Microsoft Word Копия Test A. docx

Test A

1. 
   a,b,c haqiqiy musbat sonlar:
   

a+3c + 4b − 8c ifodaning

a+2b+c a+b+2c a+b+3c eng kichik qiymatini toping?

(^A)12 2−1⁵ (^B)2 ² (C)12 2−17

(D)15 2−19

2. 
   x, y haqiqiy sonlar uchun,
   

(x+5)² +(y−12)² =196 o'rinli bo'lsa x² +y² ni eng kichik qiymatini toping?

(A)2 (B)1 (C) 3 (D) 2

3. f(x) funksiya haqiqiy sonlar da quyidagi shartlarni bajaradi: f(1)=1,

f(x+5)≥ f(x)+5, f(x+1)≤ f(x)+1

g(x)= f(x)+1− x bo'lsa, g(2002) ni toping?

(A)1 (B)2 (C)−2 (D)−1

4. Agar log₄(x+2y)+log₄(x−2y)=1 bo'lsa x − y ning eng kichik qiymatini toping?

(A) 3 (B) 2 (C) 5 (D)1

5. 
   sin² x+acosx+a² ≥1+cosx ushbu
   

tengsizlik ihtiyoriy x∈R da o'rinli,bo'lsa a ning manfiy qiymatini toping?

(^A)a≤−¹(B)a≤−2 (^C)a≥−² (^D)−1≤a≤1

5. 
   A(0;2) nuqta va y² =x+4 parobolaga
   

tegishli B va C nuqtalar berilgan, bunda AB⊥BC bo'lsa C nuqtaning ordinatasi qanday qiymatlarni qabulqila oladi?

(^A)y≥¹ (^B)y≥⁰ (C)y≤ 0, y≥ 4 (^D)y≤4

5. 
   Agar x∈^#_%$−⁵₁^π₂ ;−^π₃^&_(' bo'lsa quyidagi funksiyaning eng katta qiymatini toping?
   

! 2π$ ! π$ ! π$

y =tg#x+ &−tg#x+ &+cos#x+ &

" 3 % " 6% " 6%

1. 
   2 (B) 2 (C) 3 (D) 3
   

5. 
   x, y∈ (−2,2) va xy=−1 bo'lsa
   

4 ₂ 9 ₂ ning eng kichik qiymatini

A= +

4−x 9−y toping?

1. 
   (B) (C) (D)
   

5. 
   ABCD tetrayedrda AB=1, CD= 3 , AB va CD chiziqlar orasidagi masofa va burchak mos ravishda 2 va ga teng. Bu tetrayedrni hajmini toping?
   

5. 
   Tengsizlikni yeching: x³ −2x² −4x +3<0
   

(A)(−3,3)

(^B)(−1,³)

" −1+ 5% " 5 −1 % (C)$−3,− '∪$ ,3'

# 2 & # 2 &

(D)!# 5 +1,3$&

" 2 %

5. 
   Agar A⊆B bo'lsa a∈R ni toping, bunda
   

A={x x² −4x+3< 0, x∈R}

B={x 2^1−x +a≤ 0, x² −2(a+7)x+5≤ 0, x∈R}

(^A)−4≤a≤¹(B)−3≤a (C)a≤1 (D)∅

5. 
   Agar a,b,c,d natural sonlar va log_a b= ³ ,
   

2

log_c d= , a−c=9 bo'lsa b−d ni toping?

1. 
   95 (B)93 (C)97 (D)107
   
5. 
   Tengsizlikni yeching: ₂ 1 ₁ ³
   

log x−1+ log x +2 > 0

2 ₂

(^A)[2,³) (^B)(2,³] (C)[2,4) (^D)(2,⁴]

5. 
   O nuqta ΔABC ichida olingan va O!!A!"+2O!!B!"+3O!!C!^"=0 o'rinli bo'lsa. SΔABC _ni
   

SΔAOC

toping?

(A)2 (B)3 (C) (D)

15. 
    n=abc uch xonali son, a,b,c sonlardan teng yonli uch burchak qurish mumkun (muntazam uchburchak ham kiradi), bunda uch xonali sonlar nechta?
    
    1. 
       45 (B)81 (C)165 (D)216
       

15. 
    a₀,a₁,a₂,...,a_n,... ketma-­‐ketlikda
    

(3−a_n+1)⋅(6+a_n)=18 va a₀ =3 o'rinli bo'lsa

¹ + ¹ + ¹ +...+ ¹ ni hisoblang?

a0 a1 a2 a10

1. 
   1361 (B)1362 (C)1364 (D)1365
   
15. 
    M(−1;2) va N(1;4) va P(x;0) nuqtalar koordinata tekisligida berilgan ∠MPN burchak eng katta qiymatga ega bo'ladigan P nuqtaning x apsisasini toping?
    

(A)x=1 (B)x=−1 (C)x=−2 (D)x=0

15. 
    x−3+ 6−x≥k ushbu tengsislik
    

yechimga ega bo'ladigan k ning eng katta qiymatini toping?

(^A) 6− ³ (^B) ³ (^C) 6+ ³ (D) 6

!!!"

19. Fazoda A,B,C,D nuqtalar berilgan, AB=3,

!!!" !!!" !!!"

BC=7 , CD=11 va DA=9 bo'lsa

!!!" !!!"

AC⋅BD ni qiymatini toping?

(A)0 (B)10 (C)115 (D)155 20. k² −13k ∈N natural son bo'lsa k natural sonni nechta qiymati bor?

(A)1ta (B)2ta (C)0ta (C)5ta

21. ΔABC birlik aylanaga ichki chizilgan A burchagi bissikrisasi aylanani A₁ da, B burchagi bissikrisasi aylanani B₁ da, C burchagi bissikrisasi aylanani C₁ da, kesib

A B C AA₁cos +BB₁cos +CC₁cos

o'tadi. 2 2 2 ni

sinA+sinB+sinC toping?

(A)2 (B)4 (C)6 (D)8

22. 
    T={0,1,2,3,4,5,6} va
    

"a¹ a²₂ a³₃ a⁴_{4 i} %

M =# + + + ;a ∈T,i =1,2,3,4&

$ 7 7 7 7 '

Mning barcha qiymatlari kamayish tartibda yozilgan, 2017-­‐o'rindagi qiymatini toping?

22. 
    f (x) funksiya (0,∞) oraliqda kamayuvchi, agar f (2a² +a+1)< f (3a² −4a+1) bo'lsa
    

a=?

! 1$

(A)(1,3) (B)#0, &∪(1,5) (C)(1,5) (D)(0,5)

" 3%

22. 
    Agar 0<α<β<γ<2π va ∀x∈R uchun cos(x+α)+cos(x+β)+cos(x+γ)=0 bo'lsa, γ−αni toping?
    

22. 
    DABC tetrayedrning hajmi ACB=45^! ,
    

AC bo'lsa CD ni uzunligini

AD+BC+ =3

2

toping?

(A) 5 (B) 3 (C) 2 (D) 7

26. 
    Kvadratning bir tomoni y=2x−17 chiziqda, qolgan ikkita uchi y=x² parobolada bo'lsa uning yuzining eng katta qiymatini toping?
    

(A)90 (B)100 (C)80 (D)98

26. 
    R aqamlari yig'indisi 7 bo'lgan harqanday natural son «omadli son» hisobladi. Bu sonlarni o'sish tartibida yozilgan a₁,a₂,...,a_n,... shu ko'rinishda. Agar a_n =2005 bo'lsa a_5n ni toping? (A)45000 (B)50000 (C)52000 (C)54000
    
27. 
    f (x)= x³ +ax² +bx+c uchta haqiqiy
    

x₁, x₂, x₃ ildizlarga ega. a,b,c va h musbat

sonlar bunda x₁−x₂ =h va x_{3 >}¹(x₁+x₂) 2

o'rinli bo'lsa 2a3 +273c−9ab ni eng katta h

qiymatini toping?

(A) (B) (C) (D)

29. 
    Uchburchak tomonlari l,m,n. l>m>n va
    

!" 3l4$%=!"3m4$%=!"3k4$ o'rinli.

%

#10 & #10 & #10 &

{x}-­‐x ning kasir qismi. Ushbu uchburchak perimetrining eng kichik qiymatini toping?

1. 
   2002 (B)3002 (C)3003 (D)5003
   

29. 
    f (x)= log (x² −2x−3) ushbu funksiyaning o’sish oralig’ini toping?
    

(A)(−∞,−1) (B)(−∞,1) (C)(1,+∞) (^D)(3,+∞)

29. 
    x² = 4y, x² =−4y, x=4 va x=-­‐4 ushbu chiziqlar bilan chegaralangan shakilni OY o'qi atrofida aylantirishdan hosil bo'lgan jisimning hajmi V₁. x² +y² ≤16 ,
    

x² +(y−2)² ≥4 , x² +(y+2)² ≥4 bu chiziqlar

bilan chegaralangan shakilni OY o'qi atrofida aylantirishdan hosil bo'lgan jism hajmi V₂ bo'lsa quyidagilardan qaysi biri

to'g'ri:

(A)V1 =1V2 (B)V1 =2V2 (C)V1 =V2

2 3

(D)V₁ =2V₂

29. 
    f (x)= ^x _x − ^x ushbu funhsiya uchun qasi
    

1−2 2

tasdiq to'g'ri:

1. 
   juft (B)toq (C) na juft,na toq (D)juft va toq
   
29. 
    ^x₊^y₌1 bu to'g'ri chiziq ^x2 ₊^y2 ₌1 ushbu
    

4 3 16 9

ellipsni A va B nuqtalarda kesib o'tadi, P nuqta ellipisda olingan. S_ΔPBA =3 bo'lsa bunday P nuqtadan nechta mavjud?

(A)1 (B)2 (C)3 (C)4

34. 
    f (x)= x² +bx+c(a,b,c ∈ R,a ≠ 0) ushbu funksiya uchun quyidagilar o'rinli: 1) x∈R , f(x−4)= f(2− x) va f (x)≥ x
    
    2. 
       agar x∈ (0,2) bo'lsa f(x)≤^"_$^x+1%_'²
       

# 2 &

2. 
   f(x) ning ) x∈R da, eng kichik qiymati
   

0 m (m>1) ning eng katta qiymati toping bunda shunday t ∈ R borki f (x+t)≤ x o'rinli x∈[1,m] da.

(A)m=8 (B)m=9 (C)m=7 (D)m=10

34. 
    f(x)=2 x+1+ 2x−3+ 15−3x −2 19
    

"3 %da qiymatlarsohasini toping?

x∈$_#2,5'_&

(A)(−∞;0) (^B)(−∞;⁰] (C)(−∞;−1] (D)(−∞;1)

36. {1,2,3,...}barcha natural sonlar qatoridan aniq kvadratlarini olib tashlab yangi sonlar ketma-­‐ketligi tuzildi. Yangi tuzilgan ketma-­ketlikning 2003-­‐hadini toping?

(A)2046 (B)2047 (C)2048 (D)2049

tenglama

hech bo'lmasa bitta yechimga ega. α ni toping?

(A) (B)π , 5π (C)π, 5π (D)

12 12 6 12

38. 
    O'tkir burchakli uchburchak ABC da CE va BD balantliklar H nuqtada kesishadi.DE ni diametr qilib chizilgan aylana AB va AC ni mos ravishda F va G da kesib o'tadi. FG va AH chiziqlar K nuqtada kesishadi. Agar BC=25, BD=20 va BE=7 bo'lsa, AK ni uzunligini toping?
    

(A)7,84 (B)8,44 (C)8,64 (D)6,84

38. 
    xOy tekislikda _A^!_#0_, ^4$_& , B(−1,0) va C(1,0)
    

" 3%

berilgan. Shunday P nuqtalar to'plamini toping, bunda P nuqtadan BC chiziqgacha bo'lgan masofa, P dan AC va AB tomonlarga bo'lgan masofalarning o'rta giometrigiga teng.

!#S(aylana):2x²+2y²+3y-2 =0

(A)" _{2 2}

#$ T(giperbola):8x - 17y +12y- 8 = 0

!#S(aylana):4x²+4y²+3y-2 =0

(B)" 2 2

#$ T(giperbola):7x - 18y +12y- 8 = 0

!#S(aylana):3x²+3y²+4y-2 =0

(C)" 2 2

#$ T(giperbola):9x - 18y +12y+8 = 0

!#S(aylana):5x²+5y²+4y-12 =0

(D)" 2 2

#$ T(giperbola):9x - 10y +12y+2 = 0

40. Quyidagi chizmalarda P_o,P₁,P_3,....P_n,... shakillar berilgan P₀ muntazam uchburchak yuzi 1ga teng. Keyingi shakilni hosil qilish uchun oldingi shakildani har bir tomonini o'rta kesmasiga muntazam uch burchak bo'rtib tashqi qurilgan va shu ish keyingi shakil uchu ham dovom ettirilgan:

S_n -­‐ P_n shakilning yuzi bo'lsa hisoblang:

limS_n

n→∞