Funksiyaning eng
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2015-yil math
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1-VARIANT 1.
2 3 sin 2 4 cos 3 x tg x x y funksiyaning eng kichik musbat davrini toping. A) 24 B) 24 C) 12 D) 12 60 dan bo’lgan qavariq ko’pburchakka tashqi chizilgan doiraning yuzi 12
aniqlansin. A) 6
B) 9 C) 12 D) 15
3.
x x x f 9 sin 8 sin
34 uchun boshlang’ich funksiyani toping. A) 17sinx+sin17x+C B) 17cosx-cos17x+C C) -17cosx-cos17x+C D) 17sinx-sin17x+C 4.
lg 4 10 tengsizlikni yeching. A) (0.1;10) B) ( 2 1 ;1) C)
10 ; 10 1 D) (1;10) 5. 4 2 2 3 arcsin x x y funksiyaning aniqlanish sohasiga tegishli butun sonlar nechta? A) 2 B) 3 C) 1 D) 0 6. Diagonallari o’zaro perpendikulyar bo’lgan teng yonli trapetsiyaning yuzasi 289 ga teng. Uning balandligini toping. A) 13 B) 19 C) 17 D) 15 7. Ifoda qiymatining oxirgi raqamini toping: ` 2014 2015 2013
3 2014
2
A) 5 B) 0 C) 3 D) 1 8. Agar A 2 1 5 ; 4 3 3 va B(-0.8;-1.4) nuqtalar berilgan bo’lsa, AB kesma o’rtasining koordinatasini toping. A) (-0.4;-0.7) B) (-1.475;2.05) C)
05 . 2 ; 40 11 2 D) 4 1 5 ; 8 3 3
9. Kollejda 4 ta guruhda 126 ta o’quvchi bor. Birinchi guruhda jami o’quvchilarning 14 3 qismi, ikkinchi guruhda
21 5 qismi, uchunchi guruhda 42 11 qismi, qolganlari to’rtinchi guruhda o’qiydi. Har bir guruhda qanchadan o’quvchi bor? A) 27; 30; 33; 36 B) 30; 27; 36; 33 C) 36; 33; 30; 27 D) 33; 30; 27; 36 10. Tengsizlikni yeching: 0 log 2 3 7 4 7 2 x x x
A) 3 ; 2 1 B) 2 1 3 ; 1
C) ; 2 1 D) 3 ; 2 1
11. x; y sonlar jufti 9 2 9 4 y x y x tenglamalar sistemasini qanoatlantirsa, x+y ning qiymatini toping. A) 29 B) 23 C) 7 D) 9 12. 1
6 3 5 2 log
2 log
4 4 4 4 x x x x x
tengsizlikning barcha butun yechimlari yig’indisining natural bo’luvchilari yig’indisi topilsin. A) 28 B) 32 C) 24 D) 21 13. 324; 255 va 71 sonlarining har birini qanday natural songa bo’lganda qoldiqlari bir xil bo’ladi? A) 27 B) 23 C) 29 D) 25 14. Quyidagilardan o’zaro tub sonlarni toping. 1) (169; 143); 2) (n; n+1), n N; 3) (n; n+2), n N; 4) (121; 144). A) 1,2 B) 1,3 C) 1,4 D) 2,4 15. Agar n 61 49 51 148
41 79 bo’lsa, 61 12 51 5 41 3 ni n orqali ifodalang. A) 3-n B) 6+n C) 3+n D) 6-n 16.
11 cos cos 11 funksiyaning hosilasini toping. A)
x x 6 cos 5 sin
22 B) x x 6 cos 5 cos
22
C) x x 6 sin 5 cos
22 D) x x 6 sin 5 sin
22
17. 2 9 4 log 2 4 1
x x tengsizlikni qanoatlantiruvchi barcha butun sonlar ko’paytmasini toping.
A) -4 B) 4 C) 0 D) -2 18. Agar arifmetik progresiyada
93 24 2 3 2 2 2 1 5 3 1 a a a a a a
bo’lsa, dastlabki o’nta hadning yig’indisini toping. A) 150 yoki 245 B) 153 yoki 317 C) 160 yoki 317 D) 155 yoki 245 19. Agar 0 2 2
m mx x tenglamaning ildizlari a va b bo’lsa,
2 2 ifodaning qiymatini toping. A) mc B) 0 C) m+c D)
2
20. Tenglamani yeching va ildizlari yig’indisini toping: 2 3 1 3 2 3 x x x x
A) 0 B) -3 C) -2 D) -4 21. Uchburchakning tomonlari 3 va 6 ga teng, 3 ga teng tomon qarshisidagi 30 bo’lsa, uning yuzini toping.
A) 2 5 , 4
B) 3 5 , 4
C) 3 4 D)
3 5
22. a ax x 15 5 2 tenglama a ning qanday qiymatlarida kamida 2 ta ildizga ega? A) )
4 , 2 [
B) 4 , 2 ; 1
C) ; 1 D)
; 0
23. Agar 6 ; 3 2 ; 27 a va 2 6 ; 6 ; 20 b
berilgan bo’lsa, 3 2 a b ni toping. A) 3 B) 1 C) 5 D) 2 24.
3 13 2 5 5 13 2
ni hisoblang. A) 3 2 B) 4 65 3 C) 1 D) 2 3 25. Agar 5 3
va 2 7 cos bo’lsa, tga ni toping. A)
2 sin
3 , 1 B) 4 3
C)
2 3 sin 3 4 D) 3 4
26.
5 8 3 5 8 2 ni hisoblang. A) 3 B) 1 C) 2 D) 0 27. Diaganallarining soni tomonlari sonidan 3,5 marta ko’p bo’lgan muntazam ko’pburchakning har bir uchidan bittadan olingan tashqi burchaklari va bitta ichki burchagining yig’indisini toping. A)
496 B) 504 C) 500 D) 480
28. 12 6 4 2 2 y y x x tenglama bilan berilgan aylana uzunligini toping. A)
10 B) 12 C) 11 D) 8
29. 2 0 sin
2 sin
cos
e x x x ni hisoblang. A) 1
e
B) 1
e
C) 1 2 1 e
D) 1 2 1 e
30. 1 1 1 1 1 1 1 1 1 5 8 4 2 x x x x x x
tenglamaning haqiqiy ildizlari yig’indisini toping. A) 0 B) 2 C) 1 D) -1 31. Axborot nazaryasi asoschisini ko’rsating. A) K.Shennon B) J. Fon Neyman C) N. Viner D) N. Virt 32. Hisoblang va javobni 10 lik sanoq sistemada ifodalang:
8 10 2 234
4 * 1001011
A) 455 B) 450 C) 456 D) 457 33. Matnlarni tahrirlashga mo’ljallangan dasturlar to’g’ri berilgan qatorni toping? A) Abode Photoshop, CorelDraw B) Prompt, Socrat C) BEM, 1C Buxgalteriya D) Microsoft Word, WordPad, Bloknot 34. MS Excel 2003 dasturida absolyut murojaat qo’llanilgan formulani ko’rsating. A) D16+$B$6 B) =D16$+B6$ C) =D16+$B$6 D) =D16+B6 35. Web-resurs manzili to’g’ri yozilgan ko’rinishini toping.
A) www://http.gov.uz B) http://www.gov.uz C) http@www.gov.uz D) isoft.gov@uz 36. Agar a=12 va b=10 bo’lsa, Paskal dasturlash tilida berilgan ushbu ifodaning qiymatini toping. Round(a/b)+a*(b mod 4) A) 24 B) 26 C) 27 D) 25
2-VARIANT 1. 2 2 2 22 22 22 22
x x x x tenglama haqiqiy ildizlari yig’indisini yoping. A) -24 B) -23 C) -22 D) -21 2. Oltin va durdan yasalgan bezakning og’irligi 3 misqol, narxi 24 dinor. Agar 1 misqol oltin 5 dinor, 1 misqol dur 15 dinor tursa, bezakda qancha misqol oltin bor? A) 2.1 B) 1.8 C) 1.2 D) 2.4 3.
0 sin
2 x x tenglamaning nechta yechimi bor? A) 3 B) 2 C) 4 D) 5 4.
x x y 5 cos 3 3 cos 5 funksiyaning hosilasini toping.
A) x x 4 sin sin 30 B)
x x 4 cos cos 30 C)
x x 4 cos sin 30 D)
x x 4 sin cos 30
5. 10 lg 2 1 10 ni hisoblang. A) 10 B) 0.01 C) 0.1 D) 1 6. Teng yonli trapetsiyaning diagonallari o’zaro perpendikular hamda yuzi 32 ga teng bo’lsa, uning diagonali uzunligini toping. A) 6 B) 2 4
7. To’g’ri burchakli uchburchakning bir burchagi 38 ga teng bo’lsa, to’g’ri burchak uchidan tushirilgan bissektrisa va mediana orasidagi burchakni toping. A)
14 B) 7 C) 10 D) 17
8. 3 3 76 76 8 x x tenglamani yeching. A) 2209 B) 0 C) 2304 D) 2401 9.
dx x x 1 2 aniqmas integralni toping. A)
C x 1 3 2 2 B) C x x 1 1 2 2 C) C x x 1 1 3 2 2 2 D)
x x 1 1 3 1 2 2 10.
16 2 3 log
x x tenglamani yeching. A) 1 B) -7 C) 1; -7 D)
11. 729
9 1 2 3 y x y x , tenglamalar sistemasini yeching. A)
2 ; 1 B) 5 . 1 ; 5 . 1
C)
1 ; 2 D)
2 ; 2 12. 2 arcsin 2 arcsin
x x temglamani yeching. A) -1;0;1 B) 0 C) 1 D) -1 13. Aylana tashqarisidagi nuqtadan aylanaga kesuvchi o’tkazilgan. Berilgan nuqtadan aylanani kesgan nuqtalarigacha bo’lgan masofalar mos ravishda 9 va 45 ga teng bo’lsa, shu nuqtadan aylanaga o’tkazilgan urinmaning urinish nuqtasigacha bo’lgan masofa uzunligini toping. A)
3 8 B) 3 12 C) 5 6 D) 5 9
14. 2 3 3 3 3 3 3 2 2 2 x x x x x x
tenglamaning ildizlari ko’paytmasini toping. A) -5 B) -15 C) -10 D) -12 15. Radiusi 1 ga teng aylanaga ichki chizilgan uchburchakning tomonlari a, b, c bo’lsa, shu tomonlari kvadratlari yig’indisining eng katta qiymatini toping. A) 16 B) 12 C) 9 D) 4 9
16. Radiuslari bir xil 3 sm ga teng bo’lgan ikki aylana rasmdagidek ABCD trapetsiyaga ichki chizilgan. Agar uning AD va BC asoslari mos ravishda 15 sm va 10 sm bo’lsa, uning yon tomonlari AB va CD lar uzunliklari yig’indisi topilsin.
A) 12 sm B) 19 am C) 13 sm D) 25 sm 17.
0 4 2 3 1 2 3 2 x x x x x tengsizlikning eng katta manfiy butun yechimining eng kichik musbat butun yechimiga nisbatini toping. A) 4
B) 5 1
C) 3 1 D) 2 1
18.
1 2 6 3 5 2 log 2 log 4 4 4 4 x x x x x
tengsizlikning eng kichik va eng katta butun yechimlari nisbatini toping. A)
6 1 B) 5 1 C) 4 1 D) 2 1
19. 2 3 2 3 2 3 2 3 2 ni hisoblang. A) 3 B) 1 C) 2 D) 0 20.
10 10 9 2 lg lg
x x tenglamaning ildizlari ko’paytmasini toping. A) 1 B) 2 C) 2 D) 0 21. 1440 sonining barcha natural bo’luvchilari yig’indisini toping. A) 6198 B) 2317 C) 5225 D) 4914 22. Kutubxonada jami 3275 ta kitob bor. Jami kitoblarning 40% i badiiy kitoblar, qolgan qismi darsliklar. Darsliklarning sonini toping. A) 1965 B) 1970 C) 1950 D) 1967 23.
ctg 2 ni hisoblang. A)
2 cos 1 B) 2 cos 1
C)
sin 1 D) 2 sin 1
24. P(x) ko’phadni 6 5 2 x x ga bolganda, qoldiq 3x-4 bo’ladi. P(x) ko’phadni x-3 ga bo’lgandagi qoldiqni toping. A) x+3 B) -4 C) 5 D) 4 25.
5 : 15 3 : 12 ni hisoblang. A) -5 B) 0.2 C) -0.2 D) 1 26. Ifoda qiymatining oxirgi raqamini toping:
2014 2015
5 2014
2013
A) 6 B) 2 C) 4 D) 8 27. Ischining maoshi 900000 so’m edi. Uning maoshi ketma-ket ikki marta bir xil foizga oshgandan so’ng 1190250 so’m bo’ldi. Maosh har safar necha foizga oshgan? A) 18 B) 15 C) 12 D) 14 28. Diagonallarining soni tomonlarining sonidan 1.5 marta ko’p bo’lgan qavariq muntazam ko’pburchakning barcha ichki burchaklari va bitta tashqi burchagi yig’indisini toping. A)
780
B) 720 C) 900 D) 480 29.
x x x f 7 sin 6 sin
26 uchun boshlang’ich funksiyani toping. A)
13 cos
cos 13 B) C x x 13 sin
sin 13
C) C x x 13 cos cos 13 D) C x x 13 sin
sin 13
30. P(-2;2) nuqtadan o’tuvchi va
4 ; 6 a vektorga perpendikulyar bo’lgan to’g’ri chiziq tenglamasini toping.
A) 3x+2y-2=0 B) 3x-2y-2=0 C) 3x-2y+2=0 D) 3x+2y+2=0 31. Agar tasvirdagi raqamlar oq, qorq, och kulrang yoki to’q kulrang bo’lsa, bitta nuqtaning rangini kodlash uchun necha bit kerak bo’ladi? A) 3 B) 4 C) 8 D) 2 32. Ikkilik sanoq sistemasida 10111 sonni 101 songa ko’paytiring: A) 1111011 B) 1010011 C) 1110111 D) 1110011 33. Bir sanoq sistemasida berilgan sonning boshqa sanoq sistemasidagi ko’rinishini aniqlang: 16
. A) 2 111101
1110001100
B)
2 110101
1000101101
C)
2 000100
1100011100
D)
2 110111
1001111011
34. MS Excel 2003 dasturida yozilgan quyidagi funksiyaning qiymatini toping.
" " ; 1 avgust СЦЕПИТЬ A) avgust B) 1 avgust C) 1-avgust D) 1 35. HTML teglari necha turga bo’linadi? A) 3-turga: ochiq teglar, yopiq teglar va ichma-ich teglar B) 2-turga: uzun teglar va qisqa teglar C) 2-turga: juft teglar va juft emas teglar D) 2-turga: sodda teglar va murakkab teglar 36. Paskal tilida quydagi dastur qismining bajarilishi natijasida ekranga chiqariladigan axborotlarni aniqlang: a:=’informatika’; n:=Length(a); write(n). A) n=11 B) informatika C) 13 D) 11
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