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Matematika. Xorijiy va nodavlat OTM talabalari uchun davlat granti tanlovi testiga tayyorgarlik (asosiy fan bloki, 2026–2027)

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MATEMATIKA Xorijiy va nodavlat OTM talabalari uchun davlat granti tanlovi testiga tayyorgarlik (asosiy fan bloki, 2026–2027) 34 ta variant • 1020 ta topshiriq • javoblari bilan Mashq to'plami • 2025–2026 o'quv yili Matematika — davlat granti mashq variantlari | 1 Imtihon tuzilishi va yo'riqnoma • Xorijiy davlatlar OTMlarining O'zbekistondagi filiallari va nodavlat OTMlarning kunduzgi bakalavriat talabalari uchun davlat granti tanlovi: arizalar 2026-yil 10–17-oktyabr kunlari my.uzbmb.uz orqali qabul qilinadi. • Saralash ta'lim yo'nalishiga belgilangan fanlar majmuasi bo'yicha test sinovlari orqali o'tkaziladi (Bilim va malakalarni baholash agentligi). Joriy yilda davlat OTMlariga kirish imtihonlarida mos fanlar majmuasi bo'yicha qatnashgan talabalar o'z ballari bilan ham tanlovda ishtirok etishi mumkin. • Grantlar minimal o'tish balini to'plaganlar orasidan, ballar ketma-ketligiga qat'iy amal qilgan holda, kvotalar doirasida taqsimlanadi. Grant butun o'qish muddatiga beriladi; bitiruvchilar kamida 3 yil davlat yoki davlat ulushi bo'lgan tashkilotlarda ishlashi shart. • Test sanalari manbalarda hali ko'rsatilmagan — my.uzbmb.uz dagi e'lonlarni kuzatib boring. • To'plam OTMga kirish testi (DTM) formatida tuzilgan: asosiy (ixtisoslik) fanlar bloki — 30 ta savol. To'plamda 34 ta variant × 30 ta savol = 1020 ta test. To'g'ri javob har bir savol ostida yashil rangda, hujjat oxirida javoblar kaliti bor. • Muhim: rasmiy test savollari ochiq e'lon qilinmaydi. Bu umumta'lim fan dasturlari asosida tuzilgan mashq savollari. Har bir variant tuzilishi Topshiriqlar Turi Izoh 1–30 Yopiq test (4 ta variant) Asosiy (ixtisoslik) fan bloki — bitta to'g'ri javob Matematika — davlat granti mashq variantlari | 2 Mundarija № Variant Topshiriqlar 1 1-variant 1–30 2 2-variant 31–60 3 3-variant 61–90 4 4-variant 91–120 5 5-variant 121–150 6 6-variant 151–180 7 7-variant 181–210 8 8-variant 211–240 9 9-variant 241–270 10 10-variant 271–300 11 11-variant 301–330 12 12-variant 331–360 13 13-variant 361–390 14 14-variant 391–420 15 15-variant 421–450 16 16-variant 451–480 17 17-variant 481–510 18 18-variant 511–540 19 19-variant 541–570 20 20-variant 571–600 21 21-variant 601–630 22 22-variant 631–660 23 23-variant 661–690 24 24-variant 691–720 25 25-variant 721–750 26 26-variant 751–780 27 27-variant 781–810 28 28-variant 811–840 29 29-variant 841–870 30 30-variant 871–900 31 31-variant 901–930 32 32-variant 931–960 33 33-variant 961–990 34 34-variant 991–1020 Jami topshiriqlar 1020 Javoblar kaliti (hujjat oxirida) Matematika — davlat granti mashq variantlari | 3 1-variant Asosiy fan bloki • bitta to'g'ri javob 1. (x + 4)(x − 2) > 0 tengsizlikning eng katta manfiy butun yechimini toping. A) −4 B) −1 C) −3 D) −5 To'g'ri javob: D) −5✔ 2. To'g'ri burchakli uchburchakning bir kateti 7 ga teng, gipotenuza ikkinchi katetdan 1 ga uzun. Gipotenuzani toping. A) 8 B) 25 C) 24 D) 13 To'g'ri javob: B) 25 ✔ 3. Tomonlari 5, 12 va 13 ga teng uchburchakka tashqi chizilgan doira yuzini toping. A) 42,25π B) 36π C) 25π D) 169π To'g'ri javob: A) 42,25π ✔ 4. f(x) = x√x bo'lsa, f'(4) ni toping. A) 6 B) 8 C) 3/2 D) 3 To'g'ri javob: D) 3 ✔ 5. Hisoblang: log₀,₅8 − lg0,001. A) −6 B) 1 C) 3 D) 0 To'g'ri javob: D) 0 ✔ 6. Tengsizlikni yeching: x³ > x. A) −1 < x < 0 yoki x > 1 B) −1 < x < 1 C) x < −1 yoki 0 < x < 1 D) x > 1 To'g'ri javob: A) −1 < x < 0 yoki x > 1 ✔ Matematika — davlat granti mashq variantlari | 4 7. Radiuslari 5 va 3 ga teng bo'lgan konsentrik aylanalar orasidagi halqa yuzini toping. A) 4π B) 8π C) 16π D) 34π To'g'ri javob: C) 16π✔ 8. Hisoblang: log₂(log₃81). A) 3 B) 4 C) 2 D) 1 To'g'ri javob: C) 2 ✔ 9. Tengsizlikni yeching: (x − 1)/(x + 1) > (x + 1)/(x − 1). A) x < −1 yoki 0 < x < 1 B) 0 < x < 1 C) x < 0 D) −1 < x < 0 yoki x > 1 To'g'ri javob: A) x < −1 yoki 0 < x < 1 ✔ 10. f(x) = 1/x² bo'lsa, f'(−1) ni toping. A) 1 B) −1/2 C) −4 D) 2 To'g'ri javob: D) 2 ✔ 11. 0,(27) cheksiz davriy o'nli kasrni oddiy kasr ko'rinishida yozing. A) 3/10 B) 2/7 C) 27/100 D) 3/11 To'g'ri javob: D) 3/11 ✔ 12. Muntazam to'rtburchakli piramida asosining tomoni 10 ga, balandligi 12 ga teng. Piramidaning to'la sirtini toping. A) 360 B) 340 C) 400 D) 260 To'g'ri javob: A) 360 ✔ 13. Diagonallari 12 va 16 ga teng rombga ichki chizilgan aylana radiusini toping. A) 9,6 B) 4 C) 5 D) 4,8 To'g'ri javob: D) 4,8 ✔ Matematika — davlat granti mashq variantlari | 5 14. Ifodani soddalashtiring: (a⁻¹ + b⁻¹)/(a⁻² − b⁻²). A) ab/(b − a) B) 1/(b − a) C) ab/(a − b) D) a − b To'g'ri javob: A) ab/(b − a)✔ 15. Tengsizlikni yeching: 4ˣ − 5 · 2ˣ + 4 < 0. A) (0; 4) B) (2; 4) C) (1; 4) D) (0; 2) To'g'ri javob: D) (0; 2) ✔ 16. To'g'ri burchakli uchburchakda 30° li burchak qarshisidagi katet 6 ga teng. Ikkinchi katetni toping. A) 6√2 B) 12 C) 6√3 D) 3√3 To'g'ri javob: C) 6√3 ✔ 17. Uchburchak bissektrisalarining kesishish nuqtasi qanday xossaga ega? A) medianalarni 2:1 nisbatda bo'ladi B) uchala uchidan teng uzoqlikda C) uchala tomondan teng uzoqlikda D) eng katta tomonda yotadi To'g'ri javob: C) uchala tomondan teng uzoqlikda ✔ 18. Muntazam oltiburchakli piramida asosining tomoni 2 ga, balandligi 3 ga teng. Piramida hajmini toping. A) 12√3 B) 3√3 C) 18√3 D) 6√3 To'g'ri javob: D) 6√3 ✔ 19. Muntazam uchburchakka tashqi chizilgan aylana radiusi 6 ga teng. Uchburchak tomonini toping. A) 3√3 B) 9 C) 12 D) 6√3 To'g'ri javob: D) 6√3 ✔ 20. (n + 1)! / (n - 1)! = 42 tenglamani yeching. A) 5 B) 7 C) 6 D) 41 To'g'ri javob: C) 6 ✔ Matematika — davlat granti mashq variantlari | 6 21. Tavakkaliga tanlangan ikki xonali sonning raqamlari bir xil bo'lish ehtimolini toping. A) 9/100 B) 1/10 C) 1/9 D) 1/11 To'g'ri javob: B) 1/10✔ 22. Tengsizlikni yeching: 2x² − 7x + 3 ≤ 0. A) [1; 3] B) [−3; −1/2] C) [1/2; 7/2] D) [1/2; 3] To'g'ri javob: D) [1/2; 3] ✔ 23. Uchburchakda BC = 10 va A = 30°. Uchburchakka tashqi chizilgan aylana radiusini toping. ∠ A) 5 B) 20 C) 10√3 D) 10 To'g'ri javob: D) 10 ✔ 24. Qavariq ko'pyoqning 12 ta uchi va 30 ta qirrasi bor. Uning nechta yog'i bor? A) 20 B) 18 C) 22 D) 16 To'g'ri javob: A) 20 ✔ 25. Tenglamani yeching: (√2)ˣ = 8. A) 4 B) 3 C) 6 D) 3/2 To'g'ri javob: C) 6 ✔ 26. 1, 2, 3, 4, 5 raqamlarining har biridan bir martadan foydalanib nechta 5 ga bo'linadigan besh xonali son tuzish mumkin? A) 24 B) 5 C) 20 D) 120 To'g'ri javob: A) 24 ✔ 27. f(x) = x/(x² + 1) bo'lsa, f'(2) ni toping. A) 1/25 B) 1/5 C) −3/25 D) −5/9 To'g'ri javob: C) −3/25 ✔ Matematika — davlat granti mashq variantlari | 7 28. Agar x − 1/x = 2 bo'lsa, x² + 1/x² ning qiymatini toping. A) 8 B) 2 C) 6 D) 4 To'g'ri javob: C) 6✔ 29. y = x³ − 3x funksiya grafigiga abssissasi x₀ = 2 bo'lgan nuqtada o'tkazilgan urinmaning burchak koeffitsientini toping. A) 9 B) 2 C) 12 D) 3 To'g'ri javob: A) 9 ✔ 30. Hisoblang: 48² − 2 · 48 · 18 + 18². A) 900 B) 1200 C) 600 D) 3600 To'g'ri javob: A) 900 ✔ Matematika — davlat granti mashq variantlari | 8 2-variant Asosiy fan bloki • bitta to'g'ri javob 1. Ikki sonning yig'indisi 60 ga teng, ulardan biri ikkinchisining 25% ini tashkil etadi. Kichik sonni toping. A) 15 B) 20 C) 12 D) 48 To'g'ri javob: C) 12✔ 2. Parallelogrammning tomonlari 5 va 7 ga, bir diagonali 8 ga teng. Ikkinchi diagonalini toping. A) √74 B) 6 C) 2√21 D) 2√11 To'g'ri javob: C) 2√21 ✔ 3. Tenglamani yeching: 3(x − 2) − 2(x + 1) = 4. A) 12 B) 8 C) 4 D) 10 To'g'ri javob: A) 12 ✔ 4. A(1; 2; 3) va B(3; 5; 9) nuqtalar orasidagi masofani toping. A) √21 B) 49 C) 7 D) 11 To'g'ri javob: C) 7 ✔ 5. 150° ni radian o'lchovida ifodalang. A) 5π/6 B) 5π/3 C) 2π/3 D) 3π/4 To'g'ri javob: A) 5π/6 ✔ 6. F(x) funksiya f(x) = 4x³ − 2x ning boshlang'ich funksiyasi va F(1) = 5. F(2) ni toping. A) 16 B) 17 C) 12 D) 21 To'g'ri javob: B) 17 ✔ Matematika — davlat granti mashq variantlari | 9 7. Musbat hadli geometrik progressiyada b₃ · b₇ = 36. b₅ ni toping. A) 3 B) 18 C) 6 D) 36 To'g'ri javob: C) 6✔ 8. Muntazam ko'pburchakning ichki burchagi 140° ga teng. Uning nechta tomoni bor? A) 10 B) 9 C) 8 D) 7 To'g'ri javob: B) 9 ✔ 9. Integralni hisoblang: ∫₀¹ (x + 1)² dx. A) 1/3 B) 8/3 C) 7/3 D) 4/3 To'g'ri javob: C) 7/3 ✔ 10. A(1; 2) va B(4; 6) nuqtalar orasidagi masofani toping. A) 7 B) 5 C) 25 D) √13 To'g'ri javob: B) 5 ✔ 11. Barcha ikki xonali toq sonlarning yig'indisini toping. A) 2475 B) 4905 C) 2450 D) 2500 To'g'ri javob: A) 2475 ✔ 12. sin x · cos x = 1/4 tenglamani yeching (k Z). ∈ A) (−1)ᵏ · π/12 + πk/2 B) ±π/12 + πk C) (−1)ᵏ · π/12 + πk D) (−1)ᵏ · π/6 + πk To'g'ri javob: A) (−1)ᵏ · π/12 + πk/2 ✔ 13. Tomonlari 3 va 5 ga teng to'g'ri to'rtburchak uzunligi 3 ga teng tomoni atrofida aylantirildi. Hosil bo'lgan jism hajmini toping. A) 15π B) 45π C) 75π D) 25π To'g'ri javob: C) 75π ✔ Matematika — davlat granti mashq variantlari | 10 14. Ishchining maoshi avval 10% ga, keyin yana 20% ga oshirildi. Maosh jami necha foizga oshdi? A) 33% B) 30% C) 32% D) 28% To'g'ri javob: C) 32%✔ 15. Arifmetik progressiyaning dastlabki n ta hadi yig'indisi S = n² + 2n formula bilan berilgan. a₅ ni ₙ toping. A) 9 B) 13 C) 35 D) 11 To'g'ri javob: D) 11 ✔ 16. f(x) = e^(2x) funksiyaning boshlang'ich funksiyalarining umumiy ko'rinishini toping. A) e^x + C B) 2e^(2x) + C C) e^(2x)/2 + C D) e^(2x) + C To'g'ri javob: C) e^(2x)/2 + C ✔ 17. x² − 4x − 1 = 0 tenglamaning ildizlari x₁ va x₂ bo'lsa, 1/x₁ + 1/x₂ ni toping. A) −1/4 B) 2 C) −4 D) 1/2 To'g'ri javob: C) −4 ✔ 18. sin α = 0,6 va 0 < α < π/2 bo'lsa, sin2α ni toping. A) 0,96 B) 0,48 C) 0,28 D) 1,2 To'g'ri javob: A) 0,96 ✔ 19. Asosining radiusi 3 ga teng konusning hajmi radiusi 3 ga, balandligi 4 ga teng silindr hajmiga teng. Konus balandligini toping. A) 4/3 B) 12 C) 4 D) 8 To'g'ri javob: B) 12 ✔ 20. y = 2 − x² va y = x chiziqlar bilan chegaralangan figuraning yuzini toping. A) 9/2 B) 11/2 C) 7/6 D) 10/3 To'g'ri javob: A) 9/2 ✔ Matematika — davlat granti mashq variantlari | 11 21. Muntazam sakkizburchakning ichki burchagini toping. A) 135° B) 120° C) 140° D) 144° To'g'ri javob: A) 135°✔ 22. x² − 7x + 10 = 0 tenglama ildizlari kvadratlarining yig'indisini toping. A) 49 B) 39 C) 29 D) 20 To'g'ri javob: C) 29 ✔ 23. Qavariq to'rtburchakning diagonallari 7 va 10 ga, ular orasidagi burchak 30° ga teng. To'rtburchak yuzini toping. A) 70 B) 17,5√3 C) 17,5 D) 35 To'g'ri javob: C) 17,5 ✔ 24. sin2x = cos x tenglamaning [0; π] kesmadagi ildizlari yig'indisini toping. A) π B) 2π/3 C) 7π/6 D) 3π/2 To'g'ri javob: D) 3π/2 ✔ 25. (x − 2)(x + 3) = (x − 2)(2x − 1) tenglama ildizlarining ko'paytmasini toping. A) 4 B) 6 C) 8 D) −2 To'g'ri javob: C) 8 ✔ 26. Shar katta doirasining yuzi 16π ga teng. Sfera sirtini toping. A) 256π/3 B) 32π C) 16π D) 64π To'g'ri javob: D) 64π ✔ 27. 1 + 4 + 7 + … yig'indida nechta qo'shiluvchi olinsa, yig'indi 330 ga teng bo'ladi? A) 11 B) 15 C) 12 D) 20 To'g'ri javob: B) 15 ✔ Matematika — davlat granti mashq variantlari | 12 28. c(4; 3) vektor a(1; 2) va b(2; -1) vektorlar orqali c = xa + yb ko'rinishda yoyilgan. x + y ni toping. A) 2 B) 3 C) 4 D) 1 To'g'ri javob: B) 3✔ 29. A va B birgalikda ishni 12 kunda bajaradi. A yolg'iz o'zi shu ishni 20 kunda bajaradi. B yolg'iz o'zi ishni necha kunda bajaradi? A) 8 B) 30 C) 24 D) 32 To'g'ri javob: B) 30 ✔ 30. a(1; 2; 3) va b(4; -5; 6) vektorlarning skalyar ko'paytmasini toping. A) 32 B) -8 C) 12 D) 24 To'g'ri javob: C) 12 ✔ Matematika — davlat granti mashq variantlari | 13 3-variant Asosiy fan bloki • bitta to'g'ri javob 1. A va B nuqtalarda aylanaga o'tkazilgan urinmalar P nuqtada kesishadi, APB = 50°. AOB markaziy ∠ burchakni toping (O – aylana markazi). A) 65° B) 130° C) 50° D) 100° To'g'ri javob: B) 130° ✔ 2. Ikkita o'yin kubigi tashlandi. Kubiklarda turli ochkolar tushish ehtimolini toping. A) 2/3 B) 1/6 C) 5/6 D) 11/12 To'g'ri javob: C) 5/6 ✔ 3. To'g'ri burchakli uchburchakning katetlari 6 va 8 ga teng. Gipotenuzaga tushirilgan medianani toping. A) 4 B) 4,8 C) 10 D) 5 To'g'ri javob: D) 5 ✔ 4. y = ln x funksiya grafigiga abssissasi x₀ = e bo'lgan nuqtada o'tkazilgan urinma tenglamasini toping. A) y = x/e B) y = ex − 1 C) y = x − 1 D) y = x/e + 1 To'g'ri javob: A) y = x/e ✔ 5. f(x) = x² − 6x + 8 funksiyaning [0; 5] kesmadagi eng kichik qiymatini toping. A) −1 B) 8 C) 3 D) 0 To'g'ri javob: A) −1 ✔ 6. Tengsizlikni yeching: (x − 2)²(x + 1) ≤ 0. A) −1 ≤ x ≤ 2 B) x ≤ −1 C) x ≤ −1 yoki x = 2 D) x ≤ 2 To'g'ri javob: C) x ≤ −1 yoki x = 2 ✔ Matematika — davlat granti mashq variantlari | 14 7. Agar a/b = 3/4 bo'lsa, (2a + b)/(a − 2b) ning qiymatini toping. A) −2 B) −10/11 C) 5/2 D) −1/2 To'g'ri javob: A) −2✔ 8. Muntazam to'rtburchakli piramida asosining tomoni 4 ga, balandligi 6 ga teng. Piramidaning diagonal kesimi yuzini toping. A) 12√2 B) 12 C) 6√2 D) 24√2 To'g'ri javob: A) 12√2 ✔ 9. Tengsizlikni yeching: (x² − 4x + 4)/(x − 1) > 0. A) (1; 2) (2; +∞) ∪ B) (1; 2) C) (1; +∞) D) (2; +∞) To'g'ri javob: A) (1; 2) ∪ (2; +∞) ✔ 10. Muntazam to'rtburchakli piramidaning yon qirrasi 8 ga teng va asos tekisligi bilan 60° burchak tashkil etadi. Piramida hajmini toping. A) 64√3/3 B) 128√3/3 C) 256√3/3 D) 128√3 To'g'ri javob: B) 128√3/3 ✔ 11. 4x − x² > 3 tengsizlik butun yechimlarining yig'indisini toping. A) 3 B) 5 C) 2 D) 6 To'g'ri javob: C) 2 ✔ 12. lg²x − lg x² = 3 tenglama ildizlarining ko'paytmasini toping. A) 1000 B) 100 C) 0,1 D) 3 To'g'ri javob: B) 100 ✔ 13. y = x² funksiya grafigiga abssissasi x₀ = 1 bo'lgan nuqtada o'tkazilgan urinma tenglamasini toping. A) y = 2x − 1 B) y = x + 1 C) y = x D) y = 2x To'g'ri javob: A) y = 2x − 1 ✔ Matematika — davlat granti mashq variantlari | 15 14. y = x³/3 funksiya grafigiga abssissasi x₀ = 1 bo'lgan nuqtada o'tkazilgan urinma Ox o'qining musbat yo'nalishi bilan qanday burchak hosil qiladi? A) 45° B) 135° C) 60° D) 30° To'g'ri javob: A) 45°✔ 15. Tomonlari 13, 14 va 15 ga teng uchburchakka ichki chizilgan aylana radiusini toping. A) 3 B) 4 C) 6 D) 5 To'g'ri javob: B) 4 ✔ 16. Markazi (1; 2) nuqtada bo'lib, koordinatalar boshidan o'tuvchi aylana tenglamasini toping. A) (x - 2)² + (y - 1)² = 5 B) (x - 1)² + (y - 2)² = 25 C) (x - 1)² + (y - 2)² = 5 D) (x - 1)² + (y - 2)² = 3 To'g'ri javob: C) (x - 1)² + (y - 2)² = 5 ✔ 17. Aylana markazidan 13 ga teng masofada joylashgan nuqtadan aylanaga urinma o'tkazilgan. Aylana radiusi 5 ga teng. Urinma kesmasining uzunligini toping. A) 8 B) 18 C) √194 D) 12 To'g'ri javob: D) 12 ✔ 18. Muntazam uchburchakli prizma asosining tomoni 6 ga, yon yog'ining diagonali 10 ga teng. Prizma hajmini toping. A) 90√3 B) 72√3 C) 72 D) 36√3 To'g'ri javob: B) 72√3 ✔ 19. Tengsizlikni yeching: log₂x + log₂(x − 2) ≤ 3. A) (0; 8] B) [4; +∞) C) (2; 4] D) (0; 4] To'g'ri javob: C) (2; 4] ✔ 20. Hisoblang: (1 − 1/4)(1 − 1/9)(1 − 1/16) · … · (1 − 1/100). A) 9/20 B) 1/2 C) 11/20 D) 21/40 To'g'ri javob: C) 11/20 ✔ Matematika — davlat granti mashq variantlari | 16 21. 7 kishidan iborat guruhdan rais, rais o'rinbosari va kotibni necha xil usulda saylash mumkin? A) 343 B) 21 C) 35 D) 210 To'g'ri javob: D) 210✔ 22. Tomoni 6 ga teng muntazam uchburchakning yuzini toping. A) 9√3 B) 12√3 C) 6√3 D) 18√3 To'g'ri javob: A) 9√3 ✔ 23. Tenglamani yeching: logₓ16 = 2. A) 8 B) 4 C) 16 D) 2 To'g'ri javob: B) 4 ✔ 24. Tenglamani yeching: 3ˣ = 11 − x. A) 0 B) 1 C) 3 D) 2 To'g'ri javob: D) 2 ✔ 25. Tengsizlikni yeching: √(2x − 4) > x − 2. A) (2; +∞) B) (2; 6) C) (2; 4) D) (0; 4) To'g'ri javob: C) (2; 4) ✔ 26. Kub diagonali va uning qirrasi orasidagi burchak kosinusini toping. A) √3/3 B) √6/3 C) 1/2 D) √2/2 To'g'ri javob: A) √3/3 ✔ 27. Hisoblang: 0,25^(−1/2) + (1/27)^(−1/3) + 32^0,2. A) 7 B) 8 C) 6 D) 5 To'g'ri javob: A) 7 ✔ Matematika — davlat granti mashq variantlari | 17 28. 3 ta turli sovg'ani 5 o'quvchiga necha xil usulda tarqatish mumkin, agar bitta o'quvchi bir nechta sovg'a olishi mumkin bo'lsa? A) 125 B) 243 C) 60 D) 15 To'g'ri javob: A) 125✔ 29. Uchburchak tomonlarining o'rta perpendikulyarlari kesishgan nuqta nimaning markazi hisoblanadi? A) ortotsentrning B) tashqi chizilgan aylananing C) ichki chizilgan aylananing D) og'irlik markazining To'g'ri javob: B) tashqi chizilgan aylananing ✔ 30. Uchburchakda A = 45°, B = 60° va BC = √6. AC tomonni toping. ∠ ∠ A) √6 B) 2 C) 3 D) 3√2 To'g'ri javob: C) 3 ✔ Matematika — davlat granti mashq variantlari | 18 4-variant Asosiy fan bloki • bitta to'g'ri javob 1. a(1; 0) va b(1; 1) vektorlar orasidagi burchakni toping. A) 45° B) 30° C) 60° D) 90° To'g'ri javob: A) 45°✔ 2. Integralni hisoblang: ∫₁³ (2x + 1) dx. A) 8 B) 12 C) 14 D) 10 To'g'ri javob: D) 10 ✔ 3. cos2x + sin x = 0 tenglamaning [0; 2π] kesmadagi ildizlari yig'indisini toping. A) 3π B) 7π/2 C) 5π/2 D) 4π To'g'ri javob: B) 7π/2 ✔ 4. 3x − 2y = 4, x + 4y = 6 sistemaning yechimi uchun x − y ni toping. A) 2 B) 1 C) −4 D) 3 To'g'ri javob: B) 1 ✔ 5. a(2; 3) va b(4; -1) vektorlarning skalyar ko'paytmasini toping. A) 5 B) 8 C) 11 D) 14 To'g'ri javob: A) 5 ✔ 6. Ikki sonning nisbati 5 : 7 ga teng, ayirmasi esa 18 ga teng. Shu sonlarning yig'indisini toping. A) 120 B) 72 C) 108 D) 96 To'g'ri javob: C) 108 ✔ Matematika — davlat granti mashq variantlari | 19 7. y = tg(x/2) funksiyaning eng kichik musbat davrini toping. A) 4π B) π/2 C) 2π D) π To'g'ri javob: C) 2π✔ 8. 12 kg mahsulot 54 000 so'm turadi. Shunday mahsulotning 7 kg i qancha turadi (so'm)? A) 32 500 B) 31 000 C) 28 000 D) 31 500 To'g'ri javob: D) 31 500 ✔ 9. Integralni hisoblang: ∫₀^(π/4) cos2x dx. A) 2 B) 1 C) √2/2 D) 1/2 To'g'ri javob: D) 1/2 ✔ 10. 11 ta haddan iborat arifmetik progressiya hadlarining yig'indisi 132 ga teng. Uning o'rta (6-) hadini toping. A) 11 B) 6 C) 13 D) 12 To'g'ri javob: D) 12 ✔ 11. Yig'indini toping: 1 − 1/3 + 1/9 − 1/27 + … . A) 3/2 B) 2/3 C) 3/4 D) 1/2 To'g'ri javob: C) 3/4 ✔ 12. Konus yon sirtining yoyilmasi yarim doira, asos radiusi 3 ga teng. Konusning yon sirtini toping. A) 18π B) 36π C) 9π D) 27π To'g'ri javob: A) 18π ✔ 13. Agar tg α + ctg α = 3 bo'lsa, sin2α ni toping. A) 1/3 B) 3/2 C) 1/2 D) 2/3 To'g'ri javob: D) 2/3 ✔ Matematika — davlat granti mashq variantlari | 20 14. f(x) = sin x · cos x funksiyaning boshlang'ich funksiyalaridan birini ko'rsating. A) sin²x B) cos²x/2 C) sin²x/2 D) sin2x/2 To'g'ri javob: C) sin²x/2✔ 15. 18 soni 72 sonining necha foizini tashkil etadi? A) 18% B) 25% C) 40% D) 4% To'g'ri javob: B) 25% ✔ 16. f(x) = (x² + 1)/x (x > 0) funksiyaning boshlang'ich funksiyalarining umumiy ko'rinishini toping. A) (x³/3 + x)/(x²/2) + C B) x²/2 − 1/x² + C C) x + ln x + C D) x²/2 + ln x + C To'g'ri javob: D) x²/2 + ln x + C ✔ 17. Rombning yuzi 48 ga, tomoni 8 ga teng. Rombning balandligini toping. A) 6 B) 4 C) 12 D) 3 To'g'ri javob: A) 6 ✔ 18. a ning qanday qiymatlarida ax² + 4x + 1 = 0 tenglama yagona ildizga ega bo'ladi? A) 0; 4 B) −4; 4 C) 0 D) 4 To'g'ri javob: A) 0; 4 ✔ 19. (3; -5) nuqtaga koordinatalar boshiga nisbatan simmetrik nuqtani toping. A) (-3; 5) B) (3; 0) C) (-5; 3) D) (0; 5) To'g'ri javob: A) (-3; 5) ✔ 20. Konus o'q kesimining uchidagi burchak 90° ga, konus balandligi 3 ga teng. Konus hajmini toping. A) 3π B) 27π C) 18π D) 9π To'g'ri javob: D) 9π ✔ Matematika — davlat granti mashq variantlari | 21 21. 3 ga karrali barcha ikki xonali sonlarning yig'indisini toping. A) 1683 B) 1650 C) 1584 D) 1665 To'g'ri javob: D) 1665✔ 22. y = cos²x − sin²x funksiyaning eng kichik musbat davrini toping. A) π B) 4π C) 2π D) π/2 To'g'ri javob: A) π ✔ 23. x² + y² = 10, xy = 3 sistemaning yechimlari uchun x + y ning eng katta qiymatini toping. A) 3 B) 4 C) 16 D) √10 To'g'ri javob: B) 4 ✔ 24. Teng yonli trapetsiyaning asoslari 4 va 10 ga, o'tkir burchagi 45° ga teng. Trapetsiya yuzini toping. A) 18 B) 28 C) 21 D) 42 To'g'ri javob: C) 21 ✔ 25. ABC uchburchakda AM – mediana. AM vektorni AB va AC vektorlar orqali ifodalang. A) AB + AC B) (AB + AC)/3 C) AC - AB D) (AB + AC)/2 To'g'ri javob: D) (AB + AC)/2 ✔ 26. a₁ = 7, d = −2 bo'lgan arifmetik progressiya dastlabki n ta hadi yig'indisining eng katta qiymatini toping. A) 15 B) 17 C) 12 D) 16 To'g'ri javob: D) 16 ✔ 27. Hajmi 48 ga teng konus balandligining o'rtasidan asosga parallel tekislik o'tkazilgan. Ajralgan kichik konus hajmini toping. A) 6 B) 12 C) 24 D) 16 To'g'ri javob: A) 6 ✔ Matematika — davlat granti mashq variantlari | 22 28. Tomoni a ga teng muntazam oltiburchak yuzi tomoni a ga teng muntazam uchburchak yuzidan necha marta katta? A) 4 B) 6 C) 2√3 D) 3 To'g'ri javob: B) 6✔ 29. Rombning bir diagonali uning tomoniga teng. Rombning o'tmas burchagini toping. A) 100° B) 150° C) 135° D) 120° To'g'ri javob: D) 120° ✔ 30. Silindr hajmi 90 ga teng. Asosi va balandligi silindrnikiday bo'lgan konus hajmini toping. A) 45 B) 30 C) 60 D) 270 To'g'ri javob: B) 30 ✔ Matematika — davlat granti mashq variantlari | 23 5-variant Asosiy fan bloki • bitta to'g'ri javob 1. Chempionatda 10 ta jamoa qatnashadi, har bir jamoa boshqa har biri bilan ikki marta (o'z va raqib maydonida) o'ynaydi. Jami nechta o'yin o'tkaziladi? A) 100 B) 45 C) 90 D) 20 To'g'ri javob: C) 90✔ 2. To'g'ri prizmaning asosi katetlari 3 va 4 ga teng to'g'ri burchakli uchburchak, balandligi 10 ga teng. Prizmaning to'la sirtini toping. A) 120 B) 126 C) 144 D) 132 To'g'ri javob: D) 132 ✔ 3. Hajmi 64 ga teng piramida balandligining o'rtasidan asosga parallel tekislik o'tkazilgan. Ajralgan kichik piramida hajmini toping. A) 16 B) 8 C) 32 D) 4 To'g'ri javob: B) 8 ✔ 4. Tanga 3 marta tashlandi. Kamida bir marta «gerb» tushish ehtimolini toping. A) 3/8 B) 5/8 C) 7/8 D) 1/2 To'g'ri javob: C) 7/8 ✔ 5. Tengsizlikni yeching: log₅(3x − 2) > log₅(x + 4). A) (2/3; 3) B) (−4; +∞) C) (3; +∞) D) (−4; 3) To'g'ri javob: C) (3; +∞) ✔ 6. Aylanaga urinish nuqtasida o'tkazilgan urinma shu nuqtaga o'tkazilgan radiusga nisbatan qanday joylashadi? A) parallel B) 45° burchak ostida C) 60° burchak ostida D) perpendikulyar To'g'ri javob: D) perpendikulyar ✔ Matematika — davlat granti mashq variantlari | 24 7. Tengsizlikni yeching: 1/x < 1. A) 0 < x < 1 B) x < 0 yoki x > 1 C) x > 1 D) x < 0 To'g'ri javob: B) x < 0 yoki x > 1✔ 8. f(x) = √(1 − 2x) bo'lsa, f'(−4) ni toping. A) −2/3 B) 3 C) −1/3 D) −1/6 To'g'ri javob: C) −1/3 ✔ 9. Teng yonli uchburchakning yon tomonlari 10 dan, asosi 12 ga teng. Yon tomonga tushirilgan balandlikni toping. A) 4,8 B) 9,6 C) 8 D) 9 To'g'ri javob: B) 9,6 ✔ 10. Tengsizlikni yeching: x⁴ − 5x² + 4 < 0. A) (−2; −1) (1; 2) ∪ B) (1; 4) C) (1; 2) D) (−2; 2) To'g'ri javob: A) (−2; −1) ∪ (1; 2) ✔ 11. Radiusi 6 ga teng doira sektorining yuzi 15π ga teng. Sektorning markaziy burchagini toping. A) 135° B) 75° C) 150° D) 120° To'g'ri javob: C) 150° ✔ 12. Tenglamani yeching: 25ˣ − 6 · 5ˣ + 5 = 0. A) 1 B) 0; 5 C) 1; 5 D) 0; 1 To'g'ri javob: D) 0; 1 ✔ 13. To'g'ri burchakli uchburchakda to'g'ri burchak uchidan tushirilgan balandlik gipotenuzani 4 va 9 ga teng kesmalarga ajratadi. Balandlikni toping. A) 6 B) 6,5 C) 13 D) 5 To'g'ri javob: A) 6 ✔ Matematika — davlat granti mashq variantlari | 25 14. Kubning qirrasi 2 marta orttirilsa, uning hajmi necha marta ortadi? A) 6 B) 8 C) 2 D) 4 To'g'ri javob: B) 8✔ 15. Uchburchak burchaklari 2:3:4 nisbatda. Uning eng katta burchagini toping. A) 60° B) 100° C) 80° D) 90° To'g'ri javob: C) 80° ✔ 16. Oltiburchakli prizmaning nechta qirrasi bor? A) 24 B) 16 C) 12 D) 18 To'g'ri javob: D) 18 ✔ 17. x > 0 bo'lganda kasrni qisqartiring: (x^(2/3) − 1)/(x^(1/3) + 1). A) x^(1/3) B) x^(1/3) − 1 C) x^(2/3) − 1 D) 1 − x^(1/3) To'g'ri javob: B) x^(1/3) − 1 ✔ 18. b ning qanday qiymatlarida y = 3x + b to'g'ri chiziq y = x³ funksiya grafigiga urinma bo'ladi? A) 0; 3 B) 2 C) −4; 4 D) −2; 2 To'g'ri javob: D) −2; 2 ✔ 19. Ifodani soddalashtiring: (1 + 1/(x − 1)) : (1 + 1/(x² − 1)). A) (x + 1)/x B) x + 1 C) x/(x + 1) D) 1/x To'g'ri javob: A) (x + 1)/x ✔ 20. 1 dan 30 gacha bo'lgan natural sonlardan tavakkaliga bittasi tanlandi. U 3 ga yoki 5 ga bo'linish ehtimolini toping. A) 8/15 B) 7/15 C) 1/2 D) 2/5 To'g'ri javob: B) 7/15 ✔ Matematika — davlat granti mashq variantlari | 26 21. Radiusi 10 ga teng aylanada uzunliklari 12 va 16 ga teng parallel vatarlar markazning turli tomonlarida joylashgan. Vatarlar orasidagi masofani toping. A) 2 B) 10 C) 12 D) 14 To'g'ri javob: D) 14✔ 22. Kvadratga ichki chizilgan va tashqi chizilgan doiralar yuzlarining nisbatini toping. A) 1 : 2 B) 1 : 4 C) 1 : 3 D) 2 : 3 To'g'ri javob: A) 1 : 2 ✔ 23. 6 kishini 3 kishidan iborat ikkita (tartibi muhim bo'lmagan) guruhga necha xil usulda ajratish mumkin? A) 20 B) 6 C) 15 D) 10 To'g'ri javob: D) 10 ✔ 24. f(x) = tg x bo'lsa, f'(π/4) ni toping. A) 2 B) 4 C) 1 D) 1/2 To'g'ri javob: A) 2 ✔ 25. Hisoblang: log_√3 27. A) 3/2 B) 3 C) 6 D) 9 To'g'ri javob: C) 6 ✔ 26. y = lg((x − 1)/(x + 3)) funksiyaning aniqlanish sohasini toping. A) x > 1 B) x < −3 yoki x > 1 C) x ≠ −3 D) −3 < x < 1 To'g'ri javob: B) x < −3 yoki x > 1 ✔ 27. Tengsizlikni yeching: (x + 1)²(x − 4) ≥ 0. A) x ≥ 4 B) x = −1 yoki x ≥ 4 C) x ≥ −1 D) −1 ≤ x ≤ 4 To'g'ri javob: B) x = −1 yoki x ≥ 4 ✔ Matematika — davlat granti mashq variantlari | 27 28. f(x) = x³ − 3x² funksiyaning maksimum nuqtasini toping. A) 0 B) 1 C) 3 D) 2 To'g'ri javob: A) 0✔ 29. Uchburchakning ikki tomoni 6 va 10 ga, ular orasidagi burchak 150° ga teng. Uchburchak yuzini toping. A) 7,5 B) 15 C) 15√3 D) 30 To'g'ri javob: B) 15 ✔ 30. Agar x + y = 7 va x² + y² = 29 bo'lsa, (x − y)² ning qiymatini toping. A) 9 B) 29 C) 1 D) 49 To'g'ri javob: A) 9 ✔ Matematika — davlat granti mashq variantlari | 28 6-variant Asosiy fan bloki • bitta to'g'ri javob 1. Tenglamalar sistemasining yechimi (x; y) bo'lsa, xy ni toping: x + y = 7, x − y = 1. A) 7 B) 6 C) 10 D) 12 To'g'ri javob: D) 12✔ 2. y = x² − x − 6 parabola va Ox o'qi bilan chegaralangan figuraning yuzini toping. A) 25/6 B) 125/6 C) 27/2 D) 125/3 To'g'ri javob: B) 125/6 ✔ 3. Tomonlari 2 va 6 ga teng to'g'ri to'rtburchak uzun tomoni atrofida aylantirildi. Hosil bo'lgan silindrning to'la sirtini toping. A) 28π B) 96π C) 32π D) 24π To'g'ri javob: C) 32π ✔ 4. y = 4x − x² parabola va Ox o'qi bilan chegaralangan figuraning yuzini toping. A) 8 B) 64/3 C) 32/3 D) 16/3 To'g'ri javob: C) 32/3 ✔ 5. Radiusi 5 ga teng sferaning sirtini toping. A) 25π B) 50π C) 100π D) 500π/3 To'g'ri javob: C) 100π ✔ 6. ABCD parallelogrammda A(1; 1), B(4; 2), C(6; 5). D uchning koordinatalarini toping. A) (9; 6) B) (-1; 4) C) (3; 4) D) (4; 3) To'g'ri javob: C) (3; 4) ✔ Matematika — davlat granti mashq variantlari | 29 7. |a| = 3, |b| = 5 va a, b vektorlar orasidagi burchak 60° ga teng. |a + b| ni toping. A) 8 B) 7 C) √34 D) √19 To'g'ri javob: B) 7✔ 8. Kvadrat diagonali uning tomonidan necha marta katta? A) √2 B) 2√2 C) √3 D) 3/2 To'g'ri javob: A) √2 ✔ 9. Hisoblang: arctg1 + arcctg(−1). A) π/2 B) π C) 3π/2 D) 0 To'g'ri javob: B) π ✔ 10. Silindrning balandligi 2 marta orttirilib, asosining radiusi 2 marta kamaytirilsa, uning hajmi qanday o'zgaradi? A) 2 marta kamayadi B) 2 marta ortadi C) 4 marta kamayadi D) o'zgarmaydi To'g'ri javob: A) 2 marta kamayadi ✔ 11. Oralaridagi masofa 30 km bo'lgan ikki avtomobil bir yo'nalishda harakatlanmoqda: oldindagisining tezligi 50 km/soat, orqadagisiniki 70 km/soat. Necha soatdan keyin orqadagi avtomobil oldindagisiga yetib oladi? A) 0,5 B) 0,25 C) 2 D) 1,5 To'g'ri javob: D) 1,5 ✔ 12. Uchburchakning burchaklari arifmetik progressiya tashkil etadi va eng kichigi 30° ga teng. Eng katta burchakni toping. A) 100° B) 90° C) 120° D) 80° To'g'ri javob: B) 90° ✔ 13. 3x + 4y - 2 = 0 va 3x + 4y + 8 = 0 parallel to'g'ri chiziqlar orasidagi masofani toping. A) 6/5 B) 10 C) 1,2 D) 2 To'g'ri javob: D) 2 ✔ Matematika — davlat granti mashq variantlari | 30 14. Arifmetik progressiyada a₂ + a₈ = 20. Dastlabki 9 ta hadining yig'indisini toping. A) 45 B) 90 C) 180 D) 100 To'g'ri javob: B) 90✔ 15. Geometrik progressiyada b₄ = 24 va b₇ = 192. Dastlabki 4 ta hadining yig'indisini toping. A) 48 B) 90 C) 21 D) 45 To'g'ri javob: D) 45 ✔ 16. tg α = 1/2 va tg β = 1/3 bo'lsa, tg(α + β) ni toping. A) 5/6 B) 1/6 C) 1 D) 5/7 To'g'ri javob: C) 1 ✔ 17. a(2; 0) va b(-1; √3) vektorlar orasidagi burchakni toping. A) 60° B) 135° C) 150° D) 120° To'g'ri javob: D) 120° ✔ 18. Integralni hisoblang: ∫₀^(ln2) e^(2x) dx. A) 3 B) 3/2 C) 2 D) 1/2 To'g'ri javob: B) 3/2 ✔ 19. Son 50 dan 65 ga oshdi. U necha foizga oshdi? A) 23% B) 35% C) 15% D) 30% To'g'ri javob: D) 30% ✔ 20. Uzunligi 200 m bo'lgan poyezd uzunligi 400 m bo'lgan ko'prikdan 30 sekundda to'liq o'tdi. Poyezd tezligini m/s da toping. A) 20 B) 15 C) 10 D) 13,3 To'g'ri javob: A) 20 ✔ Matematika — davlat granti mashq variantlari | 31 21. Diagonallari o'zaro perpendikulyar bo'lgan teng yonli trapetsiyaning asoslari 6 va 10 ga teng. Trapetsiya yuzini toping. A) 48 B) 32 C) 80 D) 64 To'g'ri javob: D) 64✔ 22. Tenglamani yeching: (x + 6) = x. ∛ A) 2 B) 6 C) −1 D) 3 To'g'ri javob: A) 2 ✔ 23. Agar sin α + cos α = 1/2 bo'lsa, sin2α ni toping. A) −3/4 B) −1/2 C) 5/4 D) 1/4 To'g'ri javob: A) −3/4 ✔ 24. Integralni hisoblang: ∫₀² e^(x/2) dx. A) 2(e − 1) B) 2e C) e − 1 D) (e − 1)/2 To'g'ri javob: A) 2(e − 1) ✔ 25. Trapetsiyaning asoslari 4 va 6 ga teng, yuzi 20 ga teng. Yon tomonlarining davomlari kesishishidan hosil bo'lgan va katta asosga ega bo'lgan uchburchak yuzini toping. A) 45 B) 24 C) 30 D) 36 To'g'ri javob: D) 36 ✔ 26. Konus yon sirti 20π ga, asos radiusi 4 ga teng. Konus hajmini toping. A) 20π B) 16π C) 48π D) 80π/3 To'g'ri javob: B) 16π ✔ 27. Tenglamani yeching: x/(x − 2) − 8/(x² − 4) = 1. A) Yechimga ega emas B) x = 2 C) x = 6 D) x = −4 To'g'ri javob: A) Yechimga ega emas ✔ Matematika — davlat granti mashq variantlari | 32 28. Rombning diagonallari 18 va 24 ga teng. Rombning perimetrini toping. A) 48 B) 84 C) 56 D) 60 To'g'ri javob: D) 60✔ 29. Avtomobil 100 km yo'lga 8 litr yoqilg'i sarflaydi. 350 km yo'l uchun necha litr yoqilg'i kerak? A) 24 B) 28 C) 30 D) 35 To'g'ri javob: B) 28 ✔ 30. sin x + cos x = 0 tenglamani yeching (k Z). ∈ A) 3π/4 + πk B) π/2 + πk C) ±π/4 + 2πk D) π/4 + πk To'g'ri javob: A) 3π/4 + πk ✔ Matematika — davlat granti mashq variantlari | 33 7-variant Asosiy fan bloki • bitta to'g'ri javob 1. Tengsizlikni yeching: (2x − 3)/(x + 1) ≥ 1. A) −1 < x ≤ 4 B) x ≥ 4 C) x ≥ 2 D) x < −1 yoki x ≥ 4 To'g'ri javob: D) x < −1 yoki x ≥ 4✔ 2. 6 elementli to'plamning nechta qism to'plami bor (bo'sh to'plam va to'plamning o'zi ham hisobga olinadi)? A) 32 B) 64 C) 720 D) 36 To'g'ri javob: B) 64 ✔ 3. 9 ta o'quvchidan 4 tasini navbatchilikka necha xil usulda tanlash mumkin? A) 126 B) 36 C) 252 D) 3024 To'g'ri javob: A) 126 ✔ 4. Agar a² + b² − 4a + 6b + 13 = 0 bo'lsa, a + b ning qiymatini toping. A) 5 B) 2 C) −6 D) −1 To'g'ri javob: D) −1 ✔ 5. Tengsizlikni yeching: 3x − 7 > 2x + 1. A) (−6; +∞) B) (1; +∞) C) (−∞; 7) D) (8; +∞) To'g'ri javob: D) (8; +∞) ✔ 6. Tomonlari 10, 10 va 12 ga teng uchburchakka tashqi chizilgan aylana radiusini toping. A) 5 B) 6,25 C) 6,5 D) 6 To'g'ri javob: B) 6,25 ✔ Matematika — davlat granti mashq variantlari | 34 7. f(x) = x³ − 3x funksiyaning kamayish oralig'ini toping. A) [1; +∞) B) (−∞; 0] C) [0; 3] D) [−1; 1] To'g'ri javob: D) [−1; 1]✔ 8. Radiusi 3 ga teng aylanaga tashqi chizilgan kvadratning yuzini toping. A) 9 B) 36 C) 18 D) 24 To'g'ri javob: B) 36 ✔ 9. Muntazam ikosaedrning nechta yog'i bor? A) 30 B) 20 C) 8 D) 12 To'g'ri javob: B) 20 ✔ 10. y = x² parabolaning qaysi nuqtasida o'tkazilgan urinma y = 4x − 1 to'g'ri chiziqqa parallel bo'ladi? A) (4; 16) B) (3; 9) C) (1; 1) D) (2; 4) To'g'ri javob: D) (2; 4) ✔ 11. Ikki kub hajmlari 27 : 8 nisbatda. Ularning to'la sirtlari nisbatini toping. A) 27 : 8 B) 9 : 4 C) 81 : 16 D) 3 : 2 To'g'ri javob: B) 9 : 4 ✔ 12. Hisoblang: 5^(log₅3 + 1). A) 4 B) 125 C) 15 D) 8 To'g'ri javob: C) 15 ✔ 13. Uchburchak yuzi 24 ga, bir tomoni 8 ga teng. Shu tomonga tushirilgan balandlikni toping. A) 4 B) 12 C) 6 D) 3 To'g'ri javob: C) 6 ✔ Matematika — davlat granti mashq variantlari | 35 14. 1 radian necha gradusga teng? A) 180°/π B) 90°/π C) π/180° D) 360°/π To'g'ri javob: A) 180°/π✔ 15. Hisoblang: (2 + 1)(2² + 1)(2⁴ + 1)(2⁸ + 1) − 2¹⁶. A) −1 B) 2 C) 0 D) 2⁸ To'g'ri javob: A) −1 ✔ 16. Qirrasi a ga teng kubning to'la sirti S ga teng. Qirrasi 3a bo'lgan kubning to'la sirti S dan necha marta katta? A) 3 B) 9 C) 27 D) 6 To'g'ri javob: B) 9 ✔ 17. 72 sonining nechta natural bo'luvchisi bor? A) 12 B) 10 C) 8 D) 6 To'g'ri javob: A) 12 ✔ 18. Agar lg2 = a va lg3 = b bo'lsa, lg12 ni a va b orqali ifodalang. A) 2a + b B) 4ab C) a + 2b D) a + b + 1 To'g'ri javob: A) 2a + b ✔ 19. 3 ta turli sovg'ani 5 o'quvchiga har biriga ko'pi bilan bittadan necha xil usulda tarqatish mumkin? A) 15 B) 125 C) 60 D) 10 To'g'ri javob: C) 60 ✔ 20. f(x) = e^(3x) bo'lsa, f'(0) ni toping. A) 0 B) 3e C) 3 D) 1 To'g'ri javob: C) 3 ✔ Matematika — davlat granti mashq variantlari | 36 21. Uchburchak yuzi 45 ga teng. Bir tomoniga parallel to'g'ri chiziq qolgan ikki tomonni uchdan boshlab 1 : 2 nisbatda bo'ladi. Hosil bo'lgan trapetsiya yuzini toping. A) 36 B) 30 C) 35 D) 40 To'g'ri javob: D) 40✔ 22. ABC uchburchakda AB = 6, AC = 9, BC = 10. A burchak bissektrisasi BC tomonni D nuqtada kesadi. BD ni toping. A) 4 B) 5 C) 3,6 D) 6 To'g'ri javob: A) 4 ✔ 23. f(x) = 2ˣ funksiyaning hosilasini toping. A) 2ˣ B) 2ˣ · ln2 C) 2ˣ · lg2 D) x · 2ˣ⁻¹ To'g'ri javob: B) 2ˣ · ln2 ✔ 24. x⁴ + 4 ko'phadni ko'paytuvchilarga ajrating. A) (x² + x + 2)(x² − x + 2) B) (x² + 2)² C) (x² + 2x + 2)(x² − 2x + 2) D) (x² + 2)(x² − 2) To'g'ri javob: C) (x² + 2x + 2)(x² − 2x + 2) ✔ 25. a ning qanday qiymatlarida x² + ax + 4 = 0 tenglama haqiqiy ildizlarga ega bo'lmaydi? A) (−2; 2) B) (−16; 16) C) (0; 4) D) (−4; 4) To'g'ri javob: D) (−4; 4) ✔ 26. Qirrasi 4 ga teng kub sirti bo'yalgan va u qirrasi 1 ga teng kubchalarga bo'lingan. Nechta kubchaning roppa-rosa ikki yog'i bo'yalgan? A) 8 B) 24 C) 12 D) 32 To'g'ri javob: B) 24 ✔ 27. Muntazam uchburchakka ichki chizilgan va tashqi chizilgan doiralar yuzlarining nisbatini toping. A) 1 : 9 B) 1 : 3 C) 1 : 2 D) 1 : 4 To'g'ri javob: D) 1 : 4 ✔ Matematika — davlat granti mashq variantlari | 37 28. Kasrni qisqartiring: (a² − ab)/(b² − ab). A) b/a B) −a/b C) 1 − a/b D) a/(a − b) To'g'ri javob: B) −a/b✔ 29. Urinma va urinish nuqtasidan o'tgan vatar orasidagi burchak ichida 80° li yoy joylashgan. Shu burchakni toping. A) 80° B) 40° C) 100° D) 160° To'g'ri javob: B) 40° ✔ 30. Hisoblang: e^(2ln3). A) 2e B) 3 C) 9 D) 6 To'g'ri javob: C) 9 ✔ Matematika — davlat granti mashq variantlari | 38 8-variant Asosiy fan bloki • bitta to'g'ri javob 1. Qavariq to'rtburchakning diagonallari 10 va 14 ga teng. Uchlari shu to'rtburchak tomonlarining o'rtalarida bo'lgan to'rtburchak perimetrini toping. A) 12 B) 48 C) 24 D) 35 To'g'ri javob: C) 24✔ 2. Avtomobil A dan B ga 60 km/soat, B dan A ga 40 km/soat tezlik bilan harakatlandi. Uning butun yo'ldagi o'rtacha tezligini toping. A) 48 B) 45 C) 52 D) 50 To'g'ri javob: A) 48 ✔ 3. Musbat hadli geometrik progressiyada b₁ = 2 va S₃ = 26. q ni toping. A) 3 B) 5 C) 4 D) 2 To'g'ri javob: A) 3 ✔ 4. 2x - 3y + 6 = 0 to'g'ri chiziqning burchak koeffitsiyentini toping. A) 3/2 B) 1/3 C) 2/3 D) 2 To'g'ri javob: C) 2/3 ✔ 5. Soat 3:30 ni ko'rsatganda soat va minut millari orasidagi kichik burchakni toping. A) 60° B) 75° C) 90° D) 105° To'g'ri javob: B) 75° ✔ 6. Shar radiusi 2 marta orttirilsa, uning hajmi necha marta ortadi? A) 2 B) 6 C) 4 D) 8 To'g'ri javob: D) 8 ✔ Matematika — davlat granti mashq variantlari | 39 7. Mahsulot narxi 25% ga oshirildi. Dastlabki narxga qaytish uchun yangi narxni necha foizga kamaytirish kerak? A) 30% B) 15% C) 25% D) 20% To'g'ri javob: D) 20%✔ 8. y = x² va y = x chiziqlar bilan chegaralangan figuraning yuzini toping. A) 5/6 B) 1/2 C) 1/6 D) 1/3 To'g'ri javob: C) 1/6 ✔ 9. f(x) = 1/sin²x funksiyaning boshlang'ich funksiyalarining umumiy ko'rinishini toping. A) tg x + C B) −ctg x + C C) ctg²x + C D) 1/sin x + C To'g'ri javob: B) −ctg x + C ✔ 10. Rombning tomoni 6 ga, burchaklaridan biri 30° ga teng. Romb yuzini toping. A) 18 B) 9 C) 18√3 D) 36 To'g'ri javob: A) 18 ✔ 11. Ikki natural sonning ko'paytmasi 120 ga teng, ulardan biri ikkinchisidan 7 ta ortiq. Kichik sonni toping. A) 10 B) 15 C) 8 D) 12 To'g'ri javob: C) 8 ✔ 12. To'g'ri to'rtburchakning tomonlari 3 : 4 nisbatda, perimetri 56 ga teng. Uning diagonalini toping. A) 25 B) 20 C) 28 D) 16 To'g'ri javob: B) 20 ✔ 13. Soat 12:00 dan keyin soat va minut millari birinchi marta necha minutdan so'ng ustma-ust tushadi? A) 715/11 B) 720/11 C) 65 D) 60 To'g'ri javob: B) 720/11 ✔ Matematika — davlat granti mashq variantlari | 40 14. sin(2x − π/3) = 0 tenglamaning eng kichik musbat ildizini toping. A) 2π/3 B) π/6 C) π/3 D) π/2 To'g'ri javob: B) π/6✔ 15. To'g'ri burchakli uchburchakning katetlari 5 va 12 ga teng. U 12 ga teng kateti atrofida aylantirildi. Hosil bo'lgan konusning yon sirtini toping. A) 90π B) 60π C) 65π D) 156π To'g'ri javob: C) 65π ✔ 16. m ning qanday qiymatida x² − 3x + m = 0 tenglama ildizlari uchun x₁² + x₂² = 5 bo'ladi? A) 4 B) 7 C) 2 D) −1 To'g'ri javob: C) 2 ✔ 17. (1; 2) va (3; 6) nuqtalardan o'tuvchi to'g'ri chiziq tenglamasini toping. A) y = 2x B) y = x + 1 C) y = 3x - 1 D) y = 2x + 1 To'g'ri javob: A) y = 2x ✔ 18. f(x) = 2ˣ funksiyaning boshlang'ich funksiyalarining umumiy ko'rinishini toping. A) 2ˣ + C B) x · 2ˣ⁻¹ + C C) 2ˣ/ln2 + C D) 2ˣ⁺¹/(x + 1) + C To'g'ri javob: C) 2ˣ/ln2 + C ✔ 19. Arifmetik progressiyada a₁₀ = 25 va a₂₀ = 55. a₁ ni toping. A) 1 B) −2 C) 3 D) −5 To'g'ri javob: B) −2 ✔ 20. a = 3n − 2 formula bilan berilgan arifmetik progressiyaning dastlabki 20 ta hadi yig'indisini toping. ₙ A) 600 B) 590 C) 620 D) 580 To'g'ri javob: B) 590 ✔ Matematika — davlat granti mashq variantlari | 41 21. Hisoblang: sin75° + sin15°. A) √3/2 B) √2/2 C) √6/2 D) 1 To'g'ri javob: C) √6/2✔ 22. Koordinata o'qlarini (4; 0) va (0; 3) nuqtalarda kesib o'tuvchi to'g'ri chiziq tenglamasini toping. A) 4x + 3y = 7 B) 3x + 4y = 12 C) 3x + 4y = 7 D) 4x + 3y = 12 To'g'ri javob: B) 3x + 4y = 12 ✔ 23. Tenglamani yeching: (x² − 9)/(x + 3) = 0. A) 9 B) 3 C) −3; 3 D) 0 To'g'ri javob: B) 3 ✔ 24. Sharning sirti va hajmi son jihatdan teng. Shar radiusini toping. A) 4 B) 1 C) 3 D) 6 To'g'ri javob: C) 3 ✔ 25. (x² + x)² − 8(x² + x) + 12 = 0 tenglama ildizlarining ko'paytmasini toping. A) 12 B) −6 C) 8 D) 24 To'g'ri javob: A) 12 ✔ 26. Muntazam oltiburchakning tomoni unga tashqi chizilgan aylana radiusiga nisbatan qanday? A) radiusga teng B) radiusdan 2 marta kichik C) radiusdan √3 marta katta D) diametrga teng To'g'ri javob: A) radiusga teng ✔ 27. Ox o'qida A(1; 3) va B(5; 1) nuqtalardan baravar uzoqlikda joylashgan nuqtani toping. A) (4; 0) B) (1,5; 0) C) (3; 0) D) (2; 0) To'g'ri javob: D) (2; 0) ✔ Matematika — davlat granti mashq variantlari | 42 28. Konusning yasovchisi 10 ga teng va asos tekisligi bilan 60° burchak tashkil etadi. Konus hajmini toping. A) 125√3π/3 B) 125√3π C) 250π/3 D) 125π/3 To'g'ri javob: A) 125√3π/3✔ 29. Integralni hisoblang: ∫₀¹ eˣ dx. A) e − 1 B) e C) 1 D) 2e To'g'ri javob: A) e − 1 ✔ 30. Quyidagi sonlardan qaysi biri manfiy? A) cos4 B) cos6 C) sin2 D) sin3 To'g'ri javob: A) cos4 ✔ Matematika — davlat granti mashq variantlari | 43 9-variant Asosiy fan bloki • bitta to'g'ri javob 1. Kubning to'la sirti 150 ga teng. Uning hajmini toping. A) 216 B) 125 C) 150 D) 25 To'g'ri javob: B) 125✔ 2. To'g'ri burchakli parallelepipedning o'lchamlari 3, 4 va 12 ga teng. Uning diagonalini toping. A) 19 B) √153 C) 13 D) 12,5 To'g'ri javob: C) 13 ✔ 3. Tomonlari 6, 8 va 10 ga teng uchburchakning eng kichik balandligini toping. A) 6 B) 4,8 C) 5 D) 4 To'g'ri javob: B) 4,8 ✔ 4. f(x) = x⁴ − 8x² + 3 funksiyaning [−1; 2] kesmadagi eng kichik qiymatini toping. A) 3 B) −4 C) −13 D) −5 To'g'ri javob: C) −13 ✔ 5. Agar a > b > 0 bo'lsa, quyidagi tengsizliklardan qaysi biri doimo to'g'ri bo'ladi? A) b − a > 0 B) −a > −b C) 1/a < 1/b D) a² < b² To'g'ri javob: C) 1/a < 1/b ✔ 6. Ikkita o'yin kubigi tashlandi. Tushgan ochkolar yig'indisi 7 ga teng bo'lish ehtimolini toping. A) 1/6 B) 1/12 C) 7/36 D) 5/36 To'g'ri javob: A) 1/6 ✔ Matematika — davlat granti mashq variantlari | 44 7. Kubning diagonali 6√3 ga teng. Kubning hajmini toping. A) 216 B) 72√3 C) 648 D) 108 To'g'ri javob: A) 216✔ 8. Muntazam dodekaedrning yoqlari qanday ko'pburchaklardan iborat? A) kvadratlar B) muntazam oltiburchaklar C) muntazam uchburchaklar D) muntazam beshburchaklar To'g'ri javob: D) muntazam beshburchaklar ✔ 9. Radiusi 6 ga teng doiraning 60° li sektori yuzini toping. A) 2π B) 6π C) 12π D) 3π To'g'ri javob: B) 6π ✔ 10. x² − 3x − 10 ≤ 0 tengsizlik nechta butun yechimga ega? A) 9 B) 8 C) 7 D) 6 To'g'ri javob: B) 8 ✔ 11. Vatarga perpendikulyar bo'lgan diametr shu vatarni qanday bo'ladi? A) oltin kesim nisbatida bo'ladi B) 2 : 3 nisbatda bo'ladi C) 1 : 2 nisbatda bo'ladi D) teng ikkiga bo'ladi To'g'ri javob: D) teng ikkiga bo'ladi ✔ 12. a ning qanday qiymatida f(x) = x³ + ax funksiya x = 1 nuqtada ekstremumga ega bo'ladi? A) 2 B) −1 C) 0 D) −3 To'g'ri javob: D) −3 ✔ 13. Hisoblang: 7^(log₇2 · log₂5). A) 10 B) 7 C) 2 D) 5 To'g'ri javob: D) 5 ✔ Matematika — davlat granti mashq variantlari | 45 14. f(x) = x³ − 6x² + 9x + 1 funksiyaning maksimumini (maksimum nuqtadagi qiymatini) toping. A) 5 B) 1 C) 4 D) 3 To'g'ri javob: A) 5✔ 15. Uchburchakda a = 3, b = 6 va ular orasidagi burchak 120° ga teng. Shu burchak bissektrisasining uzunligini toping. A) 2 B) 1,5 C) 3 D) 2√3 To'g'ri javob: A) 2 ✔ 16. Aylanaga tashqi chizilgan to'rtburchakning perimetri 24 ga, aylana radiusi 3 ga teng. To'rtburchak yuzini toping. A) 24 B) 72 C) 18 D) 36 To'g'ri javob: D) 36 ✔ 17. Agar a − b = 3 va ab = 10 bo'lsa, a³ − b³ ning qiymatini toping. A) 87 B) 147 C) 27 D) 117 To'g'ri javob: D) 117 ✔ 18. Raqamlari turlicha bo'lgan nechta uch xonali son mavjud? A) 900 B) 648 C) 504 D) 720 To'g'ri javob: B) 648 ✔ 19. To'g'ri burchakli uchburchakda tg A = 3/4, A burchakka yopishgan katet 8 ga teng. Gipotenuzani toping. A) 6 B) 10 C) 32/3 D) 12 To'g'ri javob: B) 10 ✔ 20. 2(x − 3) > x − 8 tengsizlikning eng kichik butun yechimini toping. A) −2 B) −3 C) −1 D) 0 To'g'ri javob: C) −1 ✔ Matematika — davlat granti mashq variantlari | 46 21. Hisoblang: 16^(log₄3). A) 9 B) 81 C) 6 D) 12 To'g'ri javob: A) 9✔ 22. Nuqtadan radiusi 4 ga teng aylanaga o'tkazilgan ikki urinma orasidagi burchak 60° ga teng. Nuqtadan aylana markazigacha bo'lgan masofani toping. A) 4√2 B) 6 C) 4√3 D) 8 To'g'ri javob: D) 8 ✔ 23. Agar a = 2 + √3 va b = 2 − √3 bo'lsa, a² + b² ning qiymatini toping. A) 12 B) 16 C) 8 + 4√3 D) 14 To'g'ri javob: D) 14 ✔ 24. (x + 1)⁶ yoyilmasida x³ oldidagi koeffitsiyentni toping. A) 6 B) 15 C) 18 D) 20 To'g'ri javob: D) 20 ✔ 25. Tomonlari 10, 10 va 12 ga teng uchburchakka ichki chizilgan aylana radiusini toping. A) 4 B) 2,5 C) 3 D) 6 To'g'ri javob: C) 3 ✔ 26. Agar log₅2 = a bo'lsa, log₂25 ni a orqali ifodalang. A) a² B) 2/a C) 1/(2a) D) a/2 To'g'ri javob: B) 2/a ✔ 27. Hisoblang: (√3 − 1)² + 2√3. A) 2 B) 4 C) 2 + 2√3 D) 4 − 4√3 To'g'ri javob: B) 4 ✔ Matematika — davlat granti mashq variantlari | 47 28. a > 0 bo'lganda a + 9/a ifodaning eng kichik qiymatini toping. A) 3 B) 6 C) 9 D) 10 To'g'ri javob: B) 6✔ 29. O'yin kubigi 3 marta tashlandi. Har safar 6 ochko tushish ehtimolini toping. A) 1/216 B) 1/6 C) 1/36 D) 1/18 To'g'ri javob: A) 1/216 ✔ 30. Kasrni qisqartiring: (x³ + 8)/(x² − 2x + 4). A) x² + 2 B) x² − 2x + 4 C) (x + 2)² D) x + 2 To'g'ri javob: D) x + 2 ✔ Matematika — davlat granti mashq variantlari | 48 10-variant Asosiy fan bloki • bitta to'g'ri javob 1. Oralaridagi masofa 420 km bo'lgan ikki shahardan bir vaqtda bir-biriga qarab ikki avtomobil yo'lga chiqdi. Ularning tezliklari 60 km/soat va 80 km/soat. Necha soatdan keyin ular uchrashadi? A) 3,5 B) 7 C) 2,5 D) 3 To'g'ri javob: D) 3✔ 2. Teng yonli trapetsiyaning asoslari 4 va 10 ga, balandligi 4 ga teng. Trapetsiya diagonalini toping. A) 5 B) 7 C) √65 D) √116 To'g'ri javob: C) √65 ✔ 3. a(1; 2) va b(3; -1) vektorlar berilgan. 2a - b vektorning koordinatalarini toping. A) (-1; 5) B) (5; 3) C) (-1; 3) D) (-2; 5) To'g'ri javob: A) (-1; 5) ✔ 4. A(2; -4; 6) va B(4; 0; -2) nuqtalarni tutashtiruvchi kesma o'rtasining koordinatalarini toping. A) (3; -2; 2) B) (6; -4; 4) C) (3; -2; 4) D) (1; 2; -4) To'g'ri javob: A) (3; -2; 2) ✔ 5. Son ketma-ket ikki marta 10% dan orttirildi. Son jami necha foizga ortdi? A) 11% B) 20% C) 22% D) 21% To'g'ri javob: D) 21% ✔ 6. Ifodani soddalashtiring: sin²α/(1 + cos α). A) sin α B) 1 − cos α C) 1 − sin α D) cos α To'g'ri javob: B) 1 − cos α ✔ Matematika — davlat granti mashq variantlari | 49 7. Erkin tushayotgan jism birinchi sekundda 4,9 m, har bir keyingi sekundda oldingisidan 9,8 m ko'p yo'l o'tadi. Jism dastlabki 5 sekundda necha metr yo'l o'tadi? A) 117,6 B) 245 C) 98 D) 122,5 To'g'ri javob: D) 122,5✔ 8. a ning qanday qiymatlarida x² − 2ax + a² − 1 = 0 tenglamaning ikkala ildizi ham musbat bo'ladi? A) a > 1 B) a > 0 C) a > 2 D) 0 < a < 1 To'g'ri javob: A) a > 1 ✔ 9. 3 ta daftar va 2 ta ruchka 17 000 so'm, 2 ta daftar va 3 ta ruchka 13 000 so'm turadi. Bitta daftar narxini toping (so'm). A) 4 000 B) 3 000 C) 1 000 D) 5 000 To'g'ri javob: D) 5 000 ✔ 10. f(x) = 1/x (x > 0) funksiyaning boshlang'ich funksiyalarining umumiy ko'rinishini toping. A) −1/x² + C B) ln x + C C) lg x + C D) x + C To'g'ri javob: B) ln x + C ✔ 11. Konus asosining radiusi 3 ga, yasovchisi 9 ga teng. Konus yon sirti yoyilmasining markaziy burchagini toping. A) 150° B) 90° C) 120° D) 60° To'g'ri javob: C) 120° ✔ 12. a > 0 va ∫₀^a x dx = 8 bo'lsa, a ni toping. A) 4 B) 16 C) 8 D) 2√2 To'g'ri javob: A) 4 ✔ 13. y = 1/x, y = 0, x = 1 va x = e² chiziqlar bilan chegaralangan figuraning yuzini toping. A) e² − 1 B) e C) 1 D) 2 To'g'ri javob: D) 2 ✔ Matematika — davlat granti mashq variantlari | 50 14. Mahsulot narxi 120 000 so'm. Unga 12% qo'shilgan qiymat solig'i qo'shilgandan keyingi narxni toping (so'm). A) 132 000 B) 135 600 C) 134 400 D) 144 000 To'g'ri javob: C) 134 400✔ 15. Aylanaga tashqi chizilgan trapetsiyaning yon tomonlari 5 va 7 ga teng. Trapetsiya perimetrini toping. A) 20 B) 24 C) 12 D) 28 To'g'ri javob: B) 24 ✔ 16. Tomoni 4 ga teng kvadrat o'z diagonali atrofida aylantirildi. Hosil bo'lgan jism hajmini toping. A) 32√2π B) 16√2π/3 C) 32√2π/3 D) 64π/3 To'g'ri javob: C) 32√2π/3 ✔ 17. x² + px + q = 0 tenglamada p = −6 va ildizlardan biri ikkinchisidan 2 marta katta. q ni toping. A) 8 B) 12 C) 9 D) 6 To'g'ri javob: A) 8 ✔ 18. 2; 6; 10; … arifmetik progressiyaning dastlabki nechta hadi yig'indisi 200 ga teng? A) 10 B) 20 C) 8 D) 12 To'g'ri javob: A) 10 ✔ 19. Hisoblang: sin300° · tg240°. A) −3/2 B) −1/2 C) 3/4 D) −√3 To'g'ri javob: A) −3/2 ✔ 20. |a| = 3, |b| = 4 va a, b vektorlar orasidagi burchak 60° ga teng. a · b skalyar ko'paytmani toping. A) 6√3 B) 12 C) 6 D) 3 To'g'ri javob: C) 6 ✔ Matematika — davlat granti mashq variantlari | 51 21. Qavariq to'rtburchakning burchaklari 1 : 2 : 3 : 4 nisbatda. Uning eng katta burchagini toping. A) 120° B) 160° C) 144° D) 135° To'g'ri javob: C) 144°✔ 22. Birinchi quvur hovuzni 6 soatda, ikkinchisi 3 soatda to'ldiradi. Ikkala quvur birgalikda hovuzni necha soatda to'ldiradi? A) 2 B) 4,5 C) 3 D) 1,5 To'g'ri javob: A) 2 ✔ 23. Geometrik progressiyada b₁ = 1 va q = 2. Dastlabki 8 ta hadining yig'indisini toping. A) 127 B) 511 C) 255 D) 256 To'g'ri javob: C) 255 ✔ 24. Quyidagi sonlardan qaysi biri 4; 11; 18; … arifmetik progressiyaning hadi bo'ladi? A) 100 B) 90 C) 95 D) 83 To'g'ri javob: C) 95 ✔ 25. Katetlari 6 va 8 ga teng to'g'ri burchakli uchburchak 6 ga teng kateti atrofida aylantirildi. Hosil bo'lgan konus hajmini toping. A) 96π B) 128π C) 72π D) 384π To'g'ri javob: B) 128π ✔ 26. sin x = 0 tenglama [0; 10] kesmada nechta ildizga ega? A) 3 B) 10 C) 5 D) 4 To'g'ri javob: D) 4 ✔ 27. Muntazam ko'pburchakning tashqi burchagi 24° ga teng. Uning tomonlari sonini toping. A) 15 B) 18 C) 24 D) 12 To'g'ri javob: A) 15 ✔ Matematika — davlat granti mashq variantlari | 52 28. Tenglamani yeching: 0,2x − 0,5(x − 4) = 1,4. A) 2 B) 6 C) 4 D) −3 To'g'ri javob: A) 2✔ 29. Konusning yon sirti asosining yuzidan 2 marta katta. Konus yasovchisi asos tekisligi bilan qanday burchak tashkil etadi? A) 60° B) 75° C) 30° D) 45° To'g'ri javob: A) 60° ✔ 30. m ning qanday qiymatida a(1; m; 2) va b(2; -1; m) vektorlar perpendikulyar bo'ladi? A) -2 B) 1 C) -4 D) 3 To'g'ri javob: A) -2 ✔ Matematika — davlat granti mashq variantlari | 53 11-variant Asosiy fan bloki • bitta to'g'ri javob 1. Hisoblang: √(7 + 4√3). A) 4 + √3 B) 1 + 2√3 C) √7 + 2 D) 2 + √3 To'g'ri javob: D) 2 + √3✔ 2. Uchburchakning uchala medianasi uni 6 ta uchburchakka ajratadi. Uchburchak yuzi 36 ga teng bo'lsa, ularning har birining yuzi nechaga teng? A) 6 B) 12 C) 9 D) 4 To'g'ri javob: A) 6 ✔ 3. y = x² − 4x + 3 parabolaning qaysi nuqtasida o'tkazilgan urinma Ox o'qiga parallel bo'ladi? A) (2; −1) B) (1; 0) C) (2; 3) D) (4; 3) To'g'ri javob: A) (2; −1) ✔ 4. Asosi tomoni 9 ga teng kvadrat bo'lgan piramidaning balandligi 4 ga teng. Piramida hajmini toping. A) 54 B) 324 C) 108 D) 162 To'g'ri javob: C) 108 ✔ 5. Piramidaning barcha yon yoqlari asos tekisligiga bir xil burchak ostida og'ishgan. Piramida uchining asosga proyeksiyasi qaysi nuqta bo'ladi? A) asosga ichki chizilgan aylana markazi B) asos medianalarining kesishish nuqtasi C) asosga tashqi chizilgan aylana markazi D) asos balandliklarining kesishish nuqtasi To'g'ri javob: A) asosga ichki chizilgan aylana markazi ✔ 6. Agar a + b = 5 va ab = 3 bo'lsa, a² + b² ning qiymatini toping. A) 19 B) 25 C) 16 D) 22 To'g'ri javob: A) 19 ✔ Matematika — davlat granti mashq variantlari | 54 7. Tengsizlikni yeching: (x² − 9)/(x − 1) ≥ 0. A) −3 ≤ x < 1 yoki x ≥ 3 B) −3 ≤ x ≤ 3 C) x ≥ 3 D) x ≤ −3 yoki 1 < x ≤ 3 To'g'ri javob: A) −3 ≤ x < 1 yoki x ≥ 3✔ 8. 8 ta elementdan 5 tadan guruhlashlar sonini toping. A) 56 B) 6720 C) 40 D) 336 To'g'ri javob: A) 56 ✔ 9. y = √x funksiya grafigiga abssissasi x₀ = 4 bo'lgan nuqtada o'tkazilgan urinma tenglamasini toping. A) y = x/2 B) y = x/4 + 2 C) y = x/2 + 1 D) y = x/4 + 1 To'g'ri javob: D) y = x/4 + 1 ✔ 10. Tengsizlikni yeching: x² − 5x + 6 < 0. A) (−3; −2) B) (−6; 1) C) (1; 6) D) (2; 3) To'g'ri javob: D) (2; 3) ✔ 11. 1 dan 100 gacha bo'lgan natural sonlardan tavakkaliga tanlangan son to'la kvadrat bo'lish ehtimolini toping. A) 0,1 B) 0,01 C) 0,11 D) 0,09 To'g'ri javob: A) 0,1 ✔ 12. y = √(log₂(x − 1)) funksiyaning aniqlanish sohasini toping. A) (1; 2] B) [3; +∞) C) [2; +∞) D) (1; +∞) To'g'ri javob: C) [2; +∞) ✔ 13. To'g'ri burchakli uchburchakning katetlari 9 va 12 ga teng. Uchburchak perimetrini toping. A) 30 B) 36 C) 33 D) 42 To'g'ri javob: B) 36 ✔ Matematika — davlat granti mashq variantlari | 55 14. Kasrni qisqartiring: (x² − 9)/(x² + 6x + 9). A) (x − 3)/(x + 3) B) x/(x + 3) C) (x − 9)/(6x + 9) D) 1/(x + 3) To'g'ri javob: A) (x − 3)/(x + 3)✔ 15. Muntazam to'rtburchakli piramida asosining tomoni 6 ga, balandligi 4 ga teng. Piramidaning yon sirtini toping. A) 48 B) 96 C) 30 D) 60 To'g'ri javob: D) 60 ✔ 16. Vatar katta yoydagi nuqtadan 40° burchak ostida ko'rinadi. Shu vatar kichik yoydagi nuqtadan qanday burchak ostida ko'rinadi? A) 40° B) 140° C) 100° D) 80° To'g'ri javob: B) 140° ✔ 17. Raqamlari yig'indisi 9 ga teng bo'lgan nechta ikki xonali son mavjud? A) 9 B) 18 C) 10 D) 8 To'g'ri javob: A) 9 ✔ 18. a³ − b³ ifodani ko'paytuvchilarga ajrating. A) (a − b)(a² + 2ab + b²) B) (a − b)(a² + ab + b²) C) (a − b)³ D) (a − b)(a² + b²) To'g'ri javob: B) (a − b)(a² + ab + b²) ✔ 19. Tenglamani yeching: log₃x + x = 4. A) 9 B) 4 C) 1 D) 3 To'g'ri javob: D) 3 ✔ 20. 36 talik karta dastasidan tavakkaliga bitta karta olindi. Uning tuz (as) bo'lish ehtimolini toping. A) 1/12 B) 1/36 C) 1/4 D) 1/9 To'g'ri javob: D) 1/9 ✔ Matematika — davlat granti mashq variantlari | 56 21. f(x) = (x² − 1)³ bo'lsa, f'(2) ni toping. A) 27 B) 36 C) 108 D) 54 To'g'ri javob: C) 108✔ 22. Uchburchakda a = 5, b = 8 va ular orasidagi burchak 60° ga teng. Uchinchi tomonni toping. A) √129 B) √89 C) 7 D) 6 To'g'ri javob: C) 7 ✔ 23. 2³⁰⁰, 3²⁰⁰, 5¹⁰⁰ va 10⁵⁰ sonlaridan eng kattasini ko'rsating. A) 10⁵⁰ B) 5¹⁰⁰ C) 2³⁰⁰ D) 3²⁰⁰ To'g'ri javob: D) 3²⁰⁰ ✔ 24. x² ≤ 9 va x > −1 tengsizliklar sistemasi butun yechimlarining yig'indisini toping. A) 3 B) 6 C) 5 D) 0 To'g'ri javob: B) 6 ✔ 25. Tengsizlikni yeching: 5/(x − 2) ≥ 1. A) (2; 7] B) (−∞; 7] C) (2; 3] D) (0; 7] To'g'ri javob: A) (2; 7] ✔ 26. Muntazam oktaedrning nechta uchi bor? A) 12 B) 4 C) 6 D) 8 To'g'ri javob: C) 6 ✔ 27. To'g'ri burchakli uchburchakning katetlari 8 va 15 ga teng. Unga tashqi chizilgan aylana uzunligini toping. A) 15π B) 17π C) 34π D) 8,5π To'g'ri javob: B) 17π ✔ Matematika — davlat granti mashq variantlari | 57 28. Doira radiusi 3 marta orttirilsa, uning yuzi necha marta ortadi? A) 3 B) 27 C) 6 D) 9 To'g'ri javob: D) 9✔ 29. Agar log_a b = 2 bo'lsa, log_(a²) b³ ni toping. A) 3 B) 6 C) 12 D) 4/3 To'g'ri javob: A) 3 ✔ 30. Muntazam oltiburchakka ichki chizilgan va tashqi chizilgan doiralar yuzlarining nisbatini toping. A) 3 : 4 B) 2 : 3 C) 1 : 2 D) √3 : 2 To'g'ri javob: A) 3 : 4 ✔ Matematika — davlat granti mashq variantlari | 58 12-variant Asosiy fan bloki • bitta to'g'ri javob 1. (x − 1)/(x + 1) + (x + 1)/(x − 1) = 5/2 tenglama ildizlarining ko'paytmasini toping. A) 0 B) 1 C) −9 D) −3 To'g'ri javob: C) −9✔ 2. Integralni hisoblang: ∫₀^π sin x dx. A) 0 B) 1 C) 2 D) 4 To'g'ri javob: C) 2 ✔ 3. 1 dan 100 gacha bo'lgan, 5 ga bo'linmaydigan natural sonlarning yig'indisini toping. A) 3950 B) 4000 C) 1050 D) 4050 To'g'ri javob: B) 4000 ✔ 4. Trapetsiyaning diagonali uning o'rta chizig'ini 3 va 7 ga teng kesmalarga ajratadi. Trapetsiyaning katta asosini toping. A) 14 B) 20 C) 10 D) 7 To'g'ri javob: A) 14 ✔ 5. Xarita masshtabi 1 : 50 000. Xaritada 4 sm ga teng masofa joyda necha km ga teng? A) 20 B) 2 C) 12,5 D) 0,2 To'g'ri javob: B) 2 ✔ 6. O'suvchi geometrik progressiyada b₁ + b₃ = 20 va b₁ · b₃ = 36. Progressiya maxrajini toping. A) 1/3 B) 2 C) 9 D) 3 To'g'ri javob: D) 3 ✔ Matematika — davlat granti mashq variantlari | 59 7. Diagonallari 6 va 8 ga, asoslari 3 va 7 ga teng trapetsiyaning balandligini toping. A) 4,8 B) 2,4 C) 4 D) 5 To'g'ri javob: A) 4,8✔ 8. 2sin²x + 3cos x = 0 tenglamani yeching (k Z). ∈ A) π + 2πk B) ±π/3 + 2πk C) ±2π/3 + 2πk D) ±2π/3 + πk To'g'ri javob: C) ±2π/3 + 2πk ✔ 9. Ifodani soddalashtiring: (sin α + sin3α)/(cos α + cos3α). A) tg 2α B) tg 3α C) tg α D) ctg 2α To'g'ri javob: A) tg 2α ✔ 10. a₁ = 8 va d = −2 bo'lgan arifmetik progressiyaning dastlabki nechta hadi yig'indisi 0 ga teng? A) 8 B) 10 C) 17 D) 9 To'g'ri javob: D) 9 ✔ 11. Sinfdagi 20 o'quvchining o'rtacha yoshi 15 ga teng. O'qituvchining yoshi qo'shilsa, o'rtacha yosh 16 ga teng bo'ladi. O'qituvchi necha yoshda? A) 40 B) 36 C) 32 D) 31 To'g'ri javob: B) 36 ✔ 12. sin α = −0,8 va α (3π/2; 2π) bo'lsa, tg α ni toping. ∈ A) −4/3 B) 3/5 C) −3/4 D) −4/5 To'g'ri javob: A) −4/3 ✔ 13. Ifodani soddalashtiring: 1/cos²α − tg²α. A) tg²α B) 1 C) 2 D) sin²α To'g'ri javob: B) 1 ✔ Matematika — davlat granti mashq variantlari | 60 14. y = eˣ, y = 0, x = 0 va x = ln4 chiziqlar bilan chegaralangan figuraning yuzini toping. A) e⁴ − 1 B) 3 C) 4 D) ln4 To'g'ri javob: B) 3✔ 15. Ikki ishchi birgalikda ishlab, ishni 12 kunda tugatadi. Birinchi ishchi yolg'iz o'zi shu ishni 20 kunda bajaradi. Ikkinchi ishchi yolg'iz o'zi necha kunda bajaradi? A) 24 B) 32 C) 30 D) 8 To'g'ri javob: C) 30 ✔ 16. Konus asosining radiusi 7 ga, yasovchisi 25 ga teng. Konusning to'la sirtini toping. A) 200π B) 175π C) 224π D) 392π To'g'ri javob: C) 224π ✔ 17. √(3x + 1) − √(x − 1) = 2 tenglama ildizlarining yig'indisini toping. A) 6 B) 5 C) 1 D) 4 To'g'ri javob: A) 6 ✔ 18. |a| = 2, |b| = 5 va a · b = -5. a va b vektorlar orasidagi burchakni toping. A) 120° B) 135° C) 150° D) 60° To'g'ri javob: A) 120° ✔ 19. (3; 4) nuqtadan 3x + 4y - 5 = 0 to'g'ri chiziqqacha bo'lgan masofani toping. A) 4 B) 20 C) 3 D) 5 To'g'ri javob: A) 4 ✔ 20. 2x + 3y = 12 to'g'ri chiziq va koordinata o'qlari bilan chegaralangan uchburchakning yuzini toping. A) 12 B) 18 C) 6 D) 24 To'g'ri javob: A) 12 ✔ Matematika — davlat granti mashq variantlari | 61 21. Integralni hisoblang: ∫₀² x² dx. A) 4/3 B) 8 C) 8/3 D) 4 To'g'ri javob: C) 8/3✔ 22. A(1; 0) va B(3; 2) nuqtalar berilgan. AM = 2·AB tenglikni qanoatlantiruvchi M nuqtaning koordinatalarini toping. A) (5; 4) B) (7; 4) C) (6; 4) D) (4; 4) To'g'ri javob: A) (5; 4) ✔ 23. Silindr o'q kesimining diagonali 10 ga, balandligi 8 ga teng. Silindr hajmini toping. A) 48π B) 72π C) 288π D) 36π To'g'ri javob: B) 72π ✔ 24. To'g'ri to'rtburchakning diagonali 13 ga, bir tomoni 5 ga teng. Uning yuzini toping. A) 120 B) 65 C) 60 D) 30 To'g'ri javob: C) 60 ✔ 25. Qayiqning turg'un suvdagi tezligi 15 km/soat, oqim tezligi 3 km/soat. Qayiq 36 km oqim bo'yicha va shuncha masofa orqaga suzdi. Butun yo'lga qancha vaqt (soat) sarflandi? A) 6 B) 4 C) 5 D) 4,8 To'g'ri javob: C) 5 ✔ 26. Radiusi 8 ga teng doiraning 90° li sektori o'ralib, konus yon sirti hosil qilindi. Konus balandligini toping. A) 2√15 B) 6 C) √60/2 D) 2√3 To'g'ri javob: A) 2√15 ✔ 27. Silindrga shar ichki chizilgan (shar silindrning asoslari va yon sirtiga urinadi). Shar hajmining silindr hajmiga nisbatini toping. A) 1/2 B) 1/3 C) 3/4 D) 2/3 To'g'ri javob: D) 2/3 ✔ Matematika — davlat granti mashq variantlari | 62 28. Cheksiz kamayuvchi geometrik progressiyada b₁ = 9 va S = 12. Progressiya maxrajini toping. A) 1/2 B) 1/4 C) 3/4 D) 1/3 To'g'ri javob: B) 1/4✔ 29. Sinfdagi o'g'il va qiz bolalar soni 3 : 5 nisbatda, jami 32 o'quvchi. Qizlar sonini toping. A) 20 B) 16 C) 18 D) 12 To'g'ri javob: A) 20 ✔ 30. x + y = 1, x³ + y³ = 19 sistemaning yechimlari uchun xy ni toping. A) 3 B) −6 C) −18 D) 20 To'g'ri javob: B) −6 ✔ Matematika — davlat granti mashq variantlari | 63 13-variant Asosiy fan bloki • bitta to'g'ri javob 1. f(x) = eˣ − x funksiyaning eng kichik qiymatini toping. A) 0 B) e C) e − 1 D) 1 To'g'ri javob: D) 1✔ 2. Kubning bir uchidan chiqqan ikki qo'shni yog' diagonallari orasidagi burchakni toping. A) 90° B) 60° C) 45° D) 30° To'g'ri javob: B) 60° ✔ 3. Ifodani soddalashtiring: (a + 2)² − (a − 2)(a + 2). A) 4a B) 4a + 8 C) 2a² + 4a D) 8 To'g'ri javob: B) 4a + 8 ✔ 4. Tengsizlikni yeching: |x² − 5| < 4. A) (−3; −1) (1; 3) ∪ B) (1; 3) C) (1; 9) D) (−3; 3) To'g'ri javob: A) (−3; −1) ∪ (1; 3) ✔ 5. Radiusi 6,5 ga teng aylanaga to'g'ri burchakli uchburchak ichki chizilgan, uning bir kateti 5 ga teng. Ikkinchi katetini toping. A) 12 B) 13 C) 6 D) √17 To'g'ri javob: A) 12 ✔ 6. x > 0, y > 0 bo'lganda ifodani soddalashtiring: (x − y)/(√x + √y) + √y. A) √x + √y B) √x − 2√y C) √x D) √y To'g'ri javob: C) √x ✔ Matematika — davlat granti mashq variantlari | 64 7. Qirrasi 5 ga teng kubning ayqash qirralari orasidagi masofani toping. A) 2,5 B) 5 C) 5√3 D) 5√2 To'g'ri javob: B) 5✔ 8. f(x) = x³ − 3x² + 4 funksiyaning minimumini (minimum nuqtadagi qiymatini) toping. A) 0 B) 2 C) 4 D) 8 To'g'ri javob: A) 0 ✔ 9. Uchburchakning ikki tomoni 8 va 12 ga, ular orasidagi burchak 30° ga teng. Uchburchak yuzini toping. A) 48 B) 12 C) 24 D) 24√3 To'g'ri javob: C) 24 ✔ 10. y = log₂x funksiyaga teskari funksiyani ko'rsating. A) y = log_x 2 B) y = (1/2)ˣ C) y = 2ˣ D) y = x² To'g'ri javob: C) y = 2ˣ ✔ 11. Aylana uzunligi 10π ga teng. Shu aylana bilan chegaralangan doira yuzini toping. A) 100π B) 10π C) 25π D) 50π To'g'ri javob: C) 25π ✔ 12. Kesik piramida asoslarining yuzlari 16 va 4 ga, balandligi 6 ga teng. Kesik piramida hajmini toping. A) 60 B) 168 C) 40 D) 56 To'g'ri javob: D) 56 ✔ 13. AB vatar radiusga teng. A nuqtada aylanaga o'tkazilgan urinma bilan AB vatar orasidagi o'tkir burchakni toping. A) 45° B) 60° C) 15° D) 30° To'g'ri javob: D) 30° ✔ Matematika — davlat granti mashq variantlari | 65 14. Qutida 5 ta qizil va 3 ta ko'k shar bor. Tavakkaliga 2 ta shar olindi. Ikkalasi ham qizil bo'lish ehtimolini toping. A) 5/14 B) 3/14 C) 5/8 D) 25/64 To'g'ri javob: A) 5/14✔ 15. Tengsizlikni yeching: x² ≤ 2x. A) (−∞; 2] B) [−2; 0] C) [0; 4] D) [0; 2] To'g'ri javob: D) [0; 2] ✔ 16. Uchburchakning ikki tomoni 7 va 3 ga teng. Uchinchi tomon butun son bo'lsa, u nechta turli qiymat qabul qilishi mumkin? A) 5 B) 4 C) 6 D) 7 To'g'ri javob: A) 5 ✔ 17. Ikki mergan nishonga mos ravishda 0,7 va 0,6 ehtimol bilan tegizadi. Ular bittadan o'q uzdi. Kamida bittasi nishonga tegish ehtimolini toping. A) 0,88 B) 0,65 C) 0,12 D) 0,42 To'g'ri javob: A) 0,88 ✔ 18. Tengsizlikni yeching: |x − 1| > |x + 3|. A) (−∞; −3) B) (−3; 1) C) (−∞; −2) D) (−∞; −1) To'g'ri javob: D) (−∞; −1) ✔ 19. Ikkita o'yin kubigi tashlandi. Tushgan ochkolar yig'indisi 10 ga teng bo'lish ehtimolini toping. A) 1/6 B) 5/36 C) 1/12 D) 1/9 To'g'ri javob: C) 1/12 ✔ 20. Tengsizlikni yeching: (x − 1)/(x + 2) ≤ 0. A) x ≤ 1 B) −1 ≤ x < 2 C) x < −2 yoki x ≥ 1 D) −2 < x ≤ 1 To'g'ri javob: D) −2 < x ≤ 1 ✔ Matematika — davlat granti mashq variantlari | 66 21. Hisoblang: (8^(2/3) · 27^(1/3))/16^(1/4). A) 6 B) 12 C) 3 D) 9 To'g'ri javob: A) 6✔ 22. Tengsizlikni yeching: (1/3)ˣ ≥ 9. A) (−∞; −1/2] B) [−3; +∞) C) (−∞; −2] D) [9; +∞) To'g'ri javob: C) (−∞; −2] ✔ 23. Hisoblang: 3^(2·log₃5). A) 10 B) 125 C) 25 D) 5 To'g'ri javob: C) 25 ✔ 24. Hisoblang: log₆4 + log₆9. A) 13 B) 36 C) 2 D) log₆13 To'g'ri javob: C) 2 ✔ 25. f(x) = ln(sin x) funksiyaning hosilasini toping (sin x > 0). A) 1/sin x B) ctg x C) tg x D) cos x To'g'ri javob: B) ctg x ✔ 26. 5 o'g'il va 4 qizdan 3 kishilik guruhni necha xil usulda tuzish mumkin, agar guruhda kamida bitta qiz bo'lishi shart bo'lsa? A) 80 B) 64 C) 74 D) 84 To'g'ri javob: C) 74 ✔ 27. Uchburchak medianalari kesishish nuqtasida har bir median uchidan boshlab hisoblaganda qanday nisbatda bo'linadi? A) 3 : 1 B) 2 : 1 C) 3 : 2 D) 1 : 1 To'g'ri javob: B) 2 : 1 ✔ Matematika — davlat granti mashq variantlari | 67 28. Hisoblang: 27^(2/3) + 16^(3/4). A) 18 B) 17 C) 15 D) 12 To'g'ri javob: B) 17✔ 29. Moddiy nuqta x(t) = t³ − 6t² + 9t qonun bo'yicha harakatlanmoqda. Tezlik ikkinchi marta nolga teng bo'lgan paytdagi tezlanishni toping. A) 0 B) 3 C) 6 D) 12 To'g'ri javob: C) 6 ✔ 30. To'g'ri burchakli parallelepipedning o'lchamlari 2, 3 va 6 ga teng. Uning to'la sirtini toping. A) 66 B) 36 C) 54 D) 72 To'g'ri javob: D) 72 ✔ Matematika — davlat granti mashq variantlari | 68 14-variant Asosiy fan bloki • bitta to'g'ri javob 1. Arifmetik progressiyada a₁ = 5 va d = −2. Dastlabki 10 ta hadining yig'indisini toping. A) −20 B) −30 C) −40 D) −50 To'g'ri javob: C) −40✔ 2. Integralni hisoblang: ∫₀⁴ √(2x + 1) dx. A) 9 B) 26/3 C) 52/3 D) 13/3 To'g'ri javob: B) 26/3 ✔ 3. tg α = 3/4 bo'lsa, cos2α ni toping. A) 24/25 B) 7/25 C) 9/25 D) 16/25 To'g'ri javob: B) 7/25 ✔ 4. x − y = 2, xy = 15 sistemaning yechimlari uchun x² + y² ni toping. A) 30 B) 64 C) 34 D) 19 To'g'ri javob: C) 34 ✔ 5. Hisoblang: cos75° · cos15°. A) √3/2 B) 1/2 C) √3/4 D) 1/4 To'g'ri javob: D) 1/4 ✔ 6. Ketma-ket kelgan uchta juft sonning yig'indisi 78 ga teng. Ularning kattasini toping. A) 28 B) 24 C) 26 D) 30 To'g'ri javob: A) 28 ✔ Matematika — davlat granti mashq variantlari | 69 7. Integralni hisoblang: ∫₀¹ x · e^(x²) dx. A) (e − 1)/2 B) 2(e − 1) C) e − 1 D) e/2 To'g'ri javob: A) (e − 1)/2✔ 8. (2; -3) nuqtaga y = x to'g'ri chiziqqa nisbatan simmetrik nuqtani toping. A) (-3; 2) B) (-3; -3) C) (-2; 3) D) (1; -1) To'g'ri javob: A) (-3; 2) ✔ 9. 15 kg 40% li mis qotishmasiga necha kg sof mis qo'shilsa, 50% li qotishma hosil bo'ladi? A) 3 B) 1,5 C) 5 D) 2 To'g'ri javob: A) 3 ✔ 10. Bankka yillik 12% oddiy foiz bilan 500 000 so'm qo'yildi. 3 yilda qancha foiz daromad olinadi (so'm)? A) 202 464 B) 180 000 C) 60 000 D) 120 000 To'g'ri javob: B) 180 000 ✔ 11. Hisoblang: cos(2arcsin(1/3)). A) 7/9 B) 2/3 C) 8/9 D) 1/9 To'g'ri javob: A) 7/9 ✔ 12. Muntazam beshburchakning ichki burchagini toping. A) 72° B) 108° C) 100° D) 120° To'g'ri javob: B) 108° ✔ 13. a₁ = −10 va d = 3 bo'lgan arifmetik progressiyaning birinchi musbat hadi nechanchi had? A) 4 B) 6 C) 3 D) 5 To'g'ri javob: D) 5 ✔ Matematika — davlat granti mashq variantlari | 70 14. m ning qanday qiymatlarida x² − (m + 1)x + m = 0 tenglama ildizlari kvadratlarining yig'indisi 10 ga teng bo'ladi? A) 9 B) 1; 3 C) ±√10 D) ±3 To'g'ri javob: D) ±3✔ 15. O'lchamlari 2, 3 va 6 ga teng to'g'ri burchakli parallelepipedga tashqi chizilgan sfera sirtini toping. A) 36π B) 49π C) 49π/4 D) 196π To'g'ri javob: B) 49π ✔ 16. O'suvchi arifmetik progressiyaning ketma-ket uchta hadi yig'indisi 15 ga, ko'paytmasi 80 ga teng. Shu hadlarning kattasini toping. A) 7 B) 10 C) 8 D) 9 To'g'ri javob: C) 8 ✔ 17. y = √x va y = x² chiziqlar bilan chegaralangan figuraning yuzini toping. A) 1/6 B) 1/3 C) 2/3 D) 1 To'g'ri javob: B) 1/3 ✔ 18. To'g'ri burchakli trapetsiyaning asoslari 9 va 4 ga, balandligi 12 ga teng. Uning katta yon tomonini toping. A) √97 B) 12,5 C) 13 D) 15 To'g'ri javob: C) 13 ✔ 19. x³ − 3x² − 4x + 12 = 0 tenglama ildizlarining yig'indisini toping. A) 5 B) 7 C) 3 D) −4 To'g'ri javob: C) 3 ✔ 20. Arifmetik progressiyada a₃ + a₅ + a₇ + a₉ = 40. Dastlabki 11 ta hadining yig'indisini toping. A) 110 B) 100 C) 120 D) 440 To'g'ri javob: A) 110 ✔ Matematika — davlat granti mashq variantlari | 71 21. (3; -4; 12) nuqtadan koordinatalar boshigacha bo'lgan masofani toping. A) 12 B) 19 C) 11 D) 13 To'g'ri javob: D) 13✔ 22. a(2; -1; 2) vektorning uzunligini toping. A) 5 B) 7 C) 3 D) 9 To'g'ri javob: C) 3 ✔ 23. x + y = 5, y + z = 7, x + z = 6 sistemaning yechimida z ni toping. A) 2 B) 4 C) 3 D) 5 To'g'ri javob: B) 4 ✔ 24. Radiusi 4 ga teng aylanaga muntazam o'n ikkiburchak ichki chizilgan. Uning yuzini toping. A) 48√3 B) 96 C) 24 D) 48 To'g'ri javob: D) 48 ✔ 25. Radiusi 6 ga teng yarimsharning to'la sirtini (asosi bilan birga) toping. A) 144π B) 108π C) 72π D) 36π To'g'ri javob: B) 108π ✔ 26. Sinf o'quvchilarining 40% i qizlar, o'g'il bolalar esa 18 nafar. Sinfda jami nechta o'quvchi bor? A) 30 B) 25 C) 36 D) 45 To'g'ri javob: A) 30 ✔ 27. Sharning hajmi 288π ga teng. Uning diametrini toping. A) 12 B) 24 C) 6 D) 8 To'g'ri javob: A) 12 ✔ Matematika — davlat granti mashq variantlari | 72 28. Silindr yon sirtining yoyilmasi tomonlari 6π va 10 ga teng to'g'ri to'rtburchak (6π – asos aylanasi uzunligi). Silindr hajmini toping. A) 360π B) 90π C) 30π D) 60π To'g'ri javob: B) 90π✔ 29. Integralni hisoblang: ∫₁² dx/x². A) −1 B) 1/2 C) ln2 D) 3/8 To'g'ri javob: B) 1/2 ✔ 30. cos α = 1/3 bo'lsa, tg²α ni toping. A) 9 B) 8 C) 1/8 D) 3 To'g'ri javob: B) 8 ✔ Matematika — davlat granti mashq variantlari | 73 15-variant Asosiy fan bloki • bitta to'g'ri javob 1. Piramidaning barcha yon qirralari teng. Piramida uchining asosga proyeksiyasi qaysi nuqta bo'ladi? A) asos balandliklarining kesishish nuqtasi B) asosning istalgan uchi C) asosga ichki chizilgan aylana markazi D) asosga tashqi chizilgan aylana markazi To'g'ri javob: D) asosga tashqi chizilgan aylana markazi✔ 2. Kasrni qisqartiring: (a⁴ − 16)/((a² + 4)(a − 2)). A) a² + 2 B) (a − 2)² C) a + 2 D) a² − 4 To'g'ri javob: C) a + 2 ✔ 3. Ikki nuqtada kesishuvchi ikki aylana nechta umumiy urinmaga ega? A) 4 B) 1 C) 3 D) 2 To'g'ri javob: D) 2 ✔ 4. −3 < x < 2 bo'lganda ifodani soddalashtiring: |x − 2| + |x + 3|. A) 5 B) 2x + 5 C) 1 − 2x D) 2x + 1 To'g'ri javob: A) 5 ✔ 5. Tenglamani yeching: 4ˣ − 3 · 2ˣ − 4 = 0. A) 2 B) −1; 2 C) 0; 2 D) 4 To'g'ri javob: A) 2 ✔ 6. A hodisaning ehtimoli 0,35 ga teng. A ga qarama-qarshi hodisaning ehtimolini toping. A) 0,5 B) 1,35 C) 0,65 D) 0,35 To'g'ri javob: C) 0,65 ✔ Matematika — davlat granti mashq variantlari | 74 7. Tomonlari 3, 4 va 6 ga teng uchburchak qanday uchburchak? A) teng yonli B) to'g'ri burchakli C) o'tkir burchakli D) o'tmas burchakli To'g'ri javob: D) o'tmas burchakli✔ 8. Aylanadan tashqaridagi nuqtadan urinma va kesuvchi o'tkazilgan. Urinma kesmasi 6 ga, kesuvchining tashqi qismi 4 ga teng. Kesuvchining butun uzunligini toping. A) 10 B) 8 C) 9 D) 5 To'g'ri javob: C) 9 ✔ 9. Radiuslari 5 va 3 ga teng ikki aylananing markazlari orasidagi masofa 8 ga teng. Aylanalar o'zaro qanday joylashgan? A) umumiy nuqtasi yo'q B) tashqi urinadi C) ichki urinadi D) ikki nuqtada kesishadi To'g'ri javob: B) tashqi urinadi ✔ 10. Tenglamani yeching: 3^(2x − 1) = 27. A) 1 B) 1/2 C) 3/2 D) 2 To'g'ri javob: D) 2 ✔ 11. Tengsizlikni yeching: (x² − x − 6)/(x² − 1) ≤ 0. A) x ≤ −2 yoki x ≥ 3 B) −2 ≤ x ≤ 3 C) −1 < x < 1 D) −2 ≤ x < −1 yoki 1 < x ≤ 3 To'g'ri javob: D) −2 ≤ x < −1 yoki 1 < x ≤ 3 ✔ 12. Tavakkaliga tanlangan ikki xonali sonning 7 ga bo'linish ehtimolini toping. A) 11/90 B) 1/7 C) 7/45 D) 13/90 To'g'ri javob: D) 13/90 ✔ 13. Uchburchakka ichki chizilgan aylana radiusi 2 ga, perimetri 30 ga teng. Uchburchak yuzini toping. A) 15 B) 60 C) 45 D) 30 To'g'ri javob: D) 30 ✔ Matematika — davlat granti mashq variantlari | 75 14. Hisoblang: log₃54 − log₃2. A) 3 B) log₃52 C) 2 D) 27 To'g'ri javob: A) 3✔ 15. Asosining yuzi S va balandligi h bo'lgan piramida hajmi qaysi formula bilan hisoblanadi? A) V = Sh/3 B) V = Sh/2 C) V = Sh D) V = 2Sh/3 To'g'ri javob: A) V = Sh/3 ✔ 16. 1, 2, 3, 4, 5 raqamlaridan raqamlari takrorlanmaydigan nechta uch xonali juft son tuzish mumkin? A) 48 B) 20 C) 24 D) 30 To'g'ri javob: C) 24 ✔ 17. |x + 2| ≤ 5 tengsizlik nechta butun yechimga ega? A) 7 B) 3 C) 10 D) 11 To'g'ri javob: D) 11 ✔ 18. Tenglamani yeching: 3ˣ + 3^(x + 1) + 3^(x + 2) = 117. A) 9 B) 3 C) 2 D) 1 To'g'ri javob: C) 2 ✔ 19. f(x) = ln(x² + 1) bo'lsa, f'(1) ni toping. A) 1/2 B) 1 C) ln2 D) 2 To'g'ri javob: B) 1 ✔ 20. Tomonlari 13, 14 va 15 ga teng uchburchakka tashqi chizilgan aylana radiusini toping. A) 7 B) 33/4 C) 15/2 D) 65/8 To'g'ri javob: D) 65/8 ✔ Matematika — davlat granti mashq variantlari | 76 21. Muntazam to'rtburchakli piramidaning apofemasi 5 ga, asos tomoni 8 ga teng. Piramida hajmini toping. A) 64 B) 80 C) 192 D) 96 To'g'ri javob: A) 64✔ 22. f(x) = x · eˣ funksiyaning hosilasini toping. A) x · eˣ B) eˣ C) eˣ + x D) eˣ(x + 1) To'g'ri javob: D) eˣ(x + 1) ✔ 23. ABC uchburchakda C = 70°. A va B burchaklar bissektrisalari orasidagi AIB burchakni toping (I – ∠ bissektrisalar kesishish nuqtasi). A) 110° B) 125° C) 145° D) 135° To'g'ri javob: B) 125° ✔ 24. O'yin kubigi bir marta tashlanganda 4 dan katta son tushish ehtimolini toping. A) 1/6 B) 1/3 C) 2/3 D) 1/2 To'g'ri javob: B) 1/3 ✔ 25. f(x) = (x − 2)²(x + 1) bo'lsa, f'(1) ni toping. A) 0 B) −1 C) −3 D) 2 To'g'ri javob: C) −3 ✔ 26. Agar x > 0 va x² + 1/x² = 14 bo'lsa, x + 1/x ning qiymatini toping. A) √14 B) 4 C) 16 D) 2√3 To'g'ri javob: B) 4 ✔ 27. Nechta natural son x² < 30 tengsizlikni qanoatlantiradi? A) 30 B) 6 C) 4 D) 5 To'g'ri javob: D) 5 ✔ Matematika — davlat granti mashq variantlari | 77 28. Tomoni 12 sm bo'lgan kvadrat shaklidagi tunukaning burchaklaridan teng kvadratlar qirqib olinib, ustki qismi ochiq quti yasaldi. Qutining eng katta hajmini (sm³) toping. A) 128 B) 144 C) 108 D) 96 To'g'ri javob: A) 128✔ 29. Hisoblang: (√7 − √3)(√7 + √3). A) 10 B) 2 C) 4 D) √21 To'g'ri javob: C) 4 ✔ 30. Tengsizlikni yeching: (x − 1)(x − 2)(x − 3)(x − 4) < 0. A) (1; 2) (3; 4) ∪ B) (2; 3) C) (1; 4) D) (2; 3) (4; +∞) ∪ To'g'ri javob: A) (1; 2) ∪ (3; 4) ✔ Matematika — davlat granti mashq variantlari | 78 16-variant Asosiy fan bloki • bitta to'g'ri javob 1. Ikki nolmas vektorning skalyar ko'paytmasi manfiy bo'lsa, ular orasidagi burchak qanday bo'ladi? A) o'tkir B) o'tmas C) nolga teng D) to'g'ri To'g'ri javob: B) o'tmas✔ 2. Tomoni 6 ga teng muntazam oltiburchakning kichik diagonalini toping. A) 6√2 B) 9 C) 12 D) 6√3 To'g'ri javob: D) 6√3 ✔ 3. 5; 9; 13; … arifmetik progressiyaning dastlabki 10 ta hadi yig'indisini toping. A) 460 B) 240 C) 230 D) 220 To'g'ri javob: C) 230 ✔ 4. x + 2y = 4 va 2x + 4y = 8 tenglamalar sistemasi nechta yechimga ega? A) Cheksiz ko'p yechimga B) Ikkita yechimga C) Yechimga ega emas D) Yagona yechimga To'g'ri javob: A) Cheksiz ko'p yechimga ✔ 5. 1 va 25 sonlari orasiga 5 ta son shunday qo'yilganki, hosil bo'lgan 7 ta son arifmetik progressiya tashkil etadi. Progressiya ayirmasini toping. A) 6 B) 5 C) 3 D) 4 To'g'ri javob: D) 4 ✔ 6. 3; 1; 1/3; … cheksiz kamayuvchi geometrik progressiyaning yig'indisini toping. A) 9/2 B) 6 C) 4 D) 13/3 To'g'ri javob: A) 9/2 ✔ Matematika — davlat granti mashq variantlari | 79 7. Sistemani yeching va x + y ni toping: 2x + 3y = 13, 3x − y = 3. A) 5 B) 7 C) 4 D) 6 To'g'ri javob: A) 5✔ 8. 1/x + 1/y = 5/6, x + y = 5 sistemaning yechimlari uchun xy ni toping. A) 6 B) 25/6 C) 30 D) 5 To'g'ri javob: A) 6 ✔ 9. Uchlari (1; 2), (3; -4) va (5; 8) nuqtalarda bo'lgan uchburchak medianalari kesishish nuqtasining koordinatalarini toping. A) (3; 2) B) (3; 3) C) (9; 6) D) (2; 3) To'g'ri javob: A) (3; 2) ✔ 10. f(x) = sin3x funksiyaning boshlang'ich funksiyalarining umumiy ko'rinishini toping. A) sin3x/3 + C B) −cos3x + C C) −cos3x/3 + C D) −3cos3x + C To'g'ri javob: C) −cos3x/3 + C ✔ 11. Teng yonli trapetsiyaga aylana ichki chizilgan, trapetsiya asoslari 2 va 8 ga teng. Aylana radiusini toping. A) 2 B) 2,5 C) 3 D) 4 To'g'ri javob: A) 2 ✔ 12. Hovlida tovuqlar va quyonlar bor: jami 30 ta bosh va 84 ta oyoq. Nechta quyon bor? A) 18 B) 14 C) 12 D) 10 To'g'ri javob: C) 12 ✔ 13. Ifodani soddalashtiring: (1 + cos2α)/(2cos α). A) 2cos α B) cos2α C) cos α D) sin α To'g'ri javob: C) cos α ✔ Matematika — davlat granti mashq variantlari | 80 14. f(x) = eˣ funksiyaning grafigi (0; 4) nuqtadan o'tuvchi boshlang'ich funksiyasini toping. A) F(x) = 4eˣ B) F(x) = eˣ + 4 C) F(x) = 3eˣ D) F(x) = eˣ + 3 To'g'ri javob: D) F(x) = eˣ + 3✔ 15. y = sin²x − 2sin x + 3 funksiyaning eng kichik qiymatini toping. A) 1 B) 2 C) 3 D) 6 To'g'ri javob: B) 2 ✔ 16. sin3α ni sin α orqali ifodalang. A) 3sin α − sin³α B) 4sin³α − 3sin α C) 3sin α − 2sin³α D) 3sin α − 4sin³α To'g'ri javob: D) 3sin α − 4sin³α ✔ 17. Rombning diagonallari 2 : 3 nisbatda, yuzi 108 ga teng. Rombning kichik diagonalini toping. A) 9 B) 6√3 C) 18 D) 12 To'g'ri javob: D) 12 ✔ 18. x : y = 2 : 3 va x + y = 20 bo'lsa, y − x ni toping. A) 12 B) 8 C) 4 D) 6 To'g'ri javob: C) 4 ✔ 19. Bankka 2 000 000 so'm qo'yildi, bir yildan keyin hisobda 2 240 000 so'm bo'ldi. Bankning yillik foiz stavkasini toping. A) 24% B) 12% C) 10% D) 11,2% To'g'ri javob: B) 12% ✔ 20. Konusning hajmi 12π ga, balandligi 4 ga teng. Konus yasovchisini toping. A) 6 B) 5 C) √7 D) 3 To'g'ri javob: B) 5 ✔ Matematika — davlat granti mashq variantlari | 81 21. Ikki silindrning hajmlari teng, asos radiuslari esa 2 : 1 nisbatda. Ularning balandliklari nisbatini toping. A) 1 : 2 B) 4 : 1 C) 1 : 4 D) 2 : 1 To'g'ri javob: C) 1 : 4✔ 22. Geometrik progressiyada b₁ = 3 va q = −2. Dastlabki 6 ta hadining yig'indisini toping. A) −31 B) −21 C) 189 D) −63 To'g'ri javob: D) −63 ✔ 23. Tannarxi 400 so'm bo'lgan mahsulot 500 so'mdan sotildi. Foyda tannarxning necha foizini tashkil etadi? A) 25% B) 100% C) 20% D) 50% To'g'ri javob: A) 25% ✔ 24. Qaysi sonning 30% i 45 ga teng? A) 150 B) 13,5 C) 120 D) 180 To'g'ri javob: A) 150 ✔ 25. Muntazam ko'pburchakning ichki burchagi tashqi burchagidan 4 marta katta. Uning tomonlari sonini toping. A) 12 B) 10 C) 8 D) 9 To'g'ri javob: B) 10 ✔ 26. f(x) = 2x funksiyaning grafigi M(1; 3) nuqtadan o'tuvchi boshlang'ich funksiyasini toping. A) F(x) = x² + 1 B) F(x) = 2x² + 1 C) F(x) = x² + 3 D) F(x) = x² + 2 To'g'ri javob: D) F(x) = x² + 2 ✔ 27. cos α = −5/13 va α (π; 3π/2) bo'lsa, tg α ni toping. ∈ A) −5/13 B) 5/12 C) −12/13 D) 12/5 To'g'ri javob: D) 12/5 ✔ Matematika — davlat granti mashq variantlari | 82 28. |a| = 4, |b| = 5 va a, b orasidagi burchak 30° ga teng. a va b vektorlarga qurilgan uchburchakning yuzini toping. A) 20 B) 5√3 C) 5 D) 10 To'g'ri javob: C) 5✔ 29. Radiusi 3 ga teng sharning hajmini toping. A) 108π B) 36π C) 27π D) 12π To'g'ri javob: B) 36π ✔ 30. Agar biror oraliqning barcha nuqtalarida F'(x) = f(x) bo'lsa, F(x) funksiya shu oraliqda f(x) uchun nima deb ataladi? A) Hosila B) Boshlang'ich funksiya C) Murakkab funksiya D) Teskari funksiya To'g'ri javob: B) Boshlang'ich funksiya ✔ Matematika — davlat granti mashq variantlari | 83 17-variant Asosiy fan bloki • bitta to'g'ri javob 1. 1 dan 100 gacha bo'lgan sonlardan nechtasi na 2 ga, na 3 ga bo'linmaydi? A) 50 B) 34 C) 17 D) 33 To'g'ri javob: D) 33✔ 2. Hisoblang: (1/3)⁻² + (0,5)⁻³ − 4⁰. A) 18 B) 17 C) 16 D) 14 To'g'ri javob: C) 16 ✔ 3. Istalgan uchtasi bir to'g'ri chiziqda yotmaydigan 10 ta nuqtadan uchlari shu nuqtalarda bo'lgan nechta uchburchak yasash mumkin? A) 720 B) 120 C) 240 D) 30 To'g'ri javob: B) 120 ✔ 4. Tengsizliklar sistemasini yeching: |x| ≤ 3, x² ≥ 4. A) [−2; 2] B) [−3; 3] C) [−3; −2] [2; 3] ∪ D) [2; 3] To'g'ri javob: C) [−3; −2] ∪ [2; 3] ✔ 5. Ikki o'xshash uchburchakning mos tomonlari 2:3 nisbatda. Kichik uchburchak yuzi 12 ga teng bo'lsa, katta uchburchak yuzini toping. A) 36 B) 27 C) 18 D) 24 To'g'ri javob: B) 27 ✔ 6. Tengsizlikni yeching: (x − 3)/(x² + 2x + 5) ≤ 0. A) (−∞; −1] B) [−5; 3] C) [−1; 3] D) (−∞; 3] To'g'ri javob: D) (−∞; 3] ✔ Matematika — davlat granti mashq variantlari | 84 7. Qirrasi 4 ga teng kubning diagonalini toping. A) 4√3 B) 8 C) 12 D) 4√2 To'g'ri javob: A) 4√3✔ 8. a ning qanday qiymatlarida y = logₐx funksiya (0; +∞) oraliqda kamayuvchi bo'ladi? A) 0 < a < 1 B) a > 1 C) a > 0 D) −1 < a < 0 To'g'ri javob: A) 0 < a < 1 ✔ 9. Tengsizlikni yeching: 2^(x + 1) + 2^(x − 1) > 5. A) (2; +∞) B) (5/2; +∞) C) (0; +∞) D) (1; +∞) To'g'ri javob: D) (1; +∞) ✔ 10. Hisoblang: 1/(√2 + 1) + 1/(√3 + √2) + 1/(2 + √3). A) 2 B) 2 − √2 C) 1 D) √3 To'g'ri javob: C) 1 ✔ 11. f(x) = x + 4/x funksiyaning [1; 4] kesmadagi eng kichik qiymatini toping. A) 2 B) 3 C) 5 D) 4 To'g'ri javob: D) 4 ✔ 12. Diametrga tiralgan ichki chizilgan burchak nechaga teng? A) 90° B) 180° C) 60° D) 45° To'g'ri javob: A) 90° ✔ 13. Tomonlari 5, 6 va 7 ga teng uchburchakning eng katta burchagi kosinusini toping. A) 2/7 B) 1/7 C) 19/35 D) 1/5 To'g'ri javob: D) 1/5 ✔ Matematika — davlat granti mashq variantlari | 85 14. f(x) = sin³x funksiyaning hosilasini toping. A) cos³x B) 3cos²x C) 3sin²x · cos x D) 3sin²x To'g'ri javob: C) 3sin²x · cos x✔ 15. Radiuslari 6 va 1 ga teng aylanalar markazlari orasidagi masofa 13 ga teng. Ularning umumiy tashqi urinmasi kesmasining (urinish nuqtalari orasidagi) uzunligini toping. A) 2√30 B) 13 C) √168 D) 12 To'g'ri javob: D) 12 ✔ 16. Uchburchakda katta tomon qarshisida qanday burchak yotadi? A) kichik burchak B) har doim o'tmas burchak C) katta burchak D) har doim to'g'ri burchak To'g'ri javob: C) katta burchak ✔ 17. f(x) = x³ − 2x² + 5 bo'lsa, f'(2) ni toping. A) 5 B) 12 C) 8 D) 4 To'g'ri javob: D) 4 ✔ 18. Uchburchakda A burchak B burchakdan 20° ga katta, C burchak esa B burchakdan 2 marta katta. Eng katta burchakni toping. A) 60° B) 70° C) 90° D) 80° To'g'ri javob: D) 80° ✔ 19. Tengsizlikni yeching: |x − 3| < 2. A) (−∞; 5) B) (−5; −1) C) (3; 5) D) (1; 5) To'g'ri javob: D) (1; 5) ✔ 20. Qavariq ko'pyoqning 8 ta yog'i va 12 ta uchi bor. Uning nechta qirrasi bor? A) 18 B) 16 C) 20 D) 22 To'g'ri javob: A) 18 ✔ Matematika — davlat granti mashq variantlari | 86 21. a > 0, b > 0 va a + b = 10 bo'lsa, ab ko'paytmaning eng katta qiymatini toping. A) 20 B) 50 C) 100 D) 25 To'g'ri javob: D) 25✔ 22. Yuzi 32 ga teng kvadratga tashqi chizilgan aylana uzunligini toping. A) 8√2π B) 8π C) 4π D) 16π To'g'ri javob: B) 8π ✔ 23. Tenglamani yeching: 2ˣ · 5ˣ = 0,01. A) 0,1 B) −3 C) −1 D) −2 To'g'ri javob: D) −2 ✔ 24. P(A) = 0,5, P(B) = 0,4 va P(A·B) = 0,2. A yoki B hodisalardan kamida bittasining ro'y berish ehtimolini toping. A) 0,8 B) 0,2 C) 0,9 D) 0,7 To'g'ri javob: D) 0,7 ✔ 25. Uchburchakli piramidaning bir uchidan chiqqan yon qirralari o'zaro perpendikulyar va 3, 4, 5 ga teng. Piramida hajmini toping. A) 20 B) 60 C) 10 D) 30 To'g'ri javob: C) 10 ✔ 26. Moddiy nuqta s(t) = t³ − 2t² + 3 (m) qonun bo'yicha harakatlanmoqda. t = 2 s dagi tezligini (m/s) toping. A) 3 B) 4 C) 12 D) 8 To'g'ri javob: B) 4 ✔ 27. Hisoblang: (2 + √5) + (2 − √5). ∛ ∛ A) 2 B) 4 C) 1 D) √5 To'g'ri javob: C) 1 ✔ Matematika — davlat granti mashq variantlari | 87 28. Radiusi 5 ga teng aylananing markazidan 3 ga teng masofada o'tgan vatar uzunligini toping. A) 6 B) 4 C) √34 D) 8 To'g'ri javob: D) 8✔ 29. Tenglamani yeching: 5^(x − 2) = 7^(x − 2). A) 2 B) 1 C) 0 D) Yechimga ega emas To'g'ri javob: A) 2 ✔ 30. Agar x = √5 − 2 bo'lsa, x + 1/x ning qiymatini toping. A) 2√5 − 4 B) 2√5 C) 4 D) √5 To'g'ri javob: B) 2√5 ✔ Matematika — davlat granti mashq variantlari | 88 18-variant Asosiy fan bloki • bitta to'g'ri javob 1. Integralni hisoblang: ∫₁⁹ dx/√x. A) 8 B) 2 C) 52/3 D) 4 To'g'ri javob: D) 4✔ 2. tg²x = 3 tenglamani yeching (k Z). ∈ A) ±π/6 + πk B) π/3 + 2πk C) ±π/3 + πk D) ±π/6 + 2πk To'g'ri javob: C) ±π/3 + πk ✔ 3. a(2; -1) va b(-3; 4) vektorlar berilgan. a + b vektorning koordinatalarini toping. A) (-1; 3) B) (-1; 5) C) (5; -5) D) (-5; 3) To'g'ri javob: A) (-1; 3) ✔ 4. Kinoteatrning birinchi qatorida 20 ta o'rin bor, har bir keyingi qatorda oldingisidan 2 ta ortiq o'rin bor. Dastlabki 15 qatorda jami nechta o'rin bor? A) 510 B) 480 C) 540 D) 300 To'g'ri javob: A) 510 ✔ 5. Yig'indini toping: 2 + √2 + 1 + 1/√2 + … . A) 4 B) 4√2 C) 2 + 2√2 D) 4 + 2√2 To'g'ri javob: D) 4 + 2√2 ✔ 6. f(x) = 3x² funksiyaning boshlang'ich funksiyalarining umumiy ko'rinishini toping. A) x³ + C B) x³/3 + C C) 3x³ + C D) 6x + C To'g'ri javob: A) x³ + C ✔ Matematika — davlat granti mashq variantlari | 89 7. Aylanaga tashqi chizilgan ABCD to'rtburchakda AB = 7, BC = 6, CD = 9. AD ni toping. A) 11 B) 10 C) 8 D) 12 To'g'ri javob: B) 10✔ 8. Parallelogrammning tomonlari 6 va 10 ga, ular orasidagi burchak 30° ga teng. Parallelogramm yuzini toping. A) 60 B) 30 C) 30√3 D) 15 To'g'ri javob: B) 30 ✔ 9. tg x = √3 tenglamani yeching (k Z). ∈ A) π/3 + 2πk B) π/3 + πk C) ±π/6 + 2πk D) π/6 + πk To'g'ri javob: B) π/3 + πk ✔ 10. ABCD parallelogrammda A burchak bissektrisasi BC tomonni K nuqtada kesadi, BK = 4, KC = 3. Parallelogramm perimetrini toping. A) 14 B) 18 C) 20 D) 22 To'g'ri javob: D) 22 ✔ 11. 720 sonini 2 : 3 : 4 nisbatda bo'laklarga ajrating. Eng katta bo'lakni toping. A) 240 B) 360 C) 288 D) 320 To'g'ri javob: D) 320 ✔ 12. Integralni hisoblang: ∫₀^π cos²x dx. A) 1/2 B) π C) π/2 D) 0 To'g'ri javob: C) π/2 ✔ 13. Sfera sirtining yuzi 64π ga teng. Shar hajmini toping. A) 256π/3 B) 128π/3 C) 256π D) 64π To'g'ri javob: A) 256π/3 ✔ Matematika — davlat granti mashq variantlari | 90 14. Piyoda 4 km/soat tezlik bilan yursa, belgilangan vaqtdan 30 minut kechikadi, 5 km/soat tezlik bilan yursa, 15 minut oldin yetib keladi. Yo'l uzunligini toping (km). A) 10 B) 20 C) 15 D) 12 To'g'ri javob: C) 15✔ 15. 2; 5; 8; … arifmetik progressiyada 59 soni nechanchi had? A) 18 B) 19 C) 21 D) 20 To'g'ri javob: D) 20 ✔ 16. x² − y² = 16, x − y = 2 sistemaning yechimida x ni toping. A) 3 B) 8 C) 5 D) 4 To'g'ri javob: C) 5 ✔ 17. Radiusi 6 ga teng metall shar eritilib, radiusi 2 ga teng bir xil sharchalar quyildi. Nechta sharcha hosil bo'ldi? A) 3 B) 27 C) 36 D) 9 To'g'ri javob: B) 27 ✔ 18. x⁴ − 13x² + 36 = 0 tenglamaning eng katta ildizini toping. A) 2 B) 6 C) 3 D) 9 To'g'ri javob: C) 3 ✔ 19. Rombning diagonallari 12 va 16 ga teng. Uning yuzini toping. A) 48 B) 80 C) 96 D) 192 To'g'ri javob: C) 96 ✔ 20. Integralni hisoblang: ∫₁⁴ √x dx. A) 16/3 B) 14/3 C) 3/2 D) 7 To'g'ri javob: B) 14/3 ✔ Matematika — davlat granti mashq variantlari | 91 21. y = √3x + 1 to'g'ri chiziq Ox o'qining musbat yo'nalishi bilan qanday burchak hosil qiladi? A) 60° B) 120° C) 45° D) 30° To'g'ri javob: A) 60°✔ 22. O'suvchi arifmetik progressiyada a₁ + a₅ = 14 va a₂ · a₄ = 45. a₁ ni toping. A) 2 B) 11 C) 3 D) 5 To'g'ri javob: C) 3 ✔ 23. |x² − 4| = 3x tenglama ildizlarining yig'indisini toping. A) 3 B) 6 C) 4 D) 5 To'g'ri javob: D) 5 ✔ 24. |a| = |b| = 1 va a, b orasidagi burchak 120° ga teng. |2a + b| ni toping. A) 2 B) √7 C) 1 D) √3 To'g'ri javob: D) √3 ✔ 25. y = cos x funksiya quyidagi oraliqlardan qaysi birida kamayuvchi? A) [π/2; 3π/2] B) [π; 2π] C) [−π; 0] D) [0; π] To'g'ri javob: D) [0; π] ✔ 26. Ikki shar radiuslari 1 : 3 nisbatda. Ularning sirtlari nisbatini toping. A) 1 : 27 B) 1 : 3 C) 1 : 9 D) 1 : 6 To'g'ri javob: C) 1 : 9 ✔ 27. Tenglamani yeching: √(x + 2) + √(x − 1) = 3. A) 1 B) 7 C) 2 D) 3 To'g'ri javob: C) 2 ✔ Matematika — davlat granti mashq variantlari | 92 28. Son 15% ga kamaytirilgach, 340 ga teng bo'ldi. Dastlabki sonni toping. A) 425 B) 400 C) 289 D) 391 To'g'ri javob: B) 400✔ 29. |a| = 2, |b| = 3 va a · b = 3. |a - b| ni toping. A) √19 B) √7 C) √13 D) 1 To'g'ri javob: B) √7 ✔ 30. y = sin x · cos x funksiyaning eng katta qiymatini toping. A) √2/2 B) 1 C) 1/2 D) 2 To'g'ri javob: C) 1/2 ✔ Matematika — davlat granti mashq variantlari | 93 19-variant Asosiy fan bloki • bitta to'g'ri javob 1. y = eˣ funksiya grafigiga abssissasi x₀ = 0 bo'lgan nuqtada o'tkazilgan urinma tenglamasini toping. A) y = 1 B) y = x C) y = x + 1 D) y = 2x + 1 To'g'ri javob: C) y = x + 1✔ 2. y = 1/√(x² − 4x) funksiyaning aniqlanish sohasini toping. A) x > 4 B) x ≠ 0, x ≠ 4 C) x < 0 yoki x > 4 D) 0 < x < 4 To'g'ri javob: C) x < 0 yoki x > 4 ✔ 3. Agar a + b = 4 va ab = 2 bo'lsa, a³ + b³ ning qiymatini toping. A) 64 B) 56 C) 48 D) 40 To'g'ri javob: D) 40 ✔ 4. Muntazam ko'pyoqlarning necha turi mavjud? A) 7 B) 4 C) 5 D) 6 To'g'ri javob: C) 5 ✔ 5. To'g'ri burchakli parallelepipedning uchta turli yog'ining yuzlari 6, 8 va 12 ga teng. Parallelepiped hajmini toping. A) 24 B) 576 C) 48 D) 26 To'g'ri javob: A) 24 ✔ 6. Ifodani soddalashtiring: (m² + 2m + 1)/(m² − 1) : (m + 1)/(m − 1). A) (m + 1)/(m − 1) B) 1 C) (m + 1)²/(m − 1)² D) m + 1 To'g'ri javob: B) 1 ✔ Matematika — davlat granti mashq variantlari | 94 7. y = 2ˣ + 3 funksiyaning qiymatlar sohasini toping. A) (4; +∞) B) (0; +∞) C) (3; +∞) D) (−∞; +∞) To'g'ri javob: C) (3; +∞)✔ 8. f(x) = x² − 3x bo'lsa, f(x) = f'(x) tenglama ildizlarining yig'indisini toping. A) 3 B) 1 C) 2 D) 5 To'g'ri javob: D) 5 ✔ 9. Quyidagi sonlardan qaysi biri eng katta? A) √2 + √10 B) 4 C) √3 + 3 D) √5 + √7 To'g'ri javob: D) √5 + √7 ✔ 10. Tengsizlikni yeching: √(x² − 3x) ≤ 2. A) [−1; 0] [3; 4] ∪ B) [3; 4] C) [0; 3] D) [−1; 4] To'g'ri javob: A) [−1; 0] ∪ [3; 4] ✔ 11. Tenglamani yeching: lg(x + 1) + lg(x − 1) = lg3. A) −2; 2 B) 4 C) 2 D) 3 To'g'ri javob: C) 2 ✔ 12. a ≠ −2 bo'lganda (a² − 4)/(a + 2) − a ifoda nimaga teng? A) −2 B) 2a − 2 C) a − 4 D) 4 To'g'ri javob: A) −2 ✔ 13. x² + y² - 6x + 8y = 0 aylananing radiusini toping. A) 10 B) 5 C) 25 D) √14 To'g'ri javob: B) 5 ✔ Matematika — davlat granti mashq variantlari | 95 14. Muntazam uchburchakning balandligi 6√3 ga teng. Uning perimetrini toping. A) 24 B) 12√3 C) 36 D) 18√3 To'g'ri javob: C) 36✔ 15. Asosi 40 sm × 25 sm bo'lgan to'g'ri burchakli parallelepiped shaklidagi idishga 20 litr suv quyildi. Suv sathining balandligini toping (sm). A) 25 B) 20 C) 16 D) 2 To'g'ri javob: B) 20 ✔ 16. Uchburchakda A = 30°, B = 45° va BC = 4. AC tomonni toping. ∠ ∠ A) 8 B) 4√2 C) 2√2 D) 4√3 To'g'ri javob: B) 4√2 ✔ 17. [−5; 10] kesmadagi nechta butun son |3 − x| ≥ 4 tengsizlikni qanoatlantiradi? A) 7 B) 11 C) 9 D) 10 To'g'ri javob: C) 9 ✔ 18. Tekislikda istalgan uchtasi bir to'g'ri chiziqda yotmaydigan 8 ta nuqta berilgan. Ular orqali nechta to'g'ri chiziq o'tkazish mumkin? A) 56 B) 64 C) 16 D) 28 To'g'ri javob: D) 28 ✔ 19. Jism s(t) = −t² + 8t (m) qonun bo'yicha harakatlanmoqda. Harakat boshlangandan necha sekunddan keyin jism to'xtaydi? A) 2 B) 16 C) 4 D) 8 To'g'ri javob: C) 4 ✔ 20. Tomoni 12 ga teng muntazam uchburchakka ichki chizilgan aylana radiusini toping. A) 3√3 B) 2√3 C) 4√3 D) 6 To'g'ri javob: B) 2√3 ✔ Matematika — davlat granti mashq variantlari | 96 21. Kubning barcha qirralari uzunliklarining yig'indisi 48 ga teng. Kub hajmini toping. A) 216 B) 512 C) 48 D) 64 To'g'ri javob: D) 64✔ 22. Aylana uzunligining uning diametriga nisbati nimaga teng? A) π B) π/2 C) 2π D) 2 To'g'ri javob: A) π ✔ 23. Radiuslari 7 va 3 ga teng ikki aylana ichki urinadi. Markazlari orasidagi masofani toping. A) 21 B) 7 C) 4 D) 10 To'g'ri javob: C) 4 ✔ 24. To'g'ri burchakli uchburchakning gipotenuzasi 26 ga, bir kateti 10 ga teng. Ichki chizilgan aylana radiusini toping. A) 4 B) 3 C) 6 D) 5 To'g'ri javob: A) 4 ✔ 25. Radiusi 6 ga teng doiradan 90° li markaziy burchakka mos segment yuzini toping. A) 36π-18 B) 9π C) 9π-36 D) 9π-18 To'g'ri javob: D) 9π-18 ✔ 26. O'quvchida 4 ta ko'ylak, 3 ta shim va 2 juft poyabzal bor. U necha xil usulda kiyinishi mumkin? A) 24 B) 12 C) 9 D) 18 To'g'ri javob: A) 24 ✔ 27. 9ˣ − 4 · 3ˣ + 3 = 0 tenglama ildizlarining yig'indisini toping. A) 0 B) 1 C) 4 D) 3 To'g'ri javob: B) 1 ✔ Matematika — davlat granti mashq variantlari | 97 28. f(x) = x³ − 3x funksiyaning [0; 2] kesmadagi eng katta qiymatini toping. A) 4 B) 0 C) 8 D) 2 To'g'ri javob: D) 2✔ 29. Tengsizlikni yeching: lg(x² − 3x) ≤ 1. A) [−2; 5] B) (3; 5] C) (−∞; 0) (3; +∞) ∪ D) [−2; 0) (3; 5] ∪ To'g'ri javob: D) [−2; 0) ∪ (3; 5] ✔ 30. Sinfda 6 o'g'il va 5 qiz bor. 3 o'g'il va 2 qizdan iborat guruhni necha xil usulda tuzish mumkin? A) 462 B) 30 C) 200 D) 120 To'g'ri javob: C) 200 ✔ Matematika — davlat granti mashq variantlari | 98 20-variant Asosiy fan bloki • bitta to'g'ri javob 1. Ifodani soddalashtiring: cos⁴α − sin⁴α. A) sin2α B) 1 C) cos2α D) cos²α To'g'ri javob: C) cos2α✔ 2. 30% li eritmani suv bilan aralashtirib 1 litr 12% li eritma olish kerak. 30% li eritmadan necha ml olish kerak? A) 600 B) 400 C) 360 D) 120 To'g'ri javob: B) 400 ✔ 3. Geometrik progressiyada b₄ = 1/2 va q = 1/2. b₁ ni toping. A) 2 B) 8 C) 1/16 D) 4 To'g'ri javob: D) 4 ✔ 4. Ifodani soddalashtiring: (1 − cos2α)/sin2α. A) sin α B) ctg α C) 2 tg α D) tg α To'g'ri javob: D) tg α ✔ 5. 3π/4 radian necha gradusga teng? A) 120° B) 135° C) 270° D) 150° To'g'ri javob: B) 135° ✔ 6. Ikki xonali sonning raqamlari yig'indisi 9 ga teng. Raqamlarining o'rni almashtirilsa, son 27 ga ortadi. Shu sonni toping. A) 45 B) 27 C) 63 D) 36 To'g'ri javob: D) 36 ✔ Matematika — davlat granti mashq variantlari | 99 7. Konusning o'q kesimi tomoni 6 ga teng muntazam uchburchak. Konus hajmini toping. A) 27√3π B) 3√3π C) 18√3π D) 9√3π To'g'ri javob: D) 9√3π✔ 8. Silindr asosining radiusi 10% ga orttirildi, balandligi esa 10% ga kamaytirildi. Silindr hajmi necha foizga ortdi? A) 8,9% B) 0% C) 21% D) 10% To'g'ri javob: A) 8,9% ✔ 9. To'g'ri to'rtburchakning diagonali 12 ga teng va u bir tomon bilan 30° burchak tashkil etadi. To'g'ri to'rtburchak yuzini toping. A) 36 B) 36√3 C) 72√3 D) 72 To'g'ri javob: B) 36√3 ✔ 10. Parallelogrammning tomonlari 4 va 6 ga, o'tkir burchagi 60° ga teng. Uning kichik diagonalini toping. A) √52 B) 2√19 C) 5 D) 2√7 To'g'ri javob: D) 2√7 ✔ 11. Musbat hadli geometrik progressiyada b₁ = 2 va b₅ = 162. b₃ ni toping. A) 82 B) 54 C) 6 D) 18 To'g'ri javob: D) 18 ✔ 12. Integralni hisoblang: ∫₁^e dx/x. A) 0 B) 1 C) e − 1 D) e To'g'ri javob: B) 1 ✔ 13. 1/(x − 1) + 1/(x + 1) = 4/3 tenglama ildizlarining yig'indisini toping. A) 3/2 B) 5/2 C) 2 D) −1/2 To'g'ri javob: A) 3/2 ✔ Matematika — davlat granti mashq variantlari | 100 14. Radiusi 3 ga teng metall shar eritilib, asosining radiusi 3 ga teng silindr quyildi. Silindr balandligini toping. A) 3 B) 6 C) 4 D) 12 To'g'ri javob: C) 4✔ 15. y = √x, y = 0 va x = 4 chiziqlar bilan chegaralangan figuraning yuzini toping. A) 8 B) 16/3 C) 4 D) 8/3 To'g'ri javob: B) 16/3 ✔ 16. A(-2; 5) va B(6; -1) nuqtalarni tutashtiruvchi kesma o'rtasining koordinatalarini toping. A) (2; 2) B) (4; 3) C) (2; 3) D) (8; -6) To'g'ri javob: A) (2; 2) ✔ 17. Ayirmasi noldan farqli arifmetik progressiyada a₁ = 2, hamda a₁, a₃, a₁₁ hadlar shu tartibda geometrik progressiya tashkil etadi. d ni toping. A) 2 B) 3 C) 6 D) 4 To'g'ri javob: B) 3 ✔ 18. Tenglamani yeching: √(x + 5) = x − 1. A) −1 B) 5 C) 4 D) −1; 4 To'g'ri javob: C) 4 ✔ 19. To'g'ri to'rtburchakning perimetri 28 ga, diagonali 10 ga teng. Uning yuzini toping. A) 48 B) 96 C) 40 D) 24 To'g'ri javob: A) 48 ✔ 20. [0; 2π] kesmada cos x ≥ 1/2 tengsizlikning yechimlar to'plamini toping. A) [0; π/6] [11π/6; 2π] ∪ B) [0; π/3] C) [0; π/3] [5π/3; 2π] ∪ D) [π/3; 5π/3] To'g'ri javob: C) [0; π/3] ∪ [5π/3; 2π] ✔ Matematika — davlat granti mashq variantlari | 101 21. A(0; 0) va B(4; 2) nuqtalarni tutashtiruvchi kesmaning o'rta perpendikulyari tenglamasini toping. A) y = -2x + 4 B) y = -2x + 5 C) y = -x/2 + 2 D) y = 2x - 3 To'g'ri javob: B) y = -2x + 5✔ 22. Qayiqning oqim bo'yicha tezligi 18 km/soat, oqimga qarshi tezligi 12 km/soat. Daryo oqimining tezligini toping. A) 3 B) 15 C) 6 D) 2 To'g'ri javob: A) 3 ✔ 23. f(x) = 1/(x + 2) funksiyaning boshlang'ich funksiyalarining umumiy ko'rinishini toping. A) −1/(x + 2)² + C B) ln|x| + C C) ln|x + 2| + C D) 2ln|x + 2| + C To'g'ri javob: C) ln|x + 2| + C ✔ 24. f(x) = (2x − 1)³ funksiyaning boshlang'ich funksiyalarining umumiy ko'rinishini toping. A) (2x − 1)⁴/4 + C B) 6(2x − 1)² + C C) (2x − 1)⁴/2 + C D) (2x − 1)⁴/8 + C To'g'ri javob: D) (2x − 1)⁴/8 + C ✔ 25. Arifmetik progressiyada a₁ = 1 va dastlabki 20 ta hadi yig'indisi 400 ga teng. a₂₀ ni toping. A) 40 B) 39 C) 38 D) 41 To'g'ri javob: B) 39 ✔ 26. y = 2x - 1 va y = -x + 5 to'g'ri chiziqlarning kesishish nuqtasini toping. A) (3; 2) B) (1; 4) C) (2; 3) D) (2; 1) To'g'ri javob: C) (2; 3) ✔ 27. Bankka yillik 10% murakkab foiz bilan 1 000 000 so'm qo'yildi. 2 yildan keyin hisobda qancha pul bo'ladi? A) 1 200 000 B) 1 221 000 C) 1 100 000 D) 1 210 000 To'g'ri javob: D) 1 210 000 ✔ Matematika — davlat granti mashq variantlari | 102 28. Ko'pburchak ichki burchaklarining yig'indisi tashqi burchaklari (har bir uchda bittadan olingan) yig'indisidan 2 marta katta. Ko'pburchakning tomonlari sonini toping. A) 6 B) 5 C) 4 D) 8 To'g'ri javob: A) 6✔ 29. Qirrasi 4 ga teng kubga silindr ichki chizilgan (silindr asoslari kubning qarama-qarshi yoqlariga ichki chizilgan). Silindr hajmini toping. A) 8π B) 64π C) 32π D) 16π To'g'ri javob: D) 16π ✔ 30. k ning qanday qiymatida a(1; -2; 3) va b(-2; 4; k) vektorlar kollinear bo'ladi? A) -3 B) -8 C) -6 D) 4 To'g'ri javob: C) -6 ✔ Matematika — davlat granti mashq variantlari | 103 21-variant Asosiy fan bloki • bitta to'g'ri javob 1. A shahardan B shaharga 3 ta, B dan C ga 4 ta yo'l bor. A dan B orqali C ga necha xil yo'l bilan borish mumkin? A) 64 B) 12 C) 7 D) 24 To'g'ri javob: B) 12✔ 2. x ning qanday qiymatlarida y = x² − 8x + 12 funksiya manfiy qiymatlar qabul qiladi? A) (0; 8) B) (2; 6) C) (−6; −2) D) (4; 6) To'g'ri javob: B) (2; 6) ✔ 3. Ikki konsentrik aylana uzunliklarining ayirmasi 6π ga teng. Ularning radiuslari ayirmasini toping. A) 3π B) 6 C) 1,5 D) 3 To'g'ri javob: D) 3 ✔ 4. x < 3 bo'lganda ifodani soddalashtiring: √(x² − 6x + 9) − x. A) 3 − 2x B) 3 − x C) −3 D) 2x − 3 To'g'ri javob: A) 3 − 2x ✔ 5. To'g'ri burchakli uchburchakda sin A = 3/5, gipotenuza esa 20 ga teng. A burchak qarshisidagi katetni toping. A) 15 B) 16 C) 12 D) 9 To'g'ri javob: C) 12 ✔ 6. 0, 1, 2, 3 raqamlarining har biridan bir martadan foydalanib nechta to'rt xonali son tuzish mumkin? A) 24 B) 18 C) 12 D) 6 To'g'ri javob: B) 18 ✔ Matematika — davlat granti mashq variantlari | 104 7. f(x) = x · ln x funksiyaning hosilasini toping. A) ln x + 1 B) 1/x C) ln x D) x + ln x To'g'ri javob: A) ln x + 1✔ 8. Tengsizlikni yeching: (x + 3)(x − 1)(x − 4) > 0. A) −3 < x < 4 B) 1 < x < 4 C) x < −3 yoki 1 < x < 4 D) −3 < x < 1 yoki x > 4 To'g'ri javob: D) −3 < x < 1 yoki x > 4 ✔ 9. Uchrashuvda 12 kishi bir-biri bilan bir martadan qo'l berib ko'rishdi. Jami nechta qo'l berib ko'rishish bo'ldi? A) 144 B) 66 C) 132 D) 78 To'g'ri javob: B) 66 ✔ 10. Agar x/y = 2 bo'lsa, (x² + y²)/(xy) ning qiymatini toping. A) 5/2 B) 3/2 C) 2 D) 5 To'g'ri javob: A) 5/2 ✔ 11. Agar log₂5 = a bo'lsa, log₂40 ni a orqali ifodalang. A) 5a B) 8a C) 3 + a D) 2 + a To'g'ri javob: C) 3 + a ✔ 12. Ifodani soddalashtiring: 1/(x − 1) − 1/(x + 1). A) 1/(x² − 1) B) 2x/(x² − 1) C) 2/(x − 1)² D) 2/(x² − 1) To'g'ri javob: D) 2/(x² − 1) ✔ 13. Uchburchak uchlari tashqi chizilgan aylanani 2 : 3 : 4 nisbatdagi yoylarga ajratadi. Uchburchakning eng kichik burchagini toping. A) 20° B) 80° C) 40° D) 60° To'g'ri javob: C) 40° ✔ Matematika — davlat granti mashq variantlari | 105 14. Radiusi 6 ga teng doiraning 90° li sektori perimetrini toping. A) 3π B) 12+6π C) 12+3π D) 6+3π To'g'ri javob: C) 12+3π✔ 15. Piramidaning 20 ta qirrasi bor. Uning nechta uchi bor? A) 10 B) 20 C) 12 D) 11 To'g'ri javob: D) 11 ✔ 16. To'g'ri burchakli uchburchakning gipotenuzasi 13 ga, bir kateti 5 ga teng. Uchburchakning kichik burchagi sinusini toping. A) 12/13 B) 5/12 C) 5/13 D) 12/5 To'g'ri javob: C) 5/13 ✔ 17. Moddiy nuqta s(t) = 2t³ + t² (m) qonun bo'yicha harakatlanmoqda. t = 1 s dagi tezlanishini (m/s²) toping. A) 3 B) 14 C) 12 D) 8 To'g'ri javob: B) 14 ✔ 18. f'(x₀) hosilaning geometrik ma'nosi nima? A) Funksiyaning x₀ nuqtadagi qiymati B) Grafikka x₀ nuqtada o'tkazilgan urinmaning burchak koeffitsienti C) Grafik ostidagi egri chiziqli trapetsiya yuzi D) Grafikning Oy o'qi bilan kesishish nuqtasi ordinatasi To'g'ri javob: B) Grafikka x₀ nuqtada o'tkazilgan urinmaning burchak koeffitsienti ✔ 19. To'g'ri prizmaning asosi tomoni 4 ga va o'tkir burchagi 30° ga teng romb, prizma balandligi 5 ga teng. Prizma hajmini toping. A) 40√3 B) 20 C) 40 D) 80 To'g'ri javob: C) 40 ✔ 20. To'g'ri prizmaning asosi diagonallari 6 va 8 ga teng romb, balandligi 10 ga teng. Prizmaning yon sirtini toping. A) 200 B) 140 C) 280 D) 240 To'g'ri javob: A) 200 ✔ Matematika — davlat granti mashq variantlari | 106 21. n ning qanday qiymatida n ta elementdan 2 tadan o'rinlashtirishlar soni 56 ga teng bo'ladi? A) 7 B) 28 C) 14 D) 8 To'g'ri javob: D) 8✔ 22. 0,2^(x²) = 5⁻⁴ tenglamaning musbat ildizini toping. A) 4 B) 2 C) 16 D) 1/2 To'g'ri javob: B) 2 ✔ 23. f(x) = ln x − x funksiyaning eng katta qiymatini toping. A) e − 1 B) 0 C) −2 D) −1 To'g'ri javob: D) −1 ✔ 24. Aylana ichida kesishuvchi ikki vatar orasidagi burchak qarshisidagi yoylar 100° va 40° ga teng. Vatarlar orasidagi burchakni toping. A) 140° B) 70° C) 30° D) 60° To'g'ri javob: B) 70° ✔ 25. Tengsizlikni yeching: log₂(x − 3) < 2. A) (3; 7) B) (−∞; 7) C) (0; 7) D) (3; 5) To'g'ri javob: A) (3; 7) ✔ 26. Muntazam uchburchakning yuzi 16√3 ga teng. Uning balandligini toping. A) 4√3 B) 8√3 C) 2√3 D) 8 To'g'ri javob: A) 4√3 ✔ 27. Muntazam oltiburchakli prizma asosining tomoni 4 ga, balandligi 6 ga teng. Prizmaning eng katta diagonalini toping. A) √52 B) 2√13 C) 4√3 D) 10 To'g'ri javob: D) 10 ✔ Matematika — davlat granti mashq variantlari | 107 28. Tengsizlikni yeching: √(x − 2) < 3. A) (−∞; 11) B) [2; 5) C) [2; 11) D) [0; 9) To'g'ri javob: C) [2; 11)✔ 29. y = 3ˣ funksiya grafigi quyidagi nuqtalardan qaysi biri orqali o'tadi? A) (0; 1) B) (1; 1) C) (0; 3) D) (1; 0) To'g'ri javob: A) (0; 1) ✔ 30. To'g'ri burchakli uchburchakning gipotenuzasi 25 ga, bir katetining gipotenuzadagi proyeksiyasi 9 ga teng. Shu katetni toping. A) 20 B) 16 C) 15 D) 12 To'g'ri javob: C) 15 ✔ Matematika — davlat granti mashq variantlari | 108 22-variant Asosiy fan bloki • bitta to'g'ri javob 1. Sonning yarmi va uchdan birining yig'indisi 40 ga teng. Shu sonni toping. A) 24 B) 60 C) 36 D) 48 To'g'ri javob: D) 48✔ 2. Geometrik progressiya hadlarining yig'indisini toping: 3 + 6 + 12 + … + 384. A) 768 B) 1533 C) 765 D) 381 To'g'ri javob: C) 765 ✔ 3. Hisoblang: sin(arccos(3/5)). A) 4/5 B) 3/5 C) 5/4 D) 3/4 To'g'ri javob: A) 4/5 ✔ 4. cos2x = 1/2 tenglamani yeching (k Z). ∈ A) ±π/6 + 2πk B) ±π/6 + πk C) ±π/3 + πk D) ±π/3 + 2πk To'g'ri javob: B) ±π/6 + πk ✔ 5. Trapetsiyaning asoslari 15 va 7 ga teng. Uning diagonallari o'rtalarini tutashtiruvchi kesma uzunligini toping. A) 8 B) 4 C) 11 D) 3,5 To'g'ri javob: B) 4 ✔ 6. Integralni hisoblang: ∫₀^(π/6) sin3x dx. A) 1/2 B) 1 C) 1/3 D) 2/3 To'g'ri javob: C) 1/3 ✔ Matematika — davlat granti mashq variantlari | 109 7. Parallelogrammning tomonlari 8 va 12 ga teng, 8 ga teng tomonga tushirilgan balandlik 9 ga teng. Ikkinchi balandlikni toping. A) 13,5 B) 6 C) 8 D) 4 To'g'ri javob: B) 6✔ 8. |x − 1| + |x − 3| = 2 tenglama nechta butun yechimga ega? A) 3 B) 1 C) 2 D) 4 To'g'ri javob: A) 3 ✔ 9. Tomoni 2 ga teng muntazam uchburchak o'z tomoni atrofida aylantirildi. Hosil bo'lgan jism hajmini toping. A) π B) 2√3π C) 4π D) 2π To'g'ri javob: D) 2π ✔ 10. Arifmetik progressiyada a₁ = 3 va d = 4. a₁₀ ni toping. A) 36 B) 39 C) 43 D) 40 To'g'ri javob: B) 39 ✔ 11. Qavariq o'nburchakning nechta diagonali bor? A) 35 B) 30 C) 45 D) 40 To'g'ri javob: A) 35 ✔ 12. Tomoni 6 ga teng muntazam oltiburchakning katta diagonalini toping. A) 18 B) 6√2 C) 6√3 D) 12 To'g'ri javob: D) 12 ✔ 13. 6 ishchi ishni 15 kunda bajaradi. Xuddi shunday unumdorlik bilan 9 ishchi shu ishni necha kunda bajaradi? A) 10 B) 9 C) 12 D) 22,5 To'g'ri javob: A) 10 ✔ Matematika — davlat granti mashq variantlari | 110 14. x² + bx + c = 0 tenglamaning ildizlari −2 va 5 ga teng. b + c ni toping. A) −13 B) 7 C) 3 D) −10 To'g'ri javob: A) −13✔ 15. Jismning tezligi v(t) = 10 − 2t (m/s). Jism to'xtaguncha qancha yo'l (m) bosib o'tadi? A) 100 B) 50 C) 5 D) 25 To'g'ri javob: D) 25 ✔ 16. x − 1; x + 1; 2x + 5 sonlar shu tartibda geometrik progressiya tashkil etadi. x ning musbat qiymatini toping. A) 2 B) 1 C) 6 D) 3 To'g'ri javob: A) 2 ✔ 17. To'g'ri to'rtburchakning uzunligi 30% ga orttirildi, eni esa 20% ga kamaytirildi. Uning yuzi qanday o'zgardi? A) 4% ga kamaydi B) 4% ga ortdi C) o'zgarmadi D) 10% ga ortdi To'g'ri javob: B) 4% ga ortdi ✔ 18. m > 0 bo'lsa, m ning qanday qiymatida a(m; 3) vektorning uzunligi 5 ga teng bo'ladi? A) 3 B) 2 C) 4 D) √34 To'g'ri javob: C) 4 ✔ 19. sin x = 1/2 tenglamani yeching (k Z). ∈ A) π/6 + πk B) ±π/6 + 2πk C) ±π/3 + 2πk D) (−1)ᵏ · π/6 + πk To'g'ri javob: D) (−1)ᵏ · π/6 + πk ✔ 20. k ning qanday qiymatida a(2; k) va b(3; -6) vektorlar perpendikulyar bo'ladi? A) 4 B) 1 C) 2 D) -3 To'g'ri javob: B) 1 ✔ Matematika — davlat granti mashq variantlari | 111 21. α va β o'tkir burchaklar, sin α = 4/5, cos β = 5/13. cos(α + β) ni toping. A) −33/65 B) −16/65 C) 63/65 D) 56/65 To'g'ri javob: A) −33/65✔ 22. 20% li eritmadan 3 kg va 45% li eritmadan 2 kg aralashtirildi. Hosil bo'lgan aralashmaning konsentratsiyasini toping. A) 35% B) 25% C) 32,5% D) 30% To'g'ri javob: D) 30% ✔ 23. Katetlari 3 va 4 ga teng to'g'ri burchakli uchburchak gipotenuzasi atrofida aylantirildi. Hosil bo'lgan jism hajmini toping. A) 16π B) 12π C) 4,8π D) 9,6π To'g'ri javob: D) 9,6π ✔ 24. a(3; 4) va b(4; 3) vektorlar orasidagi burchak kosinusini toping. A) 12/25 B) 7/25 C) 24/25 D) 3/5 To'g'ri javob: C) 24/25 ✔ 25. Integralni hisoblang: ∫₋₁¹ (x² + x³ + x) dx. A) 2/3 B) 2 C) 4/3 D) 0 To'g'ri javob: A) 2/3 ✔ 26. a(3; -4) vektor bilan bir xil yo'nalgan birlik vektorni toping. A) (0,3; -0,4) B) (0,6; -0,8) C) (3/7; -4/7) D) (0,8; -0,6) To'g'ri javob: B) (0,6; -0,8) ✔ 27. Integralni hisoblang: ∫₋₂² (x⁵ + 3) dx. A) 0 B) 6 C) 12 D) 24 To'g'ri javob: C) 12 ✔ Matematika — davlat granti mashq variantlari | 112 28. Silindrga shar ichki chizilishi uchun silindrning o'q kesimi qanday bo'lishi kerak? A) kvadrat B) teng yonli trapetsiya C) romb D) muntazam uchburchak To'g'ri javob: A) kvadrat✔ 29. Ildizlari 2 − √3 va 2 + √3 bo'lgan keltirilgan kvadrat tenglamani ko'rsating. A) x² + 4x + 3 = 0 B) x² − 4x + 1 = 0 C) x² − 2x + 1 = 0 D) x² − 4x + 7 = 0 To'g'ri javob: B) x² − 4x + 1 = 0 ✔ 30. Silindr asosining radiusi 3 ga, balandligi 5 ga teng. Silindr hajmini toping. A) 15π B) 45π C) 30π D) 75π To'g'ri javob: B) 45π ✔ Matematika — davlat granti mashq variantlari | 113 23-variant Asosiy fan bloki • bitta to'g'ri javob 1. Agar log₃x = 2 va log₃y = 3 bo'lsa, log₃(x²y) ni toping. A) 12 B) 7 C) 5 D) 8 To'g'ri javob: B) 7✔ 2. AB – aylana diametri, C – aylanadagi nuqta, CAB = 25°. CBA ni toping. ∠ ∠ A) 50° B) 75° C) 25° D) 65° To'g'ri javob: D) 65° ✔ 3. f(x) = cos²x funksiyaning hosilasini toping. A) 2cos x B) sin2x C) −2sin x · cos x D) −2sin x To'g'ri javob: C) −2sin x · cos x ✔ 4. Hisoblang: lg25 + lg4. A) 100 B) 1 C) 2 D) lg29 To'g'ri javob: C) 2 ✔ 5. a = 17,5 va b = 2,5 bo'lganda (a³ + b³)/(a² − ab + b²) ifodaning qiymatini toping. A) 25 B) 400 C) 15 D) 20 To'g'ri javob: D) 20 ✔ 6. Tengsizlikni yeching: |2x + 1| ≥ 3. A) x ≤ −2 yoki x ≥ 1 B) x ≤ −1 yoki x ≥ 2 C) x ≥ 1 D) −2 ≤ x ≤ 1 To'g'ri javob: A) x ≤ −2 yoki x ≥ 1 ✔ Matematika — davlat granti mashq variantlari | 114 7. Uchburchakda a = 4, b = 6 va ular orasidagi burchak 120° ga teng. Uchinchi tomonni toping. A) √52 B) 2√7 C) 10 D) 2√19 To'g'ri javob: D) 2√19✔ 8. Ifodani soddalashtiring: ((a + b)/(a − b) − (a − b)/(a + b)) · (a² − b²)/(ab). A) 4ab B) 4 C) 2 D) a + b To'g'ri javob: B) 4 ✔ 9. f(x) = x³ − 6x² funksiya grafigining egilish (burilish) nuqtasi abssissasini toping. A) 2 B) 4 C) 0 D) 6 To'g'ri javob: A) 2 ✔ 10. Uchburchakning tomonlari a = 7, b = 9, c = 8. c tomonga tushirilgan medianani toping. A) 7 B) 6 C) 8 D) √65 To'g'ri javob: A) 7 ✔ 11. Qirrasi 4 ga teng muntazam tetraedrning to'la sirtini toping. A) 64√3 B) 4√3 C) 8√3 D) 16√3 To'g'ri javob: D) 16√3 ✔ 12. Kub diagonali va uning yog'i tekisligi orasidagi burchak sinusini toping. A) √3/3 B) √2/2 C) 1/2 D) √6/3 To'g'ri javob: A) √3/3 ✔ 13. (x - 2)² + (y + 3)² = 16 aylananing markazi va radiusini toping. A) (-2; 3), R = 2 B) (3; -2), R = 4 C) (2; -3), R = 4 D) (2; -3), R = 16 To'g'ri javob: C) (2; -3), R = 4 ✔ Matematika — davlat granti mashq variantlari | 115 14. Limitni hisoblang: lim(h→0) ((2 + h)² − 4)/h. A) 0 B) 4 C) ∞ D) 2 To'g'ri javob: B) 4✔ 15. (2x - 1)⁵ yoyilmasida x² oldidagi koeffitsiyentni toping. A) -20 B) -80 C) -10 D) -40 To'g'ri javob: D) -40 ✔ 16. Tengsizlikni yeching: |x − 2| ≤ x. A) [1; 2] B) [1; +∞) C) [0; +∞) D) [2; +∞) To'g'ri javob: B) [1; +∞) ✔ 17. f(x) = |x| funksiya x = 0 nuqtada qanday xossaga ega? A) Uzilishga ega B) Uzluksiz, ammo differensiallanuvchi emas C) Differensiallanuvchi va f'(0) = 1 D) Differensiallanuvchi va f'(0) = 0 To'g'ri javob: B) Uzluksiz, ammo differensiallanuvchi emas ✔ 18. (x − 5)/(x − 2) > 2 tengsizlik nechta butun yechimga ega? A) 3 B) 4 C) 1 D) 2 To'g'ri javob: D) 2 ✔ 19. Piramidaning asosi tomonlari 6 va 8 ga teng to'g'ri to'rtburchak, barcha yon qirralari 13 ga teng. Piramida hajmini toping. A) 208 B) 192 C) 96 D) 576 To'g'ri javob: B) 192 ✔ 20. Qutida 4 ta oq va 6 ta qora shar bor. Tavakkaliga olingan bitta sharning oq bo'lish ehtimolini toping. A) 3/5 B) 2/3 C) 2/5 D) 1/4 To'g'ri javob: C) 2/5 ✔ Matematika — davlat granti mashq variantlari | 116 21. Teng yonli uchburchakning yon tomoni 10 ga, asosi 12 ga teng. Uchburchak yuzini toping. A) 48 B) 40 C) 96 D) 60 To'g'ri javob: A) 48✔ 22. To'g'ri burchakli parallelepipedning har bir o'lchami 10% ga orttirilsa, uning hajmi necha foizga ortadi? A) 33% B) 33,1% C) 30% D) 21% To'g'ri javob: B) 33,1% ✔ 23. Agar x + 1/x = 3 bo'lsa, x² + 1/x² ning qiymatini toping. A) 9 B) 5 C) 7 D) 11 To'g'ri javob: C) 7 ✔ 24. Tomonlari 6 va 8 ga teng to'g'ri to'rtburchakka tashqi chizilgan aylana radiusini toping. A) 10 B) 7 C) 4 D) 5 To'g'ri javob: D) 5 ✔ 25. x = −2 bo'lganda (x³ − 1)/(x² + x + 1) ifodaning qiymatini toping. A) −9 B) −3 C) −7 D) 1/3 To'g'ri javob: B) −3 ✔ 26. Bir-biridan tashqarida joylashgan (umumiy nuqtasi yo'q, biri ikkinchisining ichida emas) ikki aylana nechta umumiy urinmaga ega? A) 4 B) 1 C) 3 D) 2 To'g'ri javob: A) 4 ✔ 27. C(7, 3) + C(7, 4) yig'indini hisoblang (C(n, k) – n ta elementdan k tadan guruhlashlar soni). A) 35 B) 120 C) 70 D) 56 To'g'ri javob: C) 70 ✔ Matematika — davlat granti mashq variantlari | 117 28. «ANANAS» so'zidagi harflarning o'rinlarini almashtirib nechta turli «so'z» (harflar ketma-ketligi) hosil qilish mumkin? A) 120 B) 60 C) 720 D) 30 To'g'ri javob: B) 60✔ 29. Hisoblang: log₂3 · log₃8. A) 8 B) 3 C) log₆24 D) 24 To'g'ri javob: B) 3 ✔ 30. Katetlari 3 va 4 ga teng to'g'ri burchakli uchburchakning gipotenuzaga tushirilgan balandligini toping. A) 2,5 B) 1,2 C) 2,4 D) 2 To'g'ri javob: C) 2,4 ✔ Matematika — davlat granti mashq variantlari | 118 24-variant Asosiy fan bloki • bitta to'g'ri javob 1. Kesik konus asoslarining radiuslari 5 va 2 ga, balandligi 4 ga teng. Kesik konusning yon sirtini toping. A) 35π B) 15π C) 70π D) 28π To'g'ri javob: A) 35π✔ 2. a ning qanday qiymatida (a − 2)x = a² − 4 tenglama cheksiz ko'p yechimga ega bo'ladi? A) 0 B) 1 C) 2 D) −4 To'g'ri javob: C) 2 ✔ 3. Arifmetik progressiyada a₃ = 7 va a₇ = 19. a₁₀ ni toping. A) 25 B) 30 C) 31 D) 28 To'g'ri javob: D) 28 ✔ 4. k ning qanday qiymatida A(1; 2), B(3; 6) va C(5; k) nuqtalar bir to'g'ri chiziqda yotadi? A) 10 B) 8 C) 9 D) 12 To'g'ri javob: A) 10 ✔ 5. 12; 6; 3; … cheksiz kamayuvchi geometrik progressiyaning yig'indisini toping. A) 24 B) 18 C) 21 D) 36 To'g'ri javob: A) 24 ✔ 6. f(x) = cos(2x + 1) funksiyaning boshlang'ich funksiyalarining umumiy ko'rinishini toping. A) sin(2x + 1) + C B) 2sin(2x + 1) + C C) sin(2x + 1)/2 + C D) −cos(2x + 1)/2 + C To'g'ri javob: C) sin(2x + 1)/2 + C ✔ Matematika — davlat granti mashq variantlari | 119 7. a(1; 2) va b(3; 1) vektorlar berilgan. λ ning qanday qiymatida a + λb vektor a vektorga perpendikulyar bo'ladi? A) 5 B) -2 C) -1/2 D) -1 To'g'ri javob: D) -1✔ 8. (2; 7) nuqtaga Ox o'qiga nisbatan simmetrik nuqtani toping. A) (2; 0) B) (0; -7) C) (7; 2) D) (2; -7) To'g'ri javob: D) (2; -7) ✔ 9. Parallelogrammning diagonallari 10 va 16 ga, ular orasidagi burchak 30° ga teng. Parallelogramm yuzini toping. A) 80 B) 40√3 C) 40 D) 20 To'g'ri javob: C) 40 ✔ 10. Ota o'g'lidan 3 marta katta. 12 yildan keyin ota o'g'lidan 2 marta katta bo'ladi. Hozir o'g'il necha yoshda? A) 36 B) 12 C) 10 D) 14 To'g'ri javob: B) 12 ✔ 11. f(x) = cos x funksiyaning boshlang'ich funksiyalarining umumiy ko'rinishini toping. A) cos x + C B) tg x + C C) sin x + C D) sin²x/2 + C To'g'ri javob: C) sin x + C ✔ 12. Silindr asosining radiusi 2 ga teng, o'q kesimining yuzi 20 ga teng. Silindrning yon sirtini toping. A) 28π B) 40π C) 10π D) 20π To'g'ri javob: D) 20π ✔ 13. Geometrik progressiyada b₂ = −6 va b₃ = 12. b₁ ni toping. A) 3 B) −12 C) 6 D) −24 To'g'ri javob: A) 3 ✔ Matematika — davlat granti mashq variantlari | 120 14. Hisoblang: sin40° · cos20° + cos40° · sin20°. A) √2/2 B) √3/2 C) sin20° D) 1/2 To'g'ri javob: B) √3/2✔ 15. Silindrning o'q kesimi tomoni 4 ga teng kvadrat. Silindrning to'la sirtini toping. A) 20π B) 24π C) 32π D) 16π To'g'ri javob: B) 24π ✔ 16. Parallelogrammning ikki burchagi 1 : 2 nisbatda. Uning katta burchagini toping. A) 150° B) 120° C) 60° D) 135° To'g'ri javob: B) 120° ✔ 17. Trapetsiyaning o'rta chizig'i 10 ga, asoslaridan biri 6 ga teng. Ikkinchi asosini toping. A) 16 B) 12 C) 14 D) 8 To'g'ri javob: C) 14 ✔ 18. y = √x, y = 0 va x = 4 chiziqlar bilan chegaralangan figura Ox o'qi atrofida aylantirilishidan hosil bo'lgan jismning hajmini toping. A) 16π B) 8π C) 4π D) 16π/3 To'g'ri javob: B) 8π ✔ 19. f(x) = 1/√x funksiyaning boshlang'ich funksiyalarining umumiy ko'rinishini toping. A) √x/2 + C B) 2√x + C C) √x + C D) 1/(2√x) + C To'g'ri javob: B) 2√x + C ✔ 20. Uchlari A(1; 1), B(5; 2) va C(3; 6) nuqtalarda bo'lgan uchburchakning yuzini toping. A) 9 B) 10 C) 18 D) 8 To'g'ri javob: A) 9 ✔ Matematika — davlat granti mashq variantlari | 121 21. Qayiq oqim bo'yicha 3 soatda 36 km, oqimga qarshi 4 soatda 32 km yo'l bosdi. Daryo oqimining tezligini (km/soat) toping. A) 4 B) 2 C) 10 D) 3 To'g'ri javob: B) 2✔ 22. 2x² − 5x + 2 = 0 tenglamaning ildizlari x₁ va x₂ bo'lsa, x₁/x₂ + x₂/x₁ ni toping. A) 17/4 B) 5/2 C) 4 D) 21/4 To'g'ri javob: A) 17/4 ✔ 23. Avtomobil A dan B ga 60 km/soat, B dan A ga 40 km/soat tezlik bilan yurdi. Butun yo'ldagi o'rtacha tezlikni (km/soat) toping. A) 45 B) 50 C) 52 D) 48 To'g'ri javob: D) 48 ✔ 24. Radiusi 5 ga teng shar markazidan 3 ga teng masofada tekislik bilan kesilgan. Kesim yuzini toping. A) 25π B) 4π C) 16π D) 9π To'g'ri javob: C) 16π ✔ 25. 200 g 15% li tuz eritmasiga 100 g suv qo'shildi. Hosil bo'lgan eritmaning konsentratsiyasini toping. A) 12% B) 5% C) 7,5% D) 10% To'g'ri javob: D) 10% ✔ 26. Qavariq o'n ikkiburchakning bitta uchidan nechta diagonal o'tkazish mumkin? A) 12 B) 54 C) 10 D) 9 To'g'ri javob: D) 9 ✔ 27. y = 3sin x − 4cos x funksiyaning eng katta qiymatini toping. A) 1 B) 7 C) 5 D) 3 To'g'ri javob: C) 5 ✔ Matematika — davlat granti mashq variantlari | 122 28. A mahsulot B mahsulotdan 60% qimmat. B mahsulot A mahsulotdan necha foiz arzon? A) 62,5% B) 60% C) 40% D) 37,5% To'g'ri javob: D) 37,5%✔ 29. sin15° ning qiymatini toping. A) (√3 + 1)/4 B) (√3 − 1)/2 C) (√2 − 1)/2 D) (√6 − √2)/4 To'g'ri javob: D) (√6 − √2)/4 ✔ 30. Mahsulot narxi ketma-ket ikki marta 10% dan arzonlashtirildi. Narx jami necha foizga kamaydi? A) 20% B) 21% C) 19% D) 18% To'g'ri javob: C) 19% ✔ Matematika — davlat granti mashq variantlari | 123 25-variant Asosiy fan bloki • bitta to'g'ri javob 1. O'tkir burchakli ABC uchburchakda C = 50°, H – balandliklar kesishish nuqtasi. AHB burchakni ∠ toping. A) 115° B) 100° C) 130° D) 140° To'g'ri javob: C) 130° ✔ 2. f(x) = x² · e^(−x) funksiyaning o'sish oralig'ini toping. A) (−∞; 0] B) [−2; 0] C) [0; 2] D) [2; +∞) To'g'ri javob: C) [0; 2] ✔ 3. Prizmaning 15 ta qirrasi bor. Uning nechta uchi bor? A) 10 B) 15 C) 12 D) 5 To'g'ri javob: A) 10 ✔ 4. Ikkita o'yin kubigi tashlandi. Tushgan ochkolar ko'paytmasi juft son bo'lish ehtimolini toping. A) 2/3 B) 1/4 C) 1/2 D) 3/4 To'g'ri javob: D) 3/4 ✔ 5. «ALGEBRA» so'zidan tavakkaliga bitta harf tanlandi. Uning «A» harfi bo'lish ehtimolini toping. A) 1/6 B) 1/3 C) 2/7 D) 1/7 To'g'ri javob: C) 2/7 ✔ 6. Aylanaga ichki chizilgan burchak 140° li yoyga tiralgan. Shu burchakni toping. A) 140° B) 70° C) 35° D) 110° To'g'ri javob: B) 70° ✔ Matematika — davlat granti mashq variantlari | 124 7. Tenglamani yeching: log₂(x + 2) + log₂(x − 2) = 5. A) 6 B) −6; 6 C) 34 D) 4 To'g'ri javob: A) 6✔ 8. y = x³ funksiya grafigiga abssissasi x₀ = 1 bo'lgan nuqtada o'tkazilgan urinma Oy o'qini qanday ordinatali nuqtada kesib o'tadi? A) −2 B) 1 C) 3 D) 4 To'g'ri javob: A) −2 ✔ 9. Hisoblang: 101² − 99². A) 400 B) 40 C) 4000 D) 200 To'g'ri javob: A) 400 ✔ 10. Agar 7a = 3b (a ≠ 0) bo'lsa, (a + b)/(b − a) ning qiymatini toping. A) 5/2 B) 7/4 C) 2/5 D) 10/3 To'g'ri javob: A) 5/2 ✔ 11. a = log₂3 va b = log₃2 bo'lsa, a · b ko'paytmani toping. A) 1 B) 2 C) 0 D) log₂6 To'g'ri javob: A) 1 ✔ 12. To'g'ri burchakli parallelepipedning asosi tomoni 4 ga teng kvadrat, diagonali esa 9 ga teng. Parallelepiped hajmini toping. A) 96 B) 144 C) 112 D) 128 To'g'ri javob: C) 112 ✔ 13. 2^(x² − 3x) = 1/4 tenglama ildizlarining ko'paytmasini toping. A) 2 B) −1 C) 3 D) 4 To'g'ri javob: A) 2 ✔ Matematika — davlat granti mashq variantlari | 125 14. n ning qanday qiymatida n ta elementdan 2 tadan guruhlashlar soni 36 ga teng bo'ladi? A) 9 B) 8 C) 12 D) 6 To'g'ri javob: A) 9✔ 15. a > 0, b > 0, a ≠ b bo'lganda ifodani soddalashtiring: (a^(3/2) − b^(3/2))/(a^(1/2) − b^(1/2)). A) a + √(ab) + b B) a + b C) a + 2√(ab) + b D) a² + ab + b² To'g'ri javob: A) a + √(ab) + b ✔ 16. Teng yonli uchburchakning perimetri 32 ga teng, asosi yon tomonidan 4 ga qisqa. Yon tomonni toping. A) 12 B) 10 C) 14 D) 8 To'g'ri javob: A) 12 ✔ 17. Agar (a; b) oraliqning har bir nuqtasida f'(x) > 0 bo'lsa, f funksiya shu oraliqda qanday bo'ladi? A) Juft B) Kamayuvchi C) O'suvchi D) O'zgarmas To'g'ri javob: C) O'suvchi ✔ 18. Mergan nishonga 0,8 ehtimol bilan tegizadi. U ikki marta o'q uzdi. Ikkala o'q ham nishonga tegmaslik ehtimolini toping. A) 0,2 B) 0,04 C) 0,64 D) 0,4 To'g'ri javob: B) 0,04 ✔ 19. Qo'sh tengsizlikni yeching: −3 < 2x − 1 ≤ 5. A) (−2; 2] B) (−1; 2] C) (−2; 3] D) (−1; 3] To'g'ri javob: D) (−1; 3] ✔ 20. (x − 4)/(x + 1) < 0 tengsizlikning eng katta butun yechimini toping. A) 3 B) 4 C) 0 D) −1 To'g'ri javob: A) 3 ✔ Matematika — davlat granti mashq variantlari | 126 21. Aylanaga ichki chizilgan muntazam oltiburchakning perimetri 36 ga teng. Aylana uzunligini toping. A) 24π B) 6π C) 12π D) 36π To'g'ri javob: C) 12π✔ 22. x² − 6x + 5 < 0 tengsizlikning eng kichik butun yechimini toping. A) 0 B) 2 C) 3 D) 1 To'g'ri javob: B) 2 ✔ 23. Nechta butun son 2 < |x| < 6 qo'sh tengsizlikni qanoatlantiradi? A) 3 B) 4 C) 8 D) 6 To'g'ri javob: D) 6 ✔ 24. Radiusi 9 ga teng aylana yoyining uzunligi 3π ga teng. Shu yoyga mos markaziy burchakni toping. A) 120° B) 90° C) 60° D) 30° To'g'ri javob: C) 60° ✔ 25. Teng yonli uchburchakning asosidagi burchagi 70° ga teng. Uchidagi burchakni toping. A) 110° B) 70° C) 20° D) 40° To'g'ri javob: D) 40° ✔ 26. Ko'paytuvchilarga ajrating: ax − ay + bx − by. A) (a + x)(b − y) B) (a − y)(x + b) C) (a + b)(x − y) D) (x + y)(a − b) To'g'ri javob: C) (a + b)(x − y) ✔ 27. Muntazam to'rtburchakli piramida asosining tomoni 6 ga, yon qirrasi 5 ga teng. Piramidaning yon sirtini toping. A) 60 B) 48 C) 96 D) 24 To'g'ri javob: B) 48 ✔ Matematika — davlat granti mashq variantlari | 127 28. Uzunligi radiusga teng vatar qanday markaziy burchakka tiraladi? A) 60° B) 90° C) 45° D) 30° To'g'ri javob: A) 60°✔ 29. Kubning nechta diagonali (fazoviy diagonali) bor? A) 4 B) 8 C) 12 D) 6 To'g'ri javob: A) 4 ✔ 30. ABC uchburchakda AB = BC va B = 36°. A burchak bissektrisasi va BC tomon orasidagi ∠ burchaklardan o'tkirini, ya'ni ADC ni toping (D – bissektrisaning BC bilan kesishish nuqtasi). ∠ A) 108° B) 72° C) 54° D) 36° To'g'ri javob: B) 72° ✔ Matematika — davlat granti mashq variantlari | 128 26-variant Asosiy fan bloki • bitta to'g'ri javob 1. Hisoblang: cos20° · cos40° · cos80°. A) 1/16 B) 1/4 C) √3/8 D) 1/8 To'g'ri javob: D) 1/8✔ 2. Kesik konusning o'q kesimi asoslari 4 va 10 ga, balandligi 4 ga teng teng yonli trapetsiya. Kesik konus hajmini toping. A) 39π B) 52π C) 156π D) 116π/3 To'g'ri javob: B) 52π ✔ 3. Uchlari A(0; 0), B(6; 0) va C(3; 4) nuqtalarda bo'lgan uchburchakning perimetrini toping. A) 12 B) 16 C) 15 D) 18 To'g'ri javob: B) 16 ✔ 4. Qirrasi 2 ga teng kub sharga ichki chizilgan. Shar radiusini toping. A) 1 B) √3 C) 2√3 D) √2 To'g'ri javob: B) √3 ✔ 5. Uzunligi 300 m bo'lgan poyezd ustun yonidan 15 sekundda o'tdi. Poyezd tezligini km/soat da toping. A) 20 B) 54 C) 80 D) 72 To'g'ri javob: D) 72 ✔ 6. (2; 1) nuqtadan o'tuvchi va y = 2x + 1 to'g'ri chiziqqa perpendikulyar to'g'ri chiziq tenglamasini toping. A) y = -x/2 + 2 B) y = 2x - 3 C) y = -2x + 5 D) y = x/2 To'g'ri javob: A) y = -x/2 + 2 ✔ Matematika — davlat granti mashq variantlari | 129 7. k ning qanday qiymatida a(2; 3) va b(6; k) vektorlar kollinear bo'ladi? A) 18 B) 4 C) 9 D) 6 To'g'ri javob: C) 9✔ 8. Hisoblang: sin30° + cos60°. A) 1/2 B) √3/2 C) 1 D) √3 To'g'ri javob: C) 1 ✔ 9. Radiusi 5 ga teng aylanaga ichki chizilgan kvadratning yuzini toping. A) 25 B) 100 C) 25√2 D) 50 To'g'ri javob: D) 50 ✔ 10. Asos radiusi R, yasovchisi l bo'lgan konusning yon sirti qaysi formula bilan hisoblanadi? A) 2πRl B) πR(R + l) C) πR²l D) πRl To'g'ri javob: D) πRl ✔ 11. x(x + 1)(x + 2)(x + 3) = 24 tenglama haqiqiy ildizlarining yig'indisini toping. A) −3 B) 1 C) −6 D) 4 To'g'ri javob: A) −3 ✔ 12. y = 2 − 3cos x funksiyaning qiymatlar sohasini toping. A) [2; 5] B) [−3; 3] C) [−1; 2] D) [−1; 5] To'g'ri javob: D) [−1; 5] ✔ 13. Qirrasi 6 ga teng kubga shar ichki chizilgan. Shar sirtini toping. A) 36π B) 144π C) 72π D) 9π To'g'ri javob: A) 36π ✔ Matematika — davlat granti mashq variantlari | 130 14. Uch ishchi ishni alohida-alohida mos ravishda 10, 15 va 30 kunda bajaradi. Ular birgalikda ishlasa, ish necha kunda bajariladi? A) 6 B) 4 C) 5 D) 55/3 To'g'ri javob: C) 5✔ 15. Trapetsiyaning o'rta chizig'i 12 ga, balandligi 7 ga teng. Uning yuzini toping. A) 42 B) 168 C) 76 D) 84 To'g'ri javob: D) 84 ✔ 16. 1 dan 200 gacha bo'lgan, 7 ga karrali barcha natural sonlarning yig'indisini toping. A) 3045 B) 2800 C) 2849 D) 2842 To'g'ri javob: D) 2842 ✔ 17. 1 + 2 + 3 + … + n = 210 tenglikda n ni toping. A) 30 B) 20 C) 21 D) 19 To'g'ri javob: B) 20 ✔ 18. x³ − 4x = 0 tenglama nechta ildizga ega? A) 1 B) 4 C) 3 D) 2 To'g'ri javob: C) 3 ✔ 19. x² + y² = 25, x + y = 7 sistemaning yechimlari uchun |x − y| ni toping. A) 7 B) 5 C) 2 D) 1 To'g'ri javob: D) 1 ✔ 20. y = x², y = 0 va x = 3 chiziqlar bilan chegaralangan figuraning yuzini toping. A) 9 B) 27 C) 18 D) 3 To'g'ri javob: A) 9 ✔ Matematika — davlat granti mashq variantlari | 131 21. Aylanaga ichki chizilgan ABCD to'rtburchakda A = 75°. C ni toping.∠ ∠ A) 105° B) 95° C) 75° D) 115° To'g'ri javob: A) 105° ✔ 22. 20 ta tangadan iborat to'plamda 500 so'mlik va 1000 so'mlik tangalar bor, ularning umumiy qiymati 14 000 so'm. Nechta 1000 so'mlik tanga bor? A) 8 B) 10 C) 6 D) 12 To'g'ri javob: A) 8 ✔ 23. x⁴ − 5x² + 4 = 0 tenglama ildizlarining ko'paytmasini toping. A) 2 B) 0 C) 4 D) 5 To'g'ri javob: C) 4 ✔ 24. Cheksiz kamayuvchi geometrik progressiya hadlarining yig'indisi 16 ga, hadlari kvadratlarining yig'indisi 256/3 ga teng. b₁ ni toping. A) 8 B) 6 C) 4 D) 12 To'g'ri javob: A) 8 ✔ 25. ∫ₐᵇ f(x)dx = F(b) − F(a) (bu yerda F — f ning boshlang'ich funksiyasi) formula qanday nomlanadi? A) Viyet formulasi B) Lagranj formulasi C) Teylor formulasi D) Nyuton–Leybnits formulasi To'g'ri javob: D) Nyuton–Leybnits formulasi ✔ 26. A(3; -2) va B(-1; 4) nuqtalar berilgan. AB vektorning koordinatalarini toping. A) (-4; 6) B) (2; 2) C) (2; 6) D) (-4; 2) To'g'ri javob: A) (-4; 6) ✔ 27. Qanday trapetsiyaga tashqi aylana chizish mumkin? A) teng yonli trapetsiyaga B) to'g'ri burchakli trapetsiyaga C) istalgan trapetsiyaga D) diagonallari perpendikulyar trapetsiyaga To'g'ri javob: A) teng yonli trapetsiyaga ✔ Matematika — davlat granti mashq variantlari | 132 28. Birinchi quvur hovuzni 4 soatda to'ldiradi, ikkinchi quvur to'la hovuzni 6 soatda bo'shatadi. Ikkala quvur bir vaqtda ochilsa, bo'sh hovuz necha soatda to'ladi? A) 2,4 B) 12 C) 10 D) 5 To'g'ri javob: B) 12✔ 29. Geometrik progressiyada b₁ = 2 va q = 3. b₅ ni toping. A) 54 B) 30 C) 486 D) 162 To'g'ri javob: D) 162 ✔ 30. Integralni hisoblang: ∫₋₁² x² dx. A) 9 B) 5/3 C) 3 D) 7/3 To'g'ri javob: C) 3 ✔ Matematika — davlat granti mashq variantlari | 133 27-variant Asosiy fan bloki • bitta to'g'ri javob 1. Hisoblang: (2¹⁰ · 3⁵)/(6⁵ · 4²). A) 1/2 B) 2 C) 4 D) 1 To'g'ri javob: B) 2✔ 2. To'g'ri burchakli uchburchakka tashqi chizilgan aylananing markazi qayerda joylashadi? A) kichik katet o'rtasida B) to'g'ri burchak uchida C) gipotenuzaning o'rtasida D) uchburchak ichida To'g'ri javob: C) gipotenuzaning o'rtasida ✔ 3. Quyidagi funksiyalardan qaysi biri butun aniqlanish sohasida kamayuvchi? A) y = lg x B) y = log₃x C) y = (0,5)ˣ D) y = 2ˣ To'g'ri javob: C) y = (0,5)ˣ ✔ 4. y = √(6 − x − x²) funksiyaning aniqlanish sohasini toping. A) [−1; 6] B) [−3; 2] C) [−2; 3] D) [−6; 1] To'g'ri javob: B) [−3; 2] ✔ 5. (a + b)⁷ yoyilmasidagi binomial koeffitsiyentlar yig'indisini toping. A) 256 B) 128 C) 49 D) 64 To'g'ri javob: B) 128 ✔ 6. Piramidaning 10 ta qirrasi bor. Uning nechta yog'i bor? A) 7 B) 10 C) 6 D) 5 To'g'ri javob: C) 6 ✔ Matematika — davlat granti mashq variantlari | 134 7. Tomoni 2 ga teng kvadrat ichidan tavakkaliga nuqta tanlandi. Nuqtaning kvadratga ichki chizilgan doiraga tushish ehtimolini toping. A) π/8 B) 1/2 C) π/4 D) π/2 To'g'ri javob: C) π/4✔ 8. Muntazam to'rtburchakli piramidaning yon yog'i asos tekisligi bilan 45° burchak tashkil etadi, asos tomoni 8 ga teng. Piramida hajmini toping. A) 256/3 B) 256 C) 128/3 D) 512/3 To'g'ri javob: A) 256/3 ✔ 9. Tenglamani yeching: log₂(2ˣ − 7) = 3 − x. A) 3 B) 2 C) 8 D) 0 To'g'ri javob: A) 3 ✔ 10. Muntazam tetraedrning ayqash qirralari orasidagi burchak nechaga teng? A) 30° B) 60° C) 90° D) 45° To'g'ri javob: C) 90° ✔ 11. Tengsizlikni yeching: √(x + 3) > x + 1. A) [−1; 1) B) [−3; −2) C) [−3; 1) D) (−2; 1) To'g'ri javob: C) [−3; 1) ✔ 12. Teng yonli to'g'ri burchakli uchburchakning gipotenuzasi 8 ga teng. Uning yuzini toping. A) 16√2 B) 32 C) 16 D) 8 To'g'ri javob: C) 16 ✔ 13. Hisoblang: (√3 + √2)²⁰²⁴ · (√3 − √2)²⁰²⁴. A) 1 B) 0 C) 2 D) 5²⁰²⁴ To'g'ri javob: A) 1 ✔ Matematika — davlat granti mashq variantlari | 135 14. Ko'paytuvchilarga ajrating: x² − 5x + 6. A) (x − 2)(x − 3) B) (x − 5)(x + 1) C) (x − 1)(x − 6) D) (x + 6)(x − 1) To'g'ri javob: A) (x − 2)(x − 3)✔ 15. f(x) = x⁴ bo'lsa, f''(1) ni toping. A) 6 B) 24 C) 12 D) 4 To'g'ri javob: C) 12 ✔ 16. Javonga 6 ta turli kitobni necha xil usulda terib qo'yish mumkin? A) 720 B) 36 C) 120 D) 360 To'g'ri javob: A) 720 ✔ 17. f(x) = (2x + 1)⁵ bo'lsa, f'(0) ni toping. A) 1 B) 10 C) 32 D) 5 To'g'ri javob: B) 10 ✔ 18. (a + b)¹⁰ ko'phad standart ko'rinishga keltirilsa, nechta haddan iborat bo'ladi? A) 20 B) 11 C) 10 D) 12 To'g'ri javob: B) 11 ✔ 19. Tengsizlikni yeching: 2ˣ > 8. A) (2; +∞) B) (3; +∞) C) (8; +∞) D) (4; +∞) To'g'ri javob: B) (3; +∞) ✔ 20. x² + x + 1 > 0 tengsizlikning yechimlar to'plamini toping. A) (0; +∞) B) (−1; 0) C) (−∞; +∞) D) Yechimga ega emas To'g'ri javob: C) (−∞; +∞) ✔ Matematika — davlat granti mashq variantlari | 136 21. Tengsizliklar sistemasini yeching: x² − 4x < 0, x² ≥ 4. A) (0; 2] B) [−2; 0) [2; 4)∪ C) (0; 4) D) [2; 4) To'g'ri javob: D) [2; 4) ✔ 22. Radiusi 6 ga teng aylananing 120° li markaziy burchakka mos yoyi uzunligini toping. A) 12π B) 6π C) 2π D) 4π To'g'ri javob: D) 4π ✔ 23. Og'ma prizmaning yon qirrasi 10 ga teng va asos tekisligi bilan 30° burchak tashkil etadi. Asos yuzi 12 ga teng. Prizma hajmini toping. A) 120 B) 40 C) 60√3 D) 60 To'g'ri javob: D) 60 ✔ 24. Uchburchakning tomonlari 4, 13 va 15 ga teng. Uning yuzini toping. A) 24 B) 28 C) 26 D) 30 To'g'ri javob: A) 24 ✔ 25. Aylanadan tashqaridagi nuqtadan o'tkazilgan ikki kesuvchi orasidagi burchak ichidagi yoylar 110° va 30° ga teng. Kesuvchilar orasidagi burchakni toping. A) 40° B) 55° C) 70° D) 80° To'g'ri javob: A) 40° ✔ 26. Tengsizlikni yeching: log₁/₂(x + 1) > −1. A) (−∞; 3) B) (−1; 3) C) (−1; 1) D) (1; +∞) To'g'ri javob: C) (−1; 1) ✔ 27. Ko'paytuvchilarga ajrating: 8x³ − 1. A) (2x − 1)(4x² + 2x + 1) B) (2x − 1)(4x² + 4x + 1) C) (2x − 1)³ D) (2x − 1)(4x² + 1) To'g'ri javob: A) (2x − 1)(4x² + 2x + 1) ✔ Matematika — davlat granti mashq variantlari | 137 28. f(x) = (x + 1)/(x − 1) funksiyaning hosilasini toping. A) 2/(x² − 1) B) −2/(x − 1)² C) 1 D) −1/(x − 1)² To'g'ri javob: B) −2/(x − 1)²✔ 29. Aylananing ikki vatari kesishadi. Birinchi vatar 4 va 9 ga teng kesmalarga bo'lingan, ikkinchi vatarning kesmalari 1 : 4 nisbatda. Ikkinchi vatar uzunligini toping. A) 13 B) 15 C) 18 D) 12 To'g'ri javob: B) 15 ✔ 30. ABC uchburchakda A = 30° va BC = 7. Uchburchakka tashqi chizilgan aylana radiusini toping. ∠ A) 3,5 B) 7√3 C) 7 D) 14 To'g'ri javob: C) 7 ✔ Matematika — davlat granti mashq variantlari | 138 28-variant Asosiy fan bloki • bitta to'g'ri javob 1. Oralaridagi masofa 24 km bo'lgan A va B punktlardan bir vaqtda bir-biriga qarab velosipedchi va piyoda yo'lga chiqdi va 2 soatdan keyin uchrashdi. Velosipedchining tezligi piyodanikidan 3 marta katta. Velosipedchi tezligini toping (km/soat). A) 6 B) 12 C) 3 D) 9 To'g'ri javob: D) 9✔ 2. Konus asosining radiusi 3 ga, balandligi 4 ga teng. Konusning yon sirtini toping. A) 20π B) 12π C) 24π D) 15π To'g'ri javob: D) 15π ✔ 3. Integralni hisoblang: ∫₀^(π/2) sin2x dx. A) 1/2 B) 0 C) 2 D) 1 To'g'ri javob: D) 1 ✔ 4. a(3; 4) vektorning uzunligini toping. A) 4 B) 5 C) 25 D) 7 To'g'ri javob: B) 5 ✔ 5. Trapetsiyaning asoslari 3 va 7 ga, diagonallari 6 va 8 ga teng. Trapetsiya yuzini toping. A) 20 B) 48 C) 24 D) 30 To'g'ri javob: C) 24 ✔ 6. Mahsulot narxi 800 so'mdan 680 so'mga tushirildi. Narx necha foizga kamaydi? A) 20% B) 12% C) 15% D) 18% To'g'ri javob: C) 15% ✔ Matematika — davlat granti mashq variantlari | 139 7. a = 25 − 3n formula bilan berilgan arifmetik progressiyaning nechta hadi musbat?ₙ A) 9 B) 25 C) 7 D) 8 To'g'ri javob: D) 8 ✔ 8. a(1; 2; 2) va b(2; 1; -2) vektorlar orasidagi burchakni toping. A) 45° B) 120° C) 60° D) 90° To'g'ri javob: D) 90° ✔ 9. Integralni hisoblang: ∫₀³ |x − 1| dx. A) 5/2 B) 3 C) 3/2 D) 2 To'g'ri javob: A) 5/2 ✔ 10. y = sin x va y = cos x chiziqlar hamda x = 0 to'g'ri chiziq bilan [0; π/4] oraliqda chegaralangan figuraning yuzini toping. A) √2 B) 1 C) √2/2 D) √2 − 1 To'g'ri javob: D) √2 − 1 ✔ 11. Rombning tomoni 10 ga, o'tkir burchagi 60° ga teng. Rombning kichik diagonalini toping. A) 5√3 B) 10 C) 10√3 D) 5 To'g'ri javob: B) 10 ✔ 12. sin α = 3/5 va α (π/2; π) bo'lsa, cos α ni toping. ∈ A) −3/5 B) −4/5 C) −3/4 D) 4/3 To'g'ri javob: B) −4/5 ✔ 13. m ning qanday qiymatlarida x² + 4x + m = 0 tenglama ikkita turli haqiqiy ildizga ega bo'ladi? A) m < 16 B) m > 0 C) m < 4 D) m < 2 To'g'ri javob: C) m < 4 ✔ Matematika — davlat granti mashq variantlari | 140 14. Kvadratning diagonali 8 ga teng. Kvadrat yuzini toping. A) 32 B) 16 C) 16√2 D) 64 To'g'ri javob: A) 32✔ 15. Arifmetik progressiyaning dastlabki n ta hadi yig'indisi S = 2n² − n. Progressiya ayirmasini toping. ₙ A) 5 B) 3 C) 4 D) 2 To'g'ri javob: C) 4 ✔ 16. Ikki xonali son raqamlari yig'indisidan 4 marta, raqamlari ko'paytmasidan 3 marta katta. Shu sonni toping. A) 12 B) 36 C) 48 D) 24 To'g'ri javob: D) 24 ✔ 17. Parallel ko'chirish (1; 4) nuqtani (3; 1) nuqtaga o'tkazadi. Bu ko'chirish vektorini toping. A) (3; -2) B) (4; 5) C) (2; -3) D) (-1; 3) To'g'ri javob: C) (2; -3) ✔ 18. tg15° ning qiymatini toping. A) √3 − 1 B) (√3 − 1)/2 C) √3/3 D) 2 − √3 To'g'ri javob: D) 2 − √3 ✔ 19. Geometrik progressiyada b₁ = 5 va b₄ = 40. Dastlabki 5 ta hadining yig'indisini toping. A) 160 B) 315 C) 155 D) 75 To'g'ri javob: C) 155 ✔ 20. Ikki sonning yig'indisi 40 ga, ayirmasi 12 ga teng. Shu sonlarning kattasini toping. A) 14 B) 28 C) 24 D) 26 To'g'ri javob: D) 26 ✔ Matematika — davlat granti mashq variantlari | 141 21. x + y = 4, x² − xy + y² = 7 sistemaning yechimlari uchun x³ + y³ ni toping. A) 36 B) 64 C) 28 D) 52 To'g'ri javob: C) 28✔ 22. sin x < 0 tengsizlikni yeching (k Z). ∈ A) (π + 2πk; 2π + 2πk) B) (2πk; π + 2πk) C) (−π/2 + 2πk; π/2 + 2πk) D) (π/2 + 2πk; 3π/2 + 2πk) To'g'ri javob: A) (π + 2πk; 2π + 2πk) ✔ 23. Quyidagi funksiyalardan qaysi biri juft? A) y = x cos x B) y = tg x C) y = sin x + cos x D) y = x sin x To'g'ri javob: D) y = x sin x ✔ 24. b = 3 · 2ⁿ⁻¹ formula bilan berilgan geometrik progressiyaning nechanchi hadi 96 ga teng? ₙ A) 5 B) 7 C) 6 D) 32 To'g'ri javob: C) 6 ✔ 25. Silindr asosining radiusi 3 ga, balandligi 7 ga teng. Silindrning to'la sirtini toping. A) 60π B) 51π C) 42π D) 63π To'g'ri javob: A) 60π ✔ 26. a ning qanday qiymatida 2x + ay = 5, 4x + 6y = 7 sistema yechimga ega bo'lmaydi? A) 12 B) 3 C) 6 D) 2 To'g'ri javob: B) 3 ✔ 27. Uzunligi 400 m bo'lgan aylana yo'lakda bir nuqtadan bir yo'nalishda 5 m/s va 3 m/s tezlik bilan ikki yuguruvchi yugura boshladi. Necha sekunddan keyin tezroq yuguruvchi ikkinchisini birinchi marta quvib yetadi? A) 100 B) 50 C) 80 D) 200 To'g'ri javob: D) 200 ✔ Matematika — davlat granti mashq variantlari | 142 28. (2; 3; 6) nuqtadan Oxy tekisligigacha bo'lgan masofani toping. A) 7 B) √13 C) 6 D) 2 To'g'ri javob: C) 6✔ 29. Balandligi asos radiusiga teng silindrning yon sirti to'la sirtining qanday qismini tashkil etadi? A) 2/3 B) 1/3 C) 1/2 D) 1/4 To'g'ri javob: C) 1/2 ✔ 30. Kesik konus asoslarining radiuslari 3 va 6 ga, yasovchisi 5 ga teng. Kesik konus balandligini toping. A) 3 B) 4 C) 5 D) √34 To'g'ri javob: B) 4 ✔ Matematika — davlat granti mashq variantlari | 143 29-variant Asosiy fan bloki • bitta to'g'ri javob 1. Kasr maxrajini irratsionallikdan qutqaring: 6/(3 − √3). A) 3 + 2√3 B) (3 + √3)/2 C) 3 + √3 D) 2(3 + √3) To'g'ri javob: C) 3 + √3✔ 2. Agar x² − 3x + 1 = 0 bo'lsa, x⁴ + 1/x⁴ ning qiymatini toping. A) 81 B) 49 C) 47 D) 45 To'g'ri javob: C) 47 ✔ 3. Uchburchakning tashqi burchagi 120° ga, unga qo'shni bo'lmagan ichki burchaklaridan biri 50° ga teng. Ikkinchi qo'shni bo'lmagan ichki burchakni toping. A) 60° B) 70° C) 130° D) 50° To'g'ri javob: B) 70° ✔ 4. Tomoni 9 ga teng muntazam uchburchakka tashqi chizilgan aylana radiusini toping. A) 3√3/2 B) 9/2 C) 9√3/2 D) 3√3 To'g'ri javob: D) 3√3 ✔ 5. Tengsizlikni yeching: x² − 2|x| − 3 < 0. A) (−3; −1) (1; 3) ∪ B) (0; 3) C) (−3; 3) D) (−1; 3) To'g'ri javob: C) (−3; 3) ✔ 6. 5 ta matematika va 4 ta fizika kitobidan 2 ta matematika va 1 ta fizika kitobini necha xil usulda tanlash mumkin? A) 40 B) 60 C) 20 D) 84 To'g'ri javob: A) 40 ✔ Matematika — davlat granti mashq variantlari | 144 7. Katetlari 5 va 12 ga teng to'g'ri burchakli uchburchakka ichki chizilgan aylana radiusini toping. A) 2,5 B) 3 C) 2 D) 6,5 To'g'ri javob: C) 2✔ 8. f(x) = x³ − 3x² − 9x funksiyaning kamayish oralig'ini toping. A) (−∞; −1] B) [3; +∞) C) [−3; 1] D) [−1; 3] To'g'ri javob: D) [−1; 3] ✔ 9. Har bir sinovda A hodisaning ro'y berish ehtimoli 0,3 ga teng. 3 ta erkli sinovda A hodisaning roppa- rosa bir marta ro'y berish ehtimolini toping. A) 0,147 B) 0,441 C) 0,9 D) 0,3 To'g'ri javob: B) 0,441 ✔ 10. Quyidagi tengsizliklardan qaysi biri x ning barcha haqiqiy qiymatlarida to'g'ri? A) x + 1/x ≥ 2 B) x² > x C) |x| > x D) x² + 4 ≥ 4x To'g'ri javob: D) x² + 4 ≥ 4x ✔ 11. Hisoblang: (√5 + √3)² + (√5 − √3)². A) 16 + 4√15 B) 2√15 C) 8 D) 16 To'g'ri javob: D) 16 ✔ 12. To'g'ri burchakli parallelepipedning o'lchamlari 1 : 2 : 3 nisbatda, hajmi 48 ga teng. Uning to'la sirtini toping. A) 88 B) 44 C) 96 D) 72 To'g'ri javob: A) 88 ✔ 13. Raqamlari turlicha bo'lgan nechta to'rt xonali kod (0 bilan boshlanishi mumkin) mavjud? A) 210 B) 10000 C) 5040 D) 4536 To'g'ri javob: C) 5040 ✔ Matematika — davlat granti mashq variantlari | 145 14. Tengsizlikni yeching: x(x − 3) ≥ 4x. A) 0 ≤ x ≤ 7 B) x ≤ 0 yoki x ≥ 7 C) x ≥ 7 D) x ≤ −7 yoki x ≥ 0 To'g'ri javob: B) x ≤ 0 yoki x ≥ 7✔ 15. Ikki konsentrik aylanadan kattasining vatari kichik aylanaga urinadi va uning uzunligi 10 ga teng. Aylanalar orasidagi halqa yuzini toping. A) 50π B) 25π C) 100π D) 10π To'g'ri javob: B) 25π ✔ 16. Tenglamani yeching: log₃(x + 1) = log₃(2x − 3). A) 2 B) 4 C) Yechimga ega emas D) −1 To'g'ri javob: B) 4 ✔ 17. Hisoblang: √(3 − 2√2) + √(3 + 2√2). A) 2 B) 2 + 2√2 C) 2√2 D) √6 To'g'ri javob: C) 2√2 ✔ 18. Tomoni 8 ga teng kvadratga ichki chizilgan doira yuzini toping. A) 16π B) 32π C) 8π D) 64π To'g'ri javob: A) 16π ✔ 19. Muntazam to'rtburchakli kesik piramida asoslarining tomonlari 4 va 10 ga, balandligi 4 ga teng. Uning yon sirtini toping. A) 136 B) 280 C) 140 D) 112 To'g'ri javob: C) 140 ✔ 20. Uchburchak tomonlari 7, 8 va 13 ga teng. Eng katta burchakni toping. A) 135° B) 105° C) 120° D) 150° To'g'ri javob: C) 120° ✔ Matematika — davlat granti mashq variantlari | 146 21. Tanga 4 marta tashlandi. Roppa-rosa 2 marta «gerb» tushish ehtimolini toping. A) 1/8 B) 3/8 C) 1/2 D) 1/4 To'g'ri javob: B) 3/8✔ 22. log₂²x − 3log₂x + 2 = 0 tenglama ildizlarining ko'paytmasini toping. A) 8 B) 6 C) 3 D) 2 To'g'ri javob: A) 8 ✔ 23. f(x) = x + 1/x funksiyaning maksimumini (maksimum nuqtadagi qiymatini) toping. A) 1/2 B) −1 C) −2 D) 0 To'g'ri javob: C) −2 ✔ 24. f(x) = 2x³ − 3x² − 12x + 1 funksiyaning o'sish oraliqlarini toping. A) [−2; 1] B) (−∞; −2] va [1; +∞) C) [−1; 2] D) (−∞; −1] va [2; +∞) To'g'ri javob: D) (−∞; −1] va [2; +∞) ✔ 25. Tengsizlikni yeching: (2/3)ˣ > (2/3)⁵. A) (−∞; 2/3) B) (−5; 5) C) (−∞; 5) D) (0; 5) To'g'ri javob: C) (−∞; 5) ✔ 26. Aylana markazidan 10 ga teng masofadagi nuqtadan radiusi 6 ga teng aylanaga o'tkazilgan urinma kesmasining uzunligini toping. A) 4 B) 8 C) 2√34 D) 16 To'g'ri javob: B) 8 ✔ 27. Muntazam to'rtburchakli piramidaning barcha qirralari 6 ga teng. Piramida balandligini toping. A) √30 B) 3√3 C) 3√2 D) 6√2 To'g'ri javob: C) 3√2 ✔ Matematika — davlat granti mashq variantlari | 147 28. x ≠ 0 bo'lganda x² + 4/x² ifodaning eng kichik qiymatini toping. A) 4 B) 5 C) 8 D) 2 To'g'ri javob: A) 4✔ 29. Qirrasi 4 ga teng kubning diagonal kesimi (ikki qarama-qarshi parallel qirradan o'tuvchi kesim) yuzini toping. A) 16√3 B) 16√2 C) 16 D) 32 To'g'ri javob: B) 16√2 ✔ 30. Tenglamani yeching: log₂(x − 1) = 3. A) 10 B) 7 C) 9 D) 4 To'g'ri javob: C) 9 ✔ Matematika — davlat granti mashq variantlari | 148 30-variant Asosiy fan bloki • bitta to'g'ri javob 1. 300 g 10% li tuz eritmasidan qancha suv bug'latilsa, 15% li eritma hosil bo'ladi (g)? A) 50 B) 200 C) 100 D) 150 To'g'ri javob: C) 100✔ 2. Bankka yillik 10 % murakkab foiz bilan 1 000 000 so'm qo'yildi. 2 yildan keyin hisobda qancha pul bo'ladi? A) 1 210 000 so'm B) 1 100 000 so'm C) 1 200 000 so'm D) 1 331 000 so'm To'g'ri javob: A) 1 210 000 so'm ✔ 3. O'suvchi arifmetik progressiyaning ketma-ket uchta hadi yig'indisi 21 ga teng. Agar ularga mos ravishda 2, 3 va 9 qo'shilsa, geometrik progressiya hosil bo'ladi. Shu hadlarning kattasini toping. A) 15 B) 18 C) 11 D) 9 To'g'ri javob: C) 11 ✔ 4. Tuzning 20 % li 200 g eritmasiga necha gramm suv qo'shilsa, 16 % li eritma hosil bo'ladi? A) 25 B) 50 C) 40 D) 60 To'g'ri javob: B) 50 ✔ 5. O'q kesimi tomoni 6 ga teng muntazam uchburchak bo'lgan konusga shar ichki chizilgan. Shar hajmini toping. A) 36π B) 12√3π C) 32π/3 D) 4√3π To'g'ri javob: D) 4√3π ✔ 6. (-1; 4) va (3; -4) nuqtalardan o'tuvchi to'g'ri chiziqning burchak koeffitsiyentini toping. A) 0 B) -1/2 C) -4 D) -2 To'g'ri javob: D) -2 ✔ Matematika — davlat granti mashq variantlari | 149 7. Qavariq ko'pburchak ichki burchaklarining yig'indisi 1800° ga teng. Uning tomonlari sonini toping. A) 12 B) 14 C) 11 D) 10 To'g'ri javob: A) 12✔ 8. (1; 5) nuqtadan o'tuvchi va y = 3x - 1 to'g'ri chiziqqa parallel to'g'ri chiziq tenglamasini toping. A) y = 3x + 5 B) y = x/3 + 14/3 C) y = 3x + 2 D) y = -3x + 8 To'g'ri javob: C) y = 3x + 2 ✔ 9. Birinchi ishchi ishni 6 soatda, ikkinchisi 3 soatda bajaradi. Ikkalasi birgalikda shu ishni necha soatda bajaradi? A) 3 B) 2 C) 4,5 D) 1,5 To'g'ri javob: B) 2 ✔ 10. Ifodani soddalashtiring: sin(π − α) + cos(π/2 + α). A) sin α + cos α B) 2cos α C) 2sin α D) 0 To'g'ri javob: D) 0 ✔ 11. Radiusi 5 ga teng sharning tekislik bilan kesimi yuzi 9π ga teng. Shar markazidan kesim tekisligigacha bo'lgan masofani toping. A) √34 B) 4 C) 3 D) 2 To'g'ri javob: B) 4 ✔ 12. Trapetsiyaning asoslari 8 va 14 ga, balandligi 5 ga teng. Trapetsiya yuzini toping. A) 110 B) 55 C) 60 D) 50 To'g'ri javob: B) 55 ✔ 13. Ikki xonali sonning raqamlari yig'indisi 9 ga teng. Raqamlari o'rni almashtirilsa, son 27 ga ortadi. Shu sonni toping. A) 45 B) 63 C) 36 D) 27 To'g'ri javob: C) 36 ✔ Matematika — davlat granti mashq variantlari | 150 14. a ning qanday qiymatida x² − 6x + a = 0 tenglama ikkita teng ildizga ega bo'ladi? A) 6 B) 3 C) 9 D) 36 To'g'ri javob: C) 9✔ 15. Hisoblang: 1 − 2sin²75°. A) −√3/2 B) 0 C) 1/2 D) √2/2 To'g'ri javob: A) −√3/2 ✔ 16. Qavariq oltiburchak ichki burchaklarining yig'indisini toping. A) 900° B) 1080° C) 540° D) 720° To'g'ri javob: D) 720° ✔ 17. 2x² − 3|x| − 2 = 0 tenglama ildizlari modullarining yig'indisini toping. A) 0 B) 4 C) 2 D) 5 To'g'ri javob: B) 4 ✔ 18. Geometrik progressiyada b₁ + b₂ = 8 va b₂ + b₃ = 24. b₁ ni toping. A) 6 B) 4 C) 3 D) 2 To'g'ri javob: D) 2 ✔ 19. Agar tg α = 2 bo'lsa, (sin α + cos α)/(sin α − cos α) ning qiymatini toping. A) 1/3 B) 2 C) −1 D) 3 To'g'ri javob: D) 3 ✔ 20. Oy o'qida (4; 1) nuqtadan 5 birlik masofada joylashgan va musbat ordinataga ega nuqtani toping. A) (0; 3) B) (0; 6) C) (0; 5) D) (0; 4) To'g'ri javob: D) (0; 4) ✔ Matematika — davlat granti mashq variantlari | 151 21. Silindrning o'q kesimi yuzi 36 ga teng kvadrat. Silindr hajmini toping. A) 216π B) 54π C) 108π D) 36π To'g'ri javob: B) 54π✔ 22. f(x) = 1/cos²x funksiyaning boshlang'ich funksiyalarining umumiy ko'rinishini toping. A) tg x + C B) 1/cos x + C C) tg²x + C D) ctg x + C To'g'ri javob: A) tg x + C ✔ 23. Qavariq ko'pburchakning 20 ta diagonali bor. Uning nechta tomoni bor? A) 8 B) 7 C) 10 D) 9 To'g'ri javob: A) 8 ✔ 24. Konus asosining radiusi 6 ga, balandligi 8 ga teng. Konus hajmini toping. A) 96π B) 48π C) 192π D) 288π To'g'ri javob: A) 96π ✔ 25. |2x − 3| = 5 tenglama ildizlarining yig'indisini toping. A) 5 B) 4 C) 3 D) −1 To'g'ri javob: C) 3 ✔ 26. Hisoblang: cos15° − sin15°. A) √2/2 B) √3/2 C) 1/2 D) √6/2 To'g'ri javob: A) √2/2 ✔ 27. Arifmetik progressiyada a₄ + a₆ = 18 va a₃ · a₇ = 45. Progressiya ayirmasining modulini toping. A) 3 B) 9 C) 2 D) 4 To'g'ri javob: A) 3 ✔ Matematika — davlat granti mashq variantlari | 152 28. F(x) = x³ − 2x + 7 funksiya quyidagi funksiyalardan qaysi birining boshlang'ich funksiyasi? A) 3x² + 5 B) 3x² − 2 C) x⁴/4 − x² D) 3x² To'g'ri javob: B) 3x² − 2✔ 29. a > 1 va ∫₁^a (2x − 1) dx = 6 bo'lsa, a ni toping. A) 2 B) 4 C) 6 D) 3 To'g'ri javob: D) 3 ✔ 30. 5 ta sonning o'rta arifmetigi 12 ga teng. Ularga oltinchi son qo'shilgandan so'ng o'rta arifmetik 13 ga teng bo'ldi. Oltinchi sonni toping. A) 15 B) 13 C) 18 D) 25 To'g'ri javob: C) 18 ✔ Matematika — davlat granti mashq variantlari | 153 31-variant Asosiy fan bloki • bitta to'g'ri javob 1. Agar a + b + c = 0 va abc ≠ 0 bo'lsa, (a³ + b³ + c³)/(abc) ning qiymatini toping. A) 1 B) 3 C) 6 D) 0 To'g'ri javob: B) 3✔ 2. To'g'ri burchakli uchburchakning o'tkir burchaklari ayirmasi 30° ga, gipotenuzasi 14 ga teng. Kichik katetni toping. A) 14√3/3 B) 7√2 C) 7 D) 7√3 To'g'ri javob: C) 7 ✔ 3. Hisoblang: log₂32 + log₃(1/9). A) 4 B) 3 C) −1 D) 7 To'g'ri javob: B) 3 ✔ 4. Diametri 10 ga teng aylanada uzunligi 6 ga teng vatar o'tkazilgan. Markazdan vatargacha bo'lgan masofani toping. A) 3 B) √91 C) 8 D) 4 To'g'ri javob: D) 4 ✔ 5. Aylanaga ichki chizilgan ABCD to'rtburchakda A = 80°, B = 110°. D ni toping. ∠ ∠ ∠ A) 110° B) 70° C) 100° D) 80° To'g'ri javob: B) 70° ✔ 6. f(x) = x³ − 12x funksiyaning minimum nuqtasini toping. A) 0 B) 16 C) 4 D) 2 To'g'ri javob: D) 2 ✔ Matematika — davlat granti mashq variantlari | 154 7. Qirrasi 6 ga teng muntazam tetraedrning hajmini toping. A) 36√2 B) 72 C) 9√2 D) 18√2 To'g'ri javob: D) 18√2✔ 8. 6 kishini dumaloq stol atrofiga necha xil usulda o'tqazish mumkin (faqat o'zaro joylashuv hisobga olinadi)? A) 120 B) 720 C) 60 D) 360 To'g'ri javob: A) 120 ✔ 9. Tengsizliklar sistemasini yeching: 2x − 1 > 3, 3x − 2 < 13. A) (−∞; 2) B) (2; 11/3) C) (5; +∞) D) (2; 5) To'g'ri javob: D) (2; 5) ✔ 10. log₃(x² − 8x) = 2 tenglama ildizlarining ko'paytmasini toping. A) 8 B) 1 C) −9 D) −18 To'g'ri javob: C) −9 ✔ 11. Hisoblang: 2√8 + 3√32 − √50. A) 21√2 B) 11√2 C) 9√2 D) 13√2 To'g'ri javob: B) 11√2 ✔ 12. Uchburchakning tomonlari 8, 10 va 12 ga teng. Uchlari shu uchburchak tomonlarining o'rtalarida bo'lgan uchburchak perimetrini toping. A) 15 B) 10 C) 20 D) 30 To'g'ri javob: A) 15 ✔ 13. f(x) = √(x² + 9) bo'lsa, f'(4) ni toping. A) 5/4 B) 4/5 C) 8/5 D) 1/10 To'g'ri javob: B) 4/5 ✔ Matematika — davlat granti mashq variantlari | 155 14. Hisoblang: log₄8. A) 2/3 B) 3/2 C) 2 D) 1/2 To'g'ri javob: B) 3/2✔ 15. 10 ta lampochkadan 2 tasi nosoz. Tavakkaliga 2 ta lampochka olindi. Ikkalasi ham soz bo'lish ehtimolini toping. A) 4/5 B) 7/9 C) 16/25 D) 28/45 To'g'ri javob: D) 28/45 ✔ 16. Quyidagi uchlik kesmalardan qaysi biridan uchburchak yasab bo'lmaydi? A) 3; 4; 6 B) 4; 7; 10 C) 5; 5; 9 D) 2; 3; 6 To'g'ri javob: D) 2; 3; 6 ✔ 17. Ifodani soddalashtiring: (a + b)² − (a − b)². A) 2a² + 2b² B) 2ab C) 4b² D) 4ab To'g'ri javob: D) 4ab ✔ 18. Tengsizlikni yeching: (3 − x)(x + 2) > 0. A) (−∞; −2) B) (−3; 2) C) (−2; 3) D) (3; +∞) To'g'ri javob: C) (−2; 3) ✔ 19. Perimetri 20 sm bo'lgan to'g'ri to'rtburchaklar ichida yuzi eng katta bo'lganining yuzini (sm²) toping. A) 24 B) 100 C) 25 D) 20 To'g'ri javob: C) 25 ✔ 20. 8 o'quvchini bir qatorga necha xil usulda turg'izish mumkin, agar ulardan ikkitasi albatta yonma- yon turishi kerak bo'lsa? A) 40320 B) 20160 C) 5040 D) 10080 To'g'ri javob: D) 10080 ✔ Matematika — davlat granti mashq variantlari | 156 21. Tenglamani yeching: 2^(x + 2) − 2ˣ = 24. A) 4 B) 2 C) 3 D) 8 To'g'ri javob: C) 3✔ 22. Hisoblang: (2/3)⁻² · (3/2)⁻³. A) 1 B) 2/3 C) 3/2 D) 4/9 To'g'ri javob: B) 2/3 ✔ 23. 0, 1, 2, 3, 4 raqamlaridan raqamlari takrorlanmaydigan nechta uch xonali son tuzish mumkin? A) 48 B) 100 C) 36 D) 60 To'g'ri javob: A) 48 ✔ 24. a ning qanday qiymatlarida x² − 2x + a > 0 tengsizlik x ning barcha haqiqiy qiymatlarida bajariladi? A) a < 0 B) a > 2 C) a > 1 D) a > 4 To'g'ri javob: C) a > 1 ✔ 25. Doira yuzi 49π ga teng. Uning diametrini toping. A) 14 B) 49 C) 24,5 D) 7 To'g'ri javob: A) 14 ✔ 26. Muntazam oltiburchakli prizma asosining tomoni 3 ga, balandligi 10 ga teng. Prizmaning yon sirtini toping. A) 360 B) 150 C) 180 D) 90 To'g'ri javob: C) 180 ✔ 27. f(x) = sin2x bo'lsa, f'(π/6) ni toping. A) √3/2 B) 1 C) 1/2 D) √3 To'g'ri javob: B) 1 ✔ Matematika — davlat granti mashq variantlari | 157 28. Doira diametri 20% ga orttirilsa, uning yuzi necha foizga ortadi? A) 20% B) 44% C) 40% D) 21% To'g'ri javob: B) 44%✔ 29. −x² + 2x − 3 > 0 tengsizlikning yechimlar to'plamini toping. A) (−1; 3) B) Yechimga ega emas C) (−∞; +∞) D) (−3; 1) To'g'ri javob: B) Yechimga ega emas ✔ 30. Qirrasi 6 ga teng muntazam tetraedrning balandligini toping. A) 2√6 B) √30 C) 3√2 D) 3√3 To'g'ri javob: A) 2√6 ✔ Matematika — davlat granti mashq variantlari | 158 32-variant Asosiy fan bloki • bitta to'g'ri javob 1. Yangi uzilgan mevada 90% suv bor, quritilgan mevada esa 20% suv bor. 50 kg yangi mevadan qancha quritilgan meva olinadi (kg)? A) 5 B) 10 C) 6,25 D) 8 To'g'ri javob: C) 6,25✔ 2. Radiusi 5 ga teng sharga balandligi 8 ga teng silindr ichki chizilgan. Silindrning to'la sirtini toping. A) 57π B) 66π C) 48π D) 84π To'g'ri javob: B) 66π ✔ 3. A(1; 1) va B(7; 4) nuqtalar berilgan. AB kesmada AM : MB = 1 : 2 bo'ladigan M nuqtaning koordinatalarini toping. A) (2; 3) B) (3; 2) C) (5; 3) D) (4; 2,5) To'g'ri javob: B) (3; 2) ✔ 4. x² + 2x − 15 = 0 tenglamaning katta ildizini toping. A) 2 B) 5 C) 3 D) 15 To'g'ri javob: C) 3 ✔ 5. Birinchi chorakda y = x³ va y = x chiziqlar bilan chegaralangan figuraning yuzini toping. A) 1/4 B) 3/4 C) 1/2 D) 1/12 To'g'ri javob: A) 1/4 ✔ 6. Radiusi 13 ga teng sharning markazdan bir tomonda yotgan ikkita parallel kesimlarining radiuslari 5 va 12 ga teng. Kesimlar orasidagi masofani toping. A) 17 B) 5 C) 7 D) 8 To'g'ri javob: C) 7 ✔ Matematika — davlat granti mashq variantlari | 159 7. Geometrik progressiyada b₅ − b₁ = 15 va b₄ − b₂ = 6. Agar q > 1 bo'lsa, b₁ ni toping. A) −16 B) 3 C) 1 D) 2 To'g'ri javob: C) 1✔ 8. Tomoni 4 ga teng muntazam oltiburchakning yuzini toping. A) 48√3 B) 24√3 C) 16√3 D) 12√3 To'g'ri javob: B) 24√3 ✔ 9. 2cos²x − cos x − 1 = 0 tenglama [0; 2π] kesmada nechta ildizga ega? A) 3 B) 2 C) 5 D) 4 To'g'ri javob: D) 4 ✔ 10. Integralni hisoblang: ∫₀^(π/3) dx/cos²x. A) 1/2 B) √3 C) 2 D) √3/3 To'g'ri javob: B) √3 ✔ 11. Cheksiz kamayuvchi geometrik progressiyaning har bir hadi o'zidan keyingi barcha hadlar yig'indisidan 2 marta katta. Progressiya maxrajini toping. A) 1/4 B) 1/2 C) 2/3 D) 1/3 To'g'ri javob: D) 1/3 ✔ 12. 240 sonining 15% ini toping. A) 36 B) 24 C) 48 D) 16 To'g'ri javob: A) 36 ✔ 13. Rombning perimetri 52 ga, diagonallaridan biri 10 ga teng. Ikkinchi diagonalini toping. A) 24 B) 20 C) 12 D) 26 To'g'ri javob: A) 24 ✔ Matematika — davlat granti mashq variantlari | 160 14. (3; -4; 12) nuqtadan Oz o'qigacha bo'lgan masofani toping. A) 12 B) 5 C) 13 D) 4 To'g'ri javob: B) 5✔ 15. Integralni hisoblang: ∫₀² (3x² − 4x + 1) dx. A) 2 B) 0 C) 4 D) 6 To'g'ri javob: A) 2 ✔ 16. Kvadratning perimetri 24 ga teng. Uning diagonalini toping. A) 6 B) 6√2 C) 3√2 D) 12 To'g'ri javob: B) 6√2 ✔ 17. a(2; 3) vektorning b(4; 3) vektor yo'nalishidagi proyeksiyasini (skalyar proyeksiyasini) toping. A) 2,6 B) 3,4 C) 17 D) 17/√13 To'g'ri javob: B) 3,4 ✔ 18. Bakteriyalar soni har 20 minutda 2 marta ortadi. Boshida 1 ta bakteriya bo'lsa, 2 soatdan keyin nechta bakteriya bo'ladi? A) 32 B) 128 C) 64 D) 12 To'g'ri javob: C) 64 ✔ 19. Hisoblang: arcsin(1/2) + arccos(−1/2). A) π/3 B) 5π/6 C) π D) π/2 To'g'ri javob: B) 5π/6 ✔ 20. Sotuvchi sotuv summasining 5% ini mukofot sifatida oladi. U 3 600 000 so'mlik mahsulot sotdi. Mukofot miqdorini toping (so'm). A) 360 000 B) 180 000 C) 150 000 D) 18 000 To'g'ri javob: B) 180 000 ✔ Matematika — davlat granti mashq variantlari | 161 21. Silindr asosining radiusi 4 ga, balandligi 6 ga teng. Silindrning yon sirtini toping. A) 80π B) 96π C) 24π D) 48π To'g'ri javob: D) 48π✔ 22. Musbat hadli geometrik progressiyada b₂ = 6 va b₄ = 54. b₆ ni toping. A) 162 B) 324 C) 1458 D) 486 To'g'ri javob: D) 486 ✔ 23. 4x⁴ − 5x² + 1 = 0 tenglama musbat ildizlarining yig'indisini toping. A) 2 B) 1 C) 3/2 D) 5/4 To'g'ri javob: C) 3/2 ✔ 24. x² − 5x − 3 = 0 tenglamaning ildizlari x₁ va x₂ bo'lsa, x₁²x₂ + x₁x₂² ni toping. A) 5 B) −15 C) −8 D) 2 To'g'ri javob: B) −15 ✔ 25. F(x) funksiya f(x) = cos x ning boshlang'ich funksiyasi va F(π/2) = 3. F(0) ni toping. A) 3 B) 1 C) 4 D) 2 To'g'ri javob: D) 2 ✔ 26. Tenglamani yeching: (x + 3)/(x − 2) = 2. A) 7 B) −5 C) 1 D) 3 To'g'ri javob: A) 7 ✔ 27. ABCD parallelogrammda AB + AD vektorlar yig'indisi qaysi vektorga teng? A) CA B) AC C) BD D) DB To'g'ri javob: B) AC ✔ Matematika — davlat granti mashq variantlari | 162 28. Mahsulot 20% zarar bilan 640 so'mga sotildi. Uning tannarxini toping. A) 768 B) 800 C) 820 D) 780 To'g'ri javob: B) 800✔ 29. cos α = 1/3 bo'lsa, cos2α ni toping. A) −7/9 B) 2/3 C) −1/3 D) 8/9 To'g'ri javob: A) −7/9 ✔ 30. y = sin3x funksiyaning eng kichik musbat davrini toping. A) π/3 B) 2π/3 C) 3π D) 6π To'g'ri javob: B) 2π/3 ✔ Matematika — davlat granti mashq variantlari | 163 33-variant Asosiy fan bloki • bitta to'g'ri javob 1. Hisoblang: 999 · 1001. A) 999999 B) 1000001 C) 999001 D) 998999 To'g'ri javob: A) 999999✔ 2. f(x) = −x² + 4x + 1 funksiyaning eng katta qiymatini toping. A) 4 B) 2 C) 1 D) 5 To'g'ri javob: D) 5 ✔ 3. 3^(x²) < 9^(x + 4) tengsizlik nechta butun yechimga ega? A) 5 B) 6 C) 7 D) 4 To'g'ri javob: A) 5 ✔ 4. Markaziy burchak 72° ga teng. Unga mos yoy butun aylananing qanday qismini tashkil etadi? A) 1/4 B) 2/9 C) 1/5 D) 1/6 To'g'ri javob: C) 1/5 ✔ 5. ABC uchburchakning BC tomonida D nuqta olingan, BD : DC = 2 : 5. ABC uchburchak yuzi 35 ga teng bo'lsa, ABD uchburchak yuzini toping. A) 14 B) 7 C) 25 D) 10 To'g'ri javob: D) 10 ✔ 6. Hisoblang: 1/(1·2) + 1/(2·3) + 1/(3·4) + … + 1/(99·100). A) 100/101 B) 99/100 C) 98/99 D) 1 To'g'ri javob: B) 99/100 ✔ Matematika — davlat granti mashq variantlari | 164 7. 48 sonini ikkita musbat qo'shiluvchiga shunday ajratingki, ularning kvadratlari yig'indisi eng kichik bo'lsin. Shu eng kichik yig'indini toping. A) 1152 B) 2304 C) 576 D) 1160 To'g'ri javob: A) 1152✔ 8. A va B erkli hodisalar, P(A) = 0,6 va P(B) = 0,5. A va B ning birgalikda ro'y berish ehtimolini toping. A) 0,8 B) 0,3 C) 0,55 D) 1,1 To'g'ri javob: B) 0,3 ✔ 9. x² − 6x + 11 ifodaning eng kichik qiymatini toping. A) 2 B) 11 C) 3 D) −9 To'g'ri javob: A) 2 ✔ 10. y = log₃(4 − x²) funksiyaning aniqlanish sohasini toping. A) (0; 2) B) (0; 4) C) (−2; 2) D) (−4; 4) To'g'ri javob: C) (−2; 2) ✔ 11. Uchburchak medianasining uzunligi 12 ga teng. Medianalar kesishish nuqtasidan shu median chiqqan uchgacha bo'lgan masofani toping. A) 8 B) 6 C) 4 D) 9 To'g'ri javob: A) 8 ✔ 12. Hisoblang: (−27) · √0,04 + 5⁰. ∛ A) −1,6 B) 0,4 C) 0,94 D) −0,8 To'g'ri javob: B) 0,4 ✔ 13. Kubning qirrasi 1 ga orttirilganda uning hajmi 61 ga ortdi. Kubning dastlabki qirrasini toping. A) 5 B) 3 C) 6 D) 4 To'g'ri javob: D) 4 ✔ Matematika — davlat granti mashq variantlari | 165 14. 1, 2, 3, 4, 5 raqamlaridan (raqamlar takrorlanishi mumkin) nechta uch xonali son tuzish mumkin? A) 125 B) 15 C) 60 D) 243 To'g'ri javob: A) 125✔ 15. Tengsizlikni yeching: (x² + 1)(x − 3) < 0. A) (−∞; 3) B) (−1; 3) C) (0; 3) D) (−∞; −1) (1; 3) ∪ To'g'ri javob: A) (−∞; 3) ✔ 16. Barcha qirralari 6 ga teng bo'lgan muntazam to'rtburchakli piramidaning hajmini toping. A) 108√2 B) 36√2 C) 18√2 D) 72 To'g'ri javob: B) 36√2 ✔ 17. Tengsizlikni yeching: (x + 5)/(x − 3) > 2. A) (−∞; 11) B) (3; 11) C) (−5; 3) D) (3; +∞) To'g'ri javob: B) (3; 11) ✔ 18. 25 o'quvchidan iborat sinfda sinf sardori va uning o'rinbosarini necha xil usulda saylash mumkin? A) 600 B) 625 C) 50 D) 300 To'g'ri javob: A) 600 ✔ 19. Tenglamani yeching: 2ˣ = 1/16. A) −4 B) 1/4 C) −8 D) −2 To'g'ri javob: A) −4 ✔ 20. Tomonlari 13, 14 va 15 ga teng uchburchakning yuzini toping. A) 96 B) 84 C) 42 D) 168 To'g'ri javob: B) 84 ✔ Matematika — davlat granti mashq variantlari | 166 21. Muntazam uchburchakli piramida asosining tomoni 6 ga, balandligi 4 ga teng. Piramida hajmini toping. A) 12√3 B) 36√3 C) 18√3 D) 9√3 To'g'ri javob: A) 12√3✔ 22. Radiusi 13 ga teng aylanada uzunligi 24 ga teng vatar o'tkazilgan. Aylana markazidan vatargacha bo'lgan masofani toping. A) √145 B) 5 C) 12 D) 6 To'g'ri javob: B) 5 ✔ 23. Tengsizlikni yeching: x² − 4 ≥ 0. A) x ≤ −2 yoki x ≥ 2 B) x ≥ 4 C) −2 ≤ x ≤ 2 D) x ≥ 2 To'g'ri javob: A) x ≤ −2 yoki x ≥ 2 ✔ 24. f(x) = x⁴ − 2x² funksiya nechta ekstremum nuqtaga ega? A) 4 B) 2 C) 3 D) 1 To'g'ri javob: C) 3 ✔ 25. Aylana radiusi 2 ga orttirilsa, uning uzunligi qanchaga ortadi? A) 4π B) 8π C) 4 D) 2π To'g'ri javob: A) 4π ✔ 26. Hisoblang: log₃5 · log₅7 · log₇9. A) 1 B) log₃21 C) 3 D) 2 To'g'ri javob: D) 2 ✔ 27. f(x) = sin x · cos x bo'lsa, f'(π/3) ni toping. A) √3/2 B) −1/2 C) √3/4 D) 1/4 To'g'ri javob: B) −1/2 ✔ Matematika — davlat granti mashq variantlari | 167 28. Tengsizliklar sistemasini yeching: (x − 1)(x + 5) < 0, x ≥ −2. A) (−5; 1) B) [−2; 5) C) [−2; 1) D) [−2; +∞) To'g'ri javob: C) [−2; 1)✔ 29. Muntazam uchburchakli prizma asosining tomoni 4 ga, balandligi 5 ga teng. Prizma hajmini toping. A) 80 B) 20√3 C) 20√3/3 D) 40√3 To'g'ri javob: B) 20√3 ✔ 30. ABC uchburchakda AC ga parallel to'g'ri chiziq AB ni M nuqtada, BC ni N nuqtada kesadi. AM : MB = 2 : 3 va AC = 15 bo'lsa, MN ni toping. A) 9 B) 6 C) 10 D) 7,5 To'g'ri javob: A) 9 ✔ Matematika — davlat granti mashq variantlari | 168 34-variant Asosiy fan bloki • bitta to'g'ri javob 1. ABCD kvadratda A(0; 0), B(3; 1), C(2; 4). D uchning koordinatalarini toping. A) (-1; 3) B) (-1; 4) C) (4; 5) D) (5; 5) To'g'ri javob: A) (-1; 3)✔ 2. Perimetri 20 ga teng to'g'ri to'rtburchaklar ichida eng katta yuzga egasining yuzini toping. A) 25 B) 24 C) 100 D) 20 To'g'ri javob: A) 25 ✔ 3. Mahsulotning 3/5 qismi sotilgandan keyin 240 kg qoldi. Dastlab necha kg mahsulot bo'lgan? A) 720 B) 384 C) 400 D) 600 To'g'ri javob: D) 600 ✔ 4. Kodli qulf 3 ta g'ildirakdan iborat, har birida 0 dan 9 gacha raqamlar bor. Kodni bilmagan kishi birinchi urinishda qulfni ochish ehtimolini toping. A) 0,003 B) 0,0001 C) 0,001 D) 0,01 To'g'ri javob: C) 0,001 ✔ 5. Integralni hisoblang: ∫₀¹ (x³ + 2x) dx. A) 7/4 B) 3/4 C) 5 D) 5/4 To'g'ri javob: D) 5/4 ✔ 6. ∫(6x² − 2x + 3) dx integralni toping. A) 12x − 2 + C B) 2x³ − x² + C C) 6x³ − 2x² + 3x + C D) 2x³ − x² + 3x + C To'g'ri javob: D) 2x³ − x² + 3x + C ✔ Matematika — davlat granti mashq variantlari | 169 7. Ona va qizi yoshlarining yig'indisi 50 ga teng. 5 yil oldin ona qizidan 4 marta katta bo'lgan. Qizi hozir necha yoshda? A) 15 B) 13 C) 12 D) 10 To'g'ri javob: B) 13✔ 8. Trapetsiyaning bir yon tomoniga yopishgan burchaklaridan biri 65° ga teng. Shu yon tomonga yopishgan ikkinchi burchakni toping. A) 125° B) 105° C) 115° D) 65° To'g'ri javob: C) 115° ✔ 9. Geometrik progressiyada b₃ = 2. Uning dastlabki 5 ta hadi ko'paytmasini toping. A) 16 B) 10 C) 32 D) 64 To'g'ri javob: C) 32 ✔ 10. Arifmetik progressiyada a₆ = 7. Uning dastlabki 11 ta hadi yig'indisini toping. A) 154 B) 70 C) 84 D) 77 To'g'ri javob: D) 77 ✔ 11. ABCD parallelogrammning yuzi 40 ga teng. BC tomonida ixtiyoriy M nuqta olingan. AMD uchburchak yuzini toping. A) 20 B) 40 C) 10 D) 30 To'g'ri javob: A) 20 ✔ 12. cos x = 0 tenglamani yeching (k Z). ∈ A) 2πk B) πk C) π/2 + πk D) π/2 + 2πk To'g'ri javob: C) π/2 + πk ✔ 13. Arifmetik progressiyada a₁ = 2, a = 62 va S = 320. n ni toping. ₙ ₙ A) 12 B) 10 C) 20 D) 8 To'g'ri javob: B) 10 ✔ Matematika — davlat granti mashq variantlari | 170 14. cos225° ning qiymatini toping. A) −1/2 B) −1 C) −√2/2 D) √3/2 To'g'ri javob: C) −√2/2✔ 15. y = x² parabola va y = 1 to'g'ri chiziq bilan chegaralangan figuraning yuzini toping. A) 2/3 B) 8/3 C) 4/3 D) 2 To'g'ri javob: C) 4/3 ✔ 16. x² + px + 12 = 0 tenglamaning ildizlaridan biri 3 ga teng. p ni toping. A) −4 B) −7 C) −5 D) −12 To'g'ri javob: B) −7 ✔ 17. Silindrning hajmi 128π ga teng, balandligi esa asos diametriga teng. Silindr balandligini toping. A) 4 B) 16 C) 6 D) 8 To'g'ri javob: D) 8 ✔ 18. Muntazam uchburchak markazidan uning uchlariga yo'nalgan uchta vektor yig'indisi nimaga teng? A) medianaga teng vektorga B) uchburchak tomoniga teng vektorga C) nol vektorga D) birlik vektorga To'g'ri javob: C) nol vektorga ✔ 19. Moddiy nuqtaning tezligi v(t) = 3t² + 2 (m/s). U t = 0 dan t = 2 s gacha qancha yo'l (m) bosib o'tadi? A) 14 B) 10 C) 12 D) 16 To'g'ri javob: C) 12 ✔ 20. sin²15° ning qiymatini toping. A) 1/4 B) (√3 − 1)/4 C) (2 − √3)/4 D) (2 − √3)/2 To'g'ri javob: C) (2 − √3)/4 ✔ Matematika — davlat granti mashq variantlari | 171 21. Hisoblang: tg135° + sin150°. A) 0 B) 3/2 C) 1 − √3/2 D) −1/2 To'g'ri javob: D) −1/2✔ 22. Teng yonli trapetsiyaning asoslari 6 va 14 ga, yon tomoni 5 ga teng. Trapetsiya yuzini toping. A) 30 B) 40 C) 60 D) 50 To'g'ri javob: A) 30 ✔ 23. y = x² − 3, y = 2x sistemaning yechimlari (x₁; y₁), (x₂; y₂) bo'lsa, x₁ + x₂ + y₁ + y₂ ni toping. A) 8 B) 4 C) 6 D) 2 To'g'ri javob: C) 6 ✔ 24. Uchlari A(1; 1), B(4; 5) va C(5; -2) nuqtalarda bo'lgan uchburchakning qaysi burchagi to'g'ri burchak? A) A burchak B) C burchak C) to'g'ri burchak yo'q D) B burchak To'g'ri javob: A) A burchak ✔ 25. Mahsulot narxi avval 20% ga oshirildi, so'ngra yangi narx 20% ga kamaytirildi. Natijada dastlabki narx qanday o'zgardi? A) 4% ga kamaydi B) 2% ga kamaydi C) o'zgarmadi D) 4% ga oshdi To'g'ri javob: A) 4% ga kamaydi ✔ 26. Kesik konus asoslarining radiuslari 4 va 2 ga, balandligi 3 ga teng. Kesik konus hajmini toping. A) 20π B) 28π C) 84π D) 36π To'g'ri javob: B) 28π ✔ 27. Barcha ikki xonali sonlarning yig'indisini toping. A) 4905 B) 4860 C) 4950 D) 5050 To'g'ri javob: A) 4905 ✔ Matematika — davlat granti mashq variantlari | 172 28. Konus asosining radiusi 6 ga, yasovchisi 10 ga teng. Konus o'q kesimining yuzini toping. A) 60 B) 96 C) 48 D) 24 To'g'ri javob: C) 48✔ 29. 5x² − 3x − 2 = 0 tenglamaning kichik ildizini toping. A) −1 B) 0,6 C) −0,4 D) −2 To'g'ri javob: C) −0,4 ✔ 30. Tenglamani yeching: (2x − 1)/3 − (x + 2)/4 = 1. A) 4,4 B) 3,6 C) 2,8 D) 4 To'g'ri javob: A) 4,4 ✔ Matematika — davlat granti mashq variantlari | 173 Javoblar kaliti Har bir variant bo'yicha: topshiriq raqami va to'g'ri javob. 1-variant 1- D 2- B 3- A 4- D 5- D 6- A 7- C 8- C 9- A 10- D 11- D 12- A 13- D 14- A 15- D 16- C 17- C 18- D 19- D 20- C 21- B 22- D 23- D 24- A 25- C 26- A 27- C 28- C 29- A 30- A 2-variant 1- C 2- C 3- A 4- C 5- A 6- B 7- C 8- B 9- C 10- B 11- A 12- A 13- C 14- C 15- D 16- C 17- C 18- A 19- B 20- A 21- A 22- C 23- C 24- D 25- C 26- D 27- B 28- B 29- B 30- C 3-variant 1- B 2- C 3- D 4- A 5- A 6- C 7- A 8- A 9- A 10- B 11- C 12- B 13- A 14- A 15- B 16- C 17- D 18- B 19- C 20- C 21- D 22- A 23- B 24- D 25- C 26- A 27- A 28- A 29- B 30- C 4-variant 1- A 2- D 3- B 4- B 5- A 6- C 7- C 8- D 9- D 10- D 11- C 12- A 13- D 14- C 15- B 16- D 17- A 18- A 19- A 20- D 21- D 22- A 23- B 24- C 25- D 26- D 27- A 28- B 29- D 30- B 5-variant 1- C 2- D 3- B 4- C 5- C 6- D 7- B 8- C 9- B 10- A 11- C 12- D 13- A 14- B 15- C 16- D 17- B 18- D 19- A 20- B 21- D 22- A 23- D 24- A 25- C 26- B 27- B 28- A 29- B 30- A 6-variant 1- D 2- B 3- C 4- C 5- C 6- C 7- B 8- A 9- B 10- A 11- D 12- B 13- D 14- B 15- D 16- C 17- D 18- B 19- D 20- A 21- D 22- A 23- A 24- A 25- D 26- B 27- A 28- D 29- B 30- A 7-variant 1- D 2- B 3- A 4- D 5- D 6- B 7- D 8- B 9- B 10- D 11- B 12- C 13- C 14- A 15- A 16- B 17- A 18- A 19- C 20- C 21- D 22- A 23- B 24- C 25- D 26- B 27- D 28- B 29- B 30- C 8-variant 1- C 2- A 3- A 4- C 5- B 6- D 7- D 8- C 9- B 10- A 11- C 12- B 13- B 14- B 15- C 16- C 17- A 18- C 19- B 20- B Matematika — davlat granti mashq variantlari | 174 21- C 22- B 23- B 24- C 25- A 26- A 27- D 28- A 29- A 30- A 9-variant 1- B 2- C 3- B 4- C 5- C 6- A 7- A 8- D 9- B 10- B 11- D 12- D 13- D 14- A 15- A 16- D 17- D 18- B 19- B 20- C 21- A 22- D 23- D 24- D 25- C 26- B 27- B 28- B 29- A 30- D 10-variant 1- D 2- C 3- A 4- A 5- D 6- B 7- D 8- A 9- D 10- B 11- C 12- A 13- D 14- C 15- B 16- C 17- A 18- A 19- A 20- C 21- C 22- A 23- C 24- C 25- B 26- D 27- A 28- A 29- A 30- A 11-variant 1- D 2- A 3- A 4- C 5- A 6- A 7- A 8- A 9- D 10- D 11- A 12- C 13- B 14- A 15- D 16- B 17- A 18- B 19- D 20- D 21- C 22- C 23- D 24- B 25- A 26- C 27- B 28- D 29- A 30- A 12-variant 1- C 2- C 3- B 4- A 5- B 6- D 7- A 8- C 9- A 10- D 11- B 12- A 13- B 14- B 15- C 16- C 17- A 18- A 19- A 20- A 21- C 22- A 23- B 24- C 25- C 26- A 27- D 28- B 29- A 30- B 13-variant 1- D 2- B 3- B 4- A 5- A 6- C 7- B 8- A 9- C 10- C 11- C 12- D 13- D 14- A 15- D 16- A 17- A 18- D 19- C 20- D 21- A 22- C 23- C 24- C 25- B 26- C 27- B 28- B 29- C 30- D 14-variant 1- C 2- B 3- B 4- C 5- D 6- A 7- A 8- A 9- A 10- B 11- A 12- B 13- D 14- D 15- B 16- C 17- B 18- C 19- C 20- A 21- D 22- C 23- B 24- D 25- B 26- A 27- A 28- B 29- B 30- B 15-variant 1- D 2- C 3- D 4- A 5- A 6- C 7- D 8- C 9- B 10- D 11- D 12- D 13- D 14- A 15- A 16- C 17- D 18- C 19- B 20- D 21- A 22- D 23- B 24- B 25- C 26- B 27- D 28- A 29- C 30- A 16-variant 1- B 2- D 3- C 4- A 5- D 6- A 7- A 8- A 9- A 10- C 11- A 12- C 13- C 14- D 15- B 16- D 17- D 18- C 19- B 20- B 21- C 22- D 23- A 24- A 25- B 26- D 27- D 28- C 29- B 30- B Matematika — davlat granti mashq variantlari | 175 17-variant 1- D 2- C 3- B 4- C 5- B 6- D 7- A 8- A 9- D 10- C 11- D 12- A 13- D 14- C 15- D 16- C 17- D 18- D 19- D 20- A 21- D 22- B 23- D 24- D 25- C 26- B 27- C 28- D 29- A 30- B 18-variant 1- D 2- C 3- A 4- A 5- D 6- A 7- B 8- B 9- B 10- D 11- D 12- C 13- A 14- C 15- D 16- C 17- B 18- C 19- C 20- B 21- A 22- C 23- D 24- D 25- D 26- C 27- C 28- B 29- B 30- C 19-variant 1- C 2- C 3- D 4- C 5- A 6- B 7- C 8- D 9- D 10- A 11- C 12- A 13- B 14- C 15- B 16- B 17- C 18- D 19- C 20- B 21- D 22- A 23- C 24- A 25- D 26- A 27- B 28- D 29- D 30- C 20-variant 1- C 2- B 3- D 4- D 5- B 6- D 7- D 8- A 9- B 10- D 11- D 12- B 13- A 14- C 15- B 16- A 17- B 18- C 19- A 20- C 21- B 22- A 23- C 24- D 25- B 26- C 27- D 28- A 29- D 30- C 21-variant 1- B 2- B 3- D 4- A 5- C 6- B 7- A 8- D 9- B 10- A 11- C 12- D 13- C 14- C 15- D 16- C 17- B 18- B 19- C 20- A 21- D 22- B 23- D 24- B 25- A 26- A 27- D 28- C 29- A 30- C 22-variant 1- D 2- C 3- A 4- B 5- B 6- C 7- B 8- A 9- D 10- B 11- A 12- D 13- A 14- A 15- D 16- A 17- B 18- C 19- D 20- B 21- A 22- D 23- D 24- C 25- A 26- B 27- C 28- A 29- B 30- B 23-variant 1- B 2- D 3- C 4- C 5- D 6- A 7- D 8- B 9- A 10- A 11- D 12- A 13- C 14- B 15- D 16- B 17- B 18- D 19- B 20- C 21- A 22- B 23- C 24- D 25- B 26- A 27- C 28- B 29- B 30- C 24-variant 1- A 2- C 3- D 4- A 5- A 6- C 7- D 8- D 9- C 10- B 11- C 12- D 13- A 14- B 15- B 16- B 17- C 18- B 19- B 20- A 21- B 22- A 23- D 24- C 25- D 26- D 27- C 28- D 29- D 30- C Matematika — davlat granti mashq variantlari | 176 25-variant 1- C 2- C 3- A 4- D 5- C 6- B 7- A 8- A 9- A 10- A 11- A 12- C 13- A 14- A 15- A 16- A 17- C 18- B 19- D 20- A 21- C 22- B 23- D 24- C 25- D 26- C 27- B 28- A 29- A 30- B 26-variant 1- D 2- B 3- B 4- B 5- D 6- A 7- C 8- C 9- D 10- D 11- A 12- D 13- A 14- C 15- D 16- D 17- B 18- C 19- D 20- A 21- A 22- A 23- C 24- A 25- D 26- A 27- A 28- B 29- D 30- C 27-variant 1- B 2- C 3- C 4- B 5- B 6- C 7- C 8- A 9- A 10- C 11- C 12- C 13- A 14- A 15- C 16- A 17- B 18- B 19- B 20- C 21- D 22- D 23- D 24- A 25- A 26- C 27- A 28- B 29- B 30- C 28-variant 1- D 2- D 3- D 4- B 5- C 6- C 7- D 8- D 9- A 10- D 11- B 12- B 13- C 14- A 15- C 16- D 17- C 18- D 19- C 20- D 21- C 22- A 23- D 24- C 25- A 26- B 27- D 28- C 29- C 30- B 29-variant 1- C 2- C 3- B 4- D 5- C 6- A 7- C 8- D 9- B 10- D 11- D 12- A 13- C 14- B 15- B 16- B 17- C 18- A 19- C 20- C 21- B 22- A 23- C 24- D 25- C 26- B 27- C 28- A 29- B 30- C 30-variant 1- C 2- A 3- C 4- B 5- D 6- D 7- A 8- C 9- B 10- D 11- B 12- B 13- C 14- C 15- A 16- D 17- B 18- D 19- D 20- D 21- B 22- A 23- A 24- A 25- C 26- A 27- A 28- B 29- D 30- C 31-variant 1- B 2- C 3- B 4- D 5- B 6- D 7- D 8- A 9- D 10- C 11- B 12- A 13- B 14- B 15- D 16- D 17- D 18- C 19- C 20- D 21- C 22- B 23- A 24- C 25- A 26- C 27- B 28- B 29- B 30- A 32-variant 1- C 2- B 3- B 4- C 5- A 6- C 7- C 8- B 9- D 10- B 11- D 12- A 13- A 14- B 15- A 16- B 17- B 18- C 19- B 20- B 21- D 22- D 23- C 24- B 25- D 26- A 27- B 28- B 29- A 30- B Matematika — davlat granti mashq variantlari | 177 33-variant 1- A 2- D 3- A 4- C 5- D 6- B 7- A 8- B 9- A 10- C 11- A 12- B 13- D 14- A 15- A 16- B 17- B 18- A 19- A 20- B 21- A 22- B 23- A 24- C 25- A 26- D 27- B 28- C 29- B 30- A 34-variant 1- A 2- A 3- D 4- C 5- D 6- D 7- B 8- C 9- C 10- D 11- A 12- C 13- B 14- C 15- C 16- B 17- D 18- C 19- C 20- C 21- D 22- A 23- C 24- A 25- A 26- B 27- A 28- C 29- C 30- A Matematika — davlat granti mashq variantlari | 178

MATEMATIKA

Xorijiy va nodavlat OTM talabalari uchun davlat granti tanlovi testiga tayyorgarlik (asosiy fan bloki, 2026–2027)

34 ta variant • 1020 ta topshiriq • javoblari bilan

Mashq to'plami • 2025–2026 o'quv yili

Imtihon tuzilishi va yo'riqnoma

• Xorijiy davlatlar OTMlarining O'zbekistondagi filiallari va nodavlat OTMlarning kunduzgi bakalavriat talabalari uchun davlat granti tanlovi: arizalar 2026-yil 10–17-oktyabr kunlari my.uzbmb.uz orqali qabul qilinadi.

• Saralash ta'lim yo'nalishiga belgilangan fanlar majmuasi bo'yicha test sinovlari orqali o'tkaziladi (Bilim va malakalarni baholash agentligi). Joriy yilda davlat OTMlariga kirish imtihonlarida mos fanlar majmuasi bo'yicha qatnashgan talabalar o'z ballari bilan ham tanlovda ishtirok etishi mumkin.

• Grantlar minimal o'tish balini to'plaganlar orasidan, ballar ketma-ketligiga qat'iy amal qilgan holda, kvotalar doirasida taqsimlanadi. Grant butun o'qish muddatiga beriladi; bitiruvchilar kamida 3 yil davlat yoki davlat ulushi bo'lgan tashkilotlarda ishlashi shart.

• Test sanalari manbalarda hali ko'rsatilmagan — my.uzbmb.uz dagi e'lonlarni kuzatib boring.

• To'plam OTMga kirish testi (DTM) formatida tuzilgan: asosiy (ixtisoslik) fanlar bloki — 30 ta savol. To'plamda 34 ta variant × 30 ta savol = 1020 ta test. To'g'ri javob har bir savol ostida yashil rangda, hujjat oxirida javoblar kaliti bor.

• Muhim: rasmiy test savollari ochiq e'lon qilinmaydi. Bu umumta'lim fan dasturlari asosida tuzilgan mashq savollari.

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