§. Natural va butun sonlar

21. ifodanisoddalashtiring.
A)1 B)x C) x²⁰¹⁸D) x²⁰¹⁹
22. ifodanisoddalashtiring.
A)1 B)xC)x²⁰²⁰D)x²⁰¹⁹
23.Agar x² + x+1=0 bo’lsa, x²⁶ + x^–26ifodaningqiymatini toping.
A) -1 B)2 C)0 D)1
24. Agar x² + x+1=0 bo’lsa, x²⁹ + x^–29 ifodaningqiymatinitoping.
A) -1 B)2 C)0 D)1
25. Agar x² + x+1=0 bo’lsa, x³² + x^–32ifodaningqiymatini toping.
A) 1 B)2 C)0 D)– 1
26. Agar x² + x+1=0 bo’lsa, x⁹⁹ + x^–99ifodaningqiymatini toping.
A) 1 B)2 C)0 D)–1
27. Agar x² + x+1=0 bo’lsa, x³³³³ + x³³³ + x³³ + x³ +2018 ifodaningqiymatini toping.
A)2018 B)2020 C)2022 D)2014
28.(a² + b²)(x² + y²) = P²(x,y) + Q²(x, y) ayniyatbajarilsa, P(0;0) + Q(0; 0) ifodaningqiymatini toping.
A) 0 B) a+b C) a–b D) 2a
29. (a² + b²)(x² + y²) = P²(x,y) + Q²(x,y)ayniyatbajarilsa, P(1;0) + Q(1; 0) ifodaningqiymatinitoping.
A) 0B) a+b C) a– b D) 2a
30. (a² + b²)(x² + y²) = P²(x,y) + Q²(x, y) ayniyatbajarilsa, P(0; 1) + Q(0; 1) ifodaningqiymatini toping.
A) 0B) a+bC) a-b D) 2a
31. (a² + b²)(x² + y²) = P²(x,y) + Q²(x, y) ayniyatbajarilsa, P(1;1) + Q(1; 1) ifodaningqiymatini toping.
A) 0B) a+b C) a– b D) 2a

32. n ning qanday qiymatlarida 1+x²+x⁴+……+x^2n-2 ifoda 1+x+x²+x³+……+x^n-1 ifodaga qoldiqsiz bo’linadi?

A) n=1 , n=3 B) n=2, n=4 C) barcha toq sonlarda D) barcha juft sonlarda
33. 1+x²+x⁴+……+x^2n-2 ifoda 1+x+x²+x³+……+x^n-1 ifodaga qoldiqsiz bo’linadigan n ning barcha natural qiymatlari yig’indisini toping.
A) 4 B) 6 C) bunday qiymatlar mavjud emas D) cheksiz kattalikka ega
34. ayniyatdan B ni toping.
A)2 B)3 C)1 D) -1
35. Yig’indini hisoblang.

A)0 B)1 C) a+b+c D) aniqlab bo’lmaydi
36. Yig’indini hisoblang.

A)0 B)1 C) a+b+c D) aniqlab bo’lmaydi
37. Yig’indini hisoblang.

A)0 B)1 C) a+b+c D) aniqlab bo’lmaydi
38. Yig’indini hisoblang.

A)0 B)1 C) a+b+c D) aniqlab bo’lmaydi
39. Yig’indini hisoblang.

A)0 B)1 C) a+b+c D) aniqlab bo’lmaydi
40. Yig’indini hisoblang.

A)0 B)1 C) a+b+c D) aniqlab bo’lmaydi
41. Yig’indini hisoblang.

A)0 B)1 C) a+b+c D) aniqlab bo’lmaydi
42. P( ) = x²+x+1 shartniqanoatlantiruvchi P(x) ko’phadberilgan. P(3x) = 7 shartiniqanoatlantiradiganbarchax ningqiymatlariyig’indisini toping.
A)–1/9 B) 1/9 C)–2/27 D) 2/27
43. P( ) = x²+x+1 shartniqanoatlantiruvchi P(x) ko’phadberilgan. P(3x) = 7 shartiniqanoatlantiradiganbarchax ningqiymatlariko’paytmasini toping.
A)– 1/9 B)1/9 C)– 2/27 D) 2/27
44. P(x) = (1+2x–x²)⁴ko’phadning x⁷oldidagikoeffitsiyentinianiqlang.
A)– 6 B)6 C)8 D)– 8
45. Agar 2²⁰⁰⁷ – 2²⁰⁰⁶ – 2²⁰⁰⁵ + 2²⁰⁰⁴ = k∙2²⁰⁰⁴ifodaberilganbo’lsa, k ningqiymatini toping.
A) 1 B)2 C)3 D)4
46. Agar x² + y² = 1 bo’lsa, 3x⁴ + 2y⁴ +5x²y² + y²ningqiymatini toping.
A) 2 B)3 C)9 D)10
47. Agar x² + y² = 1 bo’lsa, 9x⁴ + 6y⁴ +15x²y² +3 y²ningqiymatini toping.
A) 6 B)18C)9 D)10
48. Agar x² + y² = 1 bo’lsa, 6x⁴ + 4y⁴ +10x²y² + 2y²ningqiymatini toping.
A) 4B)6 C)9 D)10
49. Agar x² + y² = 1 bo’lsa, 12x⁴ + 8y⁴ +20x²y² + 4y²ningqiymatini toping.
A) 8 B)12 C)16 D)10
50. (a+1)⁴ + 4 (a+1)³ + 4a(a+ 2) ko’phadnechtaratsionalhadliko’paytuvchilargaajraladi.
A) 3 B)2 C)4 D) ko’paytuvchilargaajralmaydi
51. (a+1)⁴ + 4 (a+1)³ + 4a(a+2)= P(x)∙Q(x) shaklidaberilganifodadan|P(x) – Q(x)|ningqiymatini toping. ( Bunda P(x) va Q(x) ratsionalhadliko’phadlar)
A) 8a+6 B) 2a² + 8a+6 C) 4 D) 8a+4
52. (a+1)⁴ + 4 (a+1)³ + 4a(a+2)= P(x)∙Q(x) shaklidaberilganifodadan P(x) +Q(x)ningqiymatini toping. ( Bunda P(x) va Q(x) ratsionalhadliko’phadlar)
A) 2a² + 8a+4 B) 2a² + 8a+6C) 4 D) 8a+4
53.a³ + b³ +c³ +3a²(b+c)+3b²(a+c)+3c²(a+b)+6abc ifodani ko’paytuvchilarga ajrating.
A) (a+b+c)(a²+b²+c²) B) (a+b+c)(a²+b²+c²-2ab-2bc-2ac) C) (a+b+c)³ D) ko’paytuvchilarga ajralmaydi
54. a³ + b³ +c³ +3a²(b+c)+3b²(a+c)+3c²(a+b)+6abc I fodani a=7, b=2, c=1 bo’lgandagi qiymatini toping.
A) 540 B) 80 C) 1000 D) 900
55. P(x)= (2x²-2x+1)¹⁹⁹⁹ (x³-2x²)²⁰⁰¹ ko’phadni barcha koeffitsientlarini yig’indisini toping.
A) 1 B)-1 C)0 D)2
56. P(x,y)=(5x²-xy-2y)¹² ko’phadni barcha koeffitsientlarini yig’indisini toping.
A)512 B)1024 C)2048 D)4096
57.Agar 3z+4(2─z)=8 bo’lsa, 1+ ifodaning qiymatini toping.
A)2,5 B)3,5 C)1,5 D)4,5
58.(a+b+c)³─a³─b³─c³ifodaquyidagilarningqaysibirigabo’linmaydi?
A) a+bB) a+b+c C) 3 D) barchasigabo’linadi
59.(a+b+c)³─a³─b³─c³ifodanechtako’paytuvchigaajraladi?
A)3 B)5 C)4 D)6
60. Agar a:b:c=2:4:7 bo’lsa, (7a+b)/(c─2) ningqiymatini toping.
A) aniqlabbo’lmaydi B)6 C)8 D)9
61. P(x) ko’phadni (x-1) ga bo’lganda qoldiq 2 chiqadi. Agar (x-2) ga bo’lganda qoldiq 1 bo’lsa, P(x) ko’phadni (x-1)(x-2) ga bo’lganda qoldiqni toping.
A) 3-x B) x+3 C)x-1 D)x-2
62. M=x³-7x²+2 ko’phad
M=(x+1)³+a(x+1)²+b(x+1)+c ko’phad ko’rinishida
keltirilsa, a ning qiymatini toping.
A)17 B)-6 C)-10 D) aniqlab bo’lmaydi
63. M=x³-7x²+2 ko’phad
M=(x+1)³+a(x+1)²+b(x+1)+c ko’phad ko’rinishida
keltirilsa, b ning qiymatini toping.
A)17 B)-6 C)-10 D) aniqlab bo’lmaydi
64. M=x³-7x²+2 ko’phad
M=(x+1)³+a(x+1)²+b(x+1)+c ko’phad ko’rinishida
keltirilsa, c ning qiymatini toping.
A)17 B)-6 C)-10 D) aniqlab bo’lmaydi
65. Soddalashtiring.

66. Soddalashtiring.

67. Soddalashtiring.

68. x, y va z haqiqiy sonlar bo’lsa, (x+y+z)³- (y+z-x)³-(z+x-y)³-(x+y-z)³ ifoda quyidagilardan qaysi biriga teng.
A)36 xyz B)24 xyz C)12 x²y²z² D) 12 xyz
69. x, y va z haqiqiy sonlar bo’lsa, (x-y)(y+z)(z+x)+(y-z)(z+x)(x+y)+(z-x)(x+y)(y+z) ifoda quyidagilardan qaysi biriga teng.
A)(x-y)(y-z)(z-x) B) -(x-y)(y-z)(z-x) C) (x+y)(y+z)(z-x) D) (x+y)(y+z)(z+x)
70.x, y va z haqiqiy sonlar bo’lsa, P(x,y,z)=x³+y³+z³-3xyz ko’phad uchun quyidagilardan qaysi biri qanoatlantiradi.
A) P(x,y,z)=P(x+y,y+z,z+x) B) P(x,y,z)=P(x-y,y-z,z+x) C) P(x,y,z)= P(x+y,y+z,z+x)
D) P(x,y,z)=P(x+2y,y+2z,z+2x)
71.x, y va z haqiqiy sonlar bo’lsa, P(x,y,z)=x³+y³+z³-3xyz ko’phad uchun quyidagilardan qaysi biri qanoatlantiradi.
A) P(x,y,z)= P(-x+y+z,x-y+z,x+y-z) B) P(x,y,z)=P(-x+y+z,x-y+z,x+y-z) C) P(x,y,z)= P(-x+y+z,x-y+z,x+y-z) D) P(x,y,z)=P(-2x+y+z,x-2y+z,x+y-2z)
72. a,b,c nol bo’lmagan haqiqiy sonlar uchun a+ shart qanoatlantirsa, ning qiymatini hisoblang.
A)2 B) 3 C)1 D) aniqlab bo’lmaydi.
73. a,b,c nol bo’lmagan haqiqiy sonlar uchun a+ shart qanoatlantirsa, ning qiymatini hisoblang.
A)2 B) 3 C)4 D) aniqlab bo’lmaydi.
74. ko’phadni ko’phadga bo’lgandagi qoldiqni toping.
A) B) x+1 C)0 D) aniqlab bo’lmaydi
75. a va b o’zaro tub sonlarning nechta juftida kasr qisqaradi.
A) 2 B) 1 C)bunday juftliklar mavjud emas D) aniqlab bo’lmaydi
76. Ifodani soddalashtiring.
A) a+b+c B) a+b-c C) a+2b-2c D) 2a-2b+2c
77. kasr P²(x;y)+3Q² (x;y) ko’rinishida yozilgan bo’lsa, P(x;y) ko’phadni aniqlang.
A) B) C) D) shart yetarli emas
78. kasr P²(x;y)+3Q² (x;y) ko’rinishida
yozilgan bo’lsa, Q(x;y) ko’phadni aniqlang.
A) B) C) D) shart yetarli emas
79. kasr P²(x;y)+3Q² (x;y) ko’rinishida
yozilgan bo’lsa, P(x;y) ko’phadni aniqlang.
A) B) C) D) shart yetarli emas
80. kasr P²(x;y)+3Q² (x;y) ko’rinishida
yozilgan bo’lsa, Q(x;y) ko’phadni aniqlang.
A) B) C) D) shart yetarli emas
81. kasr 5P²(x;y) -Q² (x;y) ko’rinishida
yozilgan bo’lsa, P(x;y) ko’phadni aniqlang.
A) B) C) D) aniqlab
bo’lmaydi
82. kasr 5P²(x;y) -Q² (x;y) ko’rinishida
yozilgan bo’lsa, Q(x;y) ko’phadni aniqlang.
A) B) C) D) aniqlab bo’lmaydi
83. kasr 5P²(x;y)-Q² (x;y) ko’rinishida yozilgan
bo’lsa, P(x;y) ko’phadni aniqlang.
A) B) C) D) aniqlab
bo’lmaydi

84. kasr 5P²(x;y)-Q² (x;y) ko’rinishida yozilgan

bo’lsa, Q(x;y) ko’phadni aniqlang.
A) B) C) D) aniqlab bo’lmaydi
85. Agar x+y+z=0 bo’lsa, x³+y³+z³ ning qiymati
quyidagilarning qaysi biriga doimo teng bo’ladi.
A) xyz B) 3xyz C) 3x²y²z² D) 0
86. (a+b+c)³-a³-b³-c³ ifoda nechta ratsional
ko’paytuvchilarga ajraladi.
A) 3 B)5 C)4 D)2
87. kasrni soddalash€tiring.
A) 3 B) C)1 D)
88. a va b sonlar uchun shart qanoatlantisa, kasrning qabul qilishi mumkin bo’lgan qiymatlarini toping.
A) 1 B)2 C)3 D) A va C
89. a va b sonlar uchun shart qanoatlantirsa, kasrning qabul qilishi mumkin bo’lgan qiymatlarini toping.
A) 1 B) C) D)2
90. Agar x² –x-1= 0 shart qanoatlantirsa, x³ - ning qiymatini toping.
A) 4 B)3 C)2 D)1
91. Agar x² –x-1= 0 shart qanoatlantirsa, x⁴ + ning qiymatini toping.
A) 7 B)5 C)6 D)4
90. a⁴ – 47 a²+1=0 shart qanoatlantirsa, ( a>0) ning qiymatini toping.
A) 2 B)3 C)4 D)1
92. Agar 16x² + 144x + (a+ b) to’lakvadrathamda b – a =– 7shartlarbajarilsa, a ningqiymatni toping.
A)165,5 B) 158,5 C)166 D)159
93. Agar 16x² + 144x + (a + b) to’lakvadrathamda b – a = – 7shartlarbajarilsa, b ningqiymatni toping.
A)165,5B) 158,5 C)166 D)159
94. ayniyatdana ningqiymatni toping.
A)1 B)2 C)0 D) aniqlabbo’lmaydi
95. ayniyatdanb ningqiymatni toping.
A)1B)2 C)0 D) aniqlabbo’lmaydi
96. ayniyatdanc ningqiymatni toping.
A)1B)2C)0 D) aniqlabbo’lmaydi
97. Soddalashtiring.

98. Agar n juft son bo’lsa, S = 1-2+3-4+…+(-1)ⁿ⁺¹n yig’indini hisoblang.
A) –n B) C) D)
99. Agar n toq son bo’lsa, S = 1-2+3-4+…+(-1)ⁿ⁺¹n yig’indini hisoblang.
A) –n B) C) D)

100. Agar n juft son bo’lsa, S = 1² -2² +3² -4² +…+(-1)ⁿ⁺¹n² yig’indini hisoblang.

A) B) C) D)
101. Agar n toq son bo’lsa, S = 1² -2² +3² -4² +…+(-1)ⁿ⁺¹n² yig’indini hisoblang.
A) B) C) D)
102. Agar a, b va c haqiqiy sonlar uchun shart o’rinli bo’lsa, ifodaning qabul qilishi mumkin bo’lgan qiymatlaridan eng kattasini toping.
A)0 B)-1 C)2 D) bir tomonlama aniqlanmaydi
103. . Agar a, b va c haqiqiy sonlar uchun shart o’rinli bo’lsa, ifodaning qabul qilishi mumkin bo’lgan qiymatlaridan eng kichigini toping.
A)0 B)-1 C)2 D) bir tomonlama aniqlanmaydi
104. Ko’phadningozodhadini toping.
f(x)=(3x²─1)³⁰(4x+1)¹⁵─x³⁰+25
A) 24 B) 25 C) 26 D) 125
105) Ko’phadningozodhadini toping.
f(x)=(4x³+1)¹⁵(3x⁴+1)⁴+(x─3)²+17
A) 24 B) 33 C) 27 D) 17
106) Ko’phadningozodhadini toping.
f(x)=(3x+1)³(4x+5)⁴(x+1)²⁰⁰+(x─1)¹⁹+19
A) 18 B) 20C) 643 D) 606