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Matematika olimpiada Tuman 2019-2020 o'quv yili

11-sinf Matematika olimpiada №2

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Avgust 19, 2024

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11-sinf Matematika olimpiada №2

2019-yil tuman bosqichida tushgan savollar

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1. Koordinata boshidan o‘tuvchi, simmetriya o‘qi ordinata o‘qiga parallel, cho‘qqisi y=x va y+x-2=0 to‘g‘ri chiziqlar kesishgan nuqtada bo‘lgan parabolaning tenglamasini toping.

A) y=-x²+2x

B) y=x²-2x

C) y=-x²-2x

D) y=-x²+1

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2. tenglama nechta natural yechimga ega?

A) 2

B) 4

C) 1

D) 3

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3. funksiyaning aniqlanish sohasini toping.

A) (2/3;∞)

B) (-∞;4/3)

C) (-∞;2/3)∪(2/3;∞)

D) (-∞;4/3)∪(4/3;∞)

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4. Tengsizlikni yeching.

A) (1/2;∞)

B) (2/3;2)

C) (5/3;2)

D) (4/3;3)

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5. Perimetri 4 ga o`tkir burchagi 30^oga va shu burchak qarshisidagi tomoni √3 ga teng bo`lgan uchburchakka ichki chizlgan aylana radiusini toping.

A) 7-4√3

B) (√3-1)/2

C) (1+√3)/2

D) 4√3+7

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6. ifodani soddalshtiring

A) 2sinα

B) cosα

C) 1

D) 2cosα

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7. Asosi ga teng bo`lgan muntazam to`rtburchakli piramidaning uchidan o`tkazilgan kesma asos tomonini 2:4 nisbatda bo`ladi va asos tekisligi bilan 60^o li burchakhosilqiladi. Piramidahajmini toping.

A) 12√30

B) √30

C) 6

D) √10

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8. ABCD tetraedrning D uchidagi barcha yassi burchaklari to`g`ri. Shu tetraedrda kub shunday ichki chizilganki, kubning bitta uchi D nuqtada, unga qarama−qarshi uchi esa ABC yoqda yotibdi. Agar DA=5, DB=6 va DC=10 bo`lsa, kub qirrasining uzunligini toping.

A) 25/12

B) 2√2

C) 15/7

D) 2

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9. Agar 2^a=27, 3^c=16 bo’lsa a ∙ ? ning qiymatini toping.

A) 13

B) 12

C) 10

D) 11

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10. Agar lg5=a va lg3=b bo`lsa, log₃₀⁡8 ni toping.

A) 3(1−a)

B) (3(1-a))/(1+b)

C) 1+b

D) (1−a)(1+b)

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11. Tenglamani yeching: |x²-3x-2|=x²+3|x+2|+4

A) (−∞;−2]

B) [−2;0]

C) [2;∞)

D) [−2;∞)

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12. GH kesmani O nuqta, G nuqtadan boshlab hisoblaganda, 5 : 7 kabi, P nuqtaesa 5:11 kabi nisbatda bo’ladi. O va P nuqtalar orasidagi masofa 30 sm bo’lsa, GH kesmaning uzunligini toping.

A) 288

B) 18

C) 72

D) 234

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13. Agar f(g(x))= − x+13 bo`lsa, f(x) va g(x) to`g`ri chiziqlar orasidagi burchakni toping .

A) π/2

B) π/3

C) π/4

D) 0

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14. |x²+2x-8|=3a tenglama a ning qanday qiymatlarida 3 ta haqiqiy yechimga ega bo`ladi.

A) a>3, a=0

B) (0;3)

C) a=3

D) 1

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15. Bitta tekislikda yotuvchi n ta turli tog`ri chiziq o`tkazilgan. Ularning ixtiyoriy ikkitasi parallel emas va ixtiyoriy uchtasi bitta nuqtadan o`tmaydi ,ya`ni bitta nuqtada kesishmaydi. Bu to`g`ri chiziqlar tekislikni 1276 qismga ajratadi. n ni aniqlang?

A) 50

B) 52

C) 51

D) 49

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16. Bir savdogar 1 mеtrini 1200 tiyindan olgan matosini yuvib, kuritgandan so`ng 1800 tiyindan sotyapti. Mato yuvilib kuritilganidan so`ng 20 foizi qisqardi. Bularga ko`ra savdogar nеcha foiz foyda ko`radi?

A) 10

B) 18

C) 20

D) 15

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17. Poyezd 3 minutda 7 kilometrmasofani , motosikl 5 minutda 7 kilometrmasofanibosibo`tdi. Mototsikltezligipoyezdtezliginingnecha % initashkilqiladi?

A) 61%

B) 71%

C) 60%

D) 70%

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18. y=6sin2x+sin12x funksiyaning hosilasini toping.

A) −24sin7xcos5x

B) 24sin7xsin5x

C) 24sin5xcos7x

D) 24cos7xcos5x

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19. f(x)=70cosxcos6x uchun boshlang`ich funksiya toping.

A) −7cos5x−5cos7x+c

B) 7cos5x−5cos7x+c

C) 7sin5x+5sin7x+C

D) 7sin5x−5sin7x+c

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20. Ifodani soddalashtiring:

A) √(a²-1)

B) 1−√(a-1)

C) 1+√(a+1)

D) 0

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21. a+b=−1 a+c=6 va b+c=1 bo`lsa, a² (3b+3c+2a)+b² (3a+3c+2b)+c² (3a+3b+2c) ning son qiymatini toping.

A) 27

B) 100

C) 45

D) 216

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22. funksiyaning boshlang`ich funksiyasini toping.

A) IV

B) II

C) I

D) III

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23. 3cos2x-3 sin2x=0 trigonometrik tenglamani yeching.

A) π/12+πk/2; k∈Z)

B) π/12+2πk; k∈Z

C) π/12+πk; k∈Z

D) π/6+πk; k∈Z

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24. Radiusi 6 ga teng bo`lgan uchta aylana o`zaro tashqi urinishidan hosil bo`lgan egri chiziqli uchburchakka ichki chizilgan aylana radiusini toping.

A) 2√2−1

B) 1

C) 4√3-6

D) 6-2√3

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25. f(x)=x³/3-x²-35x+2 funksiya uchun f `(x)=0 bo`lsa x ni toping.

A) −7 va −5

B) −5 va 7

C) 5 va 7

D) −7 va 5