", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ "name": "opt1", "problem": "##25##přímek" }, | |
{ "name": "opt2", "problem": "##60##přímek" }, | |
{ "name": "opt3", "problem": "##120##přímek" }, | |
{ "name": "opt4", "problem": "##45##přímek" }, | |
{ "name": "opt5", "problem": "jiný počet " } | |
], | |
"correctAnswer": ["opt4"], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S02T03U15", | |
"title": "S02T03U15", | |
"taskText": "Silniční válec má průměr 80cm a délku 1,5m.", | |
"question": | |
"Určete obsah plochy, kterou uválcuje za 1 hodinu, otočí-li se kolem své osy jednou za 15 sekund.", | |
"maxPoints": 2, | |
"type": "options", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ "name": "opt1", "problem": "##933m^2##" }, | |
{ "name": "opt2", "problem": "##1002m^2##" }, | |
{ "name": "opt3", "problem": "##856m^2##" }, | |
{ "name": "opt4", "problem": "##905m^2##" }, | |
{ "name": "opt5", "problem": "jiná hodnota " } | |
], | |
"correctAnswer": ["opt4"], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S02T03U16", | |
"title": "S02T03U16", | |
"question": | |
"K jednotlivým rovnicím přiřaďte množinu jejích řešení.", | |
"maxPoints": 3, | |
"partPoints": [0, 1, 2, 4], | |
"type": "pairs", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ | |
"name": "opt1", | |
"problem": "##{{\\log(x)}\\over{\\log(3x-5)}}=1##", | |
"part": "opt" | |
}, | |
{ | |
"name": "opt2", | |
"problem": "##\\log_5(x)=2##", | |
"part": "opt" | |
}, | |
{ | |
"name": "opt3", | |
"problem": "##\\log_5\\sqrt{1\\over{125}}=x##", | |
"part": "opt" | |
}, | |
{ "name": "ans1", "problem": "##25##", "part": "ans" }, | |
{ | |
"name": "ans2", | |
"problem": "##x={5\\over2}##", | |
"part": "ans" | |
}, | |
{ "name": "ans3", "problem": "##x=5##", "part": "ans" }, | |
{ | |
"name": "ans4", | |
"problem": "##2\\over5##", | |
"part": "ans" | |
}, | |
{ | |
"name": "ans5", | |
"problem": "##-{3\\over2}##", | |
"part": "ans" | |
} | |
], | |
"correctAnswer": [ | |
{ "name": "opt1", "correct": "ans2" }, | |
{ "name": "opt2", "correct": "ans1" }, | |
{ "name": "opt3", "correct": "ans5" } | |
], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S02T03U17", | |
"title": "S02T03U17", | |
"question": | |
"Určete číslo ##p## tak, aby bod C ležel na přímce AB. A[-2;-1], B[1;3], C[2p-1;p-3]", | |
"maxPoints": 2, | |
"type": "options", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ "name": "opt1", "problem": "##p=-1##" }, | |
{ "name": "opt2", "problem": "##p=-2##" }, | |
{ "name": "opt3", "problem": "##p=2##" }, | |
{ "name": "opt4", "problem": "##p=3##" }, | |
{ "name": "opt5", "problem": "##p=-3##" } | |
], | |
"correctAnswer": ["opt2"], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S02T03U18", | |
"title": "S02T03U18", | |
"question": | |
"Určete odchylku přímek ##p,q## je-li ##q:2x+y-1=0;~p:x=1+t;~y=2+3t;~t\\in\\mathbb{R}##", | |
"maxPoints": 2, | |
"type": "options", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ "name": "opt1", "problem": "##\\pi\\over2##" }, | |
{ "name": "opt2", "problem": "##\\pi##" }, | |
{ "name": "opt3", "problem": "##\\pi\\over3##" }, | |
{ "name": "opt4", "problem": "##\\pi\\over4##" }, | |
{ "name": "opt5", "problem": "##3\\pi\\over2##" } | |
], | |
"correctAnswer": ["opt4"], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S02T03U19", | |
"title": "S02T03U19", | |
"question": | |
"Určete, zda je zobrazená množina bodů grafem funkce.", | |
"maxPoints": 3, | |
"partPoints": [0, 0, 2, 3, 3], | |
"type": "yes-no", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ | |
"name": "opt1", | |
"problem": | |
"&&\\images\\tasks\\S02T03\\S02T03U019_A.jpg&&" | |
}, | |
{ | |
"name": "opt2", | |
"problem": | |
"&&\\images\\tasks\\S02T03\\S02T03U019_B.jpg&&" | |
}, | |
{ | |
"name": "opt3", | |
"problem": | |
"&&\\images\\tasks\\S02T03\\S02T03U019_C.jpg&&" | |
}, | |
{ | |
"name": "opt4", | |
"problem": | |
"&&\\images\\tasks\\S02T03\\S02T03U019_D.jpg&&" | |
} | |
], | |
"correctAnswer": [ | |
{ "name": "opt1", "correct": true }, | |
{ "name": "opt2", "correct": false }, | |
{ "name": "opt3", "correct": true }, | |
{ "name": "opt4", "correct": true } | |
], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S02T03U20", | |
"title": "S02T03U20", | |
"question": "Přiřaďte správný definiční obor k funkcím:", | |
"maxPoints": 4, | |
"partPoints": [0, 0, 1, 2, 4], | |
"type": "pairs", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ | |
"name": "opt1", | |
"problem": "##x^2+3x-1##", | |
"part": "opt" | |
}, | |
{ | |
"name": "opt2", | |
"problem": "##\\sqrt{{x+2}\\over{{4x-6}}}##", | |
"part": "opt" | |
}, | |
{ | |
"name": "opt3", | |
"problem": "##\\log(x-2)##", | |
"part": "opt" | |
}, | |
{ | |
"name": "opt4", | |
"problem": "##\\sqrt{x+2}##", | |
"part": "opt" | |
}, | |
{ | |
"name": "ans1", | |
"problem": "##x\\in(2;\\infty)##", | |
"part": "ans" | |
}, | |
{ | |
"name": "ans2", | |
"problem": "##x\\in\\langle-2;\\infty)##", | |
"part": "ans" | |
}, | |
{ | |
"name": "ans3", | |
"problem": "##x\\in(-\\infty;-2\\rangle##", | |
"part": "ans" | |
}, | |
{ | |
"name": "ans4", | |
"problem": | |
"##x\\in(-\\infty,-2\\rangle\\cup({3\\over2},\\infty)##", | |
"part": "ans" | |
}, | |
{ | |
"name": "ans5", | |
"problem": "##x\\in\\mathbb{R}##", | |
"part": "ans" | |
} | |
], | |
"correctAnswer": [ | |
{ "name": "opt1", "correct": "ans5" }, | |
{ "name": "opt2", "correct": "ans4" }, | |
{ "name": "opt3", "correct": "ans1" }, | |
{ "name": "opt4", "correct": "ans2" } | |
], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S02T03U21", | |
"title": "S02T03U21", | |
"taskText": | |
"Jsou dány dvě funkce ##f(x)=3x+1## a ##g(x)=x^2+3x+2##", | |
"question": "Vypočítejte ##f(g(1))##", | |
"maxPoints": 1, | |
"type": "options", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ "name": "opt1", "problem": "##17##" }, | |
{ "name": "opt2", "problem": "##15##" }, | |
{ "name": "opt3", "problem": "##23##" }, | |
{ "name": "opt4", "problem": "##19##" }, | |
{ "name": "opt5", "problem": "##25##" } | |
], | |
"correctAnswer": ["opt4"], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S02T03U22", | |
"title": "S02T03U22", | |
"taskText": "Ve třídě 1A se vyučuje 11 různých předmětů.", | |
"question": | |
"Kolika způsoby lze sestavit rozvrh na jeden den, vyučuje-li se tento den 6 různých předmětů.", | |
"maxPoints": 1, | |
"type": "options", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ "name": "opt1", "problem": "##11!\\over5!##" }, | |
{ "name": "opt2", "problem": "##{11\\choose5}##" }, | |
{ "name": "opt3", "problem": "##{11\\choose6}##" }, | |
{ "name": "opt4", "problem": "##11!\\over6!##" }, | |
{ "name": "opt5", "problem": "##11!-5!##" } | |
], | |
"correctAnswer": ["opt1"], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S02T03U23", | |
"title": "S02T03U23", | |
"taskText": | |
"Řešte nerovnici s neznámou ##n\\in\\mathbb{N}## $${n!\\over{n-2}}+24\\geq10n$$.", | |
"maxPoints": 2, | |
"type": "options", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ | |
"name": "opt1", | |
"problem": "##n\\in\\mathbb{N}-\\langle3;8\\rangle##" | |
}, | |
{ | |
"name": "opt2", | |
"problem": "##n\\in\\langle8,\\infty)\\cup\\{2;3\\}##" | |
}, | |
{ "name": "opt3", "problem": "##\\{0;1;2;3\\}##" }, | |
{ | |
"name": "opt4", | |
"problem": "##n\\in\\langle3;8\\rangle##" | |
}, | |
{ "name": "opt5", "problem": "jiná množina" } | |
], | |
"correctAnswer": ["opt2"], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S02T03U24", | |
"title": "S02T03U24", | |
"question": | |
"Kolikrát je pravděpodobnější, že padnou na kostkách všechna čísla stejná při hodu dvěma kostkama než při hodu třema?", | |
"maxPoints": 2, | |
"type": "options", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ "name": "opt1", "problem": "##4x##" }, | |
{ "name": "opt2", "problem": "##2x##" }, | |
{ "name": "opt3", "problem": "##8x##" }, | |
{ "name": "opt4", "problem": "##6x##" }, | |
{ "name": "opt5", "problem": "##3x##" } | |
], | |
"correctAnswer": ["opt4"], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S02T03U25", | |
"title": "S02T03U25", | |
"question": | |
"Vypočtěte výšku komolého rotačního kužele, je-li dán jeho objem ##V=516~cm^3## a poloměr podstavy ##r_1=9,4~cm##. ", | |
"maxPoints": 2, | |
"type": "options", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ "name": "opt1", "problem": "##5,9##" }, | |
{ "name": "opt2", "problem": "##3,5##" }, | |
{ "name": "opt3", "problem": "##6,3##" }, | |
{ "name": "opt4", "problem": "##4,4##" }, | |
{ "name": "opt5", "problem": "jiná hodnota " } | |
], | |
"correctAnswer": ["opt4"], | |
"solutions": [{}] | |
}, | |
{ | |
"slug": "S02T03U26", | |
"title": "S02T03U26", | |
"question": | |
"Určete rozlohu obdélníkového pozemku, který je na plánku s měřítkem 1:500 nakreslen s rozměry 0,83dm a 0,2dm.", | |
"maxPoints": 1, | |
"type": "options", | |
"categories": ["59eba1833ed54d1200c8d3f1"], | |
"options": [ | |
{ "name": "opt1", "problem": "##415m^2##" }, | |
{ "name": "opt2", "problem": "##41,5m^2##" }, | |
{ "name": "opt3", "problem": "##66,4m^2##" }, | |
{ "name": "opt4", "problem": "##664m^2##" }, | |
{ "name": "opt5", "problem": "jiná hodnota " } | |
], | |
"correctAnswer": ["opt1"], | |
"solutions": [{}] | |
} | |
] | |
} | |
} |
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