\(f\left( x \right) = 4\sin \left( {x + \frac{\pi }{2}} \right) + 6\cos \left( {\frac{x}{5} + \frac{\pi }{3}} \right)\) funksiyaning eng kichik musbat davrini toping.

\(f\left( x \right) = 2{x^2} - 3x + c\) funksiya \(A\left( {1;2} \right)\) nuqtadan o‘tsa, \(c\) ning qiymatini toping.

Aniq integralni hisoblang:
\(\mathop \smallint \limits_1^e \ln \left( {{x^2}} \right)dx\)

\({2^{18}} + 1\) soni quyidagilardan qaysi biriga qoldiqsiz bo‘linadi?

\(2,\;\;3,\;\;4,\;\;5,\;\;6,\;\;7,\;\;8\) raqamlaridan nechta turli raqamli \(3\) xonali son tuzish mumkin?

\({2^n} - {2^{2 - n}} = 3\) bo‘lsa, \(n\) ning qiymatini toping.

Agar \(a = {\rm{ct}}{{\rm{g}}^{2024}}\left( {\lg \left( {2 + \sqrt 3 } \right)} \right)\) bo‘lsa, \({\rm{ct}}{{\rm{g}}^{2024}}\left( {\lg \left( {2 - \sqrt 3 } \right)} \right)\) ni \(a\) orqali ifodalang.

\(28\) ta olmadan birini ko‘pi bilan necha xil usulda olish mumkin?

\(ABCD\) trapetsiyaning asoslari \(BC = 18\;{\rm{sm}}\) va \(AD = 50\;{\rm{sm}}\) ga teng. Agar \(\angle BAC = \angle ADC\) bo‘lsa, \(AC\) diagonalning uzunligini \(\left( {{\rm{sm}}} \right)\) toping.

\(A = \frac{{\sin 31^\circ }}{{\cos 59^\circ }} + \frac{{\tan 47^\circ }}{{\cot 43^\circ }}\) bo’lsa, \(\sin \frac{\pi }{{3A}} + \tan \frac{\pi }{{2A}}\) ning qiymatini toping.

Aniq integralni hisoblang:
\(\mathop \smallint \nolimits_e^{{e^2}} \frac{{dx}}{{x \cdot {\rm{l}}{{\rm{n}}^2}x}}\)

\(m = 400 \cdot \left( {{7^4} + 1} \right) \cdot \left( {{7^8} + 1} \right)\) bo‘lsa, \(\sqrt[8]{{6m + 1}}\) ning qiymatini toping.

Sfera sirtidagi uchta nuqta orasidagi masofa \(26\;{\rm{sm}},\;\;24\;{\rm{sm}}\) va \(10\;{\rm{sm}}\) ga, sfera sirtining yuzi \(900\pi \;{\rm{s}}{{\rm{m}}^2}\) ga teng. Shu uchta nuqta orqali o‘tgan tekislikdan sferaning markazigacha bo‘lgan masofani \(\left( {{\rm{sm}}} \right)\) toping.

\({2024^{{0^{2024}}}} - {\left( {{{\left( {{2^0}} \right)}^2}} \right)^4}\) ni hisoblang.

\({x^2} + ax + 1 = 0\;\)va \({x^2} + x + a = 0\) tenglamalar bitta umumiy ildizga ega bo‘lsa,\(\;a\) ning qiymatini toping.

Quyidagi rasmda Sardor Salohiddinovning o‘quv xonasi tasvirlangan:

Xonaning eni \(5\;{\rm{m}}\) ga teng va uning \(4\) ta yon devori bo‘yalgan. Agar xonaning derazalari kvadrat shaklida va ularning soni \(4\) ta bo‘lsa, necha \(\left( {{{\rm{m}}^2}} \right)\) yuza bo‘yalgan?

\(f\left( x \right) = {\rm{tg}}x\) funksiyaning \({x_0} = \frac{\pi }{3}\) nuqtadagi hosilasini toping.

\({\log _{1 - x}}\left( {3 - x} \right) = {\log _{3 - x}}\left( {1 - x} \right)\) tenglamaning nechta haqiqiy ildizi bor?

\({\left( {xy + x + y + 1} \right)^{20}}\) ifoda ko‘phad ko‘rinishida keltirilganda nechta haddan iborat bo‘ladi?

\({\sin ^2}x;\;\;\cos \left( {90^\circ - x} \right);\;\;{\cos ^2}x\) lar ko‘rsatilgan tartibda arifmetik progressiyani tashkil qilsa, \(\frac{3}{2}\) soni bu progressiyani nechanchi nomerli hadi bo’ladi?

Quyidagi rasmda teng yonli \(ABC\) uchburchak tasvirlangan:

\(\angle DCB - \angle DBC = 40^\circ \) bo‘lsa, \(\angle BAC\) ning qiymatini toping.

Quyidagi rasmda \(\# \) amalini ishlash tartibi ko’rsatilgan:

Rasmda berilgan ma’lumotlardan foydalanib, \(\# 12 + 15\# - 11\# + \# 9\) ning qiymatini toping.

Bir xil o‘lchamdagi shakllar ustida turgan jirafaning bo‘yi uzunligini \(\left( {{\rm{cm}}} \right)\) toping.

To‘g‘ri burchakli uchburchakning katetlari \({\log _2}27\;{\rm{sm}}\) va \({\log _3}64\;{\rm{sm}}\) bo‘lsa, uning yuzini \(\left( {{\rm{s}}{{\rm{m}}^2}} \right)\) toping.

Quyidagi rasmda \(2\) ta chelak va \(1\) ta bak tasvirlangan:

Agar bakni to‘ldirish uchun ikkita chelak bilan jami \(20\) marta suv quyilgan bo‘lsa, birinchi chelak bilan necha marta suv quyilgan?

G‘ishtning og‘irligi \(1,4\) kg va yana yarimta g‘ishtni og‘irligiga bo‘lsa, g‘ishtning og‘irligini \(\left( {{\rm{kg}}} \right)\) toping.

\({2^{2013}}\) sonining oxirgi ikkita raqamini toping.

\(P\left( x \right) = 5{x^{\frac{{12}}{n}}} + {x^{\frac{4}{n}}} + 3\) ifoda ko’phad bo’ladigan \(n\) ning barcha qiymatlari yig’indisini toping.

Qavariq oltiburchakning birinchi, ikkinchi va uchinchi tomonlari uzunliklari o‘zaro teng, to‘rtinchi tomoni birinchisidan \(2\) marta katta, beshinchi tomoni to‘rtinchisidan \(3\) \({\rm{sm}}\) kichik, oltinchi tomoni esa ikkinchisidan \(1{\rm{\;sm}}\) ga katta. Aga oltiburchakning perimetri \(30\;{\rm{sm}}\) bo‘lsa, uning eng katta tomoni uzunligi \(\left( {{\rm{sm}}} \right)\) topilsin.

Quyidagi rasmda kvadrat va muntazam beshburchaklar tasvirlangan:

Agar shaklning perimetri \(96\;{\rm{sm}}\) bo‘lsa, kvadratning yuzini \(\left( {{\rm{s}}{{\rm{m}}^2}} \right)\) toping.