11-sinf Matematika olimpiada №1

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

A) 12/35

B) 15/31

C) 21

D) 23/35

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2. 3²⁰¹⁷ sonning oxirgi ikkita raqamini toping.

A) 83

B) 03

C) 13

D) 63

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3. tenglama t ning qanday qiymatida uchta ildizga ega bo‘ladi?

A) Ø

B) 5

C) 2

D) 3

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4. funksiyaning qiymatlar to‘plamini toping.

A) [-2;2]

B) [1;3]

C) [1;4]

D) [-1;3]

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5. tenglamaning ildizlari yig‘indisini toping.

A) 10

B) 6

C) -6

D) -2

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6. Ifodaning oxirgi raqamini aniqlang: $3^{279}\cdot 7^{298}-3^{178}\cdot 7^{197}$

A) 3

B) 0

C) 6

D) 1

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7. Agar va bo‘lsa, ni toping.

A) 39

B) 31

C) 11

D) 25

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8. Sonlarni kamayish tartibida joylashtiring:

A) a>b>c

B) c>a>b

C) c>b>a

D) b>c>a

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9. Beshyulduzning uchidagi burchaklarining yig‘indisini toping.

A) 240°

B) 270°

C) 180°

D) 90°

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10. 1!+2!+3!+.....+10! sonining oxirgi raqamini toping.

A) 6

B) 3

C) 0

D) 7

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11. ko‘phadning barcha koeffitsientlari va ozod hadining yig‘indisini toping.

A) 245

B) -247

C) -238

D) 125

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12. Doiraga ichki chizilgan kvadrat undan yuzasi $2\pi-4$ ga teng bo‘lgan segmentni ajratadi. Kvadratning yuzasini toping.

A) 8

B) 4

C) 16

D) 2

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13. ABC uchburchakka aylana tashqi chizilgan. Uchburchakning AM medianasi aylana bilan K nuqtada kesishguncha davom ettirilgan. Agar AM=18,MK=8,BK=10 bo‘lsa, AC tomonini toping.

A) 15

B) 12

C) 16

D) 14

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14. tenglama nechta natural yechimga ega?

A) 3

B) 4

C) 2

D) 1

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15. tenglama nechta ildizga ega?

A) 3

B) 4

C) 2

D) 1

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16. Tenglamani yeching:

A) (1;-2)

B) (2;1)

C) (1;-2)

D) (-2;1)

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17. a,b-to‘g‘ri burchakli uchburchakning katetlari va h-gipotenuzaga tushirilgan balandligi bo‘lsa, yig‘indini toping.

A) 4

B) 3

C) 2

D) 1

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18. 7⁵⁰ning oxirgi ikkita raqamini toping.

A) 25

B) 35

C) 49

D) 51

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19. bo‘lsa, nimaga teng?

A) 3

B) 7

C) 5

D) 9

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20. va a,b>0 bo‘lsa, ifodaning eng kichik qiymatini toping.

A) 3

B) 4

C) 2

D) 1

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21. 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+1

C) y=-x²+2x

D) y=-x²-2x

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22. To‘g‘ri burchakli uchburchakka ichki va tashqi chizilgan aylanalar radiuslari 2 va 5 ga teng. Katetlarning yig‘indisini toping.

A) 7

B) 14

C) 12

D) 9

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23. tengsizlik yechimlari joylashgan interval uzunligini toping.

A) 0,25

B) 0,5

C) 0,75

D) 0,125

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24. funksiyaning grafigi qaysi choraklardan o‘tadi?

A) I,II,III,IV

B) II,III

C) I,II

D) III,IV

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25. 2, 3, 4, 5, 6, 7, 8, 9, 10 sonlariga bo‘lganda mos ravishda 1, 2, 3, 4, 5, 6, 7, 8, 9 qoldiqlar hosil bo‘ladigan eng kichik natural sonni toping

A) 1519

B) 2519

C) 5039

D) 1019

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11-sinf Matematika olimpiada №1

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