Hisoblang. A b c d e 2

1. 2146, 1991 va 1805 sonlarining har birini qanday natural songa bo'lganda, qoldiqlari bir xil chiqadi? A) 7 B) 13 C) 21 D) 31 E) 37
2. Hisoblang. A) 3 B) 1 C) D) 2 E) 2
3. Ushbu ifoda n ning nechta butun qiymatida natural son bo'ladi?
A) 1 B) 3 C) 4 D) 2 E) hech bir qiymatida
4. Hisoblang. A) –2 B) 1– C) –1 D) 1– E) –1
5. Tenglamani yeching. (1,7:( x–3,75)): =
A) 5,2 B) C) 4 D) E) 4,5
6. x₁ va x₂ 3x²– 5x + 2 = 0 kvadrat tenglamaning ildizlari. Ildizlari va ga teng bo'lgan kvadrat tenglama tuzing.
A) 3x² –7x + 4 = 0 B) 7x² + 9x–2 = 0 C) 7x² + 9x + 2 = 0
D) 7x²– 9x + 2 = 0 E) 3x² + 7x– 4 = 0
7. k ning (k² –3k + 1)x = k– x–4 va (k + 1)x + 1 = k + x tenglamalardan hech bo'lmaganda birining cheksiz ko'p yechimga ega bo'ladigan nechta qiymati mavjud?
A) bunday qiymat yo'q B) 1 C) 2 D) 3 E) cheksiz ko'p
8. x^–4 + y^–4 = 162 va x^–3 + y^–3 = 0 shartlarini qanoatlantiradigan (x; y) nuqtalar orasidagi kesmaning uzunligini aniqlang.
A) B) C) D) E)
9. Ushbu c = + , d = + sonlar uchun qaysi munosabat o'rinli?
A) c < d B) c > d C) c + 1 = d D) c = d E) c² + 1 + = d²
10. Tengsizlikni yeching. ≥2
A) [ ; 2) B) [ ; 4) C) yechimi yo'q D) [–10; 10] E) (– ; 0)
11. Tengsizlikni qanoatlantiruvchi butun sonlar nechta? >x–1
A) 5 B) 3 C) 4 D) 2 E) 1
12. >2 –1 tengsizlikni yeching.
A) (1; 1,5) B) ( ; ) C) (0; ) D) (2; 5) E) ( ; )
13. 1, 8, 22, 43, … sonlar ketma – ketligi shunday xususiyatga egaki,ikkita qo'shni hadlar- ining ayirmasi 7, 14, 21, … arifmetik progressiyani tashkil etadi. Berilgan ketma – ketlikning nechanchi hadi 35351 ga teng bo'ladi?
A) 97 B) 99 C) 101 D) 103 E) 107
14. (03-7-5) 1*4+2*8+3*12+. . .+30*120 yig'indida har bir qo'shiluvchining ikkinchi ko'paytuvchisi bittadan kamaytirilsa bu yig'indi qanchaga kamayadi?
A) 60 B) 120 C) 210 D) 375 E) 465
15. Kamayuvchi geometrik progressiya tashkil etuvchi uchta sondan uchinchisi 18 ga teng. Bu son o'rniga 10 soni olinsa, uchta son arifmetik progressiya tashkil etadi. Birinchi sonni toping. A) 50 B)60 C) 40 D) 27 E) 36
16. Xaritada ikki shahar orasidagi masofa 4,5 sm ga teng. Xaritadagi masshtab 1 : 2000000 bo'lsa, shaharlar orasidagi haqiqiy masofa necha km bo'ladi?
A) 0,9 B) 9 C) 90 D) 900 E) 9000
17. Ikki shahardan bir vaqtning o'zida turli tezlik bilan ikkita avtomobil bir-biriga qarab yo'lga chiqdi. Avtomobillarning har biri uchrashish joyigacha bo'lgan masofaning yarmini bosib o'tgandan keyin, haydovchilar tezlikni 1,5 baravar oshirishdi, natijada avtomobillar belgilangan muddatdan 1 soat oldin uchrashishdi. Harakat boshlangandan necha soatdan keyin avtomobillar uchrashishdi?
A) 3 B) 4 C) 5 D) 6 E) aniqlab bo'lmaydi
18. Eritma tarkibida 60 g tuz bor. Unga 400 g toza suv qo'shilsa, tuzning konsentrasiyasi 1,5 marta kamaydi. Dastlabki eritma necha gramm bo'lgan?
A) 800 B) 840 C) 780 D) 900 E) 640
19. y = f(x) funksiyani aniqlanish sohasi [-1;2] dan iborat. y = f(1 + x) funksiyaning aniqlanish sohasini toping. A) [-2;-1] B) [-2;1] C) [-4;2] D) [-1;0] E) [0;3]
20. Agar log₇2 = a log₂10 = b bo'lsa, log₄39,2 ni a va b orqali toping.
A) + – B) + – C) – + D) – + E) – +
21. k ning qanday qiymatlarida (2x– k)*log₂x=0 tenglama bitta ildizga ega?
A) 0 < k ≤ 1 B) k > 2 C) k = 1 D) 1 ≤ k < 2 E) k ≤ 0; k = 2
22. Ushbu 7cos2x–6 = cos4x tenglamaning [0; 628] kesmaga tegishli ildizlari yig'indisini toping. A)200 B)199 C)20100 D)1990 E)19900
23. Tenglamani yeching. = sinx–cosx
A) +2n, n Z B) – + n, n Z C) +2n, n Z D) – +2n, n Z E) +n, n Z
24. cos2x + =0 tenglama [–; 4] oraliqda nechta ildizga ega? A) 9 B) 7 C) 10 D) 8 E) 5
25. y = log₃(1–2cosx) funksiyaning qiymatlar to'plamini toping.
A) (–∞; 1] B)(0; 1) C)(0; 3) D) (0; 1] E)[1; 3]
26. Agar f(x) = funksiya grafigi (2; 0) nuqtada absissa o'qiga urinib o'tsa, a + b nimaga teng? A) 0 B) 20 C) –21 D) 28 E) –56
27. A(1; 4) nuqtadan y = –2– funksiyaning grafigiga ikkita urinma o'tkazilgan. Urinish nuqtalari abssissalarining yig'indisini toping.
A) –1 B) 1 C) D) E) –
28. Integralni hisoblang.
A) B) C) D) E)
29. y = , y = x–6 va y = 0 chiziqlar bilan chegaralangan shaklning yuzini toping.
A) 18,5 B) 36 C) 4,5 D) 18 E) 13,5
30. arcsin +2arccosx = tenglama nechta ildizga ega?
A) 1 B) 2 C) yechimi yo'q D) 3 E) cheksiz ko'p yechimga ega
31. Ushbu y = ln²x – lnx funksiyaning OX o'qi bilan kesishish nuqtalaridan hamda funksiya grafigining eng quyi nuqtasini tutashtirishdan hosil bo'lgan uchburchakning yuzini hisoblang.
A) B) C) D) E)
32. Uchburchakning burchaklaridan biri 60⁰, unga tashqi chizilgan aylana radiusi ga, ichki chizilgan aylana radiusi ga teng. Uchburchakning yuzini toping.
A) 10 B) 5 C) 20 D) 8 E) 16
33. Doiraga ichki chizilgan muntazam uchburchakning yuzi unga ichki chizilgan kvadratning yuzidan 18,5 ga kam. Shu doiraga ichki chizilgan muntazam oltiburchakning yuzini toping.
A) 8 +15 B) 9 +6 C) 12 +13,5 D) 13 + 12,5 E) 24 + 27
34. Muntazam ABC uchburchak to'g'ri burchakli ABC₁ uchburchakka proyeksiyalanadi. Shu uchburchaklarning tekisliklari orasidagi burchakni toping.
A) 30⁰ B) 45⁰ C) 60⁰ D) arccos E) arccos
35. Radiusi ga teng yarim sharga kub ichki chizilgan bo'lib, uning to'rtta uchi yarim shar asosida, qolgan to'rttasi shar sirtida yotadi. Kubning hajmini toping.
A) 1 B) C) 2,25 D) 2 E) 1,5
36. R radiusli yarim sharga asosining markazi bilan ustma-ust tushadigan konus tashqi chizilgan. Konusning balandligi qanday bo'lganda, uning hajmi eng kichik bo'ladi?
A) R B) R C) R D) R E) R