Is a cube number. What is X + Y? (Xyyx) ̅ kub soni X + Y nima?

1. 
   is a cube number. What is X + Y?
   

(XYYX) ̅ - kub soni. X + Y nima?

2. 
   What is the units digit of the simplest form of ?
   Eng oddiy shaklning birlik raqami nima
   

3. 
   What is the highest power of 36 in 30! ?
   

30 dagi 36 ning eng katta kuchi nima

4. 
   What is the last two digits of 2⁵⁸⁴?
   

2darajasi584 sonining oxirgi ikki raqami nima?

5. 
   How many numbers from 1 to 1000 are relatively prime to both 6 and 35?
   1 dan 1000 gacha bo‘lgan nechta son 6 va 35 ga nisbatan tub son hisoblanadi?
   

6. 
   There are n ordered pairs (a, b) that satisfy the equation ab=442. If a and b are integers, what is n?
   ab=442 tenglamani qanoatlantiradigan n ta tartiblangan juft (a, b) mavjud. Agar a va b butun sonlar bo'lsa, n nima?
   

7. 
   If b < a < 0, c > 0, and |c|> |b | > |a|, simplify
   

2|a + b| + |c + b| + |c + a|?
Agar b < a < 0, c > 0 va |c|> |b | > |a|, soddalashtiring
2|a + b| + |c + b| + |c + a|?

8. 
   If (153x + 765y) is a square number and both x and y are positive integers, what is the minimum value of (x + y)?
   

9. 
   In the equation 15x + 16y + 17z = 208, where x, y, and z are integers, find the value of 4(x + y + z).
   

15x + 16y + 17z = 208 tenglamada x, y va z butun sonlar, 4(x + y + z) ning qiymatini toping.

Find the sum of the coefficients of the polynomial Ko‘phadning koeffitsientlari yig‘indisini toping

10. 
    

(4x³ - 7x + 12)(11 + 5x - 10x²)²(5x – 2)³.

11. 
    What is the remainder when (x + 5)²⁰¹⁹ + (x + 4)²⁰²¹ is divided by
    

(x² + 9x + 20)?
(x + 5)2019 + (x + 4)2021 ga bo'linganda qoldiq qancha bo'ladi
(x2 + 9x + 20)?

12. 
    Given that (A + B) = 12 and is a square number, find .
    

(A + B) = 12 va ((AB) ̅-(BA) ̅ ) kvadrat son ekanligini hisobga olib, ((AB) ̅-(BA) ̅ ) ni toping.

13. 
    If x is a real number, what is the maximum value of the graph of
    

y = 5 – 6x – x²?

Agar x haqiqiy son bo'lsa, grafigining maksimal qiymati qancha bo'ladi y = 5 – 6x – x2?

14. 
    Two squares overlap as shown below. The side of the bigger square is x cm while the smaller square is y cm. Both x and y are integers. The shaded region between the squares is 32 cm². Find the sum of all possible values (x + y) that satisfy the condition.
    . Ikki kvadrat quyida ko'rsatilganidek, bir-birining ustiga chiqadi. Katta kvadratning tomoni x sm, kichik kvadrati esa y sm. X ham, y ham butun sonlar. Kvadratchalar orasidagi soyali hudud 32 sm2 ni tashkil qiladi. Shartni qanoatlantiradigan barcha mumkin bo'lgan qiymatlar yig'indisini toping (x + y).
    

15. 
    The ratio of the areas of circles A and B is 3:2. Circle A has the equation
    

x² + y² – 6x + 4y + 4 = 0. If circle B has center at (-2, 5), what is the equation of circle B in standard (center-radius) form?
A va B doiralar maydonlarining nisbati 3:2 ga teng. A doirasi tenglamaga ega
x2 + y2 – 6x + 4y + 4 = 0. Agar B aylana markazi (-2, 5) da bo'lsa, B aylana standart (markaz radiusi) ko'rinishdagi tenglamasi qanday?

16. 
    In the composite figure below, the total shaded area is cm². Given that , and , calculate the area of .
    

Quyidagi kompozit rasmda umumiy soyali maydon 25p/2 sm2 ni tashkil qiladi. PH⊥HI, PI=LI va PH⊥LI ekanligini hisobga olib, ∆PIL maydonini hisoblang.

17. 
    Given the three sides of ΔPHL as shown below, find the area of the inscribed circle in the triangle.
    

Quyida ko'rsatilganidek, DPHL ning uchta tomoni berilgan, uchburchakda chizilgan aylananing maydonini toping.

18. 
    A circle of radius 10 cm overlaps right triangle QRS as shown below. QR = 16 cm and RS = 25 cm. Find the difference between the shaded areas X and Y. Use π = 3.14.
    

Radiusi 10 sm bo'lgan doira quyida ko'rsatilganidek, QRS to'g'ri burchakli uchburchakni kesib o'tadi. QR = 16 sm va RS = 25 sm. X va Y soyali maydonlar orasidagi farqni toping. p = 3.14 dan foydalaning.

19. 
    How many trailing zeroes are there in 2021!?
    2021-yilda qancha nol bor!?
    

20. 
    Mother bought a watch, a cellphone and a necklace for her 3 daughters Anita, Benita, and Catriona. At any situation, one of the following statements is true and the other three are false. Which statement is true?
    

1. 
   Anita received the watch.
   
2. 
   Benita received the cellphone.
   
3. 
   Catriona did not receive the necklace.
   
4. 
   Neither Catriona nor Anita received the cellphone.
   
5. 
   Onam 3 qizi Anita, Benita va Katriona uchun soat, uyali telefon va marjon sotib oldi. Har qanday vaziyatda quyidagi bayonotlardan biri to'g'ri, qolgan uchtasi noto'g'ri. Qaysi bayonot to'g'ri?
   
6. 
   i. Anita soatni oldi.
   

ii. Benita uyali telefonni oldi.

7. 
   iii. Katriona marjonlarni olmadi.
   
8. 
   iv. Katriona ham, Anita ham uyali telefonni olishmadi.
   

21. 
    11, 101, 1001 are palindromic numbers. How many palindromic numbers less than 2021 are there?
    11, 101, 1001 palindromik sonlar. 2021 dan qancha palindromik sonlar kichik?
    

22. 
    What is the sum of the angles marked with dots in the drawing below if the identical triangles are all right-angled?
    Agar bir xil uchburchaklar to‘g‘ri burchakli bo‘lsa, quyidagi chizmada nuqta bilan belgilangan burchaklar yig‘indisi qancha bo‘ladi?
    

23. 
    The numbers 1 to 7 are to put in each circle such that in each of the triangle shown below the sum of the 3 numbers are equal. Find the value of P + H?
    1 dan 7 gacha raqamlar har bir aylanaga shunday qo'yiladiki, quyida ko'rsatilgan uchburchakning har birida 3 ta raqamning yig'indisi teng bo'lsin. P + H qiymatini toping?
    

24. 
    Phil multiplied at least 2 consecutive numbers and got the 6-digit product A. The first two digits and the last two digits of A are 11 and 44, respectively. Find the sum of the numbers.
    Fil kamida 2 ta ketma-ket sonni ko'paytirdi va 6 xonali A mahsulotini oldi. A ning birinchi ikkita raqami va oxirgi ikki raqami mos ravishda 11 va 44 ga teng. Raqamlar yig‘indisini toping.
    

25. 
    What is the numerical coefficient of the middle term of the binomial expansion of ?
    〖(2x+3y)〗^10 ning binomial kengayishining oʻrta hadining son koeffitsienti nimaga teng?
    

26. 
    How many possible divisors does 15! or 15 x 14 x 13 x 12 x … x 3 x 2 x 1 have?
    15 ning nechta mumkin bo'luvchisi bor! yoki 15 x 14 x 13 x 12 x … x 3 x 2 x 1 bormi?
    

27. 
    If and , find .
    

Agar (0)=1 va f(n+1)=(n+1)f(n), f(3) toping.

28. 
    Among the 2021 participants of PIMSO Mathematics, what is the least number of people that must be born on the same month?
    PIMSO Matematikasining 2021 yil ishtirokchilari orasida bir oyda tug'ilishi kerak bo'lgan eng kam odamlar soni qancha?
    

29. 
    Fifteen cards are numbered 1 to 15 and then put in a bag. Two cards are drawn at random and without replacement. What is the probability that the numbers in the cards are both prime?
    O'n beshta karta 1 dan 15 gacha raqamlangan va keyin sumkaga solingan. Ikkita karta tasodifiy va almashtirilmasdan chiqariladi. Kartochkalardagi raqamlarning ikkalasi ham tub son bo'lish ehtimoli qanday?
    

Abby was asked by his teacher to name as many triangles as she can in the diagram below. What is the most number of triangles did Abby name?

Ebbidan o'qituvchisi quyidagi diagrammada iloji boricha ko'proq uchburchaklarni nomlashni so'radi. Abbi eng ko'p uchburchaklar soni qancha?

30. 
    

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