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Matematika abituriyent testi №1

InfoMaster

Aprel 5, 2022

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Matematika abituriyentlar uchun №1

1 / 30

Radiusi 25 bo’lgan doirada 48 ga teng vatar o’tkazilgan. Doira markazidan shu vatargacha masofani toping.

A) 10

B) 9

C) 7

D) 8

2 / 30

AA₁A₂A₃A₄A₅A₆ muntazam oltiburchakli piramidaning hajmi ga va balandligi 2 ga teng bo‘lsa, u holda AA₂A₆ kesim yuzini toping.

A) √5

B) 3

C) √15

D) 2

3 / 30

Tengsizlikni yeching.

A) (-1/³ √2 ;0)

B) (0;+∞)

C) to'g'ri javob yo'q

D) 0

4 / 30

Fazoda (1;2;3) nuqtalardan o’tuvchi to’g’ri chiziq tenglamasini tuzing.

A) -x-y+z=0

B) x=y/3=z/2

C) 2x+3y+z=0

D) x-1/2=y-2/3=z-3/4

5 / 30

Ushbu (y⁶+y³+1)(y³+1)(y³-1)-y⁶+y³+1 ifodani soddalashtish natijasida ko’phad hosil qilindi. Uning nechta hadi bor?

A) 2

B) 3

C) 1

D) 4

6 / 30

ABCD kvadrat ichidan olingan O nuqtadan A, B, C uchlarigacha bo’lgan masofalar mos ravishda 3, 4, 5 ga teng bo’lsa, u holda OD kesma uzunligini toping.

A) 3

B) √32

C) √37

D) 6

7 / 30

n ning qanday qiymatida ushbu

8^{1 .}8^{2 .}8^{3 .}…^.8ⁿ=512²² tenglik o’rinli bo’ladi?

A) 14

B) 10

C) 12

D) 11

8 / 30

A) 2

B) 1

C) √6

D) 0

9 / 30

|x²-5x-14|+20≥5|x+2|+4|x-7| tengsizlikni yeching.

A) (-∞;-6]v{2}v[12;∞)

B) [1;6]

C) [-2;4]v{6}

D) [2;4]v{2}v[3;∞)

10 / 30

7 sonini uchta natural sonlar yig’indisi ko’rinishida necha xil usulda yozish mumkin?

A) 4

B) 5

C) 6

D) 3

11 / 30

Perimetri 60 ga teng bo’lgan parallelogrammning tomonlari nisbati 2:3 ga, o’tkir burchagi esa 30⁰ ga teng. Parallelogrammning yuzini toping.

A) 54

B) 52√3

C) 108

D) 48√3

12 / 30

Ostki asosining yuzi 16π ga va ustki asosining yuzi 4π ga teng bo‘lgan kesik konus berilgan. Agar kesik konusga shar ichki chizilgan bo‘lsa, u holda sharning hajmini toping.

A) 8√2π/5

B) 64√2π/3

C) 3√2π/4

D) (5√3+3)π/3

13 / 30

Muntazam uchburchakli piramidaning yon qirrasi asos tekisligi bilan 45^o li burchak tashkil etgan bo‘lsa, u holda piramidaning yon sirti yuzining uning asosi yuziga nisbatini toping.

A) 2√3

B) 3√3

C) 4

D) 2√5

14 / 30

Ostki asosining yuzi 20π va ustki asosining yuzi 10π ga teng bo‘lgan kesik konus berilgan. Agar kesik konusga shar ichki chizilgan bo‘lsa, u holda kesik konus hajmining shar hajmiga nisbatini toping.

A) 3√3+1/5

B) 3√2+2/4

C) 5√3+3/3

D) 2√2/3

15 / 30

To’g’ri to’rtburchakning perimetri 50 ga teng. Bir tomoni boshqa tomonidan 5 ga ko’p. To’g’ri to’rtburchakning yuzini toping.

A) 225

B) 150

C) 60

D) 50

16 / 30

Bir vaqtning o’zida 9,13, . . . ,405 va 15,21, . . . ,255 ketma–ketliklarning hadlari bo’lgan sonlarning eng kattasi va eng kichigining ayirmasini toping

A) 147

B) 150

C) 231

D) 228

17 / 30

Quyidagi 2x-y+3z=2018 va x+5y+z=2019 tekisliklarning holatini aniqlang.

A) o’zaro perpendikulyar

B) aniqlab bo’lmaydi

C) o’zaro parallel

D) ayqash

18 / 30

tenglamalar sistemasini yeching

A) (-4;-4)

B) (4;–4)

C) (4;4)

D) (-4;4)

19 / 30

A(2;-2,5) nuqtadan y= - 4x parabolagacha bo’lgan eng qisqa masofani toping.

A) 1,5

B) √3/2

C) 1

D) √5/2

20 / 30

Ifodani soddalashtiring. [ln(ln x)-ln(log_e10)]^.log₁₀e

A) lg(lg x)

B) lg(ln x)

C) ln(lg x)

D) ln(ln x)

21 / 30

sistema yagona yechimga ega bo’ladigan a ning barcha qiymatlari to’plamini toping.

A) {1;2}

B) {-1;2}

C) {-1;3}

D) {2;4}

22 / 30

x(t)=t²+7t-6 qonuniyat bo’yicha harakatlanayotgan moddiy nuqtaning tezligi harakat boshlangandan necha sekund o’tgach 87 m/s ga teng bo’ladi?

A) 40

B) 50

C) 54

D) 36

23 / 30

Ostki asosining yuzi 32π va ustki asosining yuzi 18π ga teng bo‘lgan kesik konus berilgan. Agar kesik konusga shar ichki chizilgan bo‘lsa, u holda sharning sirtini toping.

A) 56π

B) 72π

C) 96π

D) 100π

24 / 30

Tenglamani yeching.

|x²-11x+10|=x²-11x+10

A) [10;∞)

B) (-∞;1]v[10;∞)

C) (-∞;1]

D) 1; 10

25 / 30

Ag ar tgα=2 bo’lsa, u holda ni hisoblang

A) 10/27

B) 10/3

C) -10/3

D) -10/27

26 / 30

x²-5|x|-6=0 tenglama ildizini toping

A) -1;6

B) ±6

C) -1;-6

D) ±;±6

27 / 30

To’rtburchakli muntazam piramidaning yon qirrasidagi ikki yoqli burchak 120 ga teng. Diagonal kesimining yuzasi S ga teng bo’lsa, uning yon sirtini toping.

A) 2S

B) 3S

C) 0,5S

D) 4S

28 / 30

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