1. O`zaro teng bo`lmagan x va y sonlari x

1. O`zaro teng bo`lmagan x va y sonlari x²+36y=y²+36x tenglikni qanoatlintirsa x+y ni toping
A)24 B)18 C)36 D)0
2. x²+4|x|-a+3=0 tenglama yagona yechimga ega bo`ladigan a ning barcha butun manfiy qiymatlari yig`indisini toping
A)Ø B)-2 C)-3 D)1
3. Arifmetik progressiyada a₁+a₂+a₃=0 va a₁²+a₂²+a₃²=98 bo’lsa shu o’suvchi arfimetrik progressiyada a₄ ni toping.
A)14 B)-14 C)-49 D)49
4.a va b sonlari 4va 7 sonlariga proporsional, a va c sonlari 5 va 8 sonlariga teskari proporsional. Bu uch sonning yig’indisi 81 ga teng b sonini toping.
_{A)24 B)42 C)15 D)9}
5. (x²+3x+2)(x²+3x+7)=24 tenglama nechta haqiqiy ildizga ega?
A)0 B)1 C)2 D)4
6. 3ab-a(10b-28)-b(a-10b)-35b ko’phadni ko’paytuvchilarga ajrating
A)(5a-4)(7b-2a) B) (7a-2)(4a-5b) C) (7b-2a)(4-5a) D (4a-5b)(7-2b)
7. qisqarmas kasirning surati maxrajidan 6 ga kam , kasirning suratiga 3 maxrajiga 17 qo’shilsa, uning qiymati 0.5 ga teng bo’ladi. Kasrning surati va maxraji yig’indisini toping.
A) 20 B) 32 C)28 D)40 E)55
8. 9*8²⁴*625¹⁷ ko’paytma necha xonali son?
A) 71 B)73 C) 72 D) 70
9. Natural a sonni natural b songa bo’lganda bo’linma c ga va qoldiq d gat eng bo’ldi. Agar bo’linuvchi va bo’luvchi 2 marta ortirilsa d qanday o’zgaradi?
A) o’zgarmaydi B)2 marta kamayadi C) bittaga ortadi D)2 marta ko’payadi
10. a⁴+4b⁴ ni ratsional ko’paytuvchilarga ajrating .
A) (a²-2ab+2b²)(a²+2ab+2b²) B) (a²-2ab²)² C) (a²+2b²)² D)(a²-2b²)(a²+2b²)
11. Ikki natural sonning yig’indisi 462 ga teng. Ulardan birining oxrigi raqami 0 bilan tugaydi . Agar bu 0 o’chirilsa 2-son hosil bo’ladi. Berilgan sonlardan kichigini toping.
A) 46 B) 44 C) 42 D) 38
12. Tenglamani yeching: 4.5-1.6(5x-3)=1.2(4x-1)-15.1
A) 20 B) 2 C) 0.2 D) T J Y
13. 123.2*10⁵ berilgan sonni standart shaklga keltiring.
A)1.232*10⁶ B) 12.32*10⁷ C) 1.232*10⁷ D) 0.1232*10⁷
14. 12^(n-3)*8⁽ⁿ⁺²⁾ ko’paytmaning natural bo’luvchilari soni 42 ga teng bo’lsa n=?
A) 4 B) 3 C) 5 D) 6
15. a va b 1 dan farqli o’zaro tub sonlar. Bu sonlarning EKUKi 200 ga teng. a+b=?
A) aniqlab bo’lmaydi B) 45 C) 54 D) 33 E) 102
16. Ikki natural sonni 5 ga bo’lganda mos ravishda 1 va 3 qoldiq qoladi bu sonlarni kvadratlarining yig’indisini 5 ga bo;lganda qoldiq nechiga teng bo’ladi
A) 4 B) 1 C) 0 D) 2
17. b²+ab-2a²-b+a ko’paytuvchilarga ajrating
A) (a-b)(2a-b) B) (a+b)(2a-b-1) C) (a-b)(2a-b-1) D) (b-2a)(a-b+1) E)(b-a)(2a+b-1)
18. Ushbu (k²-4k+2)x=k-x-3 yoki (k+2)x-1=k+x tenglamalardan biri cheksiz ko’p yechimga ega bo’ladigan k ning nechta qiymati bor
A) 0 B) 3 C) 2 D) 1 E)cheksiz ko’p
19. kx²+3kx+2k-1=0 tenglama yechimga ega bo’lmaydigan k ning butun qiymatlari o’rta arifmetigini toping
A) -3 B) -2 C) -1.5 D) 3 E)1.5
20. n²(n²-n-6)<0 tengsizlik o’rinli bo’ladigan n ning barcha natural qiymatkari yig’indisini toping.
A) 4 B) 2 C) 5 D) 3 E) 6
21. √0.25+2x-√1+8x+√2.25+18x=2 tenglamaning ildizlari quyidagi oraliqlardan qaysi biriga tegishli
A) [5;7) B) (2;4) C) (0;2] D) (-1;0) E) (7;8]
22. log₃(x+3)+5=x²-5x+11 tenglama nechta ildizga ega?
A) 1 B) 2 C) 3 D) 4 E) Ø
23. k ning qanday eng kichik butun qiymatida x²-2(k+3)x+20+k²=0 tenglama 2 ta turli xil haqiqiy ildizlarga ega bo’ladi
A) 3 B) 2 C) 1 D) -2 E) -1
24. 1/3 va 1/48 sonlari orasiga shunday 3 ta musbat sonni joylashtiringki natijada geometric progressiya hosil bo’lsin. Qo’yilgan 3 ta snning yig’indisi topilsin
A) 0.5 B) 7/12 C) 0.375 D)5/24 E) 7/24
25. O’zidan oldingi natural sonlar yig’indisining 1/12 qismiga teng bo’lgan natural sonni toping
A) 25 B) 14 C) 26 D) 32
26. n-3 ta n-5 ning ko’paytmasining n-5 ta n-5 yig’indisiga nisbatini toping
A)2(n-5)(n-4) B) (n-5)^n-3) C) (n-5)^(n-5) D) (n-3)^(n-3)
27. 2*4+3*5+4*6+…+21*23 yig’indida har bir qo’shiluvchining 2-ko’paytuvchisi bittadan kamaytirilsa bu yig’indi qanchaga kamayadi?
A) 230 B) 235 C) 225 D) 460 E) 130
28. 7 ga bo’lganda 4 qoldiq qoladigan dastlbki 32 ta son yigg’indisini toping
A) 3600 B) 3824 C) 3985 D) 3271 E) 3817
29. log₂5=a va log₃2=b bo’lsa log₁₈100 ni a va b orqali ifodalang
A) (2ab+2b)/(b+2) B) (2a+b)/(ab+2a) C) (2+2ab)/(b+1) D) (4ab+2b)/(2b+1)
E) (a+b)/(2ab-2)
30. log_ma=6 va log_na=9 bo’lsa log_mna=?
A) 5/18 B) 1/18 C) 3.6 D) 1.8 E) 1
31. Agar m ushbu log_5+2x(5x²+19x+19)=2 tenglama ildizlarining soni, x₀ esa shu tenglamaning musbat ildizi bo’lsa , (2m+4)/x₀ ning qiymati nimaga teng?
A) 1 B) 2 C) 1/3 D) 6/5 E)8/3
32. (1+2/3)(1+2/4)(1+2/5) … (1+2/98) ni hisoblang.
A) 825 B) 1 C) 625 D) 980
33. 120 soni 64 sonidan necha % ortiq?
A) 46.(6) B) 20 C) 87.5 D) 25 E) 47
34. Agar x²y=50, xy²=20 bo’lsa xy=?
A) 8 B) 10 C) 6 D) 12
35. 20%li tuzli suvga 300 l suv quyilganda undagi tuzning miqdori 12% bo’ldi. Dastlabki tuzli suv necha l bo’lgan
A) 450 B) 320 C) 360 D) 60 E) 500
36. 2²⁰+2¹⁹+2¹⁸+…+1 yig;indini hisoblang
A) 2²¹ B) 2²⁰ -1 C) 2²⁰-0.5 D) 2²¹-1 E) 2²²