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

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

\(ABCD\) 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.

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

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

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

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

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.

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

\(P\left( x \right) = 5{x^{\frac{{12}}{n}}} + {x^{\frac{4}{n}}} + 3\) 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.

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

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

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

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

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 kvadrat va muntazam beshburchaklar tasvirlangan:

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

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

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

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

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

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

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.

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.

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

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

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

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

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