Skip to content

1. Begin — kiritish, chiqarish va o'zlashtirish

Barcha masalalarda kirish ma'lumotlari haqiqiy sonlar. Natijani ekranga chiqaring. Zarur bo'lsa π ≈ 3.14159 oling.

1. Kvadratning tomoni a berilgan. Uning diagonali d ni toping.
\(\displaystyle d = a\sqrt{2}\)
Misol: a = 4 → d = 5.6569

2. Teng tomonli uchburchakning tomoni a berilgan. Uning perimetri va yuzasini toping.
\(\displaystyle P = 3a\), \(\displaystyle S = \dfrac{a^2\sqrt{3}}{4}\)
Misol: a = 6 → P = 18, S = 15.5885

3. Rombning diagonallari d₁ va d₂ berilgan. Uning yuzasini toping.
\(\displaystyle S = \dfrac{d_1 d_2}{2}\)
Misol: d₁ = 6, d₂ = 8 → S = 24

4. Trapetsiyaning asoslari a, b va balandligi h berilgan. Uning yuzasini toping.
\(\displaystyle S = \dfrac{(a + b)\,h}{2}\)
Misol: a = 5, b = 7, h = 4 → S = 24

5. Silindrning radiusi R va balandligi h berilgan. Uning hajmi va to'la sirtini toping.
\(\displaystyle V = \pi R^2 h\), \(\displaystyle S = 2\pi R\,(R + h)\)
Misol: R = 3, h = 5 → V = 141.3715, S = 150.7963

6. Konusning radiusi R va balandligi h berilgan. Uning yasovchisi l va hajmini toping.
\(\displaystyle l = \sqrt{R^2 + h^2}\), \(\displaystyle V = \dfrac{\pi R^2 h}{3}\)
Misol: R = 3, h = 4 → l = 5, V = 37.6991

7. Sharning radiusi R berilgan. Uning hajmi va sirtini toping.
\(\displaystyle V = \dfrac{4\pi R^3}{3}\), \(\displaystyle S = 4\pi R^2\)
Misol: R = 6 → V = 904.7779, S = 452.389

8. Doira sektorining radiusi R va markaziy burchagi φ (gradusda) berilgan. Yoy uzunligi va sektor yuzasini toping.
\(\displaystyle l = \dfrac{\pi R \varphi}{180}\), \(\displaystyle S = \dfrac{\pi R^2 \varphi}{360}\)
Misol: R = 10, φ = 90 → l = 15.708, S = 78.5397

9. Uchta son a, b, c berilgan. Ularning o'rta arifmetigi va o'rta kvadratik qiymatini toping.
\(\displaystyle \dfrac{a + b + c}{3}\), \(\displaystyle \sqrt{\dfrac{a^2 + b^2 + c^2}{3}}\)
Misol: a = 1, b = 2, c = 3 → o'rta arifmetik = 2, o'rta kvadratik = 2.1602

10. Ikkita son a va b berilgan. Quyidagi ifodalarning qiymatlarini toping.
\(\displaystyle (a + b)^2\), \(\displaystyle (a - b)^2\), \(\displaystyle a^2 - b^2\)
Misol: a = 5, b = 3 → (a+b)² = 64, (a-b)² = 4, a²-b² = 16

11. Uchburchakning asosi a va unga tushirilgan balandligi h berilgan. Uning yuzasini toping.
Misol: a = 6, h = 4 → S = 12

12. Parallelogrammning tomonlari a, b va ular orasidagi burchak α (gradusda) berilgan. Uning yuzasini toping.
\(\displaystyle S = a\,b\sin\alpha\)
Misol: a = 4, b = 5, α = 30 → S = 10

13. Uchburchakning ikki tomoni a, b va ular orasidagi burchak γ (gradusda) berilgan. Uchinchi tomonini toping.
\(\displaystyle c = \sqrt{a^2 + b^2 - 2ab\cos\gamma}\)
Misol: a = 3, b = 4, γ = 90 → c = 5

14. Mahsulot narxi P so'm va chegirma p% berilgan. Chegirmadan keyingi narxni va tejalgan pulni toping.
Misol: P = 200000, p = 15 → yangi narx = 170000, tejalgan = 30000

15. Ikkita musbat son a va b berilgan. a soni b ning necha foizini tashkil qilishini aniqlang.
Misol: a = 30, b = 120 → foiz = 25

16. Shaharning boshlang'ich aholisi S kishi. Aholi soni har yili r% ga ortib boradi (har yilgi o'sish oldingi yil natijasiga qo'llanadi). n yildan keyingi aholi sonini toping.
\(\displaystyle S\left(1 + \dfrac{r}{100}\right)^{n}\)
Misol: S = 1000000, r = 10, n = 3 → aholi soni = 1331000

17. Yo'l uzunligi S km va avtomobil tezligi v km/soat berilgan. Yo'lga ketadigan vaqtni soatlarda va minutlarda (haqiqiy son sifatida) toping.
Misol: S = 150, v = 60 → soat = 2.5, minut = 150

18. Jism boshlang'ich tezligi v₀, tezlanishi a bilan t sekund harakatlandi. Bosib o'tgan yo'li va oxirgi tezligini toping.
\(\displaystyle s = v_0 t + \dfrac{a t^2}{2}\), \(\displaystyle v = v_0 + a t\)
Misol: v₀ = 2, a = 3, t = 4 → s = 32, v = 14

19. Jism h metr balandlikdan erkin tushmoqda (g = 9.8 m/s²). Yerga tushish vaqti va tushish paytidagi tezligini toping.
\(\displaystyle t = \sqrt{\dfrac{2h}{g}}\), \(\displaystyle v = g t\)
Misol: h = 19.6 → t = 2, v = 19.6

20. Zanjir uchastkasida kuchlanish U (V) va qarshilik R (Ω) berilgan. Tok kuchi va quvvatni toping.
\(\displaystyle I = \dfrac{U}{R}\), \(\displaystyle P = U I\)
Misol: U = 12, R = 4 → I = 3, P = 36

21. Ikki qarshilik R₁ va R₂ berilgan. Ularni ketma-ket va parallel ulaganda umumiy qarshilikni toping.
\(\displaystyle R = R_1 + R_2\), \(\displaystyle R = \dfrac{R_1 R_2}{R_1 + R_2}\)
Misol: R₁ = 6, R₂ = 3 → ketma-ket = 9, parallel = 2

22. Massasi m (kg) va tezligi v (m/s) bo'lgan jismning kinetik energiyasi va impulsini toping.
\(\displaystyle E = \dfrac{m v^2}{2}\), \(\displaystyle p = m v\)
Misol: m = 2, v = 5 → E = 25, p = 10

23. Kubning hajmi V berilgan. Uning tomoni va yon sirtini toping.
\(\displaystyle a = \sqrt[3]{V}\), \(\displaystyle S = 4a^2\)
Misol: V = 27 → a = 3, S = 36

24. A, B, C koeffitsientlar berilgan. Kvadrat tenglamaning diskriminantini toping.
\(\displaystyle D = B^2 - 4AC\)
Misol: A = 1, B = 5, C = 6 → D = 1

25. Tekislikda ikki nuqta (x₁, y₁) va (x₂, y₂) berilgan. Ularni tutashtiruvchi kesmaning o'rta nuqtasi koordinatalarini toping.

\(\displaystyle x = \frac{x_1+x_2}{2}\) \(\displaystyle y = \frac{y_1+y_2}{2}\)

Misol: (1, 2) va (5, 8) → x = 3, y = 5

26. Fazoda vektor (x, y, z) berilgan. Uning uzunligini toping.
\(\displaystyle |\vec v| = \sqrt{x^2 + y^2 + z^2}\)
Misol: x = 2, y = 3, z = 6 → uzunlik = 7

27. A va B sonlari berilgan. Uchinchi o'zgaruvchisiz, faqat qo'shish va ayirish orqali ularning qiymatlarini almashtiring.
Misol: A = 3, B = 7 → A = 7, B = 3

28. A, B, C, D sonlari berilgan. Ularning qiymatlarini chapga aylanma siljiting: A ← B, B ← C, C ← D, D ← A.
Misol: A = 1, B = 2, C = 3, D = 4 → A = 2, B = 3, C = 4, D = 1

29. Arifmetik progressiyaning birinchi hadi a₁, ayirmasi d va hadlar soni n berilgan. n-hadini va dastlabki n ta hadining yig'indisini toping.
\(\displaystyle a_n = a_1 + (n - 1)\,d\), \(\displaystyle S_n = \dfrac{(a_1 + a_n)\,n}{2}\)
Misol: a₁ = 2, d = 3, n = 5 → aₙ = 14, Sₙ = 40

30. Geometrik progressiyaning birinchi hadi b₁, maxraji q va n berilgan. n-hadini toping.
\(\displaystyle b_n = b_1 q^{\,n-1}\)
Misol: b₁ = 2, q = 3, n = 4 → bₙ = 54

31. x soni (x ≥ 0) berilgan. Uning kvadrati, kubi va kvadrat ildizini toping.
Misol: x = 16 → kvadrat = 256, kub = 4096, ildiz = 4

32. Uzunlik L santimetrda berilgan. Uni dyuymlarda ifodalang (1 dyuym = 2.54 sm).
Misol: L = 25.4 → dyuym = 10

33. Masofa M milyada berilgan. Uni kilometrlarda ifodalang (1 milya ≈ 1.609 km).
Misol: M = 10 → km = 16.09

34. Akvariumning o'lchamlari a, b, h santimetrda berilgan. Uning sig'imini litrlarda toping (1 l = 1000 sm³).
Misol: a = 50, b = 40, h = 30 → litr = 60

V=a×b×h / 1000

35. Xona poli a × b metr. 1 m² ga q gramm bo'yoq sarflanadi. Butun pol uchun necha kilogramm bo'yoq kerak?

Misol: a = 5, b = 4, q = 150 → kg = 3

36. Avtomobil 100 km ga q litr yoqilg'i sarflaydi, 1 litr narxi c so'm. d km yo'l uchun yoqilg'i narxini toping.
Misol: q = 8, c = 10000, d = 250 → narx = 200000

37. Dollar kursi K so'm. X dollar necha so'm bo'lishini va Y so'm necha dollar bo'lishini aniqlang.
Misol: K = 12500, X = 20, Y = 250000 → X dollar (so'm) = 250000, Y so'm (dollar) = 20

38. Birinchi ishchi ishni A soatda, ikkinchisi B soatda bajaradi. Birgalikda ishlasa, ish necha soatda bajarilishini toping.
\(\displaystyle T = \dfrac{A B}{A + B}\)
Misol: A = 6, B = 3 → T = 2

39. To'g'ri burchakli uchburchakning katetlari a va b berilgan. Unga tashqi chizilgan aylananing radiusi R va ichki chizilgan aylananing radiusi r ni toping.
\(\displaystyle R = \dfrac{c}{2}\), \(\displaystyle r = \dfrac{a + b - c}{2}\), bunda \(\displaystyle c = \sqrt{a^2 + b^2}\)
Misol: a = 6, b = 8 → R = 5, r = 2

40. Uchburchakning uch tomoni a, b, c berilgan (uchburchak mavjud deb hisoblang). Uning yuzasini Geron formulasi bilan toping.
\(\displaystyle p = \dfrac{a + b + c}{2}\), \(\displaystyle S = \sqrt{p(p - a)(p - b)(p - c)}\)
Misol: a = 3, b = 4, c = 5 → S = 6