Matematika – 2025 Matematika Pro

Attestatsiya Mock 16- Test

1. 𝑥 musbat butun son uchun, 𝐸𝐾𝑈𝐵(𝑥, 2𝑥 + 7) = 𝑥 tenglik o’rinli. 𝑥 soni qancha turli
qiymatlarni qabul qilishi mumkin?
A) 1
B) 2
C) 3
D) 4
2. Agar 2𝑎+𝑏+𝑐 = 2𝑎+𝑏 + 2𝑎+𝑐 + 2𝑏+𝑐 tenglik o’rinli bo’lsa, 2−𝑎 + 2−𝑏 + 2−𝑐
ifodaning qiymatini toping.
1
A) 2
B) 1
3
C) 2
D) 2
3. Ifodaning qiymatini toping.
√√5 + 2 + √√5 − 2
− √3 − 2√2
√√5 + 1
A) 1
B) 2√2 − 1
√5
C)
4
√2
D)
5
1231
4. 12 + 144324 ifodani 13 ga bo'lgandagi qoldiqni toping?
A) 0
B) 1
C) 2
D) 3
5. Ifodani soddalashtiring.
𝑥 2 + 𝑦 2 + 2𝑥𝑦 + 2𝑥 + 2𝑦 + 1 𝑥 2 + 𝑥𝑦 − 𝑥
⋅ 2
𝑦 2 + 𝑥𝑦 + 𝑦 𝑥 + 𝑦 2 + 2𝑥𝑦 − 1
A) 1
B) x
C) y
𝑥
D)
𝑦
(𝑥+2)2010 ⋅(𝑥 2 −𝑥−2)
6. ≤ 0 tengsizlikning yechimlari to’plamining eng katta manfiy butun
(1−𝑥)2011
qiymatini toping.
A) -5
B) -4
C) -1
D) -2
7. Tenglamaning musbat ildizini toping.
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(𝑥 + 1)1+log (𝑥+1) = 10(𝑥 + 1)
A) 5
B) 6
C) 7
D) 8
8. 15 dona yangi o‘rik 750 gramm, 20 dona quritilgan o‘rik esa 600 gramm. Kilogrami
𝑥 so’mga sotib olingan yangi o'rik miqdori quritilganda 4 kilogramm yengillashadi va
bir kilogramm quritilgan o'rik 2𝑥 so’mga sotiladi va 12 so’m foyda keltiradi. Shunga
ko'ra, boshida yangi o'rik uchun jami necha so’m to'langan?
A) 40
B) 50
C) 56
D) 60
9. Farxodning ish tezligi Olimning ish tezligining 3 barobari va Kamronning ish
tezligining yarmi. Farxod va Kamron birga ishlay boshlaydi va 3 kun ishlagandan
so'ng Kamron ishdan ketadi va uning o'rnida Olimni davom etadi. Agar butun ish 19
kunda bajarilsa, Kamron va Olim butun ishni birga necha kunda tugatadilar?
A) 8
B) 10
C) 13
D) 15
10.Tengsizlikni yeching.
log 1 (𝑥 + 2) ⋅ log 3 (5 − 𝑥) ≤ 0
2
A) (−2,5)
B) [−1,4]
C) (−∞, 4]
D) (−∞, −1] ∪ [4, ∞)
11. Berilgan qatorning:
13,11,17,14,18,21,21, 𝑥, 25,26
medianasi 19 bo’lsa, 𝑥 ning qiymatini toping.
A) 6
B) 7
C) 8
D) 9
12. 3 ta quyon va 4 ta mushuk tasodifiy yonma-yon tizilgan.Shunga ko'ra, har qanday 2
ta mushukning birga kelmaslik ehtimoli qanday?
A) 1/35
B) 2/35
C) 3/35
D) 1/7
13.Tenglamaning ildizlari ko′ paytmasini toping.
𝑥 + 3 12𝑥 − 6
+ =5
2𝑥 − 1 𝑥+3
A) 1

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B) 2
C) 3
D) 4
𝑎𝑥 2 +𝑏𝑥𝑦+𝑐𝑦 2 𝑥 2 −4𝑥𝑦+3𝑦 2 𝑥−2𝑦
14. Agar : = tenglik o’rinli bo’lsa, a + b + c yig’indini
2𝑥 2 +𝑥𝑦−𝑦 2 𝑥 2 −𝑦 2 𝑥−3𝑦
qiymatini toping.
A) 2
B) 1
C) -1
D) -2
15. Bu yerda a va b natural sonlar, 4𝑎 = 7𝑏 = 2𝑐 va 𝐸𝐾𝑈𝐵(𝑎, 𝑏, 𝑐) = 3. Agar shunday
bo'lsa, 𝑎 + 𝑏 + 𝑐 yig'indisi nechaga teng?
A) 78
B) 75
C) 72
D) 64
16.A va B kranlari mos ravishda 4 va 6 soat ichida tankni to'ldiradi va C va D kranlari
mos ravishda 8 va 12 soat ichida to'liq tankni o'z darajalariga tushiradi. D krani
rezervuarning pastki qismida joylashganligi va C krani tank balandligining 1/3
qismini tashkil etganligi sababli, idish bo'sh bo'lganda to'rtta kran bir vaqtning o'zida
ochilgan bo'lsa, uni to'ldirish uchun qancha vaqt kerak bo'ladi?
A) 11
B) 11/2
C) 11/3
D) 11/4

17. Yotoqxonada ikkita 3 kishilik va bitta 2 kishilik xona mavjud. Akbar va Ali bir
xonada qolmasligi sharti bilan, 8 kishi, jumladan, Akbar va Ali bu yotoqxonaga necha
xil usulda joylashishi mumkin?
A) 360
B) 380
C) 420
D) 432
1 1
18. 𝑥 2 − (2𝑎 + 2)𝑥 + 9 = 0 tenglamaning ildizlari 𝑥1 va 𝑥2 dir. + = 2 tenglik
√𝑥1 √𝑥2
o’rinli bo’lsa, 𝑎 ning qiymatini toping.
A) 15
B) 14
C) 13
D) 12

19. Quyida aylanada bir xil masofada joylashgan 12 ta nuqta bor. Shunga ko'ra,
rasmdagi istalgan uchta nuqtani burchak sifatida qabul qiladigan nechta to'g'ri
burchakli uchburchak chizish mumkin?

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A) 10
B) 18
C) 30
D) 60

20.Tenglamaning ildizlari yig’indisini toping.

𝑥 2 − 𝑥 − √𝑥 2 − 𝑥 − 1 = 1
A) 0
B) 1
C) 2
D) 3
1 2 1 1
21. (𝑥 + ) − 8 (𝑥 + ) + 16 = 0 tenglamaning ildizlaridan biri 𝑥1 bo’lsa, 𝑥1 2 + 2
𝑥 𝑥 𝑥1
ifodaning qiymati nimaga teng?
A) 11
B) 12
C) 13
D) 14
22. Ifodani soddalashtiring.
2𝑥 2𝑦 1 1
( − ) : ( − )
1 + 2𝑥−𝑦 1 − 2𝑦−𝑥 2𝑥 + 2𝑦 2𝑥 − 2𝑦
A) 2𝑥
B) 2𝑦
C) 2𝑥+𝑦
D) 2𝑥−𝑦
23. 518 ⋅ 154 ⋅ 222 necha xonali son?
A) 18
B) 21
C) 23
D) 24
24. 𝑥 2 − (√2 − 1)𝑥 − √2 = 0 tenglamaning ildizlari 𝑥1 va 𝑥2 dir. Bunga ko’ra,
𝑥13 + 𝑥23 ifodaning qiymatini toping?
A) √2 − 1
B) √2 − 3
C) 2√2 − 1
D) 2√2 − 3
25. Ifodani soddalashtiring.
3 1 4
𝑥−2− −
𝑥 ⋅ 𝑥 𝑥2
4 1 9
𝑥−3−𝑥 −
𝑥 𝑥3
𝑥+2
A)
𝑥−3
𝑥+3
B)
𝑥−2

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𝑥−4
C)
𝑥+3
𝑥
D)
𝑥+3
26. 𝑎(𝑎 + 3)𝑥 2 + (2𝑎 + 6)𝑥 − 3𝑎 − 9 = 0 tenglama bitta ildizga ega bo'ladigan a ning
qiymatlari yig'indisini toping.
A) −3
2
B) −2
3
1
C) −
3
1
D) −4
3
−2 4
27. Rasmdagi 𝑓(𝑥) funksiya grafigi tasvirlangan. ∫−3 𝑓(𝑥)𝑑𝑥 = −4 va ∫−2 |𝑓(𝑥)|𝑑𝑥 =
4 4
6 bo'lsa, ∫−3 𝑓(𝑥)𝑑𝑥 − ∫−3 |𝑓(𝑥)|𝑑𝑥 ni toping.
A) -2
B) -10
C) -12
D) -8

28. 𝐴𝐵𝐶 Uchburchakda ∠𝐵𝐴𝐶 = 90∘ , 𝐵𝐷 = 4, 𝐷𝐶 = 4√2 bo’lib, D nuqta

bissektrissalar kesishish nuqatasi bo'lsa, BC ni toping.
A) 4√3
B) 4√5
C) 5√5
D) 6√3

29. y = x, y = 0 va √𝑥 + √𝑦 = 2 funksiyalar bilan chegaralangan sohaning yuzini

toping.
5
A) 2
6
1
B) 1
3
C) 1,5
D) 1,2
30. Uch o'lchovli fazoda uchlari 𝐴(3; 0; 0), 𝐵(0; 4; 0) va 𝐶(0; 0; 5) nuqtalarda bo'lgan
parallelepipedning to'la sirtini toping.
A) 84
B) 94
C) 104
D) 114
31. Asosi rombdan iborat bo'lgan piramidaning yon qirralari asos tekisligi bilan 60
gradusli burchak tashqil qiladi. Agar rombning tomoni 12 ga teng bo'lsa,
piramidaning hajmini toping.

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A) 144√6
B) 216√6
C) 288√6
D) 288
32. Agar 𝑎⃗ = (−3, −1), 𝑏⃗⃗ = (2, −1), 𝑐⃗ = (5, −4) vektorlar uchun 3𝑐⃗ = 𝑚𝑎⃗ + 𝑛𝑏⃗⃗
tenglik o’rinli bo’lsa, 𝑛 + 𝑚 ning qiymatini toping.
A) 13
B) 12
C) 15
D) 11
33. Asosining tomonlari 3 va 7 ga teng bo'lgan muntazam uchburchakli kesik pramidaga
shar ichki chizilgan. Kesik pramidaning yon sirtini toping?
25
A)
√3
50
B)
√3
100
C)
√3
75
D)
√3

34. 𝑦 ′ = √𝑦 differensial tenglamani yeching. Bunda 𝑦(1) = 4 bo'lsa, y ni toping.

(𝑥+3)2
A) 𝑦 =
4
(𝑥−3)2
B) 𝑦 =
4
(𝑥+3)2
C) 𝑦 =
2
D) 𝑦 = 𝑥 − 3
35. √3sin 𝑥 + cos 𝑥 = 2 tenglamani yeching.
𝜋
A) + 2𝜋𝑛
2
𝜋
B) + 2𝜋𝑛
3
𝜋
C) + 2𝜋𝑛
4
𝜋
D) + 2𝜋𝑛
6

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