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

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

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

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

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.

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

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

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

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

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

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

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

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?

\(ABCD\) 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.

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

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

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.

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

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.

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.

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

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

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

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

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

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

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

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

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.

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?