1

10. 𝑎 ning qanday qiymatida (𝑎; 𝑎 − 1)

𝑼𝒁𝑴𝑰𝑨𝒕𝒆𝒔𝒕 nuqtaning 3𝑥 + 𝑦 = 6𝑎 chiziqga nisbatan
1. Uchburchakning balantliklar kesishgan nuqtasi va simmetrik nuqtasi (𝑎2 + 1; 𝑎) bo’ladi?
𝐴) − 2 𝐵) 3 𝐶) 1 𝐷) 2
tashqi chizilgan aylana markazi koordinatalari mos
ravishda (1; 1) va (3; 2) bo’lsa, bu uchburchakning 11. 𝑓(𝑥) va 𝑔(𝑥) funksiyalarning hosilari
medianalari kesishgan nuqtasining koordinatasini mavjud. 𝑓′′(𝑥) − 𝑔′′(𝑥) = 0, 𝑓 ′ (1) = 2,
toping? 𝑔′ (1) = 4, 𝑓(2) = 3, 𝑔(2) = 9 bo’lsa
7 5 5 7 3 3
𝐴) ( ; ) 𝐵) ( ; ) 𝐶) (7; 5) 𝐷) 𝑡. 𝑗. 𝑦
3 3 3 3
𝑓 (2) − 𝑔 (2) ning qiymatini toping?
2. 2𝑎⃗ + 3𝑏⃗⃗ + 𝑐⃗ = 0 bo’lsa, 𝑎⃗ ∙ 𝑏⃗⃗ + 𝑏⃗⃗ ∙ 𝑐⃗ + 𝑐⃗ ∙ 𝑎⃗ ifoda 𝐴) − 5 𝐵) 3 𝐶) 5 𝐷) − 3
qaysi jovobga teng? 12. [0; 2𝜋] oralig’ida quyidagi tenglama
𝐴) 6 ∙ (𝑏⃗⃗ ∙ 𝑐⃗) 𝐵) 3 ∙ (𝑏⃗⃗ ∙ 𝑐⃗) 𝐶) 2 ∙ (𝑏⃗⃗ ∙ 𝑐⃗) 𝐷) 0 nechta yechimga ega?
3. Quyidagi ifodaning yoyolmasidagi 𝑥 5 ning cos 6𝑥 + tg 2 𝑥 + cos 6𝑥 ∙ tg 2 𝑥 = 1
𝐴) 5 𝑡𝑎 𝐵) 6 𝑡𝑎 𝐶) 7 𝑡𝑎 𝐷) 4 𝑡𝑎
koeffisentini toping?
1 10 1 9 13. Ikki parallel chiziqning birida 6 ta nuqta
(𝑥 + ) ∙ (𝑥 − ) ikkinchisida esa 8 ta nuqta berilgan bu nuqtalar
𝑥 𝑥
𝐴) 𝐶93 𝐵) 𝐶94 𝐶) − 𝐶93 𝐷) − 𝐶94 orqali o’tkazilgan barcha chiziqlarning, ikki
parallel chiziqlar orasidagi, kesishish nuqtalari
4. Agar 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 va 𝑏𝑥 2 + 𝑐𝑥 + 𝑎 = 0
𝑎3 +𝑏 3 +𝑐 3
nechta?
tenglamalar umumiy ildizga ega bo’lsa, ni 𝐴) 210 𝑡𝑎 𝐵) 315 𝑡𝑎 𝐶) 420 𝑡𝑎 𝐷) 840 𝑡𝑎
𝑎𝑏𝑐
toping? 14. 𝑥 2 + 𝑦 2 − 4𝑥 − 4𝑦 + 4 = 0 aylanaga (6; 4)
𝐴) 0 𝐵) 3 𝐶) − 1 𝐷) − 3 nuqtadan o’tkazilgan urinma 𝑜𝑦 o’qini 𝐴 va 𝐵
5. 2,4,5,7,8,9 sonlaridan tuzilgan uch xonli 𝑥𝑦𝑧
̅̅̅̅̅ nuqtada kesib o’tadi. |𝐴𝐵| masofani toping?
sonlar uchun 𝑥 < 𝑦 va 𝑧 < 𝑦 (takroriy hollarsiz) 𝐴) 6 𝐵) 8 𝐶) 10 𝐷) 12
shartlari o’rinli bo’ladigan nechta shunday uch
15. (2; 5) nuqtadan 3𝑥 − 4𝑦 + 8 = 0 chiziqga parallel
xonali sonlar mavjud?
𝐴) 20 𝑡𝑎 𝐵) 40 𝑡𝑎 𝐶) 60 𝑡𝑎 𝐷) 30 𝑡𝑎 ravishda 3𝑥 + 𝑦 + 4 = 0 chiziqgacha bo’lgan
6. {𝑎𝑛 } arifmetik progressiyada 𝑎7 = 15 masofani toping?
15 9
bo’lsa, 𝑎2 𝑎7 𝑎12 ifoda eng katta qiymatga 𝐴) 𝐵) 𝐶) 5 𝐷) 𝑡. 𝑗. 𝑦
2 2
ega bo’ladigan arifmetik progressiyaning 16. (3; 2) nuqtadan o’tuvchi to’g’ri chiziqning
ayirmasini toping? quyidagi chiziqlar orasidfagi kesmasi uzunligi 2 ga
9
𝐴) 9 𝐵) 𝐶) 0 𝐷) 18 teng bo’lsa bu chizqning tenglamasini toping?
4
7. Agar funksiya, 3𝑥 + 4𝑦 = 11 va 3𝑥 + 4𝑦 = 1
𝑎𝑥 3 + 𝐵, 0≤𝑥≤1 𝐴) 2𝑥 + 𝑦 − 8 = 0 𝐵) 3𝑦 − 4𝑥 + 6 = 0
𝑓(𝑥) = { 𝐶) 3𝑥 + 4𝑦 − 17 = 0 𝐷) 2𝑥 − 𝑦 − 4 = 0
2 cos(𝜋𝑥) + arctg 𝑥 , 1 < 𝑥 ≤ 2
[0; 2] oraliqda hosilasi mavjud bo’lsa 17. 𝑧 kopleks son uchun, |𝑧 − 3 − 2𝑖| = |𝑧 + 2𝑖|
tenglik o’rinli bo’lsa |𝑧| ning eng kichik qiymatini
quyidagi qaysi javob to’g’ri?
𝜋−8 28−3𝜋 toping?
𝐴) 𝐴 + 𝐵 = 𝐵) 𝐴 − 𝐵 = 1 4 7 9
4 12
𝐴 2 𝐴) 𝐵) 𝐶) 𝐷)
𝐶) = 𝐷) ℎ𝑎𝑚𝑚𝑎 𝑗𝑎𝑣𝑜𝑏 𝑡𝑜′𝑔′𝑟𝑖 2 5 10 10
𝐵 3𝜋−26 19
𝑢(𝑥) 18. Quyidagi ko’phadda 𝑥 oldidagi koeffisentni
8. 𝑓(𝑥) = ln (𝑣(𝑥)) bunda 𝑢′ (2) = 4, toping?
𝑣 ′ (2) = 2, 𝑢(2) = 2, 𝑣(2) = 1 bo’lsa (𝑥 − 1)(𝑥 − 21 )(𝑥 − 22 ) … (𝑥 − 219 )
𝑓 ′ (2) ni toping? 𝐴) 220 − 219 𝐵) − (220 − 1) 𝐶) 220 𝐷) 0
𝐴) 0 𝐵) 1 𝐶) − 1 𝐷) 𝑡. 𝑗. 𝑦 19. Quyidagi ketma-ketliklar 100 tadan hadga ega
9. 𝑥𝑦 + 𝑎𝑥 + 𝑏𝑦 = 0 chiziqga (1; 1) bo’lsa ularning eng oxiregi umumiy hadini toping?
nuqtada o’tkazilgan urunma 𝑜𝑥 o’qi bilan 1, 11, 21, 31, …
holsil qilgan burchagi arctg 2 bo’lsa, 𝑎 va 31, 36, 41, 46, …
𝑏 ni toping? 𝐴) 381 𝐵) 521 𝐶) 281 𝐷) 𝑡. 𝑗. 𝑦
𝐴) 𝑎 = 1; 𝑏 = 2 𝐵) 𝑎 = 1; 𝑏 = −2 20. 𝑦 = 𝑥 ∙ 𝑒 |𝑥| , |𝑥| = 1, 𝑦 = 0 ushbu chiziqlar bilan
𝐶) 𝑎 = −1; 𝑏 = 2 𝐷) 𝑎 = −1; 𝑏 = −2 chegaralangan sohaning yuzini toping?
𝐴) 4 𝐵) 1 𝐶) 2 𝐷) 6

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21. Hisoblang: 32. Hisoblang:
2 1
𝑎𝑥 − 𝑏
∫ 𝑑𝑥 ∫ (𝑥 − [2𝑥])𝑑𝑥
𝑥√𝑐 2 𝑥 2 − (𝑎𝑥 2 + 𝑏)2 −1
𝑎𝑥−
𝑏
1 𝑎𝑥+
𝑏 𝐴) 1 𝐵) 2 𝐶) 3 𝐷) 0
𝑥 𝑥
𝐴) arcsin ( ) + 𝐾 𝐵) arcsin ( )+𝐾 33. Quyidagi ko’phadda 𝑥 49 oldidagi koeffisentini
𝑐 2 𝑐

𝑎𝑥+
𝑏 toping?
𝑥
𝐶) arcsin ( )+𝐾 𝐷) 𝑡. 𝑗. 𝑦 (2𝑥 + 1)(2𝑥 + 3)(2𝑥 + 5) … (2𝑥 + 99)
𝑐
𝐴) 250 ∙ 2500 𝐵) 249 ∙ 2500
22. 𝑦 = 2𝑥 4 − 𝑥 2 chiziq, bu chiziqning minimum
𝐶) − 250 ∙ 2500 𝐷) − 249 ∙ 2500
nuqtalari ordinatlari va 𝑜𝑥 bilan chegaralangan
soha yuzini toping? 34. Differensial tenglamani yeching:
9 7 11 13 𝑑𝑦 𝑥+𝑦+1
𝐴) 𝐵) 𝐶) 𝐷) =
120 120 120 120 𝑑𝑥 2𝑥 + 2𝑦 + 1
2
23. 𝑓(𝑥) = { arcsin 𝑎 + 𝑥 , 0 < 𝑥 < 1 𝐴) ln|3𝑥 + 3𝑦 + 2| + 3𝑥 + 6𝑦 = 𝑐
2𝑥, 𝑥≥1
𝐵) ln|3𝑥 + 3𝑦 + 2| − 3𝑥 + 6𝑦 = 𝑐
Bu 𝑓(𝑥) funksiya 𝑥 = 1 da minimumga ega bo’lsa,
𝐶) ln|3𝑥 + 3𝑦 + 2| − 3𝑥 − 6𝑦 = 𝑐
𝑎 ni toping?
𝐷) ln|3𝑥 + 3𝑦 + 2| + 3𝑥 − 6𝑦 = 𝑐
𝐴) sin 1 𝐵) − sin 1 𝐶) 0 𝐷) 𝑡. 𝑗. 𝑦
35. Hisoblang:
24. ∀ 𝑥, 𝑦 lar uchun, 𝑓(𝑥 + 𝑦) = 𝑓(𝑥) + 𝑓(𝑦) o’rinli. 3𝑛
𝑓(𝑥) = (2𝑥 2 + 3𝑥)𝑔(𝑥) barcha 𝑥 uchun 𝑔(𝑥) 𝑛
lim ∑
usliksiz, 𝑔(0) = 3. U holda 𝑓 ′ (𝑥) qaysi jovobga 𝑛→∞ 𝑟 2 − 𝑛2
𝑟=2𝑛+1
teng? 3 2
𝐴) ln √2 𝐵) ln √ 𝐶) ln √ 𝐷) ln √3
𝐴) 9 𝐵) 3 𝐶) 6 𝐷) 𝑡. 𝑗. 𝑦 2 3

25. Hisoblang: 36. 10 ta talaba bir qator turibdi, necha xil usulda 4 ta
sin2 𝑥 talabani shunday tanlab olish mumkinki bunda hech
1/ sin2 𝑥 1/ sin2 𝑥 1/ sin2 𝑥
lim(1 +2 +⋯+𝑛 )
𝑥→0 bir ikkitasi yonma-yon turgan emas edi?
𝑛(𝑛+1)
𝐴) ∞ 𝐵) 0 𝐶) 𝐷) 𝑛 𝐴) 35 𝐵) 36 𝐶) 40 𝐷) 41
2
100
26. 17 256 ̅̅̅ soning oxirgi ikki raqami yig’indisi
=. . . 𝑎𝑏 37. (√2 + 4√3) ifodanni yoyilmasida nechta had
𝑎 + 𝑏 ni toping? irratsional had?
𝐴) 9 𝐵) 3 𝐶) 6 𝐷) 10 𝐴) 25 𝐵) 26 𝐶) 76 𝐷) 𝑡. 𝑗. 𝑦
27. Hisoblang: 38. 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 tenglamaning ildizlari 𝛼 va 𝛽.
sin(𝜋 cos 2(tg(sin 𝑥)) Agar 𝑎 + 𝑏 + 𝑐 < 0, 𝑎 − 𝑏 + 𝑐 < 0 va 𝑐 > 0
lim
𝑛→0 𝑥2 bo’lsa [𝛼] + [𝛽] ning qiymatini toping?
𝜋 𝜋
𝐴) 𝜋 𝐵) 𝐶) 𝐷) − 𝜋 𝐴) 1 𝐵) − 1 𝐶) 0 𝐷) 𝑡. 𝑗. 𝑦
4 2
|𝑥 − 1|([𝑥] − 𝑥), 𝑥 ≠ 1 39. Agar quyidagi tenglik o’rinli bo’lsa 𝑘 ni toping?
28. 𝑓(𝑥) = { berilgan bo’lsa 𝜋
0, 𝑥=1 3 tg 𝑥 √cos 𝑥 1
qaysi javob to’g’ri? ∫ = 1−
𝐴) 𝑓 ′ (1+ ) = 2 𝐵) 𝑓 ′ (1− ) = 0 𝐶) 𝑓 ′ (1− ) = −1 0 √2𝑘 √2
𝐴) 2 𝐵) 6 𝐶) 3 𝐷) 𝑡. 𝑗. 𝑦
𝐷) 𝑓(𝑥) 𝑑𝑎 𝑥 = 1 𝑑𝑎 ℎ𝑜𝑠𝑖𝑙𝑎𝑠𝑖 𝑚𝑎𝑣𝑗𝑢𝑑 𝑒𝑚𝑎𝑠;
5𝑥 8 +7𝑥 6 40. Agar ∫ 𝑒 𝑥 (𝑓(𝑥) − 𝑓 ′ (𝑥))𝑑𝑥 = 𝑔(𝑥) bo’lsa, u
29. 𝑓(𝑥) = ∫ (𝑥2+1+2𝑥7)2 𝑑𝑥 da 𝑓(0) = 0 bo’lsa, 𝑓(1) holda ∫ 𝑒 𝑥 𝑓(𝑥) 𝑑𝑥 qaysi javobga teng?
ni toping? 𝐴) 𝑔(𝑥) + 𝑒 𝑥 𝑓(𝑥) + 𝐶
1 1 1 1
𝐴) − 𝐵) 𝐶) 𝐷) − 𝐵) 𝑔(𝑥) − 𝑒 𝑥 𝑓(𝑥) + 𝐶
2 4 2 4
1
30. Hisoblang: 𝐶) (𝑔(𝑥) + 𝑒 𝑥 𝑓(𝑥)) + 𝐶
2
2021 1
∫ (𝑥 − 1)(𝑥 − 2)(𝑥 − 3) … (𝑥 − 2021) 𝑑𝑥 𝐷) (𝑔(𝑥) + 𝑒 𝑥 𝑓′(𝑥)) + 𝐶
2
1
𝐴) 20212 𝐵) 2020 ∙ 2021 ∙ 2022
𝐶) 2021! 𝐷) 0
31. 𝑓(𝑥) = min(𝑥 + 1; √1 − 𝑥 ) bunda 𝑥 ≤ 1, bu
𝑓(𝑥) va 𝑜𝑥 o’qi bilan chegaralangan sohaning
yuzini toping?
7 1 11 7
𝐴) 𝐵) 𝐶) 𝐷)
3 6 6 6

𝐎’𝐳𝐛𝐞𝐤𝐢𝐬𝐭𝐨𝐧 𝐌𝐚𝐭𝐞𝐦𝐚𝐭𝐢𝐤𝐥𝐚𝐫𝐢 𝐯𝐚 𝐈𝐧𝐟𝐨𝐫𝐦𝐚𝐭𝐢𝐤𝐚 𝐀𝐬𝐬𝐨𝐭𝐬𝐢𝐚𝐭𝐬𝐢𝐲𝐚𝐬𝐢 HTTPS://T.ME/UZMIA31

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Javoblar:
1. A
2. B
3. C
4. B
5. B
6. C
7. D
8. A
9. B
10. D
11. A
12. C
13. C
14. B
15. C
16. B
17. D
18. B
19. B
20. C
21. C
22. B
23. A
24. A
25. D
26. A
27. A
28. D
29. B
30. D
31. D
32. A
33. B
34. D
35. B
36. A
37. D
38. B
39. A
40. C

𝐎’𝐳𝐛𝐞𝐤𝐢𝐬𝐭𝐨𝐧 𝐌𝐚𝐭𝐞𝐦𝐚𝐭𝐢𝐤𝐥𝐚𝐫𝐢 𝐯𝐚 𝐈𝐧𝐟𝐨𝐫𝐦𝐚𝐭𝐢𝐤𝐚 𝐀𝐬𝐬𝐨𝐭𝐬𝐢𝐚𝐭𝐬𝐢𝐲𝐚𝐬𝐢 HTTPS://T.ME/UZMIA31