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Matematika abituriyent testi №1

InfoMaster

Aprel 5, 2022

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Matematika abituriyentlar uchun №1

1 / 30

a=sin 1; b=sin 2; c=sin 3; d=sin 4 va e=sin 5 sonlarni kamayish tartibida joylashtiring.

A) b>a>c>d>e

B) b>c>a>d>e

C) a>b>c>d>e

D) e>b>a>d>c

2 / 30

ABC muntazam uchburchak ichidan ixtiyoriy P nuqta olinib, undan BC, CA va AB tomonlarga mos ravishda PD, PE va PF perpendikulyarlar tushirilgan bo’lsa,ni toping.

A) 1/√2

B) 0,5

C) 1/√3

D) 1

3 / 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√5

B) 4

C) 2√3

D) 3√3

4 / 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) 3√2π/4

B) 64√2π/3

C) (5√3+3)π/3

D) 8√2π/5

5 / 30

Rasmda ko‘rsatilgan ko‘pyoqlardan qaysi birida 4 ta yoq, 6 ta qirra bor?

A) 2

B) 1, 3

C) 3

D) 1, 2

6 / 30

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

A) ln(lg x)

B) lg(lg x)

C) lg(ln x)

D) ln(ln x)

7 / 30

Quyidagilardan qaysi biri barcha lar uchun ma’noga ega (aniqlangan)?

A) ²ᴷ⁺⁴v2k+1/k²+1

B) ⁴ᴷ⁺³√-√2k+1

C) (512-1/2⁻⁹)°

D) 4k+1/1/8:7-1/56

8 / 30

Teng yonli uchburchakning tomonlari 5, 5 va 6 ga teng. Bu uchburchakning bissektiritsalari va medianalari kesishgan nuqtalar

A) 1,2

B) 1/2

C) 1/6

D) 1

9 / 30

Bankda qo`yilgan pul bir yildan kegin foydasi bilan 2600 so`m bo`ldi; Agar bank yillik 30% foyda to`lasa, boshida qancha pul qo`yilgan bo`ladi ?

A) 2000

B) 2100

C) 1900

D) 2200

10 / 30

Ushbu funksiyaning boshlang’ich funksiyasini toping.

A) ln|x-1/x+4|+c

B) ln(|x+4*|x-1|)+c

C) ln(|x+4+|x-1|)+c

D) ln|x+4/x-1|+c

11 / 30

Tengsizlikni yeching.

A) (2;4)

B) (-4;2)v(2;3)

C) (-3;2)v(2;4)

D) (-3;2)

12 / 30

Agar arctga+ arctgb + arctgc= bo’lsa, a+b+c ni toping.

A) ab

B) abc

C) 1

D) ab/c

13 / 30

Tengsizlikni yeching.

A) 0

B) (-1/³ √2 ;0)

C) to'g'ri javob yo'q

D) (0;+∞)

14 / 30

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

A) √3/2

B) 1,5

C) √5/2

D) 1

15 / 30

qonuniyat bo’yicha harakatlanayotgan moddiy nuqta harakatning 200- metrida qanday tezlikka (m/s) erishadi?

A) 36

B) 38

C) 32

D) 42

16 / 30

a(x+2)=2x+1 tenglama a ning qanday qiymatida yechimga ega emas?

A) (-∞;2)v(2;∞)

B) (2;∞)

C) (∞;∞)

D) (-∞;2)

17 / 30

Sin9x =4sin3x tenglamani yeching

A) πn/3, n€Ζ

B) π/3+πn, n€Ζ

C) πn, n€Ζ

D) π/2+πn, n€Ζ

18 / 30

A) 1

B) 0

C) 2

D) √6

19 / 30

x(t)=t²+6t+5 qonuniyat bo’yicha harakatlanayotgan moddiy nuqta harakat boshlangandan necha sekund o’tgach boshlang’ich nuqtaga nisbatan 77 metr masofaga siljiydi?

A) 7

B) 10

C) 8

D) 6

20 / 30

ABCD to’gri to’rtburchak ichidan olingan O nuqtadan A, B, C, D uchlarigacha bo’lgan masofalar mos ravishda 3, 4, 5, 6 ga teng bo’lsa, u holda AB tomon uzunligini toping.

A) √7

B) 2

C) √37

D) bunday to’gri to’rtburchak mavjud emas

21 / 30

y= $\sqrt{2x^{2}-4x}$ funksiyaning aniqlanish sohasini toping

A) (-∞;0)v(2;∞)

B) (0,2)

C) (2;∞)

D) (-∞;0])v[2;∞)

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) 54

B) 50

C) 40

D) 36

23 / 30

Anvar tub son o’yladi va o’ylagan sonini 5 ga ko’paytirib, 8 ni ayirgan edi, yana tub son hosil bo’ldi. Anvar qanday son o’ylagan?

A) 374389

B) 412967

C) 2

D) aniqlab bo’lmaydi

24 / 30

sin2x-cos2x=1 tenglama [-π; 2π] oraliqda nechta ildizga ega?

A) 9

B) 6

C) 7

D) 10

25 / 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) 96π

B) 56π

C) 100π

D) 72π

26 / 30

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

A) 3

B) 2

C) √15

D) √5

27 / 30

200 kishidan iborat turistlar guruxida 140 kishi ingliz tilini, 90 kishi nemis tilini va 46 kishi ikkala tilni biladi. Ikkala tilni xam bilmaydigan turistlar necha foizni tashkil qiladi.

A) 8

B) 4

C) 12

D) 16

28 / 30

Tomoni 6 ga teng bo`lgan teng tomonli uchburchakga tashqi chizilgan doiraning yuzini toping.

A) 12π

B) 7 π

C) 10 π

D) 6 π

29 / 30

To’g’ri burchakli uchburchakning gipotenuzasi 5 ga, bir katetining gipotenuzadagi proyeksiyasi 1,6 ga teng. Ikkinchi katetning kvadratini toping.

A) 16

B) 14

C) 17

D) 18

30 / 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) 150

B) 147

C) 231

D) 228