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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. To‘g‘ri burchakli uchburchakda AC=3, BC=4, CD-balandlik va CE-bissektrisa. DE ni toping.

A) 15/31

B) 23/35

C) 12/35

D) 21

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2. 7⁵⁰ning oxirgi ikkita raqamini toping.

A) 51

B) 35

C) 49

D) 25

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3. 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) 45

B) 216

C) 27

D) 100

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4. 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) 2

B) 2√2

C) 25/12

D) 15/7

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

A) 24sin7xsin5x

B) −24sin7xcos5x

C) 24cos7xcos5x

D) 24sin5xcos7x

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6. funksiyaning boshlang`ich funksiyasini toping.

A) IV

B) III

C) I

D) II

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

A) 60%

B) 71%

C) 70%

D) 61%

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

A) 13

B) 12

C) 11

D) 10

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

A) 1

B) a>3, a=0

C) a=3

D) (0;3)

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

A) 4√3-6

B) 2√2−1

C) 1

D) 6-2√3

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11. Tengsizlikni yeching.

A) (1/2;∞)

B) (2/3;2)

C) (4/3;3)

D) (5/3;2)

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12. 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

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13. 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) 234

C) 72

D) 18

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

A) 1+b

B) 3(1−a)

C) (1−a)(1+b)

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

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15. 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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16. 3cos2x-3 sin2x=0 trigonometrik tenglamani yeching.

A) π/6+πk; k∈Z

B) π/12+2πk; k∈Z

C) π/12+πk; k∈Z

D) π/12+πk/2; k∈Z)

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17. Tenglamani yeching:

A) πk; −arcctg4+πk; k∈Z

B) π −arcctg4+πk; k∈Z

C) arccos0,8+2πk; k∈Z

D) πk; π−arcctg4+πk; k∈Z

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

A) 7cos5x−5cos7x+c

B) 7sin5x−5sin7x+c

C) −7cos5x−5cos7x+c

D) 7sin5x+5sin7x+C

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19. 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) (1+√3)/2

B) 4√3+7

C) (√3-1)/2

D) 7-4√3

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20. 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) 18

B) 15

C) 10

D) 20

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21. ifodani soddalshtiring

A) 2cosα

B) 2sinα

C) 1

D) cosα

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

A) π/4

B) 0

C) π/3

D) π/2

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23. Ifodani soddalashtiring:

A) 1+√(a+1)

B) 0

C) 1−√(a-1)

D) √(a²-1)

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24. 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) 51

B) 52

C) 49

D) 50

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25. ni hisoblang.