Matematika (informatika bilan) 1

MATEMATIKA (INFORMATIKA BILAN) 11. Agar uch xonali sondan 6 ni ayirsak, ayirma
7 ga bo‘linadi, 7 ni ayirsak, ayirma 8 ga
1. aa va bb ikki xonali sonlar bo‘lib, bo‘linadi, 8 ni ayirsak, ayirma 9 ga bo‘linadi.
(aa)2 + (bb)2 = 2057 va a + b = 5 bo‘lsa, a · b ni Bu sonni toping.
toping. A) 503 B) 167 C) 143 D) 936
A) 6 B) 4 C) 8 D) 15
12. Koordinata boshidan o‘tuvchi tekislik
2. Ishchi birinchi kuni o‘ziga topshirilgan butun bir tenglamasini toping.
ishning yarmini, ikkinchi kuni qolgan ishning
A) 2x − 2y + 5z = 0 B) x + y − 1 = 0
yarmini, uchinchi kuni qolgan ishning yarmini
C) x + 3y + 9z − 1 = 0 D) x + y + 1 = 0
bajardi. U ishni tugatishi uchun to‘rtinchi kuni
butun ishning qancha qismini bajarishi kerak?
13. Balandligi asosining diametriga teng silindrning
1 1 1 1 yon sirti 16π ga teng. Silindr asosining
A) B) C) D)
2 4 8 16 diametrini toping.
A) 2 B) 1 C) 4 D) 8
3. Agar a ∈ N bo‘lsa, quyidagilardan qaysi biri
albatta juft son bo‘ladi?
14. Yon sirti 60π ga, balandligi 2 ga teng silindr
A) a3 + 2a B) a4 · (a + 1) C) a2 + 4 asosining diametrini toping.
a−1
D) A) 15 B) 10 C) 30 D) 20
5
!
π 1 1 1
4. Quyidagi tenglamalar sistemasini yeching. 15. tg − arctg − arctg − arctg ni
4 3 4 5
(
EKU B(x; y) = 45
x
= 11 hisoblang.
y 7
1 1 1 1
A) x = 220, y = 140 B) x = 143, y = 91 A) B) C) D)
47 60 45 80
C) x = 275, y = 175 D) x = 495, y = 315

5. 31 · 52 − 93 · 4 + 57 · 25 − 19 · 35 + 2 · (−10)3 16. Quyidagi rasmda berilganlarga ko‘ra x necha

gradusga teng?
A) 0 B) 1000 C) -1000 D) 4000
AE

bE A
x3 − x2 − 4x + 4
50 E Ab

E A
6. kasr qisqarishi mumkin
x2 + mx + 6
E30A
bo‘lgan m ning eng katta va eng kichik
E # #A

A
qiymatlari farqini toping.

#E
A
E x A
# E
A) 12 B) 15 C) 17 D) 18


b #
#
A
E
q
20
#b
#
E A
10
(1510 − 1010 ) : (310 − 210 ) ni hisoblang.

# A
7.
60
E
# E A
A) 25 B) 5 C) 8 D) 9
A) 40 B) 30 C) 45 D) 50
8. |(x + 3) (x + 1) + 1| ≤ 0 tengsizlikni yeching.
√
A) −2 B) ∅ C) 2 D) 0 17. f (x) =3x − 2 funksiyaning hosilasini toping.
1 √ 1 3
9. ABC uchburchakda BH -balandlik, CM - A) ( 3x − 2) B) √ C) √
2 2 3x − 2 3x − 2
mediana, M H=12 bo‘lsa, AB ni toping.
3
A) 24 B) 20 C) 28 D) 12 D) √
2 3x − 2
" #
π 3
10. Agar x ∈ 0; va log24sinx (24cosx) = 18. f (x) = x2 + x − 1 funksiya uchun f 0 (x) = 0
2 2
bo‘lsa, 24ctg 2 x ning qiymatini toping. bo‘lsa, x ning qiymatini toping.
1 64 1 1 2 3
A) 192 B) 208 C) D) A) B) − C) − D) −
192 81 3 2 3 4
2 Matematika (informatika bilan)

19. f (x) = log4 x + 4e2x , f 0 (x)−? 2

27. f (x) = e2x + , F (x)−?
1 1 1 x−1
A) + 8ex B) + 8e2x C) + 8e2x
ln4 x xln4 A) e2x + ln(x − 1) + c
x
D) xln4 + 8e B) ex − ln(x − 1) + c
1
20. f (x) = −3e− 2 x+1 − 4x2 , f 0 (x)−? C) 2e2x + ln(x − 1) + c
1
3 1 D) e2x + ln(x − 1)2 + c
A) e x + 4x 2
2
2
B) ex + 8x 1
3 28. f (x) = + x2 , F (x)−?
sin2 x
3 1
C) e− 2 x − 8x 2x2
2 A) ctgx + 2x + c B) ctgx + +c
3
3 1 x3
D) e− 2 x+1 − 8x C) ctgx + 2x2 + c D) −ctgx + +c
2 3

1 29. Berilgan chizmadan eng uzun kesmani aniqlang.

21. f (x) = sin4x − x funksiya uchun f 0 (x) = 0
4 B
bo‘lsa, x ning qiymatini toping. b
E
A 60
E
A E
πn
A) x = ; n∈Z A b E
2 A30 bE
A 64 E
π A b E
B) x = + 2πn; n ∈ Z A 110 (((E C
2 A(((
D
π
C) x = − + 2πn; n ∈ Z
2 A) AC B) DC C) AB D) BC
D) x = π + 2πn; n ∈ Z
7122 − 289
30. ni hisoblang.
695
22. f (x) = e2x−4 + 2lnx, f 0 (2)−?
A) 725 B) 695 C) 765 D) 729
A) 5 B) 2 C) 3 D) 4
R2
18
2 31. = 3 tenglamani yeching.
23. (x + 1) dx ni hisoblang. x+7
0 2+
x−3
3 4 2 5 2+
A) 4 B) 4 C) 4 D) 4 2
4 5 3 6
A) 1 B) 5 C) 3 D) 4
π
R12
24. cos2xdx ni hisoblang. 32. x3 + 12x2 + 48x = 152 tenglamani yeching.
0
A) 3 B) 4 C) 2 D) 6
1 1 1 3
A) B) C) D)
3 4 2 4 33. (x − 4)(x − 7)(x − 9) > 0 tengsizlikni yeching.
π
R4 A) x ∈ (−∞; 4) ∪ (7; 9)
25. cos2xdx ni hisoblang. B) x ∈ (4; 7)
0
√
2 1 1 √ C) x ∈ (7; 9)
A) B) C) − √ D) 2
2 2 2 D) x ∈ (4; 7) ∪ (9; ∞)

26. f (x) = cosx + ex , F (x)−? q √ q √

x x 34. x−3−2 x−4+ x−4 x−4=1
A) sinx + e + c B) −sinx + e + c
1 tenglamaning ildizlarini toping.
C) sinx − ex + c D) −cosx + ex + c A) [3; 4] B) [5; 8] C) [6; 8] D) [6; 9]
x
 Matematika (informatika bilan) 3

3−1 a−2 b−1

! !
35. Zavodning 3 ta sexida 2740 nafar ishchi ishlaydi. 1 1
44. √ + √ : ni
Ikkinchi sexda birinchisiga nisbatan 140 ta ko‘p b− a b+ a a−2 − a−1 b−2
ishchi, uchinchi sexda esa ikkinchisiga nisbatan soddalashtiring.
1,2 marta ko‘p ishchi ishlaydi. Har bir sexda 1
A) 5 B) 6 C) 7 D)
qanchadan ishchi ishlaydi? ab
A) 750; 900; 1090 B) 790; 900; 1050 q √ √
C) 760; 980; 1000 D) 760; 900; 1080 45. 4 2 + 2 6 ifodani soddalashtiring.
√ √
36. Uzunligi 19,8 m bo‘lgan arqon ikki bo‘lakka A) 4 18 − 4 2
bo‘lindi. Bo‘laklardan birining uzunligi √ √
B) 18 + 2
ikkinchisinikidan 20% ortiq bo‘lsa, har bir √ √
bo‘lakning uzunligini (m) toping. C) 4 18 + 4 2
√
A) 9 va 10,8 B) 6,8 va 13 C) 8 va 11,8 D) 18
D) 7,8 va 12
46. (x2 + 2x)2 − (x + 1)2 = 55 tenglamani yeching.
37. 2x+4 + 3 · 2x−2 ≥ 67 tengsizlikni yeching.
A) 4; 2 B) -2; 4 C) -4; -2 D) -4; 2
A) [3; ∞)
B) [2; ∞)
(
x2 − y = 23
47. tenglamalar sistemasini yeching.
C) [4; ∞) x2 y = 50
D) (−∞; 2) A) (5;4)(-5;4) B) (5;2)(-5;2) C) (4;5)(-4;5)
D) (-2;5)(-5;-2)
√ √
38. 1 + log2 x + 4log4 x − 2 = 4 tenglamani √
48. x2 + 3x − 3 = 2x − 3 tenglamani yeching.
yeching.
A) 5 B) -4 C) 3 D) 4
A) 16 B) 4 C) 32 D) 8
2 49. Yuzi 120 sm2 , diagonali esa 17 sm bo‘lgan to‘g‘ri
xe−3x dx ni hisoblang.
R
39.
to‘rtburchakning tomonlarini (sm) toping.
1 2 1 2
A) e−3x + c B) − e3x + c A) 30; 4 B) 12; 10 C) 16; 12 D) 15; 8
6 6
1 −3x2 1
C) − e + c D) e−3x + c 50. Aylanaga tashqi chizilgan√muntazam
6 6
oltiburchakning tomoni 4 2 bo‘lsa, aylanaga
ichki chizilgan kvadratning yuzini hisoblang.
40. Uchburchak tomonlari 5, 6, 7 sm. Uning
yuzasini (sm2 ) toping. A) 64 B) 48 C) 52 D) 50
√ √
A) 6 B) 5 5 C) 6 6 D) 8 51. Doiraning yuzi 6,25π ga teng. Bu doirada
uzunligi 3 ga teng bo‘lgan vatar o‘tkazilgan.
41. Kubning sirti 294 sm2 ga teng. Uning barcha
Doira markazidan vatargacha bo‘lgan masofani
qirralari yig‘indisini (sm) toping.
toping.
A) 84 B) 98 C) 147 D) 117
A) 3 B) 2 C) 2,5 D) 4
42. Idish to‘g‘ri burchakli parallelepiped shaklida
bo‘lib, uning bo‘yi 60 sm, eni 45 sm va 52. ~a(1; −2; 2) va ~b(2; −2; −1) vektorlar berilgan
balandligi 47 sm ga teng. Agar idishdagi suv bo‘lsa, 2~a2 − 4(~a~b) + 5~b2 ifodaning qiymatni
sathi 40 sm balandlikda bo‘lsa, unda necha litr toping.
suv bor? A) 44 B) 45 C) 46 D) 47
A) 135 B) 106 C) 115 D) 108
bc − a2 b2 − ac ab − c2
53. − + ifodani kasrga
a2 + 4
!
a−2 a 1 ab bc ac
43. 2 : 2 − 3 − 2 aylantiring.
a + 2a a − 2a a − 4a a + 2a
ifodani soddalashtiring. a2 − b 2 − c 2
A) B) 0 C) abc D) -1
A) a − 2 B) a C) 2 D) a + 2 abc
4 Matematika (informatika bilan)

219 · 273 + 15 · 49 · 94 61. Basseyn ikkita quvur bilan 7,5 soatda

54. ni hisoblang.
69 · 210 + 1210 to‘ldiriladi. Birinchi quvurning yolg‘iz o‘zi
1 1 basseynni ikkinchi quvurning yolg‘iz o‘zi
A) B) 1 C) 2 D) to‘ldirganidan 8 soat tezroq to‘ldiradi. Birinchi
2 3
quvurning alohida o‘zi basseynni necha soatda
to‘ldira oladi?
55. 2, 6, 10,. . ., 102 sonlarining o‘rta arifmetik A) 12 B) 15 C) 15,5 D) 16
qiymatini toping.
→
−
A) 52 B) 60 C) 62 D) 42 62. →
−
a (1; −1) va b (−2; m) vektorlar kollinear.
m ning nimaga tengligini toping.
56. To‘g‘ri to‘rtburchakning bo‘yi kvadratning A) 2 B) -2 C) 1 D) -3
tomonidan 8 m uzun, eni esa shu kvadrat
63. ABC uchburchak berilgan. AB to‘g‘ri chiziqqa
tomonidan 4 m qisqa. Kvadrat tomonini x bilan
parallel tekislik bu uchburchakning AC
belgilab, to‘g‘ri to‘rtburchak perimetri va yuzi
tomonini A1 nuqtada, BC tomonini B1 nuqtada
uchun ifoda tuzing.
kesib o‘tadi. AB=15 sm, AA1 : AC = 2 : 3
A) P = 4(x + 2); S = (x + 8)(x − 4) bo‘lsa, A1 B1 kesma uzunligini (sm) toping.
B) P = 4x + 8; S = 4(x + 8)
A) 5 B) 3 C) 2 D) 4
C) P = 4x + 4; S = x2 + 4x − 18
D) P = 4x + 2; S = (x + 8)(x − 4) 64. To‘rtburchakli muntazam prizma asosining yuzi
144 sm2 , balandligi 14 sm. Prizma diagonalini
57. Asosi a, perimetri 42 bo‘lgan to‘g‘ri (sm) toping.
to‘rtburchakning yuzini hisoblash uchun ifoda A) 22 B) 12 C) 21 D) 20
tuzing.
A) S = a(21 − a) B) S = a(a − 21) x+5
65. −2 ≤ < 2 tengsizlikning yechimini toping.
C) S = a2 − 21 D) S = ax x
#
2
A) −1 ; 5
58.
R
x sin 2xdx aniqmas integralni hisoblang. 3
#
1 1 2
A) sin2x − xcos2x + c B) −∞; −1 ∪ (0; 5)
4 2 3
#
B) 4sin2x − 2xcos2x + c 2
C) −∞; −1 ∪ (5; ∞)
C) 4sinx + xcosx + c 3
" #
1 1 2
D) sin2x + xcos2x + c D) −1 ; 0 ∪ (5; ∞)
4 2 3

66. y = x2 − 4x − 1 funksiyaga (x ≤ 2)teskari

59. Yo‘lovchi yuqoriga harakatlanib, harakatsiz funksiyani ko‘rsating.
eskalatorda 3 minutda, harakatlanayotgan √ √
A) y = 2 − x + 5 B) y = 2 + x + 5
eskalatorda 45 sekundda ko‘tariladi. √ √
C) y = 2 − x − 5 D) y = 5 − 2 − x
Eskalatorda harakatsiz turgan yo‘lovchi qancha
vaqtda (min) ko‘tariladi? 3 − 4cos2α + cos4α
A) 1 B) 1,5 C) 2,5 D) 2 67. ifodani soddalashtiring.
3 + 4cos2α + cos4α
A) tg 4 α B) ctg 4 α C) 1 + tg 4 α D) −tg 4 α
60. Teploxod ikki pristan oraligidagi masofani daryo
oqimi bo‘yicha 7 soat, oqimga qarshi 9 soatda √
o‘tadi. Agar oqimning tezligi 2 km/soat bo‘lsa, 68. y = sin3 2x ning hosilasini hisoblang.
√ √
pristanlar orasidagi masofani (km) aniqlang. A) 3cos2x sin2x B) 3 sin2x
A) 126 B) 120 C) 130 D) 128 3√ √
C) sin2x D) −3cos2x sin2x
2
 Matematika (informatika bilan) 5

2 76. Teng yonli uchburchakning uchidagi burchagi β,

69. y = √
4
funksiyaning boshlang‘ich
2x + 5 yon tomoniga o‘tkazilgan balandligi h ga teng
funksiyasini toping. bo‘lsa, uchburchakning asosini toping.
4q4 h
A) (2x + 5)3 + c A)
3 2sinβ
8q 2h
B) 4 (2x + 5)3 + c B)
3 β
cos
4q 2
C) − 4 (2x + 5)3 + c
3 h
C)
4√ β
D) 4 2x + 5 + c sin
3 2
h
D)
β
70. O‘ziga qo‘shni burchakning 20% iga teng
cos
2
bo‘lgan burchakning kattaligini toping.
A) 30◦ B) 25◦ C) 36◦ D) 45◦
77. Radiusi 1 ga teng bo‘lgan aylana uchta yoyga
bo‘lingan. Ularga mos markaziy burchaklari 1,
71. Qavariq ko‘pburchakning bir uchidan chiqqan 2 va 3 sonlariga proporsional bo‘lsa, yoylardan
diagonallari soni 47 ta. Bu ko‘pburchakning eng kattasining uzunligini toping.
nechta tomoni bor? π 3π 2π
A) B) π C) D)
A) 49 B) 48 C) 51 D) 50 3 2 3

78. Radiusi 5 ga teng bo‘lgan doiradagi uzunligi

72. Ikkita doira radiuslari 1:2 nisbatda. Katta doira
8 ga teng vatar doira markazidan qancha
aylanasining uzunligi 8π. Kichik doira yuzini
uzoqlikda bo‘ladi?
toping.
A) 3 B) 4 C) 3,6 D) 3,2
A) 4π B) 2π C) 8π D) π

79. Radiusi R ga teng bo‘lgan doiraning markazidan

73. Teng yonli trapetsiyaning diagonali yon bir tomonda ikkita bir-biriga parallel vatar
tomoniga perpendikular.
√ Trapetsiyaning kichik o‘tkazildi. Bunda ulardan biri 120◦ li, ikkinchisi
asosi 2 sm, balandligi 24 sm ga teng. 60◦ li yoylarni tortib tursa, vatarlar orasida
Trapetsiya katta asosining uzunligini (sm) joylashgan maydon yuzini toping.
toping. πR2 πR2 πR2 5πR2
√ A) B) C) D)
A) 10 B) 8 C) 2 24 D) 6 6 4 3 8

74. To‘g‘ri burchakli trapetsiyaning kichik diagonali 80. Qirralari 6 ga teng bo‘lgan kubga ichki chizilgan
15 sm ga teng bo‘lib, yon tomoniga sharning hajmini toping.
perpendikular, kichik yon tomoni 12 sm bo‘lsa, A) 72π B) 36π C) 27π D) 108π
uning yuzini (sm2 ) toping.
A) 204 B) 244 C) 200 D) 196 81. Muntazam o‘nburchakka tashqi chizilgan aylana
2
radiusi ga teng bo‘lsa, uning tomonini
sin18◦
75. m dan katta bo‘lmagan juft natural sonlarning toping.
yig‘indisi x, m dan katta bo‘lmagan, lekin A) 3 B) 4 C) 6 D) 2
10 dan katta bo‘lgan juft sonlarning yig‘indisi y
hamda x + y = 810 bo‘lsa, m ning barcha
82. Beshburchakning ichki burchaklari yig‘indisi
qiymatlari yig‘indisini toping.
nechaga teng.
A) 81 B) 210 C) 83 D) 420
A) 540◦ B) 560◦ C) 720◦ D) 580◦
6 Matematika (informatika bilan)

83. Agar x ∈ [−1; 2] bo‘lsa, y = 5x funksiya qaysi 93. Barcha ikki xonali sonlar ko‘paytmasidan
oraliqda yotadi? tashkil topgan ko‘paytmada 7 sonining eng
A) (0; ∞) B) [0, 2; 25] C) [1; 5] katta darajasini aniqlang.
D) (0; 25] A) 15 B) 16 C) 14 D) 13
√ √ √
84. 3−x = x tenglamaning eng kichik butun 94. y = x2 − 6x + 9 + x2 + 8x + 16
yechimini toping. funksiyaning qiymatlar sohasi topilsin.
A) 0 B) 1 C) 2 D) ∅ A) [7; ∞) B) [1; ∞) C) [0; ∞)
D) (−∞; ∞)
85. Rombning tomoni 4 ga, o‘tkir burchagi 30◦ ga !x
teng bo‘lsa, unga ichki chizilgan aylananing 1 x 8x
95. ·4 − = 0 tenglama ildizlarining o‘rta
uzunligini toping. 8 16
π arifmetigini toping.
A) 4π B) 2π C) π D)
2 A) 1,5 B) 3 C) 2,5 D) 2

1 1 1 1 1 1 96. cos2 x − sin2 x ≥ tgx · ctgx tengsizlikni yeching.

86. + + + + + ni hisoblang.
2 24 48 80 120 168 A) ∅
15 125 33 33 B) x = πk; k ∈ Z
A) B) C) D)
28 333 76 56 "
π π
#
C) − + 2πk; + 2πk , k ∈ Z
2 2
x2 − (m − 4) x − 4m
87. ni hisoblang.
!
x2 + (1 − m) x − m π π
D) − + 2πk; + 2πk , k ∈ Z
x−1 x+4 x−4 x−4 2 2
A) B) C) D)
x+2 x+1 x−2 x−1
97. sinx = [x] tenglamani yeching. (Bu yerda [x]−
√ √ butun qism.)
88. x + 1 + 2x + 3 = 5, tenglamaning haqiqiy
ildizlari yig‘indisini toping. π
A) 0 va
A) −3 B) 143 C) 3 D) −6 2
π
89. y = log0,5 x funksiyaga teskari funksiyani toping. B) x = πk; x = + πk; k ∈ Z
2
A) y = (0, 5)x B) x = (0, 5)y C) x = log0,5 y
D) x = log2 y π
C) 0, ,π
2
2x5 2x5 D) ∅
90. = tenglamaning barcha
x4 − 16 16 − x4
natural yechimlari yig‘indisidan eng katta 98. y = x + 3, x + 2y = 6 va y = 0 to‘g‘ri chiziqlar
manfiy butun yechimi ayirmasini toping. bilan chegaralangan figuraning yuzini toping.
A) 3 B) 1 C) 4 D) 2 A) 13,5 B) 27 C) 12,5 D) 25

2x − 5 99. Rombning balandligi 12 ga va diagonallaridan

91. > 3 tengsizlikni yeching.
x+3 biri 15 ga teng bo‘lsa, uning yuzini hisoblang.
A) (−∞; − 14) ∪ (−3; ∞) A) 150 B) 125 C) 100 D) 180
B) (−14; − 3) 100. Muntazam yigirmaburchakning eng katta va eng
C) (−14; 3) kichik diagonallari orasidagi burchakni toping.
D) (−14; − 3) ∪ (−3; ∞) A) 72◦ B) 82◦ C) 76◦ D) 80◦
√
101. ABCD parallelogrammda BD = 4 2,
3 6 ADB = 60◦ , 6 CDB = 75◦ bo‘lsa, AB ni
92. sin6 α + cos6 α + sin2 2α ni hisoblang.
4 toping.
√ √ √ √
A) 1 B) −1 C) sin2 α D) cos2 α A) 4 3 B) 3 3 C) 5 3 D) 6 2
 Matematika (informatika bilan) 7

102. Agar tengyonli trapetsiyaning perimetri 72 ga 111. To‘rtburchakli muntazam prizmaga ichki
hamda yon tomoni o‘rta chizig‘ining yarmiga chizilgan silindr yon sirtining prizma yon sirtiga
teng bo‘lsa, shu trapetsiyaning yon tomonini nisbatini toping.
toping. π π
A) B) C) 4 D) 2
A) 12 B) 16 C) 10 D) 9 4 2
√
103. y = 16 − x2 funksiyaning grafigi bo‘lgan egri 112. Balandligi 12 ga, asosining radiusi 5 ga teng
chiziq uzunligini toping. bo‘lgan konusga ichki chizilgan oltiburchakli
A) 4π B) 8π C) 6π D) aniqlab bo‘lmaydi muntazam piramidaning katta diagonal kesimi
yuzini hisoblang.
√ A) 60 B) 50 C) 72 D) 38
104. y = 25 − x2 funksiyaning grafigi bo‘lgan egri
chiziq va y = 0 to‘g‘ri chiziq bilan 113. Silindrga shar ichki chizilgan. Silindr o‘q
chegaralangan shakl yuzini toping. kesimining diagonali l ga teng bo‘lsa, shar
A) 12, 5π B) 25π C) 5π sirtining yuzini hisoblang.
D) aniqlab bo‘lmaydi π π π
A) · l2 B) π · l2 C) · l2 D) · l2
2 3 4
105. Aylananing uzunligi shu aylananing 40◦ li yoyi
uzunligidan necha foiz ko‘p?
114. Teng yonli uchburchakning uchidagi tashqi
A) 800 B) 900 C) 600 D) 700 burchagi ichki burchagi bilan 7:5 nisbatda
bo‘lsa, asosidagi tashqi burchagini toping.
106. Markazlari bir nuqtada bo‘lgan ikki doiradan
kattasining radiusi kichigining radiusidan 20% A) 127,5◦ B) 127◦ C) 120◦ D) 120,5◦
ga katta. Ularning orasidagi halqaning yuzi
katta doira yuzidan necha marta kam? 115. Agar ABC o‘tkirburchakli uchburchakda
3 3 4 4 AB=0,7; BC=0,9; sinB=0,8 bo‘lsa, uchinchi
A) 3 B) 2 C) 3 D) 2 tomonning kvadratini toping.
11 7 9 7
A) 0,544 B) 0,543 C) 0,541 D) 0,519
107. A nuqta ikki yoqli to‘g‘ri burchakning
yoqlaridan 6 va 8 ga teng uzoqlikda yotsa, shu 116. y = ln ||x| + 1| funksiyaning aniqlanish sohasini
nuqtadan ikki yoqli burchakning qirrasigacha toping.
bo‘lgan masofani toping. A) (−∞; ∞)
A) 10 B) 8 C) 9 D) 12 B) (0; ∞)
108. Uzunligi 17 ga teng bo‘lgan kesmaning uchlari C) (−∞; 0)
tekislikdan 4 va 12 ga teng uzoqlikda yotishi D) (1; ∞)
ma’lum bo‘lsa, kesmaning tekislikdagi
proyeksiyasi uzunligini toping. (
x−y =2
A) 15 B) 12 C) 16 D) 10 117. tenglamalar sistemasini yeching.
xy = 15
109. Tekislikdan h uzoqlikda joylashgan nuqtadan A) (5; 3); (−3; −5) B) (5; 3); (−5; −3)
tekislikka o‘tkazilgan va tekislik bilan 30◦ li C) (−5; −3); (3; −5) D) (−5; 3); (3; −5)
burchak hosil qiladigan og‘maning uzunligini
toping. 118. Agar to‘g‘ri to‘rtburchakda BK = KA bo‘lib,
√ √ AB = 6, AD = 4 bo‘lsa, SKCD =?
A) 2h B) 2h C) 1, 5h D) 3h
Br rC
110. Tekislikdan a uzoqlikda joylashgan nuqtadan
tekislik bilan 30◦ li burchak hosil qiluvchi ikkita
og‘ma o‘tkazilgan. Ularning tekislikdagi Kr r

proyeksiyalari o‘zaro 120◦ li burchak hosil qilsa,

og‘malarning uchlari orasidagi masofani r r
aniqlang. A D
√ √
A) 3a B) 2a C) 3a D) 2a A) 12 B) 16 C) 10 D) 14
 8 Matematika (informatika bilan)
√
119. Trapetsiyaning tomonlari a, a, a va 2a bo‘lsa, 129. x2 − 3x + x2 − 3x + 5 = 7 tenglamani katta
unga tashqi chizilgan aylananing uzunligini ildizining kichik ildiziga nisbatini toping.
toping. A) -4 B) -5 C) 4 D) 5
A) aπ B) 3aπ C) 6aπ D) 2aπ √
130. x2 + 2 x2 + 6x + 13 = −6x − 5 tenglama
120. Aylanaga tashqi chizilgan√muntazam ildizlarining yig‘indisini toping.
oltiburchakning tomoni 4 2. Shu aylanaga A) -2 B) -3 C) -13 D) -6
ichki chizilgan kvadratning yuzini hisoblang.
A) 64 B) 48 C) 36 D) 50 131. |x2 − 2x − 3| + 2 |x − 2| < 5 tengsizlikni
yeching.
121. Aylanaga tashqi chizilgan√muntazam √ √
A) ( 2; 2 3)
oltiburchakning tomoni 2 3 sm bo‘lsa, shu
aylanaga ichki chizilgan kvadratning yuzini B) (2; 3)
√
(sm2 ) hisoblang. C) ( 2; 3)
A) 18 B) 16 C) 20 D) 12 D) (−∞; ∞)
√
122. Rombning tomoni 10 3 ga, o‘tmas burchagi √ √ π
120◦ ga teng. Rombga ichki chizilgan doiraning 132. x2 − x − 12 + 5x − x2 − 4 + tg =1
2x − 4
yuzini hisoblang. tenglamani yeching.
A) 56,25π B) 48,75π C) 52,25π D) 58,6π A) 4 B) 1 C) 3 D) 1; 3
133. Sotuvchi kilosi 1500 so‘mdan 100 kg olma sotib
(x2 + x + 1)x2 oldi. 20 kg maydaroq olmalarni sotuvchi
123. < 0 tengsizlikni yeching.
x2 − 5x + 6 1750 so‘mdan, qolganlarini 2000 so‘mdan sotdi.
A) [2; 3] Bu tijoratda sotuvchi necha foiz foyda qilgan?
B) (2; 3) A) 30 B) 25 C) 35 D) 27
C) (−∞; 2] ∪ [3; ∞) 134. P (x) = (x2 − 3x + n)3 ko‘phadning
D) (−∞; 2] koeffitsientlar yig‘indisi 64 ga teng bo‘lsa, n ni
toping.
124. |x| − |x − 2| = 2 tenglamani yeching. A) 6 B) 8 C) 4 D) 2
A) [2; ∞) B) (2; ∞) C) {−2} D) {2} 135. 2x
2 +1
= 1 − x8 tenglamani yeching.
√ A) tenglama ildizga ega emas B) 1 C) 2
125. y = 7cos x funksiyaning davrini aniqlang.
D) -1
A) davriy emas B) 4π 2 C) 2π D) 2π 2
136. log2 (x2 + 2x + 4) + log2 (x − 2) <
q
4 √
3
√
3 < log2 (x3 − x2 + 4x − 3) tengsizlikni yeching.
7 54 + 15 128
126. q √ q √ ni hisoblang. A) (2; 5) B) (1; 5) C) (−1; 5) D) (−1; 2)
3 4 3 4
4 32 + 9 162
3 2 1
A) B) C) 1 D) 137. log2 (x − 1) − log2 (x + 1) + log x+1 2 > 0
5 3 4 x−1
tengsizlikni yeching.
q √ A) x > 3 B) x > 4 C) x < 3 D) x > 6
127. 5 − 2x − 7 = 2 tenglamaning ildizlari
quyidagi oraliqlardan qaysi biriga tegishli? 1 π √
138. arccos = (1 − 3 x) tenglamani yeching.
A) (−1; 1) B) [4; 6) C) [1; 3) D) [3; 4) x 2
A) ±1 B) ±8 C) 2 D) ∅
√
128. 4x − 5 x − 1 − 3 = 0 tenglama ildizlarining 60◦ va 30◦ bo‘lgan
139. Asosidagi burchaklari √
ko‘paytmasini toping. trapetsiyaga radiusi 3 3 bo‘lgan doira ichki
1 16 17 chizilgan. Trapetsiyaning perimetrini toping.
A) 4 B) 3 C) 2 D) √ √ √
4 17 8 A) 24(1+ 3) B) 2 2 C) 8 D) 3 3
 Matematika (informatika bilan) 9
!
140. Parallelogrammning diagonali 8 sm li tomoni 4 4 0 π
147. f (x) = cos x − sin x berilgan, f ni
bilan 60◦ li, ikkinchi tomoni bilan esa 75◦ li 4
burchak tashkil etadi. Ushbu diagonalning toping.
uzunligini (sm) toping. A) -2 B) 2 C) 0 D) 1
√ √ √
A) 8( 3 − 1) B) 4( 3 − 1) C) 8( 3 + 1)
√
D) 4( 3 + 1) 148. Agar arifmetik progressiyada a1 + a2 + a3 = 0
va a21 + a22 + a23 = 50 bo‘lsa, uning ayirmasini
141. Radiusi r bo‘lgan
√ aylananing vatari aylana toping.
r 3
markazidan uzoqlikda bo‘lsa, bu vatar A) ±5 B) 4 C) 2 D) 1
2
tortib turgan yoy uzunligini toping.
πr πr πr πr 149. Agar arifmetik progressiyada a1 + a2 + a3 = 15
A) B) C) D)
3 4 2 6 va a1 a2 a3 = 80 bo‘lsa, uning ayirmasini toping.
A) ±3 B) 2 C) 4 D) 5
142. Doiraning yuzasi 44% ga oshirilsa, uning radiusi
necha foizga oshadi?
sin1◦ · sin2◦ · sin3◦ · . . . · sin90◦
A) 20 B) 25 C) 30 D) 35 150. ni
sin91◦ · sin92◦ · sin93◦ · . . . · sin179◦
hisoblang.
143. Uchlari A(3; 0), B(−3; 8), C(3; 8) nuqtalarda √
bo‘lgan uchburchakka ichki chizilgan aylana π 2
A) 1 B) 2 C) D)
tenglamasini toping. 2 2
A) (x − 1)2 + (y − 6)2 = 4
B) (x − 2)2 + (y + 6)2 = 4 151. A(2; 1) nuqtadan o‘tib, koordinata o‘qlariga
C) (x + 3)2 + (y − 2)2 = 1 urinuvchi aylana tenglamasini tuzing.
D) (x − 3)2 + (y + 1)2 = 2
A) (x − 5)2 + (y − 5)2 = 25 yoki
√ (x − 1)2 + (y − 1)2 = 1
144. Asoslarining radiuslari 2 va ( 101 − 1) ga teng
bo‘lgan kesik konus va unga tengdosh B) (x − 3)2 + (y − 3)2 = 9
silindrning balandliklari ham o‘zaro teng bo‘lsa, C) (x − 2)2 + (y − 4)2 = 9
silindr asosining radiusini toping. D) (x − 1)2 + (y − 5)2 = 16
s
104
A)
3
√

2x − 1 > x,
2 104 
B) 152. x2 − 7x + 6 > 0, tengsizliklar sistemasini
3  x

2 < 128
√
208 yeching.
C) √
3 A) (6; 7)
104 B) (−∞; 6)
D)
3 C) (7; ∞)
D) (−∞; 6) ∪ (7; ∞)
145. ax = by = cz = 6 va x + y + z = 36 ekani
1 1 1
ma’lum bo‘lsa, + + ni toping.
a b c 153. ABC uchburchak uchlaridan va shu
A) 6 B) 9 C) 5 D) 12 uchburchakning medianalari kesishgan
M nuqtadan α-tekislikka tushirilgan
a+b perpendikularlar asoslari mos ravishda A1 , B1 ,
146. a > b > 0 va c = berilgan. Quyidagi
b C1 , M1 nuqtalarda yotsa, AA1 + BB1 + CC1 va
tasdiqlardan qaysi biri to‘g‘ri? M M1 uzunliklari nisbatini toping.
A) c > 2 B) c = 1 C) c = 2 D) a < c < 2 A) 3 B) 2 C) 1 D) 23
 10 Matematika (informatika bilan)

154. Muntazam ko‘pburchakning tomoni a ga, unga 162. 3; 5; 9; 17; 33; 65; . . . ketma-ketlikning
tashqi chizilgan aylana radiusi esa R ga teng dastlabki n ta hadining yig‘indisini toping.
bo‘lsa, ichki chizilgan aylana radiusini toping. A) 2n+1 + n − 2 B) 2n C) 2n + n − 2
v
D) (2 + 2n−1 ) · n
a2
u
u
A) tR2 −
4 163. Cheksiz kamayuvchi ishorasi almashinuvchi
v geometrik progressiyada ketma-ket kelgan uchta
2
a
u
u hadning yig‘indisi -21 ga, ko‘paytmasi 729 ga
B) tR2 +
4 teng bo‘lsa, shu sonlarni toping.
2aR A) 27; -9; 3 B) -28; 14; -7 C) -3; 9; -27
C) √ D) -27; 9; -3
4R2 − a2
2aR 2x − 1
D) √ 164. y = √ funksiyaning aniqlanish
4R2 + a2 x2 − 5x + 6
sohasini toping.
155. 5200 sonini 24 ga bo‘lganda qoladigan qoldiqni A) (−∞; 3)
aniqlang. B) (−2; 3)
A) 15 B) 23 C) 1 D) 3 C) (0; 2)
2010 D) (−∞; 2) ∪ (3; ∞)
156. 20122011 sonining oxirgi raqamini toping.
A) 6 B) 2 C) 4 D) 8 3x + 1
165. y = funksiyaning qiymatlar to‘plamini
x2 − 5x − 6 x+2
157. 2 ≤ 0 tengsizlikni yeching. toping.
x − 4x + 10
A) (−∞; 3) ∪ (3; ∞)
A) (0; 3)
B) (−∞; − 2)
B) [0; 5]
1
C) (−∞; − )
!
1 3
C) ; 6
2
1
D) [−1; 6] D) [−2; − ]
3

x+3
 2


 < 2, 166. 2x −16 ≤ 1 tengsizlikni yeching.

3−x A) [0; 4) B) (−2; 2) C) [−4; 4]
158. tengsizliklar sistemasini yeching.
x3 < 16x,
D) (0; 2)


4 ≥ x2


( √ √
A) [2; 3] B) (3; 5) C) (4; 6] D) (0; 1) 3 x+ y = 273 ,
167. √ tenglamalar sistemasini
√ √ lg xy = 1 + lg 2
159. x2 + 11 − x2 − 9 = 2 tenglamani yeching. yeching.
(x ∈ R) A) (0; 9) B) (16; 25), (25; 16)
A) 3 B) 5; 3 C) -3 D) -5; 5 C) (4; 9), (9; 4) D) (0; 1)
√ 1 1
x2 − 3x + 2 168. 8 , 8 , . . . arifmetik progressiyaning birinchi
160. ≥0 2 3
4x − x2 − 3 manfiy hadini toping.
A) [0; 2) B) [2; 3) C) (0; 1) D) (0; ∞) 1 1 1 1
A) − B) − C) − D) −
6 4 5 3
161. Ishorasi almashinuvchi geometrik
7 11
progressiyaning birinchi hadi −2 ga, uchinchi 0, 725 + 0, 6 + +
hadi −8 ga teng bo‘lsa, shu progressiyaning 169. 40 20 · 0, 25 ni hisoblang.
1 3
dastlabki 6 ta hadi yig‘indisini toping. 0, 128 · 6 − 0, 0345 :
4 25
A) 36 B) 42 C) −36 D) −42 A) 2 B) 1/2 C) 1 D) 4
 Matematika (informatika bilan) 11
!
1 1 2c 176. Konusning balandligi va uning yasovchisi mos
+ − (a + b + 2c)
a b ab ravishda 4 sm va 5 sm ga teng. Asosi konus
170. ifodani
1 1 2 4c2 asosida yotgan ichki chizilgan yarimsharning
+ + − hajmini (sm3 ) toping.
a2 b2 ab a2 b2
soddalashtiring va uning son qiymatini toping. 1152 125 156
5 A) π B) π C) π D) 8π
a=7,4; b = . 125 1152 137
37
4 1 16
A) 0 B) C) D) 1 177. x2 + x2
+ (x − x4 ) − 28 = 0 tenglamaning
5 2 ildizlari yig‘indisini toping.
! A) -1 B) 1 C) 4 D) 0
3x − 1 x+1
171. f = bo‘lsa, f (x) ni toping.
x+2 x−1
178. x3 − x + 3 = 0 bo‘lsa, (x3 − x + 1) · (x3 + 3) ning
x+4 x+1 2x + 1
A) B) C) qiymatini toping.
3x − 2 x−1 3−x
A) -2x B) -4x C) 0 D) 2x
3x − 1
D)
x+2
179. To‘g‘ri burchakli trapetsiyaga radiusi 5 ga teng
q aylana ichki chizilgan. Agar trapetsiyaning
172. y = log0,2 x+2
x−1
− 1 funksiyaning aniqlanish
katta asosi 17 ga teng bo‘lsa, aylana
sohasini toping.
" ! markazidan trapetsiyaning o‘tkir burchagigacha
11 bo‘lgan masofani toping.
A) − ; −2
4 A) 13 B) 7 C) 9 D) 12
B) (−∞; −2]
C) ∅ 180. Diagonali 8 ga teng, a va b tomonlari
a2 b2
D) [−2; 1) + = 10 shartni qanoatlantiruvchi
a−b b−a
to‘g‘ri to‘rtburchakning yuzini toping.
173. |log2013 x − 2| + |log2013 x − 4| < 4 tengsizlikni A) 18 B) 20 C) 16 D) 24
yeching.
A) (2013; 20135 ) 181. Anvar aka bozorga tuxum olib keldi va u
B) ∅ birinchi xaridorga tuxumlarning yarmini va
yana bitta, ikkinchi xaridorga qolganining
C) {2013; 20135 } yarmini va yana bitta, uchinchi xaridorga
D) {2013} qolgan tuxumlarning yarmini va yana bitta
tuxum sotdi. Shundan so‘ng o‘zida 14 ta tuxum
174. To‘g‘ri burchakli uchburchakning katetlaridan qoldi. Anvar aka bozorga hammasi bo‘lib,
biri 15 sm ga, ikkinchi katetning gipotenuzadagi nechta tuxum olib keldi?
proyeksiyasi esa 16 sm ga teng. Bu A) 126 ta B) 100 ta C) 96 ta D) 50 ta
uchburchakka ichki chizilgan aylananing
radiusini (sm) toping. 182. Xo‘jayin bir kishini bir yilga yollab, unga
A) 3 B) 4 C) 5 D) 6 12 so‘m pul va bir chakmon bermoqchi bo‘libdi,
lekin ishchi 7 oy ishlagandan keyin xo‘jayin
175. Teng yonli uchburchakning yon tomoni 10 sm, unga 5 so‘m pul va bir chakmon beribdi.
asosi 12 sm ga teng. Uchburchakka ichki Chakmon necha so‘m bo‘lgan.
chizilgan aylanaga o‘tkazilgan urinmalar A) 4,8 B) 5 C) 5,2 D) 5,5
uchburchakning asosiga tushirilgan balandligiga
parallel va berilgan uchburchakdan ikkita to‘g‘ri
183. ABC uchburchakda AB = 3AC.
burchakli uchburchak ajratadi. Ushbu
Uchburchakning C va B uchlaridan o‘tkazilgan
uchburchakning tomonlarini (sm) toping.
balandliklarining nisbati qanday?
A) 2; 2; 3 B) 2; 3; 4 C) 3; 4; 5 D) 3; 3; 5
A) 1:3 B) 3:1 C) 2:3 D) 1:4
 12 Matematika (informatika bilan)

2x 1
184. M va N nuqtalar ABC uchburchakning AB va 191. 4tg + 2 cos2 x − 80 = 0 tenglamani yeching.
AC tomonlari o‘rtasida yotadi. AN M
π
uchburchakning perimetri 21 sm bo‘lsa, ABC A) ± + πk, k ∈ Z
3
uchburchakning perimetrini (sm) toping.
A) 42 B) 84 C) 50 D) 63 π
B) + πk, k ∈ Z
4
185. To‘g‘ri burchakli uchburchakning katetlari C) πk, k ∈ Z
yig‘indisi gipotenuzadan 8 sm ortiq. Agar D) π(k + 1), k ∈ Z
uchburchakning perimetri 48 sm bo‘lsa, uning
yuzini (sm2 ) toping.
A) 96 B) 148 C) 52 D) 60 192. arccos(1 + x) + 2arcsinx = 0 tenglamani
yeching.
◦
186. To‘g‘ri burchakli ABC uchburchakda 6 A = 30 1 1
bo‘lib, AB=6 sm li gipotenuzasini diametri A) 0 B) −1 C) − D)
2 3
qilib, doira chizildi. Hosil bo‘lgan eng kichik
segmentning yuzini toping. 2
√ √ 193. √ √ √ √ kasrning maxrajini
6π − 9 3 12π − 9 3 10 + 15 + 14 + 21
A) B) C) 36π
4 4 irratsionallikdan qutqaring.
D) 18π √ √ √ √
A) 10 − 15 + 21 − 14
√ √ √ √ √
187. log2 3 + 2 log4 x =
log3 x
xlog9 16 tenglamani B) 10 + 15 + 14 − 21
√ √ √ √
yeching. C) 10 − 15 + 14 − 21
16 √ √ √ √
A) B) 16 C) log3 4 D) 12 D) 10 − 15 + 21 + 14
3
 √ √ !
188. logx−1 (x + 1) > 2 tengsizlikni yeching. q m3 1 m 
194.  m(1 − m) + √ : √ + :
A) (2; 3) 1−m 1+ m 1−m
q
B) (0; 1) ∪ (2; 3) m(1 − m) ifodani soddalashtiring.
C) (2; 3) ∪ (3; ∞) (m ∈ (0; 1))
D) (−∞; 0) ∪ (3; ∞) 1
A) 1 + m B) 1 − m C) 1 D)
m
189. Umumiy bahosi 225 dinor bo‘lgan ikki xil √ √
3 3
! !
qimmatbaho mo‘ynali teri xalqaro bozorda 40% 195. √a + b + √a − b − 2 : √ 1 −√
1
3 3 3 3
foydasi bilan sotildi. Agar birinchi xil teridan a−b a+b a−b a+b
25%, ikkinchisidan 50% foyda qilingan bo‘lsa, ifodani soddalashtiring. (a > b > 0)
har bir terining bahosi necha dinor bo‘lgan? √ √
A) 3 a − b − 3 a + b
A) 90; 135 B) 100; 125 C) 80; 145 √
3
√
3
D) 200; 25 B) a + b − a−b
( x−y
C) 1
y−x
2 2 + 2 2 = 2, 5 D) 0
190.
lg(2x − y) + 1 = lg(y + 2x) + lg 6
tenglamalar sistemasini yeching.  √ 
3
8 − n n 2
A) (4; 2) 196. √ : 2 + √ −
! ! 2+ 3n 2+ 3n
1 1 1 1 √ ! √
B) ;− va ;− √ 23n
3
4 − n2
2 2 4 4 − 3
n+ √ · √ √ ifodani
3
! ! 3
n−2 n 2+2 3 n
2 2 4 4
C) ;− va ;− soddalashtiring. (n 6= ±8)
3 3 3 3
1
D) (1; −1) va (1; 0) A) 1 B) 2 C) 0 D)
n
 Matematika (informatika bilan) 13
1

x2 + 1 1 sin(x − y) = 2 sin x sin y,

: 1,5 ifodani soddalashtiring.

197. 1 204. π sistemani yeching.
x + x2 + 1 x − 1  x+y =

2
A) 1 B) x + 1 C) x − 1 D) 1 − x !
π πk 5π πk
ax − b bx + a a2 + b 2 A) − + ; − , k∈Z
198. + = 2 tenglamani yeching 8 2 8 2
a+b a−b a − b2 !
6 |b|).
(|a| = π 5π
B) − + πk; − πk , k ∈ Z
8 8
A) x = 1 B) x = 0 C) x = −1 D) x = a !
π πk 5π πk
C) + ; + , k∈Z
8 2 8 2
199. (x − a − b)ab + (x − b − c)bc + (x − c − a)ac = 3abc !
tenglamani yeching. π 5π
D) + πk; + πk , k ∈ Z
A) a + b B) a − b + c C) a + b + c 8 8
D) b + c − a

2x2 − x + 1 a b c 205. Agar a2 + b2 = 1 bo‘lsa, a6 + 3a2 b2 + b6 ni

200. = + + toping.
(x + 1)(x − 2)2 x + 1 x − 2 (x − 2)2
tenglikni qanoatlantiradigan a, b, c larni toping. A) 1 B) 2 C) ab D) a + b
4 14 7
A) a = ; b = ; c = 206. 2x2 + 5y 2 − 4xy − 2y − 4x + 5 = 0 tenglamani
9 9 3
qanoatlantiruvchi nechta (x, y) juftlik mavjud?
14 4 7
B) a = ; b = ; c = A) 1 ta B) 2 ta C) 3 ta D) mavjud emas
9 9 3
4 14 7
C) a = − ; b = ; c =
9 9 3 1 1 1
4 14 7 207. ! − ! − ! ni hisoblang.
D) a = ; b = − ; c = − 1 1 1
9 9 3 log2 log3 log4
6 6 6
A) 1 B) 6 C) 2 D) 3
201. x(x + 1)(x − 1)(x + 2) = 24 tenglamani yeching.
A) x1 = x2 = 1 B) x1 = −3; x2 = 2 208. Agar x = 4 bo‘lsa,
C) x1 = 0; x2 = 1 D) x1 = −1; x2 = −2 (3x − 2) · (4x + 1) − (3x − 2) · 4x + 1 ni toping.
A) 11 B) 10 C) 0 D) 1
b 2 a2
! !
a+b b−a
202. 2 + 2 −2 · + ·
a b b −a a + b
1 1 1 1 1 1 1 1
209. n ∈ N va + + + yig‘indi butun son
 2 + 2 2 − 2 2 3 7 n
a b b a 

 1 −  ifodani soddalashtiring. bo‘lsa, quyidagilardan qaysi biri noto‘g‘ri?
1 1 1 
− + A) n > 84 B) n soni 3 ga bo‘linadi
 
b 2 a2 a2 b2
C) n soni 6 ga bo‘linadi
A) −8 B) ab C) 2ab D) 1 D) n soni 2 ga bo‘linadi
203. sinx = cos2x tenglamani yeching.
210. Agar xy + yz + zx = 16 bo‘lsa, x2 + y 2 + z 2
π 2πk
A) + , k∈Z ifoda teng bo‘lishi mumkin bo‘lgan eng kichik
6 3
qiymatni toping.
π 2πk A) 16 B) 32 C) 8 D) 48
B) + , k∈Z
3 3
2π πk 211. Agar xy + yz + zx = 16 bo‘lsa, (x + y + z)2
C) + , k∈Z
3 3 ifoda teng bo‘lishi mumkin bo‘lgan eng kichik
π πk qiymatni toping.
D) + , k∈Z
6 3 A) 48 B) 16 C) 32 D) 64
 14 Matematika (informatika bilan)
0
212. ABCD to‘g‘ri to‘rtburchakda AD = 1. AB 219. f (x) = cos2x + ex , f (x)−?
tomondan shunday P nuqta olinganki DB va A) sin2x + ex B) −sinx + ex
DP kesmalar 6 ADC ni teng uchga bo‘ladi. C) −sin2x + ex D) −2sin2x + ex
BDP uchburchakning perimetrini toping.
√ √
4 3 3 √ 220. f (x) = sin2x + 4x, f (x)−?
0

A) 2 + B) 3 + C) 2 + 2 2
3 3 A) cosx + 4 B) 2cos2x + 4 C) cos2x + 4x
√
5 D) −cos2x + 4
D) 3 +
2
1 0
221. f (x) = sin2x + x, f (x)−?
213. Radiuslari 2 va 3 ga teng bo‘lgan aylanalar 2
bir-biriga tashqi ravishda urinadi. Ularning 1
ikkalasi uchinchi aylanaga ichki ravishda urinsa A) cos2x B) cos2x + 1 C) cosx + 1
2
va markazlari bitta to‘g‘ri chiziqda yotsa, tashqi D) 2cos2x + 1
aylananing ichki aylanalardan bo‘sh qolgan
sohasi yuzini toping. √ 0
222. f (x) = 2sinx − 2x, f (x)−?
A) 12π B) 9π C) 6π D) 4π √
A) −cosx − 2 B)√− 2cos2 x − 2
C) cosx + 2 D) 2cosx − 2
214. XOY uchburchakda 6 XOY = 90◦ . M va N
nuqtalar mos ravishda OX va OY tomonlarning
R2
o‘rtalari. Agar XN =19 va Y M =22 bo‘lsa, XY 223. (x2 − 1) dx ni hisoblang.
−1
ni toping.
A) 2 B) 1 C) −2 D) 0
A) 26 B) 28 C) 13 D) 14
224. f (x) = 8x3 − 6x2 + 7 funksiyaning M (1; 0)
215. ABCDEF GH muntazam sakkizburchakning
yuzi 1 ga teng bo‘lsa, ABEF to‘g‘ri nuqtadan o‘tuvchi boshlang‘ich funksiyasini
to‘rtburchakning yuzini toping. toping.
√ √ A) 4x4 − 2x3 + 7x − 7 B) 4x4 − 2x3 + 7x − 6
1 1+ 2 2 3
A) B) C) D) C) 4x4 − 2x3 + 7x − 9 D) 2x4 − 2x3 + 7x − 7
2 4 4 2

216. Rasmda berilgan ADE va BDC uchburchaklar 0

225. f (x) = 3x2 − 4x + 2, f (−1) = 0, f (2)−?
yuzalarining ayirmasini toping.
A) 8 B) 18 C) 9 D) 10
Er
0
rC 226. f (x) = 12x5 − 4x3 − 2x + 5, f (−1) = 0, f (1)−?
8 D A) 8 B) −10 C) 10 D) −8
r
6
227. f (x + 1) = x · f (x) + 4, f (2)-?
r 4 r A) 0 B) 6 C) 8 D) 16
A B
A) 4 B) 5 C) 8 D) 2 228. 117, 177, 237 sonlarini A soniga bo‘lganda mos
ravishda 5, 9, 13 qoldiqlar chiqadi. A ning
217. To‘g‘ri burchakli uchburchakning gipotenuzasi c qabul qilishi mumkin bo‘lgan qiymatlari
ga, unga ichki chizilgan aylana radiusi r ga teng yig‘indisini toping.
bo‘lsa, uchburchakning yuzini toping. A) 42 B) 120 C) 98 D) 31
A) r2 + cr B) c2 + cr C) 2cr D) r2 + c2
6
229. = 3 tenglamani yeching.
2
218. f (x) = x + 2x + 1 funksiyaning hosilasini x−2
1+
toping. 3−x
1+
A) 2x + 2 B) x2 + 2 C) 2x − 2 2
D) 2x2 + 2 A) 1 B) 4 C) 6 D) 3
 Matematika (informatika bilan) 15

8 239. Qanday ko‘pburchak diagonallarining soni

230. = 4 tenglamani yeching.
x−4 tomonlarining sonidan 12 ta ortiq?
1+
x−6 A) oltiburchak B) sakkizburchak
2+
3 C) to‘rtburchak D) o‘nikkiburchak
A) 4 B) 3 C) 0 D) 6
240. To‘g‘ri to‘rtburchakning diagonali 17 sm,
231. x, y butun sonlar uchun −12 ≤ x < 13, tomonlaridan biri esa 8 sm. To‘g‘ri
x−y to‘rtburchakning yuzini (sm2 ) toping.
−9 < y ≤ 6 va x + y 6= 0 bo‘lsa, ning eng
x+y A) 120 B) 140 C) 80 D) 160
katta qiymatini toping.
A) 20 B) 18 C) 17 D) 14 241. Omonatchi bankga 25000 so‘m pul qo‘ydi.
Oradan 3 yil o‘tgach, u o‘ziga tegishli hamma
232. x, y butun sonlar uchun −8 ≤ x ≤ 19, pulni qaytarib oldi. Agar bank yiliga 5% foyda
x+y to‘lasa, omonatchi bankdan necha so‘m pul
−4 ≤ y ≤ 13 va x − y 6= 0 bo‘lsa, ning
x−y olgan?
eng katta qiymatini toping.
A) 28000,125 B) 59490,235 C) 28940,625
A) 27 B) 28 C) 32 D) 18 D) 27941
233. x, y butun sonlar uchun −6 ≤ x ≤ 8, 242. 2 ta parallel to‘g‘ri chiziqni uchinchi to‘g‘ri
x−y
−9 ≤ y ≤ 12 va x + y 6= 0 bo‘lsa, ning chiziq kesib o‘tganda hosil bo‘lgan ichki bir
x+y 7
eng katta qiymatini toping. tomonli burchaklar nisbatda. Ulardan
13
A) 24 B) 19 C) 32 D) 17 kattasini toping.

xy A) 117◦ B) 120◦ C) 113◦ D) 63◦

 x−y
 = −6
yz
234. x, y, z - butun sonlar bo‘lib, z−y
= 15
2
243. Teng yonli uchburchakning uchidagi tashqi
xz
= 10 burchagi 120◦ ga teng bo‘lsa, asosidagi burchak



z−x 3
bo‘lsa, x + y − z =? sinusini toping.
√ √
A) 6 B) 4 C) 0 D) -4 3 2 1
A) B) 1 C) D)
 2 2 2
xy

 x−y
 = −6
yz 244. ABC uchburchakda AB=0,6; BC=0,8;
235. x, y, z - butun sonlar bo‘lib, y−z
= − 15
2
xz
= − 10 AC=0,5 bo‘lsa, B burchak kosinusini toping.



x−z 3
bo‘lsa, x − y − z =? 25 25 24 24
A) B) C) D)
A) −8 B) 6 C) 10 D) −6 32 31 31 33

245. ABC uchburchakda a=3; b=5; 6 C=60◦ bo‘lsa,


xy

 y−x
 = − 15
2
yz c ni toping.
236. x, y, z - butun sonlar bo‘lib, z−y
= 21
4 √ √ √ √
 xz


= 35 A) 19 B) 21 C) 17 D) 23
z−x 2
bo‘lsa, x + y − z =? 246. Agar to‘g‘ri to‘rtburchak kichik tomoni
√
A) 9 B) 15 C) 4 D) 1 a = 10 2 bo‘lsa, uning ixtiyoriy burchagidan

xy
katta tomonga o‘tgan bissektrisasi uzunligi

 x−y
 = 15
2 qancha?
yz
237. x, y, z - butun sonlar bo‘lib, z−y
= 21
4 A) 20 B) 10 C) 30 D) 15
 xz

= −17, 5

x−z
bo‘lsa, x + y + z =? 247. Aylanaga teng yonli trapetsiya tashqi chizilgan.
A) 9 B) 15 C) 1 D) 4 Trapetsiyaning bir burchagi 30◦ , o‘rta chizig‘i
2 sm bo‘lsa, aylananing radiusini (sm) toping.
238. ||x − 4| − 7| > 5 tengsizlikning eng kichik A) 2 B) 2,5 C) 0,5 D) 1
musbat va eng katta manfiy butun yechimlari
ayirmasini toping. 248. |x + 1| = |x − 1| tenglamaning ildizlarini toping.
A) −12 B) 12 C) −6 D) 6 A) 0 B) -1; 1 C) -1; 0 D) ∅
 16 Matematika (informatika bilan)
1
249. 4x − 2 · 6x = 9x+ 2 tenglama ildizini toping. 258. (x2 + x)2 − 14(x2 + x) + 24 ko‘phadni
lg3 ko‘paytuvchilarga ajrating.
A) A) (x2 + x + 12)(x2 + x − 2)
2
lg B) (x2 + x + 2)(x2 + x + 12)
3
C) (x2 + 3)(x2 + 8)
B) lg3 D) (x2 + x − 2)(x2 + x − 12)
2
C) −lg
3 4x2 − y 2 x−y
259. 3 3 − 2 ni soddalashtiring.
2 x +y x − xy + y 2
D) lg
3 3x2 3(x + y) x+y
A) 3 3 B) 3 3 C) 2
x +y x +y x − xy + y 2
x2 − y 2
250. y = 1994x + 2013 funksiya grafigi qaysi D) 2
choraklardan o‘tadi? x − xy + y 2
A) I, II, III B) I, II, IV C) I, III, IV 260. 7 · 52 va 32 · 5 · 7 sonlari uchun EKUK ni toping.
D) II, III, IV
A) 3150 B) 1575 C) 315 D) 1500
251. y = 1994x2 + 2013x − 1 funksiya grafigi qaysi 261. 165 + 215 yig‘indi berilgan sonlardan qaysi
choraklardan o‘tadi? biriga qoldiqsiz bo‘linadi?
A) I, II, III, IV B) I, II, III C) II, IV A) 17 B) 29 C) 9 D) 33
D) I, II, IV
!2

−3 −8
 
−13 −2
 1
252. Oltiburchakli muntazam prizma eng katta 262. (−15) : (−15) − − ni
15
diagonal kesimining yuzi Q, prizmaning hisoblang.
qarama-qarshi yon yoqlari orasidagi masofa b 2 1
bo‘lsa, prizmaning hajmini hisoblang. A) 0 B) C) 50 D) −
225 225
3bQ 3bQ 4bQ bQ
A) B) C) D)
4 2 3 2 66 · 23 − 36
263. ni hisoblang.
66 + 63 · 33 + 36
253. Agar arifmetik progressiyada S13 = 52 bo‘lsa, A) 3 B) 7 C) 9 D) 11
a7 ni toping.
A) 4 B) 5 C) 3 D) 8 264. 1024 − 4 ni 9 ga bo‘lganda qoldiq nechaga teng?
A) 4 B) 6 C) 0 D) 3
8562 − 4 · 222 vs
254. : 180 ni hisoblang. s
3 √ 1 u
s
1
u
406 4
265. 3 3 + 18 · 4 4 − t 5 ni hisoblang.
A) 16 B) 10 C) 12 D) 8 8 2 16
√ √
√ √ √ √ √ A) 2 B) 2 3 C) 6 D) 3
255. a = 5 + 6, b = 3 + 8, c = 2 + 7 q√ √
sonlarni o‘sish tartibida joylashtiring. 266.
4 3 6
25 · 55 ni hisoblang.
√ √ √
A) b < c < a B) c < b < a C) a < b < c A) 5 12 5 B) 5 C) 3 5 D) 5 6 5
D) b < a < c
267. Velosipedchi bir soatda 15,75 km, piyoda esa
(8n+1 + 8n )2 1
256. ni soddalashtiring. (n ∈ N ) 4 km yo‘l bosadi. Velosipedchining tezligi
(4n − 4n−1 )3 2
piyodaning tezligidan necha marta ortiq?
A) 192 B) 144 C) 216 D) 96
A) 3,5 B) 11,5 C) 11,25 D) 3,75
(4n+1 + 6 · 4n )3 √
3
√ √
257. ni soddalashtiring. (n ∈ N ) 268. x + 2 + 3 x + 3 + 3 x + 4 = 0 tenglama
(8n+1 + 2 · 8n )2 ildizlarining yig‘indisini toping.
A) 10 B) 15 C) 18 D) 16 A) -5 B) -3 C) 2 D) 1
 Matematika (informatika bilan) 17
q √ q √
269. 3
5 + x + 3 4 − x = 3 tenglama ildizining 279. Rasmda qanday uchburchaklar tasvirlangan?
natural bo‘luvchilari sonini toping.
A) 2 B) 4 C) 3 D) 5
√ √ √
270. 3x2 + 7x + 2 − 2x2 + 3x − 2 = x2 + 2x
tenglama ildizlarining yig‘indisini toping.
A) 3 B) -3 C) -1 D) -2
√
3 √
271. x2 − 3 3 x − 4 = 0 tenglamaning katta va
A) tengdosh
kichik ildizlari ayirmasini toping.
A) 60 B) 65 C) 63 D) 68 B) perimetrlari bir xil
C) yuzalari har xil
√ √3
272. 3
x + 6 = x2 tenglamaning katta va kichik D) uchburchaklardan biri to‘g‘ri burchakli
ildizlari ayirmasini toping.
A) 25 B) 35 C) 45 D) 50 280. Rombning tomoni 6 sm, bitta burchagi 120◦ ga
√ teng. Romb tomoniga va kichik diagonaliga
273. x2 − 3x − 6 3x + 18 = 0 tenglama ildizlari urinuvchi aylananing radiusini (sm) toping.
√ √
ko‘paytmasining ildizlari soniga ko‘paytmasini A) 3 B) 3 C) 4 D) 2 3
toping.
2 281. Shaklda berilganlardan x ni toping.
A) -3 B) 3 C) D) 6
3

√ 6 √ 

274. 5x − 1 + √ = 5x + 15 tenglamaning r  
5x − 1 

katta ildizi m va ildizlarining soni n bo‘lsa,  
x
 ◦
30 r
m + n ni toping. 
A) 4 B) 6 C) 3 D) 8
A) 120◦ B) 80◦ C) 135◦ D) 105◦
a3 − 2a2 + 5a + 26 √
275. kasrni qisqartiring. 282. x2 + 2x + 1 − |x − 4| = 2 tenglamaning [1; 3]
a3 − 5a2 + 17a − 13
1−a a+2 a+2 a−2 kesmadagi ildizini toping.
A) B) C) D) A) 2,5 B) 2,(3) C) 1,5
a+2 a−1 a−2 a+2
D) bu oraliqda yechimi yo‘q
(z + 4)2 − 12
!
z−2 1
276. 2 + 3 − : 283. (x − 1)2 (x2 − 2x) = 12 tenglamaning haqiqiy
6z + (z − 2) z −8 z−2 ildizlari yig‘indisini toping.
z 3 + 2z 2 + 2z + 4
ni soddalashtiring. A) 2 B) 3 C) 4 D) 0
z 3 − 2z 2 + 2z − 4
1 1 284. a > 2 da ||x + 1| − 2| = a tenglama nechta
A) z − 2 B) C) D) z + 2
z−2 z+2 yechimga ega?
A) 2 B) 3 C) 4 D) ildizga ega emas
277. Cheksiz kamayuvchi geometrik progressiyaning
√
ikkinchi hadi beshinchi hadidan 8 marta katta. 23a+0,5 + 2 a+0,5
√
Agar bu geometrik progressiya hadlari yig‘indisi 285. 4a − 2a + 1 · (2 − 2) − 22a+1 ni hisoblang.
6 ga teng bo‘lsa, uning birinchi hadini toping. √
A) 2cos7π B) −2a C) 4a 2 D) 2
A) 3 B) 6 C) 4 D) 2
286. 112 soni shunday 3 bo‘lakka bo‘linganki,
Rπ
278. 8 cos2 x · sin 2xdx integralni hisoblang. 2-bo‘lak 1-bo‘lakning 10% ini, 3-bo‘lak 2-sining
π
4 20% ini tashkil etadi. O‘rta bo‘lakni toping.
A) 3 B) 2 C) -3 D) 1 A) 10 B) 112/13 C) 20 D) 5
 18 Matematika (informatika bilan)

287. 3ax − 6x2 − 8 + x3 ko‘phad to‘la kub bo‘ladigan 294. f (x + 5) = x · f (x) + 4 bo‘lsa, f (10) ni toping.
barcha a larni toping. A) 24 B) 23 C) 30 D) 25
A) 4 B) 2 C) -2 D) -4
a4 + a3 + a2 + 9
√ √ 295. Agar a3 + a − 2 = 0 bo‘lsa,
7+ 3 a5 + a2 + a + 6
288. Agar a = bo‘lsa, ifodaning qiymatini toping.
3 q
q √ √ 4 12
a − 2 a − 1 + a + 2 a − 1 ifodaning A) B) 1 C) -2 D)
qiymatini toping. 3 11
√ √
√ 7+ 3 √ ! ! ! !
A) 2 B) 2 C) D) 5 + 21 1 1 1 1
3 296. a = 1 + 1+ 1+ ... 1 + ,
2! 3! 4! 2011 !
289. a, b, c - noldan farqli raqamlar uchun a > b > c
1 1 1 1
b= 1− 1− 1− ... 1 −
munosabat o‘rinli. Agar abc + bca + cab = 999 2 3 4 2012
tenglik bajarilsa, a ning eng katta qiymati berilgan, a · b ko‘paytmani toping.
nechaga teng bo‘lishi mumkin? 1
A) B) 2 C) 3 D) 1
A) 6 B) 7 C) 5 D) 4 2
v
u v v
297. Geometrik progressiyada b9 · b19 = 9 ga teng,
b1 · b27 + 1 ni toping.
u u
u a2 u 2
ua
u 2
ua
290. t +t +t + . . . = 4 tenglikni
u
3 3 3 A) 10 B) 4 C) 2 D) 5
qanoatlantiruvchi a musbat sonni toping. 298. y = |x − 1| + |x − 2| + |x − 3| + ... + |x − 9|
A) 6 B) 4 C) 2 D) 8 funksiyaning eng kichik qiymatini toping.
A) 20 B) 21 C) 10 D) 12
f (8)
291. Quyidagi chizmaga asoslanib ning
g(8) 299. ABCD parallelogrammning A va B
qiymatini toping. burchaklaridan chiquvchi bissektrisalar
y 6 orasidagi burchakni toping.
A) 90◦ B) 40◦ C) 120◦ D) 150◦
y = f (x)
y = g(x) 300. ABCD parallelogrammning B o‘tmas
5 r burchagidan chiquvchi BL va BK balandliklar
(5; 5)
orasidagi burchak o‘tmas burchakdan 3 marta
kichik. 6 ABC ni toping.
A) 135◦ B) 120◦ C) 150◦ D) 110◦
(4; 0)
r r - 301. ABC uchburchakning AM medianasi BK
4 5 x bissektrisasiga perpendikular. Agar BC=12 sm
bo‘lsa, AB tomon uzunligini (sm) toping.
A) 6 B) 9 C) 4 D) 5

302. Tomonlari uzunliklari 6 sm, 10 sm va 12 sm

A) 4 B) 2 C) 3 D) -4 bo‘lgan uchburchakka aylana ichki chizilgan.
Bu aylanaga o‘tkazilgan urinma uchburchakning
292. Ildizlari x2 − 6x + 1 = 0 kvadrat tenglama ikkita katta tomonini kesib o‘tadi. Hosil bo‘lgan
ildizlaridan 2 marta katta bo‘lgan kvadrat uchburchakning perimetrini (sm) toping.
tenglama x2 − bx + c = 0 ko‘rinishda A) 16 B) 24 C) 28 D) 15
ifodalangan. bc ko‘paytmani toping.
A) -48 B) 60 C) 36 D) 24 303. Teng yonli trapetsiyaning diagonali 10 ga teng
va u asos bilan 60◦ li burchak tashkil etadi.
2 −4x+5 πx Trapetsiyaning o‘rta chizig‘ini toping.
293. 2x = 1 + sin2 tenglamani yeching. √
4 5 3
A) 5 B) 6 C) 4 D)
A) 2 B) 1 C) -1 D) ∅ 2
 Matematika (informatika bilan) 19
√ √ √
304. Trapetsiyaga aylana ichki chizilgan. Yon tomon 315. 3
0, 5 + 3 4 − 3 13, 5 ni hisoblang.
√ √ √
aylana markazidan qanday burchak ostida A) 0 B) 3 5 C) − 3 2 D) − 3 5
ko‘rinadi?
A) 90◦ B) 120◦ C) 10◦ D) 150◦
316. Ikki xonali son raqamlari kvadratlarining
305. To‘g‘ri burchakli trapetsiyaning bitta burchagi yig‘indisi 13 ga teng. Agar undan 9 ni ayirsak,
60◦ , katta asosi 12 sm ga teng. Agar shu son raqamlarining teskari tartibda yozilgani
trapetsiyaning kichik diagonali katta asosiga kelib chiqsa, ikki xonali sonning raqamlari
teng bo‘lsa, diagonallar o‘rtalarini yig‘indisini toping.
tutashtiruvchi kesma uzunligini (sm) toping. A) 5 B) 6 C) 7 D) 8
A) 3 B) 4 C) 5 D) 8
317. M nuqta ABC uchburchakning og‘irlik markazi.
306. O‘zaro tashqi urinuvchi 3 ta aylana radiuslari 1,
Shu uchburchak tekisligidan 7 sm uzoqlikda O
2 va 3 ga teng. Bu aylanalarning urinish
nuqta olingan. OA + OB + OC vektor bilan
nuqtalari orqali o‘tuvchi aylananing radiusini
OM vektor uzunliklari nisbatini toping.
toping.
A) 3 B) 2 C) 1 D) 4
A) 1 B) 1/2 C) 1/3 D) 1,2
(
xx−2y = 36, 318. ~a(3; 1; 2) vektorga perpendikular hamda
307. sistemaning butun
4 (x − 2y) + log6 x = 9 (4; 6; − 6) nuqtadan o‘tuvchi tekislikning
yechimlari yig‘indisini toping. koordinata o‘qlarida ajratgan kesmalar
A) 8 B) 7 C) 6 D) 5 uzunliklari yig‘indisini toping.
A) 11 B) 22 C) 10 D) 12
√ √3
x 1
308. 3
0, 5 +
4 = 13 tenglamani yechimlari
2
yig‘indisini toping. 319. ~a(3; 4) vektorga perpendikular bo‘lgan birlik
A) 3 B) 3,5 C) 2,5 D) 4 vektorni toping.
! !
4 3 4 3
309. Arifmetik progressiyada a4 + a7 = 10 bo‘lsa, A) ; − va − ;
5 5 5 5
a2 + a9 ni toping. ! !
A) 10 B) 8 C) 11 D) 9 3 4 3 4
B) ; − va − ;
5 5 5 5
310. O‘suvchi geometrik progressiyada a3 · a10 = 16 ! !
4 3 4 3
bo‘lsa, a1 · a12 ni toping. C) ; va − ; −
5 5 5 5
A) 16 B) 14 C) 8 D) 24 ! !
3 4 3 4
D) ; va − ; −
311. Dastlabki o‘nta hadining yig‘indisi 55 ga teng 5 5 5 5
bo‘lgan arifmetik progressiyaning o‘ninchi hadi
19 ga teng bo‘lsa, uning ayirmasini toping.
A) 3 B) 2 C) -3 D) -2 320. ~a va ~b vektorlar ~c vektorga perpendikular va
~a ~b = 120◦ . Agar |~a| = |~b| = |~c| = 1 bo‘lsa,
d
312. Agar arifmetik progressiyada s2n = 2013,
S3n = 2001 bo‘lsa, Sn ni toping. |~a + ~b − ~c| ni toping.
√ √
A) 1344 B) 1350 C) 1354 D) 1346 3 √ 3
A) 1 B) C) 2 D)
2 3
313. Dastlabki n ta hadining yig‘indisi
Sn = 2n2 + 3n rekurent formula bilan berilgan
ketma-ketlikning o‘ninchi hadini toping. 321. ABC uchburchak uchlaridan α-tekislikkacha
1
A) 41 B) 39 C) 27 D) 42 bo‘lgan masofalar mos ravishda 3,75; 9 va 2 ga
4
√ √ √ teng bo‘lsa, uchburchakning og‘irlik markazidan
314. Agar a + b + c = 54 bo‘lsa, 2a + 2b + 2c α-tekislikkacha bo‘lgan masofani toping.
yig‘indining eng katta qiymatini toping.
A) 5 B) 4 C) 6 D) 4,75
A) 12 B) 18 C) 13,5 D) 27
 20 Matematika (informatika bilan)

322. To‘g‘ri burchakli trapetsiyaga radiusi 3 ga teng 329. Avtomashina Toshkentdan Samarqandga tomon
bo‘lgan aylana ichki chizilgan. Agar 2
yo‘lga chiqdi. Yo‘lning qismini rejadagi
trapetsiyaning katta asosi 7 ga teng bo‘lsa, 5
aylana markazidan trapetsiya uchlarigacha tezlikda o‘tgach, tezligini 20% ga oshirdi va
bo‘lgan masofalarning eng kattasini toping. Samarqandga mo‘ljaldagidan yarim soat oldin
25 21 9 keldi. Avtomashina ikki shahar orasidagi
A) 5 B) C) D) masofani necha soatda o‘tgan?
4 4 4
A) 4 B) 3 C) 4,5 D) 2,5
323. Muntazam sakkizburchakka tashqi chizilgan
q √
aylana radiusi 2 + 2 ga teng bo‘lsa, uning (2p − q)2 + 2q 2 − 3pq 4p2 − 3pq
tomonini toping. 330. : ifodani
2p−1 + q 2 2 + pq 2
√ soddalashtiring va uning son qiymatini toping.
A) 2
q √ p=0,78, q=7/25
B) 2 − 2 A) 1 B) 0,25 C) -1 D) 0,5
C) 1
q √ 1
2+ 2 331. f (x) = + 1, 5 funksiyaning eng
D) x2 + 2x + 1 + 2
2
katta qiymatini toping.
A) 2 B) 1,5 C) 2,5 D) 0,5
324. Muntazam o‘nikkiburchakka tashqi chizilgan
q √
aylana radiusi 2 + 3 ga teng bo‘lsa, uning
332. Hosila uchun qaysi munosabatlar o‘rinli?
tomonini toping. 0
q √ √ 1) (ln sin x)
!0
= ctgx;
A) 1 B) 2 + 3 C) 2 D) 3 1 1 1
2) cos = − 2 sin ;
x x x
325. To‘rtburchakning diagonallari 10 va 12 ga teng 1
bo‘lsa, uning tomonlari o‘rtasini tutashtiruvchi 3) (log4 5x)0 = ;
√
5x ln 4
to‘rtburchakning perimetrini toping.  √ 0 2 x ln 2
A) 22 B) 11 C) 20 D) 18 4) 2 x = √
2 x
A) 1, 4 B) 1, 2 C) 3, 4 D) 1, 3
326. Silindrga muntazam uchburchakli prizma ichki
chizilgan, prizmaga esa silindr ichki chizilgan
bo‘lsa, katta silindr hajmi kichik silindr 333. Muntazam o‘nburchakning har bir ichki
hajmidan necha marta katta bo‘ladi? burchagi necha gradusga teng?
A) 4 B) 3 C) 6 D) 2 A) 146◦ B) 150◦ C) 135◦ D) 144◦

327. Uchta butun son tashkil etgan arifmetik 334. Muntazam o‘nikkiburchakning bitta ichki
progressiyada birinchi hadi 1 ga teng. Agar burchagini hisoblang.
ikkinchi hadga 3 qo‘shilsa, uchinchisi kvadratga A) 135◦ B) 150◦ C) 140◦ D) 145◦
ko‘tarilsa, geometrik progressiya hosil bo‘ladi.
Uchinchi sonni toping.
335. To‘g‘ri burchakli trapetsiyaning diagonali uning
A) 8 B) 7 C) 9 D) 6 yon tomoniga teng. Agar bu trapetsiyaning
balandligi 2 ga, yon tomoni esa 4 ga teng bo‘lsa,
4 uning o‘rta chizig‘i uzunligini toping.
328. Yig‘indisi ga, hadlar kvadratlarining yig‘indisi √ √ √ √
3 A) 5 3 B) 3 2 C) 3 3 D) 6 2
16
ga teng bo‘lgan cheksiz kamayuvchi
27
geometrik progressiya hadlari kublarining 336. x2 + y 2 + 8x − 2y − 8 = 0 aylana va x + y = 4
yig‘indisini toping. to‘g‘ri chiziqning kesishish nuqtalarini toping.
8 64 64 56 A) (0; 4), (−1; 5) B) (3; 2), (5; −1)
A) B) C) D)
27 81 189 189 C) (2; 1), (−2; 1) D) (4; 9), (−5; 1)
 Matematika (informatika bilan) 21

337. Doiraga tashqi chizilgan teng yonli 347. ABC uchurchakda A uchidan tushirilgan
2
trapetsiyaning yuzi 8 sm ga teng. Agar bissektrisa BC tomonni x va 6 ga teng
trapetsiyaning asosidagi burchak 30◦ li bo‘lsa, kesmalarga ajratadi. AB=6, AC = 2x + 1
uning yon tomonini (sm) aniqlang. bo‘lsa, x ni toping.
A) 4 B) 8 C) 12 D) 16 A) 4 B) 3 C) 2 D) 5

338. Shar sirtining unga ichki chizilgan kub sirtiga 348. Talaba besh yilda 31 ta imtihon topshirdi. U
nisbatini toping. har keyingi yilda oldingi yildagiga qaraganda
3π π π π ko‘p imtihon topshirgan. Beshinchi kursda
A) B) C) D) birinchi kursdagidan 3 marta ko‘p imtihon
2 2 4 6
topshirgan bo‘lsa, to‘rtinchi kursda nechta
m imtihon topshirgan?
339. Natural m va n sonlar uchun + n = 8 bo‘lsa, A) 8 B) 7 C) 6 D) 9
4
m qabul qilishi mumkin bo‘lgan qiymatlar
349. ABCD qavariq to‘rtburchakda AB = 9,
ichida eng kattasini toping.
CD = 12. AC va BD diagonallar E nuqtada
A) 28 B) 20 C) 24 D) 16
kesishadi. Agar AC = 14 hamda AED va BEC
 !−0,5 1 uchburchaklar yuzalari teng bo‘lsa, AE ni
2
3 1 π toping.
340.  · 3 2 log3 6 + 1 · sin ni hisoblang.
2 3 9 21 17
A) 6 B) C) D)
A) 1,5 B) 3/4 C) -1,5 D) -0,75 2 4 3

10
2 1 8 1 5 3 2 1 350. = 5 tenglamaning ildizlari
341. (2+ − )·6+( + − )·21+( − + )·14 ni x+2
3 2 21 3 7 14 7 2 3+
hisoblang. x − 11
2+
2
A) 19 B) 20 C) 18 D) 15 yig‘indisini toping.
2 A) 2 B) 3 C) 1 D) 4
342. 1 − ifoda x ning nechta qiymatida
4 12
5− 351. = 3 tenglamaning ildizlari
6 x+7
5− 3+
x x+3
ma’noga ega emas? 8+
5
A) 3 B) 4 C) 1 D) 2 yig‘indisini toping.
A) −3 B) 7 C) 2 D) 4
sin1◦ · sin2◦ · . . . · sin45◦
343. ni hisoblang.
cos46◦ · cos47◦ · . . . · cos89◦ 352. Protsessorlardan ma’lumotlarni baytlarda olib,
√ √
2 3 1 qurilmalarga bitlarda uzatadigan port turini
A) B) 1 C) D) aniqlang.
2 2 2
A) parallel B) ketma-ket C) slot
2−3lnx 2+3lnx D) shina
344. 2 +2 = 8 tenglamani yeching.
A) 1 B) 2 C) 0 D) e
353. Yunonlar foydalangan hisoblash vositasi nomini
aniqlang.
3x + 9x + 18x 24
345. Agar x = bo‘lsa, x ni toping. A) Abak B) Serobyan C) Suan-pan
2 + 6x + 12x 81
D) Cho‘t
A) -3 B) -5 C) -2 D) -4
354. Dastur asosida boshqariladigan birinchi
346. To‘g‘ri burchakli trapetsiyaga radiusi 3 ga teng hisoblash mashinasini kim va qachon ixtiro
aylana ichki chizilgan. Aylana markazidan qilgan?
trapetsiyaning to‘g‘ri burchagigacha bo‘lgan
A) 1930 yil, V.Bush B) 1941 yil, K.Suze
masofani toping.
√ √ √ C) 1944 yil, G.Eyken D) 1907 yil, Li de Fores
A) 3 2 B) 3 C) 3 3 D) 3,5
 22 Matematika (informatika bilan)

355. “Mantiq insonga shunday bir qoida beradiki, bu 365. Tashkil etish texnologiyasiga ko‘ra web-sahifalar
qoida yordamida xulosa chiqarishda xatolardan necha va qanday turga bo‘linadi?
saqlanadi”. Ushbu fikr kimga tegishli? A) 2 turga: statik, dinamik
A) Abu Nasr Farobiy B) Alisher Navoiy
B) 3 turga: statik, dinamik, interaktiv
C) Kamoliddin Behzod D) Abu Ali Ibn Sino
C) 4 turga: statik, dinamik, interaktiv, input
type
356. Kompyuter uchun yangi dasturlar tayyorlash va D) 2 turga: input type va interaktiv
tahrirlashni yengillashtiruvchi dasturlar qanday
nomlanadi?
A) Sistema dasturlari B) Amaliy dasturlar 366. Random (x) funksiyasining vazifasini aniqlang.
C) Uskunaviy dasturlar D) Utilitalar
A) Parametrli takrorlash funksiyasi
357. Tasvirli fayllarning kengaytmasi keltirilgan B) [0, x) oraliqdagi tasodifiy sonni
qatorni aniqlang. aniqlash funksiyasi
A) .bmp, .gif B) .com, .exe C) .bas, .pas C) [0, 1) oraliqdagi tasodifiy sonni aniqlash
funksiyasi
D) .xls, .doc
D) Tasodifiy harflar generatori
358. MS Excelning A5:C12 katakchalar blokida
nechta katakcha bor?
A) 22 ta B) 18 ta C) 21 ta D) 24 ta 367. Ma’lumotlar ombori undagi axborot shakliga
ko‘ra qanday turlarga ajratiladi?
359. MS Excel 2003 da berilgan shartni A) hujjatli va faktografik
qanoatlantiruvchi satrlarni ajratib olish amali B) relyatsion va to‘rli C) matnli va grafik
qanday ataladi? D) raqamli va analog
A) filtrlash B) tartiblash C) avtofiltr
D) hisobga olish
368. MS Word 2003 dasturida uskunalar panelini
360. Sakkizlik sanoq sistemasidan ikkilik sanoq sozlash bo‘limi qaysi menyuda joylashgan?
sistemasiga o‘tkazishni bajaring: 5678 → x2 A) Файл(Fayl) B) Правка(Tahrir)
A) 101101012 B) 1011101112 C) 11111012 C) Вид(Ko‘rinish) D) Формат(Format)
D) 111011102

361. Kodlashning Morze usuli qanday usulga misol 369. Kompyuter ekranida aks etgan holatni rasmga
bo‘ladi? olish uchun qaysi klavishlardan foydalaniladi?
A) Notekis kodlash usulu A) Shift + Delete B) Ctrl + Alt + Delete
C) Print Screen / Sys Rq D) Ctrl + F12
B) Tekis kodlash usuli
C) Tartib raqamlari yordamida kodlash usuli
370. Agar kitobdagi axborot hajmi 7 Kbayt bo‘lsa,
D) Alifboni surish usuli
uni nechta “Axborot” so‘zi bilan almashtirish
mumkin?
362. Hisoblang va o‘tkazishni bajaring: A) 1024 B) 2048 C) 2000 D) 14336
2710 + 1112 → x2
A) 1000102 B) 1000112 C) 1001102
D) 1001112 371. Tashkil etuvchi barcha sodda mulohazalar rost
bo‘lganda quyidagilardan qaysi birining natijasi
363. 3 terabayt axborotni baytlarda ifodalang. rost bo‘ladi?
A) 340 bayt B) 3 · 240 bayt C) 640 bayt A) (A ∨ ¬B) ∧ ¬ (C ∨ D)
D) 240 bayt B) A ∧ ¬B ∨ C ∧ ¬D
364. 63 kilobayt axborotda nechta belgi bor? C) A ∨ B ∧ ¬C ∨ ¬D
A) 516096 ta B) 516098 ta C) 64512 ta D) ¬A ∨ (B ∨ C) ∧ ¬D
D) 64500 ta
 Matematika (informatika bilan) 23

372. Agar A=rost, B=yolg‘on, C=5, D=6 bo‘lsa, 380. Paskalda quyidagi ifoda a=5, b=15, c=2 bo‘lsa
quyidagilardan qaysi birining natijasi yolg‘on qanday natija beradi?
bo‘ladi? (a+b div c ∗ 4) mod 5 div 3
A) A ∨ B ∧ (C = D) A) 4 B) 1 C) 3 D) 2
B) A ∧ B ∨ (C > D)
C) ¬A ∨ B ∨ (C < D) 381. Dastur lavhasida X qaysi qiymatni qabul qiladi?
D) A ∧ ¬B ∨ (C < D) VAR i,j,X: intejer;
BEGIN FOR i:=1 TO 2 DO;
FOR j:=2 DOWNTO 1 DO X:=i+j; END.
373. Nomi S harfidan boshlanuvchi va faqat to‘rtta A) 3 B) 7 C) 4 D) 10
belgidan iborat ixtiyoriy kengaytmali fayllar
qanday belgilanadi?
382. MS Excel 2003 da A1 dan A10 gacha bo‘lgan
A) S∗ ∗ ∗.∗ B) S???.? C) S???.∗ D) S∗.∗
katakchalardagi qiymatlarni yig‘indisini
hisoblash formulasini aniqlang.
374. Faylning xususiy nomi nechta belgidan iborat A) СУММ(А1:А10) B) =summa(A1:A10)
bo‘lishi mumkin? C) A1+A10 D) =СУММ(А1:А10)
A) 1 tadan 8 tagacha
B) 1 tadan 64 tagacha 383. Amal va o‘tkazish natijasini aniqlang.
C) operatsion sistema va dasturga bog‘liq 638 + 218 → x2
D) 1 tadan 255 tagacha A) 10001002 B) 10101002 C) 10110002
D) 10110012

375. Qaysi javobda faqat arxivlangan fayllar

384. MS Word dasturi kompyuterda ishlayotgan
kengaytmasi berilgan?
bo‘lsa, u holda . . .
A) .dll, .zip B) .xls, .rar C) .zip, .rar
D) .exe, .com A) MS Word dasturi boshqa kompyuterdan
ko‘chirib o‘tkazilgan
376. Paskal dasturi lavhasidagi write protsedurasi B) MS Office paketi installyatsiya
necha marta bajariladi? qilingan
for i:=1 to 3 do for j:=0 to 3 do write (i+j); C) MS Office paketi deinstallyatsiya qilingan
A) 1 marta B) 3 marta C) 12 marta D) MS Office paketi ko‘chirib o‘tkazilgan
D) 9 marta

377. Paskal dasturi lavhasidagi S ning qiymati 385. MS Excel 2003 da katakchadagi
nimaga teng? “=СУММ(А1:А10;B1;C5)” formula nechta
begin S:=0; for I:=1 to 3 do S:=S+2∗i; katakchadagi sonni qo‘shadi?
writeln(S); end. A) 12 ta B) 15 ta C) 10 ta D) 20 ta
A) 24 B) 48 C) 96 D) 12
386. MS Excel 2003 da AA21 katakchadagi
378. Paskal dasturi lavhasidagi natijani aniqlang. “=КОРЕНЬ(СТЕПЕНЬ(625;2))” formula
begin X:=2; p:=1; 1:P:=P∗(2∗x-2); X:=X+3; if natijasini aniqlang.
X<=6 then goto 1; writeln(P); end. A) 625 B) 390625 C) 25 D) 5
A) 16 B) 20 C) 2 D) 24

387. Windows yo‘lboshlovchisini ishga tushirish

379. Paskal dasturi lavhasidagi hisob natijasini
aniqlang. uchun Пуск menyusidagi qaysi bo‘lim
begin a:=12; b:=14; c:=10; if(a>b) or (b>c) tanlanadi?
then y:=a+b-c else y:=a-b+c; writeln(y); end. A) Программы B) Документы C) Найти
A) 8 B) 6 C) 16 D) 14 D) Настройка
 24 Matematika (informatika bilan)
1
√ √ 1
388. Elektron pochta manziliga oid mulohazalardan 395. 8 3 log2 ( 3 cos x)
+ 6 = 27 3 +log27 sin x tenglamani
xatosini aniqlang. yeching.
A) E-mail manzilida @ belgisi ishtirok 3π
etmaydi A) + 2πn, n ∈ Z
4
B) E-mail manzilida probel (bo‘shliq) belgisi 7π
ishtirok etmaydi B) + 2πn, n ∈ Z
12
C) E-mail manzilida raqamlar ishtirok etadi
5π
D) E-mail manzilida lotin harflari ishtirok etadi C) + 2πn, n ∈ Z
12
5π
389. Nuqtalar o‘rniga kerakli iborani tanlang: D) + πn, n ∈ Z
12
Foydalanuvchi elektron pochta qutisini
Internetga ulangan . . . ocha oladi.
A) faqat o‘z kompyuterida 396. (x + 2)log2 (1+x
2)
< (x + 2)log2 (2x+9) tengsizlik x
B) faqat shu pochta ochilgan kompyuterda ning qanday qiymatlarida o‘rinli?
C) ixtiyoriy kompyuterda A) (−4, 5; ∞) B) (−2; 4) C) (4; ∞)
D) faqat server kompyuterda D) (−1; 4)

2 −5x+5)
390. Axborot uzatish jarayonida quyidagi 397. (x − 2)log1/2 (x < (x − 2)log1/2 (x−3)
qismlardan qaysi biri bo‘lishi shart? tengsizlik x ning qanday qiymatlarida o‘rinli?
1) Axborot qabul qiluvchi 2) Axborot manbai A) (−∞;√2) ∪ (4; ∞) B) (2; 4)
3) Axborot uzatish vositasi 5+ 5
A) 1, 2, 3 B) 1 C) 1, 2 D) 1, 3 C) ( ; 4) D) (4; ∞)
2

391. Biror Web-saytni ochish uchun quyidagilardan

qaysi birini qo‘llash mumkin? 398. Aylananing ikkita kesishuvchi vatarlaridan
1) Web-brauzerning manzil satrida web-sayt birining uzunligi 36 sm, ikkinchisi kesishish
nomi kiritiladi va Enter klavishi bosiladi. 2) nuqtasida 18 sm va 16 sm li kesmalarga ajraladi.
Biror web-saytdan kerakli web-saytga o‘tish Birinchi vatarning kesmalarini aniqlang.
belgisi tanlanadi. 3) MS Word dasturi matnida A) 12 va 24 B) 16 va 20 C) 17 va 19
yozilgan kerakli web-sayt manzili tanlanadi. D) 22 va 14
A) 1 B) 1, 2 C) 1, 3 D) 1, 2, 3
399. To‘g‘ri burchakli uchburchak to‘g‘ri
392. Uchlari A(1; 1), B(−2; 3) va C(−1; −2) burchagining bissektrisasi gipotenuzani 1:5
nuqtalarda bo‘lgan uchburchakning A va B nisbatda bo‘ladi. Uchburchakning balandligi
burchaklarini toping. gipotenuzani qanday nisbatda bo‘ladi?
A) 60◦ ; 30◦ B) 90◦ ; 45◦ C) 30◦ ; 90◦ A) 25:1 B) 1:25 C) 1:5 D) 5:1
D) 45◦ ; 90◦
s
√ √ √
r
393. Uchburchakning tomonlari 6; 7 va 8 m. 6 m li
q
400. 1 + 8 − 3 2 − 4 + 5 2 + 6 − 4 2 ni
tomonning 8 m li tomondagi proyeksiyasi necha
metr? hisoblang.
√ √ √
3 3 1 13 A) 2 − √ 1 B) 2 − 2 C) 2 + 2
A) 4 B) 3 C) 3 D) 2
16 16 16 16 D) 3 − 2

394. Uchlari A(−2; 3), B(−1; −2) va C(1; 1) √

401. cx2 + 20x + c + 2 > 0 tengsizlik yechimga ega
nuqtalarda bo‘lgan uchburchakning A va C
bo‘lmaydigan c ning butun qiymatlari orasidan
burchaklarini toping.
eng kattasini toping.
A) 45◦ ; 90◦ B) 90◦ ; 45◦ C) 30◦ ; 90◦
A) −1 B) −2 C) −6 D) −4
D) 45◦ ; 45◦
 Matematika (informatika bilan) 25
√
48 409. To‘g‘ri burchakli uchburchakning
√ gipotenuzasi
402. Sharning radiusi √ ga teng. Radiusning
π 30 ga, katetlaridan biri 12 5 ga teng. Ikkinchi
◦
oxiridan u bilan 60 li burchak tashkil etadigan katetning gipotenuzadagi proyeksiyasini toping.
kesuvchi tekislik o‘tkazilgan. Kesimning yuzini A) 4 B) 5 C) 6 D) 7
toping.
 2
A) 8 B) 12 C) 16 D) 14 
+ 5x + 6
2 +5x+2

x

410. y = arccos 52x + lg
x+2
2 2 1 funksiyaning aniqlanish sohasini toping.
403. (13 + 7x + 3x2 )(x2 − ) log1−x2 (x2 + 2 ) ≥ 0
π x 1
tengsizlikni qanoatlantiruvchi sonlar nechta? A) (−3; ∞) B) [−2; − ] C) [−2; ∞)
2
A) 4 B) 2 C) 3 D) 1 1
D) (−2; − ]
2
√
log7 log7 ( 2 + 1) √
√ √
411. sin2x − cos2x = 2 + cos2 4x tenglamani

404. 2+1 log7 ( 2 + 1) ni soddalashtiring.
eching.
√ √
A) log7 ( 2 + 1) B) log7 ( 2 − 1) π
1 √ A) + 2πn, n ∈ Z
C) √ D) 2 + 1 4
2−1 π
B) − + πn, n ∈ Z
4
x−3
405. y = arcsin − lg(4 − x) funksiyaning 3π
2 C) + 2πn, n ∈ Z
aniqlanish sohasini toping. 4
A) [1; 4] B) [1; 5] C) (1; 4) D) [1; 4) 3π
D) + πn, n ∈ Z
8
√
π π 2
 
406. tg − sin2x = −1 tenglamani yeching. 2
2 4 
3
−ln48 − 12 7π 12
412. (3 · 128 · e
7 ) − (tg )−1 + √ ni
3π 6 6
A) ± + 2πn, n ∈ Z hisoblang.
4
A) 1 B) 2 C) 3 D) 5
3π
B) ± + πn, n ∈ Z
8 s
√
r q
π 413. 21,5 53 21,5 53 . . . ifodaning qiymatini
C) (−1)n+1 + πn, n ∈ Z
4 toping.
π πn A) 17 B) 10 C) 14 D) 12
D) (−1)n+1 + ,n ∈ Z
8 2
414. k parametrning qanday qiymatlarida
kx2 + 2(k + 3)x + k + 2 = 0 tenglamaning
407. To‘rtta nuqta aylanani yoylarga ajratadi. ildizlari nomanfiy bo‘ladi?
Yoylarning uzunliklari maxraji 2 ga teng
A) [−2, 25; −2] B) [−2, 1; −1] C) [1; 2]
geometrik progressiyani tashkil etadi. Shu
D) (−∞; −2]
to‘rtta nuqtani ketma-ket
tutashtirish natijasida hosil bo‘lgan 415. Arifmetik progressiyaning dastlabki to‘rtta hadi
to‘rtburchakning diagonallari orasidagi eng yig‘indisi 124 ga, oxirgi to‘rttasiniki 156 ga
katta burchakni toping. teng. Progressiyaning hadlari yig‘indisi 490 ga
A) 100◦ B) 120◦ C) 150◦ D) 130◦ teng. Progressiyaning nechta hadi bor?
A) 12 B) 14 C) 11 D) 10
408. cos4 (x + 1) · log4 (3 − 2x − x2 ) ≥ 1 tengsizlikni
yeching. 416. |1 − |1 − x|| = 0, 5 tenglamaning ildizlari
A) [−1; 0) B) [−2; −1] C) {−2; −1} yig‘indisini toping.
D) {−1} A) 5 B) 4 C) 3 D) 1
 26 Matematika (informatika bilan)

~ = |AC|
417. Agar |AB| ~ = |AB
~ + AC|
~ = 4 bo‘lsa, 427. Uchburchakli piramidaning asosi tomonlari 4; 4
~ ning qiymatini toping.
|CB| va 2 ga teng bo‘lgan uchburchakdan iborat.
√ √ √ Piramidaning barcha yon yoqlari asos tekisligi
A) 4 2 B) 4 3 C) 2 3 D) 4, 5
bilan 60◦ li burchak tashki etadi. Piramidaning
418. logx2 (3 − 2x) > 1 tengsizlikning butun hajmini toping.
√ √
yechimiga qarama-qarshi sonni toping. A) 3 B) 2 3 C) 3 D) 6
1
A) −4 B) C) 2 D) −2
2 428. Kubga ichki chizilgan silindrning hajmi 16π ga
teng. Shu kubga tashqi chizilgan sferaning
419. Kesik konusning yon sirti 10π ga, to‘la sirti 18π
yuzini toping.
ga teng. Konusning to‘la sirti unga ichki
chizilgan shar sirtidan qanchaga ortiq? A) 64π B) 32π C) 48π D) 24π
A) 14π B) 16π C) 15π D) 10π
32
π 429. Kubga tashqi chizilgan sharning hajmi π ga
420. sin = 1 tenglamaning [0,05; 0,1] oraliqda 3
x teng. Kubning diagonaliga tegishli bo‘lmagan
nechta ildizi bor? uchlaridan diagonalgacha bo‘lgan masofani
A) 5 B) 6 C) 2 D) 3 toping.
√
421. Uchburchakli piramidaning yon yoqlari asos 4 2
A) √
tekisligi bilan 60◦ li burchak tashkil etadi. Agar 3
piramida asosining yuzi 40 ga teng bo‘lsa, √
3 2
piramidaning to‘la sirtini toping. B)
4
A) 120 B) 80 C) 72 D) 128 √
4 2
C)
x z 9
422. Agar 3 ≤ x ≤ y ≤ z ≤ t ≤ 27 bo‘lsa, + √
y t 3 3
ifodaning eng kichik qiymatini toping. D)
2 9 3 1 8
A) B) C) D)
3 10 2 5
430. To‘g‘ri burchakli uchburchakning katetlari 3 va
x z 5 ga teng bo‘lib, bu uchburchakka u bilan
423. Agar 25 ≤ x ≤ y ≤ z ≤ t ≤ 64 bo‘lsa, +
y t umumiy to‘g‘ri burchakka ega bo‘lgan kvadrat
ifodaning eng kichik qiymatini toping. ichki chizilgan. Kvadratning yuzini toping.
25 7 15 225 225
A) 1, 25 B) 1, 6 C) D) 0, 2 A) B) C) D)
32 8 8 64 128
424. x : 2, 06(6) = 0, (27) : 0, 4(09) tenglamani
yeching. 431. k, m va n ning qanday qiymatida
A) 1, 3 B) 1, 37 C) 1, (37) D) 1, 3(7) cos2π k m n
2 = + 2 +
(x + 1) (x + 2) x + 1 (x + 1) x+2
425. 2; b2 va b3 sonlari o‘suvchi geometrik tenglik ayniyat bo‘ladi?
progressiyaning dastlabki uchta hadidan iborat. 1
A) −1; 1; 1 B) 0; 1; 2 C) 1; − 1;
Agar bu progressiyaning ikkinchi hadiga 25 2
qo‘shilsa, hosil bo‘lgan sonlar arifmetik 1
D) 2; − 2;
progressiyaning dastlabki uchta hadini tashkil 2
etadi. b2 toping.
A) 8 B) 12 C) 6 D) 10 x
432. y = 2cos2 − tgx · ctgx funksiyaning qiymatlari
2
426. Trapetsiya asoslarining uzunliklari 28 va 10 ga to‘plamini toping.
teng. Trapetsiya diagonallari o‘rtalarini
A) [1; 3] B) [0; 3] C) (1; 2) ∪ (2; 3)
tutashtiruvchi kesmaning uzunligini aniqlang.
D) (−1; 0) ∪ (0; 1)
A) 8 B) 10 C) 7 D) 9
 Matematika (informatika bilan) 27
√ √
433. (x3 + 4x2 + 4x) · 25 − x2 ≥ 0 tengsizlikning 2x + 3
442. h(x) = |x|, g(x) = , f (x) = x + 1
butun sonlardan iborat yechimlari yig‘indisini 3x − 1
toping. bo‘lsa, quyidagilardan qaysi biri to‘g‘ri?
q
A) 6 B) 10 C) 8 D) 12 A) h(f (x)) = |x + 1|
√
y 2 − 0, 25y + 1 15 5x + 4
434. 0, 25 < < tengsizlikning tub B) f (g(x)) = √
1+y 2
16 3x − 1
sonlardan iborat yechimlari nechta? 2 |x| + 3
C) g(h(x)) =
A) 5 B) 2 C) 3 D) 4 3 |x| + 1
q
435. Sferaga balandligi asosining diametriga teng D) f (h(x)) = |x| + 1
bo‘lgan konus ichki chizilgan. Agar sfera
sirtining yuzi 125 ga teng bo‘lsa, konus
asosining yuzini toping.
A) 10 B) 5π C) 15 D) 20

436. Agar tgα = −2 bo‘lsa, 1 + 5 sin 2α − 3 cos−1 2α

ning qiymatini toping.
A) 2 B) 1 C) −1, 2 D) −2

437. y = −3x2 + 2x + |x + 2| funksiyaning eng katta

qiymatini toping.
11 3 4 443. O‘suvchi geometrik progressiyaning dastlabki
A) 3 B) 10 C) 2 D) 2
12 4 5 uchta hadi yig‘indisi 35 ga teng. Agar ulardan
mos ravishda 2; 2 va 7 ni ayirsak, hosil bo‘lgan
438. Muntazam to‘rtburchakli
√ prizmaning hajmi sonlar arifmetik progressiyaning dastlabki uchta
1944 ga, yon sirti 432 2 ga teng. Prizma hadini tashkil qiladi. Shu arifmetik
asosining simmetriya markazidan ustki progressiyaning ikkinchi hadini toping.
asosining uchigacha bo‘lgan masofani toping. A) 10 B) 5 C) 8 D) 6
A) 12 B) 9 C) 15 D) 8

439. Parallelogrammning uchta ketma-ket

A(−3; − 2; 0), B(3; − 3; 1) va C(5; 0; 2)
~ va BD
uchlari berilgan. AC ~ vektorlar orasidagi
burchakni toping.
A) 60◦ B) 150◦ C) 135◦ D) 120◦

440. Asosining tomonlari 12; 9 va 15 hamda

asosidagi barcha ikki yoqli burchaklari 60◦ dan
iborat bo‘lgan uchburchakli piramidaning
hajmini toping.
√ √ √ √
A) 54 3 B) 162 3 C) 108 3 D) 27 3

441. To‘g‘ri burchakli uchburchakning gipotenuzasi

2
6 ga teng. Gipotenuza bilan o‘tkir
5
burchakning bissektrisasi 22, 5◦ li burchak
tashkil qiladi. Berilgan burchakli
uchburchakning yuzini toping.
A) 10, 24 B) 102, 4 C) 20, 48 D) 9, 8