2019 Matematika savollari Uchta tengdosh prizmaning balandliklari
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1+𝑐𝑜𝑠2𝑥
𝑠𝑖𝑛2𝑥 ∙ 1+𝑐𝑜𝑠𝑥 𝑐𝑜𝑠𝑥 − 𝑠𝑖𝑛𝑥 1−𝑐𝑜𝑠𝑥 − 2 A) −1 B) 0 C) −2 D) 1 75.
𝑥+3 √𝑥+20−2𝑥
2 ≥ 0 tengsizlikning butun yechimlari nechta? A) 6 B) 5 C) 4 D) 3 76. 𝑎 va 𝑏 ratsional son bo’lib, 𝑎 + √3 3 𝑏 = 4 tenglik o’rinli bo’lsa, 𝑎 2 + 𝑏
2 =? A) 12 B) 16 C) 28 D) 48 77. 𝑎 va 𝑏 ratsional son bo’lib, 𝑎 + √2 2
o’rinli bo’lsa, 𝑎 2 + 𝑏 2 =? A) 18 B) 17 C) 25 D) 22 78. Hisoblang. 16𝑠𝑖𝑛 2 70°𝑠𝑖𝑛
2 50°𝑠𝑖𝑛
2 10 =? A) 2 B) 1 2 C) 1 4 D) 1 8 79. Integralni hisoblang. ∫ (𝑥 2
3 (2𝑥 + 1)𝑑𝑥 =? 1 0
A) 20 B) 81 4 C) 0 D) 25 80. 𝑦
2 + 2𝑥(𝑥 + 𝑦) − 8(𝑥 − 2) = 0 bo’lsa, 3𝑥𝑦 4
A) −12 B) 12 C) 16 D) −16 81. Hisoblang. 𝑡𝑔15° − 𝑡𝑔75° =? A) − 2
B) 2 √3 C) 2√3 D) −2√3 82. 2
𝑥 > √𝑥 tengsizlikni yeching. A) 𝑥𝜖𝑅 B) (1; ∞) C) (4; ∞) D) [0; ∞) 83. 𝑥
2 − (𝑏 + 2)𝑥 + 𝑏 − 4 = 0 tenglamaning ildizlaridan biri 𝑏 ga teng bo’lsa, 𝑥 1 2 + 𝑥 2 2 ning qiymatini toping. A) 16 B) 32 C) 8 D) 20 84. Aniqmas integralni hisoblang. ∫ 𝑥 2 𝑠𝑖𝑛𝑥 𝑑𝑥 =? A) (2 − 𝑥 2 )𝑐𝑜𝑠𝑥 + 2𝑥𝑠𝑖𝑛𝑥 + 𝐶 B) −𝑥 2 𝑐𝑜𝑠𝑥 + 2𝑥𝑠𝑖𝑛𝑥 + 𝐶 C) 𝑥 2 𝑐𝑜𝑠𝑥 − 2𝑥𝑠𝑖𝑛𝑥 − 2𝑐𝑜𝑠𝑥 + 𝐶 D) (𝑥 2 − 2)𝑐𝑜𝑠𝑥 + 2𝑥𝑠𝑖𝑛𝑥 + 𝐶 85. Hisoblang. 𝑎𝑟𝑐𝑡𝑔√2 + 𝑎𝑟𝑐𝑡𝑔 1 √2 A) ∅ B) 𝜋 2
𝜋 3 D) 5𝜋 12
86. Hisoblang. sin (2𝑎𝑟𝑐𝑠𝑖𝑛 3 5 ) =? A)
12 25 B) 0,96 C) 16 25 D) − 24 25
87. |7 − 2𝑥| = |5 − 3𝑥| tenglamaning butun yechimlari nechta? A) 1 B) 2 C) 3 D) 0 88. Geometrik progressiya uchun 𝑏 1 + 𝑏
4 = 27 va
𝑏 2 𝑏 3 = 72 bo’lsa, 𝑆 4 =? A) 25 B) 36 C) 45 D) 54 89. |𝑥 − 1| + |𝑦| ≤ 4 tengsizlik bilan berilgan soha yuzini toping. A) 32 B) 64 C) 28 D) 56 90. | 6−3𝑥
1+3𝑥 | ≥ 0 tengsizlikni yeching. A) (−∞; − 1 3 ) ∪ (− 1 3 ; 2] B) [2; ∞) C) (−∞; − 1 3
1 3 ; ∞) D) (− 1 3 ; 2] 4
91. 𝑃(𝑥) = (2𝑥 − 1) 10 (𝑥 + 1)
2 ko’phadning koeffitsiyentlari yig’indisini toping. A) 1 B) 2 C) 4 D) 1024 92. 𝑓(𝑥) = √ √17−15𝑥−2𝑥 2 𝑥+3
funksiyaning aniqlanish sohasini toping. A) [−8,5; −3) ∪ (−3; 1] B) {−8,5} ∪ (−3; 1] C) [−8,5; 1] D) (−3; ∞) 93. 𝑓(𝑥) = √(𝑠𝑖𝑛𝑥 + 𝑐𝑜𝑠𝑥) 2 − 1 funksiyaning aniqlanish sohasini toping. A) [−
𝜋 4 + 𝜋𝑛; 𝜋 4 + 𝜋𝑛] B) [𝜋𝑛; 𝜋 4 + 𝜋𝑛] C) [𝜋𝑛; 𝜋 2 + 𝜋𝑛] D) [2𝜋𝑛; 𝜋 2 + 2𝜋𝑛] 94. 𝑓(𝑥) = arcsin ( 𝑥−3 2
aniqlanish sohasiga tegishli butun sonlar yig’indisini toping. A) 10 B) 11 C) 15 D) 6 95.
𝑐𝑜𝑠12𝑥 𝑐𝑜𝑠4𝑥
− 𝑠𝑖𝑛12𝑥
𝑠𝑖𝑛4𝑥 ni soddalashtiring. A) −2 B) 2 C) 4 D) −1 96.
𝑛 3 +3𝑛−20 2𝑛 ketma-ketlikning nechta hadi butun son? A) 2 B) 3 C) 1 D) 4 97. Soddalashtiring. (𝑥 − 1)(𝑥 + 1)(𝑥 2 + 1)(𝑥
4 + 1) A) 𝑥 4
8 + 1 C) 𝑥 8 − 1 D) 𝑥 4 + 1 98. 𝑛 + 3, 𝑛 + 9, 𝑛 + 15 sonlar arifmetik progressiyaning ketma-ket hadlari bo’lib, 𝑎 11 =
𝑛 ning qiymatini toping. A) 7 B) 4 C) 2 D) 5 99. 𝑎 ning qanday eng kichik qiymatida 𝑎, 𝑎 + 6, 𝑎 + 14 sonlar, tub sonlar bo’ladi? A) 7 B) 11 C) 5 D) 17 100. 𝐴𝐵𝐶 uchburchakda 𝐴𝐵 = 6 va 𝐵𝐶 = 8. 𝐵 uchidan chiqqan bissektrisa 𝐴𝐶 tomonni 𝐷 nuqtada kesadi. 𝐴𝐶: 𝐴𝐷 nisbatni toping. A) 4:3 B) 7:4 C) 7:3 D) 3:4 101. [0; 200] sonlar to’plamida nechta natural son 6 ga qoldiqsiz bo’linib, 8 ga qoldiqsiz bo’linmaydi? A) 33 B) 25 C) 27 D) 17 102. 𝑎𝜖(−2; 2) bo’lsa, |𝑎 2 −16| 4−𝑎
− |𝑎 2 −9| 3+𝑎
− |4−𝑎
2 | 2−𝑎 ifodani soddalashtiring. A) 𝑎 + 1 B) 3𝑎 + 3 C) 𝑎 + 9 D) 𝑎 − 1 103. Hisoblang. (1 − 1
2 ) (2 −
2 3 2 ) (3 − 3 4 2 ) … (8 −
8 9 2 ) A)
8! 2 B) 8! 9 C) 5 9 ∙ 8! D) 2 3 ∙ 8! 104. 2𝑡𝑔𝛼 − 𝑠𝑖𝑛𝛼 + 3𝑐𝑜𝑠𝛼 = 6 bo’lsa, 𝑐𝑜𝑠2𝛼 ni toping. A) 0,8 B) −0,8 C) 0,6 D) −0,6 105. 𝑓(𝑥) = 𝑎𝑟𝑐𝑠𝑖𝑛3 𝑥 funksiyaning aniqlanish sohasini toping. A) [−1; 1] B) (−∞; 0] C) [0; ∞) D) [0; 1] 106. Agar 𝑓(𝑥) = 𝑥 2 − 2𝑥 + 3 va 𝑔(𝑥) = 2𝑥 − 1 bo’lsa, 𝑓(𝑔(𝑥)) =? A) 2𝑥
2 − 4𝑥 + 3 B) 4𝑥 2 − 8𝑥 + 6 C) 4𝑥 2 + 6 D) 4𝑥 2 − 4𝑥 + 6 107. [1; 200] sonlar to’plamida nechta natural son 4 ga qoldiqsiz bo’linib, 6 ga qoldiqsiz bo’linmaydi? A) 50 B) 34 C) 42 D) 17 108. 𝑦 = 𝑥 2 − 5𝑥 + 3 kvadrat funksiyaning ordinatalar o’qiga nisbatan simmetrik funksiyasini toping. A) 𝑦 = 𝑥 2 − 5𝑥 + 3 B) 𝑦 = 𝑥 2 + 5𝑥 + 3 C) 𝑦 = −𝑥 2 + 5𝑥 − 3 D) 𝑦 = −𝑥 2 − 5𝑥 − 3 109. 𝑎 sonining 24%i 40 ning 3 5 qismiga teng. 𝑎 ning 1 4 qismi 15 sonidan qancha ko’p? A) 6,5 B) 10 C) 13 D) 20 110. Agar 𝑦 = 𝑙𝑛(5𝑥 + 1) 2 − 𝑙𝑛(2𝑥 + 1) 5 + 4
funksiyaning grafigiga (𝑥 0 ; 𝑦 0 ) nuqtada o’tkazilgan urinma 𝑂𝑋 o’qiga parallel bo’lsa, √𝑥 0 2 + 𝑦
0 2 ni toping. A) 3 B) 4 C) 5 D) 6 111. Markazi (0; 0) nuqtada bo’lgan aylanadagi 𝐴(0; 2) nuqtani soat mili harakati yo’nalishida aylana bo’ylab 30° ga burish natijasida hosil bo’lgan nuqtaning koordinatalari yig’indisini toping. A) 1 B) 1 + √3 C) 2 D) 1 − √3 112. Kollinear bo’lmagan 𝑎⃗ va 𝑏⃗⃗ vektorlar berilgan. Agar −3𝑎⃗ + 𝑥𝑏⃗⃗ = 𝑦𝑎⃗ + 2𝑏⃗⃗ o’rinli bo’lsa, 𝑥 va 𝑦 ning qiymatini toping. A) 𝑥 = −3; 𝑦 = 2 B) 𝑥 = 3; 𝑦 = −2 C) 𝑥 = 2; 𝑦 = −3 D) 𝑥 = −2; 𝑦 = 3 5
113. Hisoblang. 512∙(2 6 ) 4 (2 5 ) 5 ∙64 ∙ (4 −2 ) −2 ∙ 8
−4
A) 16 B) 1 8 C) 4 D) 1 4 114.
3 𝑥+2
−81 3 𝑥+1 −9 ≥ 3 tengsizlikni yeching. A) (1; ∞) B) ( 1 3 ; ∞) C) (−∞; 1) D) (0; 1) 115. Merganning nishonga tekkizish ehtimoli 0,6 ga teng. U nishonga 2 marta o’q uzganda o’qlaridan biri nishonga tegishining ehtimolligini toping. A) 0,6 B) 0,24 C) 0,48 D) 0,5 116. To’g’ri konusning balandligi 5 sm va asos radiusi 3 sm. Uning yon sirtida joylashgan asosining markaziga eng yaqin bo’lgan nuqtalar orqali tekislik o’tkazilgan. Hosil bo’lgan kesik konusning kichik asosi yuzini katta asosi yuziga nisbatini toping. A)
15 34 B) 25 34 C) 625 1156
D) 112
289
117. Ifodani soddalashtiring. (𝑥 > 0) √ 9−4√5
5𝑥 4 ∙ (5√𝑥 + √20𝑥) 0,5 ∙ 2
−1
A) 5
B) 1 C) 3 √17 D) 0,5 118. Ko’phadlarni ko’paytiring. (3𝑎 + 5)(4𝑎 − 3) A) 12𝑎 2
2 + 11𝑎 − 15 C) 12𝑎 2
2 − 29𝑎 − 15 119. Aniqmas integralni hisoblang. ∫ 𝑥−1
𝑥 2 −2𝑥+2 𝑑𝑥 A) 𝑙𝑛|𝑥
2 − 2𝑥 + 2| + 𝐶 B) 1
𝑙𝑛|𝑥 2 − 2𝑥 + 2| + 𝐶 C) 2𝑙𝑛|𝑥 2 − 2𝑥 + 2| + 𝐶 D) 1 2 𝑙𝑛|2𝑥 − 2| + 𝐶 120. Hisoblang. 18𝑠𝑖𝑛221°−6𝑐𝑜𝑠131° 4𝑐𝑜𝑠49°
A) 3 B) 2 C) −2 D) −3 121. Tengsizlikni yeching. 𝑙𝑜𝑔 3 2 𝑥 ≥ 2 − 𝑙𝑜𝑔 3 𝑥 A) (−∞; 1 9 ] ∪ [3; ∞) B) (0; 1 9 ] ∪ [3; ∞) C) [
1 9 ; 3] D) (0; 1 9 ] ∪ {3} 122. 𝑓(𝑥) = (𝑥 2 − 3𝑥 + 4)(𝑥 − 4) funksiyaning 𝑥 0 = 4 nuqtadagi hosilasini toping. A) 0 B) 16 C) 8 D) 4 123. 𝑏
𝑛 = 3 ∙ 2
𝑛 bo’lsa, 𝑏 1
+ 𝑏 2 2 + 𝑏 3 2 + ⋯ + 𝑏 7 2 =? A) 8 ∙ (2 12 − 1) B) 12 ∙ (2 12 − 1) C) 8 ∙ (2 14 − 1) D) 12 ∙ (2 14 − 1)
124. {𝑎 = 16 − 𝑥 2 𝑏 = 𝑥 2 − 4
bo’lsa, 𝑎𝑏 ning eng katta qiymatini toping. A) 64 B) 36 C) 24 D) 100 125. 𝑎 + 𝑏 ifoda 7 ga qoldiqsiz bo’linsa, 37𝑎 + 9𝑏 ifodani 7 ga bo’lgandagi qoldiqni toping. A) 0 B) 1 C) 2 D) 4 126. Uchlari 𝐴(−1; 1), 𝐵(3; 1), 𝐶(−1; 7) nuqtalarda bo’lgan uchburchak yuzini toping. A) 6 B) 10 C) 4√13 D) 12 127. To’g’ri burchakli parallelepipedning tomonlari nisbati 2:5:3 nisbatda va to’la sirti 𝑆 𝑇 = 248 𝑑𝑚 2 bo’lsa, uning hajmini toping. A) 120 B) 240 C) 360 D) 960 128. Tenglamani yeching. sin(𝜋𝑐𝑜𝑠2𝑥) = 0 A) 𝜋𝑛
B) 𝜋𝑛 C) 𝜋𝑛 4 D) 𝜋 4 + 𝜋𝑛 2 129. 𝑦 = 𝑥 ∙ 2 𝑥 funksiyaning hosilasini toping. A) 𝑥 ∙ 2 𝑥 ∙ 𝑙𝑛2 + 2 𝑥 B) 2
𝑥 + 𝑥 ∙
2 𝑥 𝑙𝑛2 C) 2
𝑥 − 𝑥 ∙ 2
𝑥 ∙ 𝑙𝑛2 D) 2 𝑥 − 𝑥 ∙
2 𝑥 𝑙𝑛2 130. Katetlari 2 va 3 bo’lgan to’g’ri burchakli uchburchak gipotenuza atrofida 2𝜋 ga aylantirildi. Hosil bo’lgan shaklning to’la sirtini toping. A)
18𝜋 √13
B) 15𝜋
√13 C)
30𝜋 √13
D) 36𝜋
√13
131. Tengsizlikni yeching. (√5 − 1) 𝑥2−2𝑥+8 𝑥−4
≥ 1 A) (4; ∞) B) (−2; 4) ∪ (4; ∞) C) (−2; ∞) D) (−∞; −2) ∪ (4; ∞) 132. 𝑓(𝑥) = 15 4𝑥
+ 12𝑥
2 5 funksiyaning eng kichik qiymatini toping. A) 7 B) 8 C) 6 D) 5 133. Hisoblang. (𝑡𝑔 7𝜋 24 + 𝑡𝑔 5𝜋 24 ) ∙ 𝑐𝑜𝑠 𝜋 12 + 2 A) 1 B) 3 C) 4 D) 2 134. 𝛼 tekislik va uni kesib o’tadigan 𝐴𝐵 kesma berilgan. Kesmaning uchlaridan 𝛼 tekislikkacha bo’lgan masofalar 𝐴𝐴 1 = 19 𝑠𝑚, 𝐵𝐵 1 = 9 𝑠𝑚 bo’lsa, 𝐴𝐵 kesmani 𝐴 uchidan boshlab hisoblaganda 3:4 nisbatda bo’luvchi 𝐶 nuqtadan 𝛼 tekislikkacha bo’lgan masofani (𝑠𝑚) toping. A) 6 B) 7,2 C) 7 D) 6,8 135. 𝐴𝐵𝐶𝐷 parallelogrammning 𝐵𝐶 va 𝐶𝐷 tomonlaridan mos ravishda 𝑀 va 𝑁 nuqtalar shunday olinganki 𝐶 uchidan boshlab hisoblaganda (𝐵𝐶 va 𝐶𝐷 tomonlarini) 2:1 6
nisbatda bo’ladi. Agar parallelogrammning yuzi 45 ga teng bo’lsa, 𝐴𝑀𝑁 uchburchakning yuzini toping. A) 15 B) 25 C) 20 D) 10 136. Agar charxpalak 5 minutda 36 2 3
aylansa, u 12 minutda necha marta aylanadi? A) 86
1 3 B) 91 C) 86 D) 88 137. Tenglamani yeching. 𝑥+4
6 −3 2 3 +4 − 𝑥−3 3 +2 2+ 1 3 = 𝑥 8 +2 2 3 ( 4 7 ) −1
A) −14 B) 30 C) 14 D) −30 138. 𝑦 = 𝑥 2 − 6𝑥 + 10 kvadrat funksiyaning 𝑦 = 2 to’g’ri chiziqqa nisbatan simmetrik funksiyasini toping. A) 𝑦 = −𝑥 2 + 6𝑥 − 10 B) 𝑦 = −𝑥 2 − 6𝑥 + 10 C) 𝑦 = −𝑥 2 + 6𝑥 − 6 D) 𝑦 = −𝑥 2 − 6𝑥 + 6 139. Soatning minut mili 15 minutda necha gradusga buriladi? A) 90° B) 60° C) 105° D) 75° 140. 650 soni 10% ga oshirildi. Hosil bo’lgan sonning 20%ini toping. A) 145 B) 133 C) 153 D) 143 141. Integralni hisoblang. ∫ (2𝑥 + 5) cos(𝑥 2 + 5𝑥) 𝑑𝑥 =? 1 0
A) 𝑐𝑜𝑠6 B) −𝑐𝑜𝑠6 C) 𝑠𝑖𝑛6 D) −𝑠𝑖𝑛6 142. Tomonlari 18 va 12 ga teng bo’lgan parallelogrammning barcha bissektrisalari kesishishidan hosil bo’lgan to’rtburchak yuzini toping. A) 18 B) 9 C) 36 D) 24 143. Sayyoh belgilangan yo’lning 1 6 qismini bosib o’tgach, yo’l yarmigacha yana 16 km qolgan bo’lsa, belgilangan yo’l uzunligini toping (km) A) 48 B) 42 C) 54 D) 36 144. 28 ta o’quvchidan 3𝑥 + 1 tasi rus tilini, 2𝑥 − 1 tasi ingliz tilini, 𝑥 − 1 tasi rus tilini ham ingliz tilini ham biladi. 3 tasi esa rus tilini ham ingliz tilini ham bilmaydi. Nechta o’quvchi ingliz tilini biladi? A) 12 B) 10 C) 11 D) 19 145. Hisoblang. 0,429
0,03 + 0,128 0,08 + 0,0096 0,012
A) 1,67 B) 16,7 C) 2,39 D) 23,9 146. 2 ta turli lavozimga nomzodlari ko’rsatilgan 7 kishidan 2 kishini necha xil usul bilan saylash mumkin? A) 49 B) 35 C) 56 D) 42 147. To’g’ri konusning balandligi 9 sm va asos radiusi 5 sm. Uning yon sirtida joylashgan asosining markaziga eng yaqin bo’lgan nuqtalardan asosiga parallel tekislik o’tkazilgan. Hosil bo’lgan kesik konusning kichik asosi radiusini (sm) toping. A)
53 14 B) 221 56 C) 405 106
D) 45 14 148. 120000 so’mning 15%i uy xarajatlariga, 2 3
boshqa xarajatlarga sarflandi. Qolgan pulning 20%ini toping (so’m). A) 4150 B) 4400 C) 4650 D) 4200 149. Agar 0 < 𝛼, 𝛽 < 𝜋 2
𝑐𝑜𝑠𝛽 = 1 3 bo’lsa, 𝑠𝑖𝑛2𝛼 + 𝑐𝑜𝑠2𝛽ni hisoblang. A) −
8 45 B) 62 45 C) 45 62 D) − 45 8
150. Hisoblang. 𝑐𝑜𝑠33°∙𝑐𝑜𝑠46°−𝑐𝑜𝑠57°∙𝑐𝑜𝑠44° 𝑐𝑜𝑠39°∙𝑐𝑜𝑠40°−𝑐𝑜𝑠50°∙𝑐𝑜𝑠51° + 2 A) 2,5 B) 3 C) 2,25 D) 2 151. Ikkita to’g’ri chiziqning kesishishidan hosil bo’lgan burchaklardan uchtasining yig’indisi 225° ga teng bo’lsa, shu burchaklardan kattasining gradus o’lchovini aniqlang. A) 125° B) 145° C) 135° D) 115° 152. 𝑦 = 𝑥 2 + 1 𝑥 funksiyaning 𝑥 = 1 2 nuqtadagi orttirmasini toping. ∆𝑥 = 1 2 A) 0 B) 1 4
1 4 D) −2 153. Teng yonli uchburchakning perimetri 64 sm ga teng. Agar teng tomonlarining o’rtalarini tutashtiruvchi kesma uzunligi 12 sm bo’lsa, uchburchakka ichki chizilgan aylana diametrini (sm) toping. A) 9 B) 8 C) 6 D) 12 154. 𝑓(𝑥) = (𝑥 − 2) 2 − 2 parabola uchining koordinatalari ko’paytmasini toping. A) 4 B) −3 C) 3 D) −4 7
155. 10 1 0 -4 -5 y= f(x ) x Y
Rasmda 𝑓(𝑥) = 𝑘𝑥 + 𝑏 funksiyaning grafigi tasvirlangan. 𝑓(2) + 𝑓(0) ning qiymatini toping. A) 18 B) 16 C) 20 D) 24 156. Parametrli tenglamani yeching. 𝑥+𝑎+2𝑐 2
+ 𝑥+𝑏
2 +2𝑎
2 𝑐+𝑎
+ 𝑥 2 +𝑐 2 +2𝑏 2 𝑎+𝑏
A) −(𝑎
2 + 𝑏
2 + 𝑐
2 ) B) 0 C) 1 D) (𝑎 2
2 + 𝑐
2 )
157. 𝐴𝐵𝐶 uchburchakda 𝐴𝐸 va 𝐵𝐹 medianalar 𝑃 nuqtada kesishadi. 𝑃𝐸𝐹 uchburchak yuzi 7,5 bo’lsa, 𝐴𝐵𝐶 uchburchak yuzini toping. A) 45 B) 90 C) 30 D) 60 158. Dastlabki 4 ta hadining yig’indisi 244 ga teng bo’lgan arifmetik progressiyada 𝑎 7
3 = −32 va 𝑎 𝑛 = 17 bo’lsa, 𝑛 =? A) 9 B) 8 C) 6 D) 5 159.
2 10 ∙ 2 100
∙ 2 1000 ∙ … ∙ 2 1 00…0 ⏟ 10 𝑡𝑎 𝑛𝑜𝑙 : 128 sonini standart shaklga keltiring. A) 2 3
−55 B) 0,8 ∙ 10 −55
C) 0,8 ∙ 10 −54
D) 8 ∙ 10 −54
160. (1 − 1 2
1 3 ) (1 − 1 4 ) ∙ … ∙ (1 − 1 8 ) 𝑥 = 11 4
bo’lsa, 2 11 𝑥 ni toping. A) 4 B) 2 C) 1 D)6 161. 520 ni 20% ga oshirib, so’ngra 25%ini toping. A) 136 B) 156 C) 123,5 D) 148 162. (𝑥
2 − 7𝑥 + 13) 2 − (𝑥 − 3)(𝑥 − 4) − 3 = 0 tenglamaning haqiqiy yechimlari ko’paytmasini toping. A) 154 B) 143 C) 11 D) 14 163. 𝑦 = √ 3 3−𝑥
funksiya 𝑥 ning qanday qiymatlarida 1 ga teng qiymatni qabul qiladi? A) 6 B) 2 C) 0 D) 9 164. 𝑥 = 0,3, 𝑦 = 6 va 𝑧 = 10 bo’lsa, 3𝑥𝑦𝑧 𝑥𝑦+𝑦𝑧+𝑥𝑧
− ( 𝑥−1
𝑥 + 𝑦−1 𝑦 + 𝑧−1 𝑧 ) : (
1 𝑥 + 1 𝑦 + 1 𝑧 ) ni hisoblang. A) 1 B) 0 C) −1 D) −2 165. Qutida a,o,t,s,m,n harflari bor. Tavakkaliga olingan 4 ta harf ketma-ket qoyilganda “soat” so’zining hosil bo’lish ehtimolini toping. A)
1 360
B) 1 180 C) 1 84 D) 1 720 166. Qirralari uzunliklari 6 ga teng bo’lgan muntazam tetraedrning hajmini toping. A) 9√6 B) 18√3 C) 18√2 D) 27√2 167. Soatning soat mili 19° ga burilsa, minut mili necha gradus buriladi? A) 178° B) 228° C) 218° D) 272° 168. Soatning soat mili 22° ga burilsa, minut mili necha gradusga buriladi? A) 96° B) 106° C) 264° D) 254° 169. To’g’ri parallelepipedning bir uchidan chiqqan qirralari uchun 1 𝑎
1 𝑏 + 1 𝑐 = 3 5 tenglik o’rinli bo’lib, to’la sirti 288 ga teng. Parallelepipedning hajmini toping. A) 240 B) 480 C) 120 D) 360 170. To’g’ri parallelepipedning bir uchidan chiqqan qirralari uchun 1 𝑎 + 1 𝑏 + 1 𝑐 = 2 5 tenglik o’rinli bo’lib, to’la sirti 288 ga teng. Parallelepipedning hajmini toping. A) 180 B) 360 C) 240 D) 480 171. ∫ 𝑥(𝑥 − 5) 4 𝑑𝑥 6 5 integralni hisoblang. A) 1 1 6 B) 1 1 7 C) 1 1 3 D) 1 1 9 172.
𝑙𝑜𝑔 2 7 𝑙𝑜𝑔 56 2 − 𝑙𝑜𝑔
2 14 𝑙𝑜𝑔 28 2 =? A) −2 B) 2 C) −1 D) 1 173.
𝑙𝑜𝑔 3 153 𝑙𝑜𝑔 51 3 − 𝑙𝑜𝑔
3 459
𝑙𝑜𝑔 17 3 =? A) 2 B) −2 C) 1 D) −1 174. Arifmetik progressiyada 𝑎 𝑛+1
= 𝑎 𝑛 + 4 va 𝑎 4 = 6 bo’lsa, 𝑆 15 =? A) 165 B) 660 C) 330 D) 495 8
175. Hisoblang. 111 333
+ 333
666 + 555 666 =? A) 5
B) 2 C) 1 D) 7 4 176. 𝑦 = 𝑙𝑛𝑥 𝑥−2 funksiya hosilasini toping. A) 𝑙𝑛𝑥 − 𝑥−2
𝑥 B) 𝑙𝑛𝑥 + 𝑥+2 𝑥
C) 𝑙𝑛𝑥
𝑥 +𝑥+2
𝑥 D) 𝑙𝑛𝑥 𝑥
𝑥
177. 𝑦 = 𝑙𝑛𝑥 𝑥 funksiya hosilasini toping. A) 𝑙𝑛𝑥 − 1 B) 𝑙𝑛𝑥+𝑥
𝑥 C) 𝑙𝑛𝑥 + 1 D) 𝑙𝑛𝑥−𝑥
𝑥
178. Agar 𝛼 = 30° bo’lsa, (1 + 𝑐𝑜𝑠 −1 2𝛼 +
𝑡𝑔2𝛼) ∙ (1 − 𝑐𝑜𝑠 −1 2𝛼 + 𝑡𝑔2𝛼) ni hisoblang. A) √3 B) −√3 C) 2√3 D) 2 √3 179. Tenglamani yeching. 𝑐𝑜𝑠 4
4 13𝑥 = 𝑐𝑜𝑠24𝑥 A) 𝜋𝑛, 𝑥𝜖𝑍 B) 𝜋𝑛 13 , 𝑥𝜖𝑍 C) 𝜋𝑛 24 , 𝑥𝜖𝑍 D)
𝜋𝑛 25 , 𝑥𝜖𝑍 180. 𝑐𝑜𝑠 4 12𝑥 − 𝑠𝑖𝑛 4 12𝑥 = 𝑐𝑜𝑠22𝑥 tenglamani yeching. A) 𝑥 =
𝜋𝑛 23 , 𝑛𝜖𝑍 B) 𝑥 = 𝜋𝑛, 𝑛𝜖𝑍 C) 𝑥𝜖𝑅 D) 𝑥 = 2𝜋𝑛
23 , 𝑥𝜖𝑍
181. 𝐴 = {𝑥|𝑥 ≥ 6, 𝑥𝜖𝑁} va 𝐵 = {𝑥| 𝑥 < 18, 𝑥𝜖𝑄} bo’lsa, 𝐴 ∩ 𝐵 =? A) {𝑥| 6 ≤ 𝑥 < 18, 𝑥𝜖𝑄} B) {𝑥| 6 ≤ 𝑥 < 18, 𝑥𝜖𝑁} C) {𝑥| 6 < 𝑥 < 18, 𝑥𝜖𝑄} D) {𝑥| 6 < 𝑥 < 18, 𝑥𝜖𝑁} 182. 𝑂 markazli aylananing radiusi 10 ga teng. Aylana tashqarisidan olingan 𝐴 nuqtadan, 𝐴𝐵 urinma va 𝐴𝑂 kesuvchi o’tkazilgan. 𝐴𝑂 kesuvchi 𝐶 nuqtada kesadi. Agar 𝐴𝐶 yoy uzunligi 9 ga teng bo’lsa, 𝐵𝐶 =? A)
10 𝑐𝑜𝑠0,9
− 10 B) 10 𝑠𝑖𝑛0,9 + 10 C) 10(1 − 𝑐𝑜𝑠0,9) D) 10(1 − 𝑠𝑖𝑛0,9) 183. A B C O Rasmga ko’ra, radiusi 10 ga teng bo’lgan aylanaga 𝐴𝐵 urinma va 𝑂𝐵 kesuvchi o’tkazilgan. 𝐴𝐶 kichik yoy uzunligi 8 ga teng bo’lsa, 𝐵𝐶 =? A)
10 𝑐𝑜𝑠0,8
− 10 B) 10 𝑠𝑖𝑛0,6 + 10 C) 10(1 − 𝑐𝑜𝑠0,8) D) 10(1 − 𝑠𝑖𝑛0,6) 184. √𝑥 − 2 3 − √𝑥 − 9 3 = 1 tenglama ildizlari yig’indisini toping. A) 11 B) 10 C) 1 D) 9 185. Bitta ildizi 1 ga teng bo’lgan 𝑥 2 + 𝑏𝑥 + 3 = 0 kvadrat tenglamaning ikkinchi ildizini toping. A) −3 B) 3 C) −4 D) 4 186. 𝑓(𝑥) = 𝑥 2 + 𝑏𝑥 + 7 funksiyaning nollaridan biri 1 ga teng bo’lsa, ushbu funksiyaning butun yechimlari yig’indisini toping. A) −8 B) 8 C) 7 D) −7 187. 𝑎⃗(−2; 6; 3) vektorga yo’nalishdosh bo’lgan birlik vektorning koordinatalarini toping. A) (−
2 7 ; 6 7 ; 3 7 ) B) (− 2 7 ; 6 7 ; − 3 7 ) C) ( 2 7 ; 6 7 ; 3 7 ) D) (− 2 7 ; − 6 7 ; − 3 7 ) 188. (𝑥
3 + 12𝑥)
2 ≤ 49𝑥
4 tengsizlikning nechta butun yechimi bor? A) 4 B) 5 C) 6 D) 7 189. Integralni hisoblang. ∫ 𝑥(𝑥 − 9) 8 𝑑𝑥 10 9
A) 1 1 9 B) 9 10 C) 1,1 D) 10 11 190. Hisoblang. √(3 −2 )
+ (2 −2 ) −2 + 1 A) 5 B) 6 C) 4 D) 2 191. 3 ta mergan 1 tadan o’q otish natijasida, nishonga tekkizish ehtimoli mos ravishda 0,5, 0,6, 0,7 bo’lsa, birinchi va ikkinchi merganning nishonga tekkizish ehtimolligini toping. A) 0,21 B) 0,09 C) 0,8 D) 0,14 9
192. 3 ta mergan 1 tadan o’q otish natijasida, nishonga tekkizish ehtimoli mos ravishda 0,5, 0,6, 0,8 bo’lsa, birinchi va ikkinchi merganning nishonga tekkizish ehtimolligini toping. A) 0,24 B) 0,9 C) 0,06 D) 0,16 193. 𝑦 = −√144 − 𝑥 2 funksiya grafigiga 𝐴(15; 0) nuqtadan o’tuvchi urinma tenglamasini toping. A) 𝑦 = 3
𝑥 − 45 4 B) 𝑦 = − 3 4 𝑥 + 45 4 C) 𝑦 =
4 3 𝑥 − 45 4 D) 𝑦 = − 4 3 𝑥 − 45 4
194. 1 0 -1 x Y -1 -3 -2
4 3 3 Chizmada 𝑓(𝑥) funksiyaning grafigi tasvirlangan. Chizmaga ko’ra, quyidagilarning qaysi biri to’g’ri? A) 𝑓
′ (5) + 𝑓(0) = 0 B) 𝑓 ′
C) 𝑓 ′ (3) + 𝑓(−2) = 0 D) 𝑓 ′ (4) + 𝑓(0) = 0 195. Tog’ga olib boradigan 6 ta yo’l bor. Borgan yo’ldan qaytib kelmaslik sharti bilan, necha xil usulda tog’ga borib kelish mumkin? A) 36 B) 30 C) 24 D) 25 196. Toqqa chiqish uchun 7 ta yo’l bor. Agar turist chiqqan yo’lidan qaytmasa, toqqa chiqib tushishni necha usulda amalga oshirish mumkin? A) 49 B) 42 C) 36 D) 48 197. 𝑦 = 𝑐𝑜𝑠𝑥(𝑠𝑖𝑛2𝑥 + 2) funksiyaning 𝑥 = 0 nuqtadagi hosilasini toping. A) 1 B) 2 C) −1 D) −2 198. Tomoni 2 sm ga teng muntazam tetraedrning asos markazidan yon qirrasigacha bo’lgan masofani toping. A)
√2 3 B) √ 2 3 C) 2√2 3 D) 2√ 2 3
199. Qirrasi 3 ga teng bo’lgan tetraedr asosiga aylana ichki chizilgan. Aylana markazidan yon qirragacha bo’lgan masofani toping. A) 2 B) √2 C) 1 2
1 √2
200. Konusning to’la sirti 48𝜋 ga teng bo’lsa, uning hajmining eng katta qiymatini toping. A) 16√6𝜋 B) 8√6𝜋 C) 12√6𝜋 D) 24𝜋 201. 𝐴 to’plamda 12 ta, 𝐵 to’plamda 13 ta, 𝐶 to’plamda 14 ta element mavjud bo’lsa, 𝐴 ∪ 𝐵 ∪ 𝐶 to’plamning elementlari soni eng kamida nechta? A) 12 B) 39 C) 13 D) 14 202. Aniqmas integralni hisoblang. ∫ 𝑥 7 𝑙𝑛7𝑥𝑑𝑥 A) 𝑥 8 𝑙𝑛7𝑥 − 𝑥 8 8 + 𝐶 B)
𝑥 8 8 𝑙𝑛7𝑥 + 𝑥 8 64 + 𝐶 C) 𝑥
8 𝑙𝑛7𝑥 −
𝑥 8 64 + 𝐶 D) −
𝑥 8 8 𝑙𝑛7𝑥 + 𝑥 8 64 + 𝐶
203. Aniqmas integralni hisoblang. ∫ 𝑥 5 𝑙𝑛5𝑥𝑑𝑥 A) 𝑥 6 𝑙𝑛5𝑥 − 𝑥 6 6 + 𝐶 B)
𝑥 6 6 𝑙𝑛5𝑥 + 𝑥 6 36 + 𝐶 C) 𝑥
6 𝑙𝑛5𝑥 −
𝑥 6 36 + 𝐶 D) −
𝑥 6 6 𝑙𝑛5𝑥 + 𝑥 6 36 + 𝐶
204. 𝑂𝑌 o’qiga perpendikulyar bo’lgan 𝑓(𝑥) = (𝑥 − 2) 2 ∙ 𝑒
𝑥 + 3 funksiya urinmasini toping. A) 𝑦 = 7 va 𝑦 = −7 B) 𝑦 = 3 va 𝑦 = −7 C) 𝑦 = −3 va 𝑦 = 7 D) 𝑦 = 3 va 𝑦 = 7 205.
A B C D C B D A 1 1 1 1 Rasmga ko’ra, 𝐴𝐶 𝐴 1 𝐶 1 = 6 5 va 𝐵𝐷 𝐵 1 𝐷 1 = 5 4 , 𝑆 𝐴 1 𝐵 1 𝐶 1 𝐷 1 =40
bo’lsa, 𝑆 𝐴𝐵𝐶𝐷
=? A) 80 B) 60 C) 100 D) 75 206. 3
+ 31 44 + 331
444 + 3331 4444 yig’indi qaysi oraliqda joylashgan? A) (1; 2) B) (2; 3) C) (3; 4) D) (4; 5) 10
207. 2 4 + 21 44 + 221 444
+ 2221
4444 yig’indi qaysi oraliqda joylashgan? A) (0; 1) B) (1; 2) C) (2; 3) D) (3; 4) 208. Birinchi qotishmaning 1 kilogrammi narxi 18000 so’m, ikkinchi qotishmaning 1 kilogrammi narxi 12000 so’m. Ikkalasidan 4:1 nisbatda olinsa, hosil bo’lgan qotishmaning 1 kilogrammi qancha? A) 13200 B) 16800 C) 84000 D) 16200 209. 𝑠𝑖𝑛𝛼 = 2 5 bo’lsa, 𝑠𝑖𝑛
6 𝛼 + 𝑐𝑜𝑠
6 𝛼 + 3𝑠𝑖𝑛
2 𝛼𝑐𝑜𝑠
2 𝛼 − 1 ni hisoblang. A) 0,6 B) 0,36 C) 1 D) 0 210. 𝑠𝑖𝑛𝛼 = 1 3 bo’lsa, 𝑠𝑖𝑛
6 𝛼 + 𝑐𝑜𝑠
6 𝛼 + 3𝑠𝑖𝑛
2 𝛼𝑐𝑜𝑠
2 𝛼 +
1 2 ni hisoblang. A)
1 2 B) 1 C) 3 2 D) 2 211. { |𝑥 − 3| = 3√𝑦 + 2 |𝑦 + 2| = 3√𝑥 − 3 sistemadan 𝑦 1 + 𝑦
2 =? A) −2 B) 29 C) 3√3 D) 27 212. {
|𝑥 − 1| = 5√𝑦 − 2 |𝑦 − 2| = 5√𝑥 − 1 sistemadan 𝑥 1 + 𝑥 2 =? A) 5 B) 1 C) 25 D) 27 213. 𝑎⃗(3; 2), 𝑏⃗⃗(1; 2), 𝑐⃗(𝑥 − 1; 𝑦 − 1) va 𝑐⃗ = 2𝑎⃗ + 3𝑏⃗⃗ bo’lsa, 𝑥𝑦 =? A) 90 B) 110 C) 100 D) 99 214. 𝑎⃗(3; 2), 𝑏⃗⃗(1; 2), 𝑐⃗(𝑥; 𝑦) va 𝑐⃗ = 2𝑎⃗ − 3𝑏⃗⃗ bo’lsa, 𝑥𝑦 =? A) 4 B) −4 C) 8 D) −8 215. √𝑥 + 6 ≥ √8 − 𝑥 tengsizlikning eng katta va eng kichik yechimlari yig’indisini toping. A) 2 B) −5 C) 9 D) 3 216. (−3; −11) nuqtadan o’tuvchi 𝑦 = 𝑘𝑥 − 5 funksiyaning abssisalar o’qiga nisbatan simmetrik funksiyasi tenglamasini toping. A) 𝑦 + 2𝑥 − 5 = 0 B) 𝑦 − 2𝑥 − 5 = 0 C) 𝑦 + 2𝑥 + 5 = 0 D) 𝑦 − 2𝑥 + 5 = 0 217. 𝑦 = 4𝑥 + 6 funksiyaga 𝑂𝑋 o’qiga nisbatan simmetrik funksiya tenglamasini toping. A) 𝑦 + 4𝑥 + 6 = 0 B) 𝑦 − 4𝑥 + 6 = 0 C) 𝑦 + 4𝑥 − 6 = 0 D) 𝑦 − 4𝑥 − 6 = 0 218. Tenglamani yeching. 𝑙𝑜𝑔 2 2
2 𝑥 8 A) 2 B) 4 C) 8 D) 1 219. 𝑥 = − 2 3 bo’lsa, (𝑥 − 4)
−1 − 𝑥+4 2𝑥−4 ∙ (
𝑥 𝑥 2 −16 − 𝑥−4 𝑥(𝑥+4) ) ni
hisoblang. A)
2 3 B) − 2 3 C) 3 2 D) − 3 2
220. Birinchi son ikkinchisidan 122 ga ortiq. Agar ularning o’rta arifmetigi 48 bo’lsa, ikkinchi sonni toping. A) −13 B) 109 C) −109 D) 13 221.
Birlik katakchalar bilan berilgan trapetsiya yuzini toping. A) 64 B) 56 C) 63 D) 72 222.
2 3 ; 3 4 ; 5 6 ; … arifmetik progressiyaning uchinchi hadi to’qqizinchi hadining necha fozini tashkil qiladi? A) 90 B) 75 C) 60 D) 80 223. 𝑓(2) + 𝑓(𝑥 − 3) = 5𝑥 + 1 berilgan bo’lsa, 𝑓(𝑥) chiziqli funksiyani toping. A) 5𝑥 + 3 B) 5𝑥 + 4 C) 5𝑥 + 2 D) 5𝑥 + 6 224. 𝑓(1) + 𝑓(𝑥 + 1) = 2 + 9𝑥 bo’lsa, 𝑓(𝑥) chiziqli funksiyani toping. A) 9𝑥 + 8 B) 9𝑥 − 8 C) 9𝑥 + 2 D) 9𝑥 − 2 225. 𝐴 = {𝑥| 𝑥 > 2, 𝑥𝜖𝑍} va 𝐵 = {𝑥| 𝑥 < 8, 𝑥𝜖𝑍} bo’lsa, 𝐴 ∩ 𝐵 to’plamning elementlari sonini toping. A) ∞ B) 9 C) 5 D) 24 226. 𝐴 = {𝑥| 𝑥 ≥ 4, 𝑥𝜖𝑍} va 𝐵 = {𝑥| 𝑥 < 13, 𝑥𝜖𝑍} bo’lsa, 𝐴 ∩ 𝐵 to’plamning elementlari sonini toping. A) 8 B) 9 C) 10 D) ∞ 227. 7
3 + 7 ∙ 11 ni 6 ga bo’lgandagi qoldiqni toping. A) 0 B) 5 C) 1 D) 4 228. 𝛼 = 45° bo’lsa, (1 +
1 𝑐𝑜𝑠𝛼
+ 𝑡𝑔𝛼)(1 − 1 𝑐𝑜𝑠𝛼 + 𝑡𝑔𝛼) ni hisoblang. A) 1 B) 2 C) −1 D) −2 11
229. 𝐴𝐵𝐶 uchburchakda ∠𝐵𝐴𝐶 = 33°. 𝐴𝐶 tomondan shunday 𝐷 nuqta olinganki, bunda 𝐵𝐷 = 𝐷𝐶. Agar ∠𝐵𝐷𝐶 = 42° bo’lsa, ∠𝐴𝐵𝐶 ning qiymatini toping. A) 78° B) 69° C) 81° D) 84° 230. Tengsizlikni yeching. (2 𝑥+3 −1)(2 𝑥 −8) 𝑥−3 > 0 A) (−3; 3) ∪ (3; ∞) B) (3; ∞) C) (0; 3) ∪ (3; ∞) D) (−∞; ∞) 231. Tengsizlikni yeching. (7 𝑥+1 −1)(2 𝑥 −4) 𝑥−2 > 0 A) (2; ∞) B) (−∞; ∞) C) (−2; 1) D) (−1; 2) ∪ (2∞) 232. Tengsizlikni yeching. 7 𝑥−1 ∙(𝑥−2) 𝑥−3
> 0 A) (−∞; 2) ∪ (3; ∞) B) (2; 3) C) (−∞; 1) ∪ (1; 2) ∪ (3; ∞) D) (−∞; 1) ∪ (1; 2) ∪ (2; 3) ∪ (3; ∞) 233. Soddalashtiring. (𝑥 > 0) 2 𝑥(𝑥+3) + 2 (𝑥+3)(𝑥+6) + 2 (𝑥+6)(𝑥+9) A)
3 𝑥(𝑥+9)
B) 6 𝑥(𝑥+9) C) 2 𝑥(𝑥+9) D) 6 𝑥 234. Soddalashtiring. (𝑥 > 0) 1 𝑥(𝑥+4)
+ 1 (𝑥+4)(𝑥+8) + 1 (𝑥+8)(𝑥+12) A)
4 𝑥(𝑥+12)
B) 8 𝑥(𝑥+12) C) 6 𝑥(𝑥+12) D)
1 𝑥(𝑥+12)
235. Arifmetik progressiyada 𝑎 4 = 4 va 𝑎 𝑛+1
= 𝑎 𝑛 − 2 bo’lsa, progressiyaning dastlabki 12 ta hadi yig’indisini toping. A) 12 B) −12 C) 22 D) −22 236. Arifmetik progressiyada 𝑎 4 = 5 va 𝑎 𝑛+1
= 𝑎 𝑛 + 4 bo’lsa, progressiyaning dastlabki 15 ta hadi yig’indisini toping. A) 315 B) 300 C) 345 D) 360 237. 6
3 0 2 y x Chizmada 𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 funksiya grafigiga 𝑥 0 = 3 nuqtasidan urinma o’tkazilgan. Berilganlarga ko’ra 𝑏 + 𝑐 ning qiymatini toping. A) 3 1
B) 3 2 3 C) 3 2 9 D) 3 4 9 238.
6 6 3 0 2 y x Chizmada 𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 funksiya grafigiga 𝑥 0 = 3 nuqtasidan urinma o’tkazilgan. Berilganlarga ko’ra 𝑏 + 𝑎 ning qiymatini toping. A) 2 2
B) 2 1 3 C) 2 2 9 D) 1 2 9 12
239. 6 6 3 0 2 y x Chizmada 𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 funksiya grafigiga 𝑥 0 = 3 nuqtasidan urinma o’tkazilgan. Berilganlarga ko’ra 𝑏 + 𝑎 ning qiymatini toping. A) 1 2
B) 1 5 9 C) 1 2 3 D) 1 8 9 240. 𝑙𝑔2 = 𝑥, 𝑙𝑔3 = 𝑦, 𝑙𝑔5 = 𝑧 bo’lsa, lg (0,96) ni 𝑥, 𝑦, 𝑧 orqali ifodalang. A) 2𝑦 + 3𝑥 − 𝑧 B) 𝑦 + 2𝑥 − 3𝑧 C) 𝑦 + 3𝑥 − 2𝑧 D) 𝑦 − 3𝑥 + 2𝑧 241. Tenglamani ildizini chorak qismini toping. 120: (24: (18: (12: (6: (𝑥 + 1))))) = 15 A) 2 B) 1 C) 1 2
242. √28 − 10√3 − 1 7+4√3 ni hisoblang. A) 2 − 3√3 B) 2 + 3√3 C) 3√3 − 2 D) −2 − 3√3 243. Dastlabki 𝑛 ta hadining yig’indisi 𝑆 𝑛
2 + 3𝑛 formula bilan aniqlanadigan arifmetik progressiya uchun 𝑎 𝑛+2 𝑑 ning
qiymatini toping. A) 𝑛 + 2 B) 𝑛 + 3 C) 𝑛 + 4 D) 𝑛 244. Dastlabki 𝑛 ta hadining yig’indisi 𝑆 𝑛 = 6𝑛 − 𝑛 2 formula bilan aniqlanadigan arifmetik progressiyaning ayirmasini toping. A) 2 B) −2 C) 1 D) −1 245. Dastlabki 𝑛 ta hadining yig’indisi 𝑆 𝑛 = 2𝑛 − 𝑛 2 formula bilan aniqlanadigan arifmetik progressiyaning ayirmasini toping. A) 2 B) −2 C) 1 D) −1 246. Qutida 𝑛, 𝑎, 𝑚, 𝑜, 𝑡 harflari bor. Tavakkaliga olingan 3 ta harfni ketma-ket qoyganda "𝑜𝑛𝑎" so’zi hosil bo’lish ehtimolini toping. A)
1 120
B) 1 60 C) 1 30 D) 1 20 247. Qutida 𝑎, 𝑏, 𝑚, 𝑜, 𝑡, 𝑐, 𝑛 harflari bor. Tavakkaliga olingan 2 ta harf ketma-ket qoyilganda "𝑜𝑡" so’zi hosil bo’lish ehtimolini toping. A)
1 42 B) 1 21 C) 1 63 D) 1 84
248. Qutida 𝑚, 𝑒, ℎ, 𝑛, 𝑎, 𝑡 harflari bor. Tavakkaliga olingan harflar ketma-ket qoyilganda "𝑚𝑒ℎ𝑛𝑎𝑡" so’zi hosil bo’lish ehtimolini toping. A) 1
B) 1 240 C) 1 360 D) 1 720 249. Markazi (0; 0) nuqtada bo’lgan aylanadagi 𝐴( √3
; 1 2 ) nuqtani soat strelkasi harakati yo’nalishida aylana bo’ylab 60° ga burish natijasida hosil bo’lgan nuqtaning koordinatalari yig’indisini toping. A) 0 B) 1 C) √3−1
2 D) 1−√3 2
250. Aniqmas integralni hisoblang. ∫ 𝑠𝑖𝑛𝑥 ∙ 𝑐𝑜𝑠 7 𝑥𝑑𝑥 =? A) 𝑐𝑜𝑠
8 𝑥 8 + 𝐶 B) − 𝑐𝑜𝑠
8 𝑥 8 + 𝐶 C)
𝑐𝑜𝑠 8 8𝑥 8 + 𝐶 D) − 𝑠𝑖𝑛 8
8 + 𝐶
251. Aniqmas integralni hisoblang. ∫ 𝑠𝑖𝑛𝑥 ∙ 𝑐𝑜𝑠 8 𝑥 𝑑𝑥 =? A) 𝑐𝑜𝑠
9 𝑥 9 + 𝐶 B) 𝑠𝑖𝑛
9 𝑥 9 + 𝐶 C) −
𝑐𝑜𝑠 9 𝑥 9 + 𝐶 D) − 𝑠𝑖𝑛 9
9 + 𝐶
252. Aniqmas integralni hisoblang. ∫ 𝑐𝑜𝑠𝑥 ∙ 𝑠𝑖𝑛 3 𝑥𝑑𝑥 =? A) 𝑠𝑖𝑛
4 𝑥 4 + 𝐶 B) − 𝑠𝑖𝑛
4 𝑥 4 + 𝐶 C)
𝑐𝑜𝑠 4 𝑥 4 + 𝐶 D) − 𝑐𝑜𝑠 4
4 + 𝐶
253. Agar 𝑎 + 𝑏 3 = 8 bo’lsa, 𝑎𝑏 ko’paytmaning eng katta qiymatini toping. A) 16 B) 12 C) 32 D) 48 254. Agar 𝑎 + 𝑏 5
eng katta qiymatini toping. A) 25 B) 125 C) 5 D) 625 255. 𝐴𝐵𝐶𝐷𝐸𝐹 muntazam oltiburchak berilgan. 𝐸𝐵 ⃗⃗⃗⃗⃗⃗ vektor quyidagilardan qaysi biriga teng? A) −2(𝐵𝐶 ⃗⃗⃗⃗⃗⃗ − 𝐵𝐴 ⃗⃗⃗⃗⃗⃗) B) 2(𝐵𝐶 ⃗⃗⃗⃗⃗⃗ − 𝐵𝐴 ⃗⃗⃗⃗⃗⃗) C) −2(𝐵𝐶
⃗⃗⃗⃗⃗⃗ + 𝐵𝐴 ⃗⃗⃗⃗⃗⃗) D) 2(𝐵𝐶 ⃗⃗⃗⃗⃗⃗ + 𝐵𝐴 ⃗⃗⃗⃗⃗⃗)
13
256. 𝑦 = −11𝑥 + 𝑏 funksiya 𝑏 ning qanday qiymatlarida kamayuvchi bo’ladi? A) 𝑏𝜖𝑅 B) [0; ∞) C) (−∞; 0] D) ∅ 257. 𝑦 = 3𝑥 + 𝑏 funksiya 𝑏 ning qanday qiymatlarida o’suvchi bo’ladi? A) 𝑏𝜖𝑅 B) [0; ∞) C) (−∞; 0] D) ∅ 258. 𝑦 = 7𝑥 + 𝑏 funksiya 𝑏 ning qanday qiymatlarida kamayuvchi bo’ladi? A) 𝑏𝜖𝑅 B) [0; ∞) C) (−∞; 0] D) ∅ 259. 0,125 ∙ 4 2𝑥−3
= ( 0,25
√2 ) −𝑥 tenglamani yeching. A) 3 B) 6 C) 2 D) 1 260. Agar 8𝑥+15
16𝑥 2 −9 = 𝑎 4𝑥+3 + 𝑏 4𝑥−3 tenglik ayniyat bo’lsa, 𝑎𝑏 =? A) −10,5 B) −5,5 C) −5,25 D) −5 261. Agar 10𝑥−8 25𝑥
2 −4 = 𝑎 5𝑥−2
+ 𝑏 5𝑥+2 tenglik ayniyat bo’lsa, 𝑎 + 𝑏 =? A) −2 B) 2 C) −1 D) 1 262. Agar 𝑥 = 14 bo’lsa, ( 𝑥√𝑥−8
𝑥−4 + 2√𝑥 √𝑥+2 ) : (
4 2−√𝑥
− 1) − 2 ifodaning qiymatini toping. A) 4 B) −4 C) √14 D) −√14 263. Agar 𝑐 > 𝑎 > 𝑏 > 0 bo’lsa, √(𝑐 − 𝑎) 2 (𝑏 − 𝑎) 2 (𝑐 − 𝑏)
2 ifodani soddalashtiring. A) (𝑐 − 𝑎)(𝑎 − 𝑏)(𝑐 − 𝑏) B) (𝑐 − 𝑎)(𝑏 − 𝑎)(𝑐 − 𝑏) C) (𝑎 − 𝑐)(𝑏 − 𝑎)(𝑏 − 𝑐) D) (𝑎 − 𝑐)(𝑎 − 𝑏)(𝑐 − 𝑏) 264. Soddalashtiring. cos( 5𝜋
−6𝛼)+sin(𝜋+4𝛼)+sin (3𝜋+𝛼) sin(
5𝜋 2 +6𝛼)+cos(4𝛼−2𝜋)+cos (𝜋+𝛼) A) 𝑐𝑡𝑔𝛼 B) 𝑡𝑔𝛼 C) 2𝑡𝑔𝛼 D) 2𝑐𝑡𝑔𝛼 265. 𝑓(𝑥) = 3 𝑥+1 +3 𝑥+2
+3 𝑥+3
5 𝑥+2
+14∙5 𝑥 bo’lsa, 9 ∙ 𝑓(−1) ning qiymatini toping. A) 24 B) 15 C) 1 2 3
2 3
266. 𝑓(𝑥) = 3 𝑥+1 +3 𝑥+2
+3 𝑥+3
5 𝑥+2
+14∙5 𝑥 bo’lsa, 15 ∙ 𝑓(−1) ning qiymatini toping. A)
5 3 B) 8 3 C) 25 D) 40 267. 𝑦 = −𝑥 2 + 6𝑥 − 5 funksiyaning qiymatlar sohasini toping. A) [4; ∞) B) [2; ∞) C) (−∞; 2] D) (−∞; 4] 268. 𝑦 = 3𝑥 2 + 4𝑥 + 5 funksiyaning qiymatlar sohasini toping. A) [
11 3 ; ∞) B) [ 8 3 ; ∞) C) [ 10 3 ; ∞) D) [ 4 3 ; ∞) 269. 𝑦 = 3 − √16 − |2𝑥 − √3| funksiyaning qiymatlar sohasini toping. A) [−3; 1] B) (−∞; 3] C) [−1; 3] D) [3; ∞) 270. Soddalashtiring. 𝑠𝑖𝑛8𝑥 + 𝑐𝑜𝑠8𝑥 ∙ 𝑐𝑡𝑔 (4𝑥 + 3𝜋 4 ) + 3 A) 3 B) −3 C) 2 D) −2 271. Soddalashtiring. 𝑠𝑖𝑛𝑥 + cos (𝑥 − 6𝜋) ∙ 𝑐𝑡𝑔( 𝑥 2
13𝜋 4 ) A) 1 B) −1 C) 2 D) −2 272. Agar 𝐴 to’plamga 1 ta element qo’shilganda, hosil bo’ladigan to’plamning qism to’plamlar soni, 𝐴 to’plamdan 1 ta element chiqarilganda hosil bo’lgan to’plamning qism to’plamlar sonidan 12 ga ko’p bo’lsa, 𝐴 to’plamning qism to’plamlari sonini toping. A) 4 B) 8 C) 16 D) 32 273. Agar 𝐴 to’plamga 1 ta element qo’shilganda, hosil bo’ladigan to’plamning qism to’plamlar soni, 𝐴 to’plamdan 1 ta element chiqarilganda hosil bo’lgan to’plamning qism to’plamlar sonidan 96 ga ko’p bo’lsa, 𝐴 to’plamning qism to’plamlari sonini toping A) 32 B) 64 C) 128 D) 256 274. Mis va rux qotishmasi 12 kg. Mis qotishmaning 40%ini tashkil qiladi. Rux qotishmaning 80%ini tashkil qilishi uchun qotishmaga necha kg rux qo’shish kerak? A) 8 B) 9,6 C) 12 D) 10 275. Mis va rux qotishmasi 18 kg. Mis qotishmaning 70%ini tashkil qiladi. Rux qotishmaning 40%ini tashkil qilishi uchun qotishmaga necha kg rux qo’shish kerak? A) 3 B) 4 C) 3,6 D) 4,8 276. Mis va rux qotishmasi 16 kg. Mis qotishmaning 80%ini tashkil qiladi. Rux qotishmaning 50%ini tashkil qilishi uchun qotishmaga necha kg rux qo’shish kerak? A) 8 B) 8,4 C) 9 D) 9,6 277. 25 𝑙𝑜𝑔
5 (1−2𝑥)
+ (2𝑥 − 1) 2
yeching. 14
A) (−2; 3) B) (−∞; −2) ∪ (0,5; ∞) C) (−2; 0,5) D) (−∞; −2) ∪ (3; ∞) 278. 9
𝑙𝑜𝑔 3 (3−𝑥) + (𝑥 − 3) 2 ≥ 50 tengsizlikni yeching. A) [−2; ∞) B) [2; ∞) C) (−∞; −2] D) (−∞; −2] ∪ [8; ∞) 279. |2
4𝑥 2 −1 − 5| = 3 tenglama nechta haqiqiy ildizga ega? A) 1 B) 2 C) 3 D) 4 280. Uchburchakli piramida asosining ikki tomoni uzunligi 9 va 10 ga teng, ular orasidagi burchak 45°. Yon qirrasi uzunligi 16 ga teng. Agar yon qirrasi va asos tekisligi orasidagi burchak 30° ni tashkil qilsa, piramida hajmini toping. A) 160√2 B) 225√2 C) 180√2 D) 200√2 281. Uchburchakli piramida asosining ikki tomoni uzunligi 6 va 7 ga teng, ular orasidagi burchak 45°. Yon qirrasi uzunligi 8 ga teng. Agar yon qirrasi va asos tekisligi orasidagi burchak 30° ni tashkil qilsa, piramida hajmini toping. A) 21√2 B) 42√2 C) 63√2 D) 84√2 282. Arifmetik progressiyada 𝑎 2 𝑎
= 60 va 𝑎 1 + 𝑎 5 = 24 o’rinli bo’lsa, progressiyaning ayirmasi va birinchi hadi ayirmasining modulini toping. A) 5 B) 9 C) 7 D) 3 283.
1 |𝑥|
= 8 𝑥 2 +3𝑥
tenglamani haqiqiy ildizlari nechta? A) 1 B) 2 C) 3 D) 4 284. 𝐴𝐵𝐶𝐷 parallelogrammda 𝐵𝐶 va 𝐴𝐷 tomonlari o’rtalarida mos ravishda 𝑀 va 𝑁 nuqtalar olingan. 𝐴𝑀 va 𝐶𝑁 kesmalar 𝐵𝐷 dioganalni mos ravishda 𝑃 va 𝑄 nuqtalarda kesib o’tadi. Agar 𝐷𝑁𝑄 uchburchak yuzi 8 ga teng bo’lsa, 𝐵𝐶𝐷 uchburchak yuzini toping. A) 24 B) 48 C) 96 D) 72 285. 𝐴𝐵𝐶𝐷 parallelogrammda 𝐵𝐶 va 𝐴𝐷 tomonlari o’rtalarida mos ravishda 𝑀 va 𝑁 nuqtalar olingan. 𝐴𝑀 va 𝐶𝑁 kesmalar 𝐵𝐷 dioganalni mos ravishda 𝑃 va 𝑄 nuqtalarda kesib o’tadi. Agar 𝐷𝑁𝑄 uchburchak yuzi 15 ga teng bo’lsa, 𝐴𝐵𝐷 uchburchak yuzini toping. A) 45 B) 90 C) 135 D) 67,5 286. 𝐴𝐵𝐶𝐷 parallelogrammda 𝐵𝐶 va 𝐴𝐷 tomonlari o’rtalarida mos ravishda 𝑀 va 𝑁 nuqtalar olingan. 𝐴𝑀 va 𝐶𝑁 kesmalar 𝐵𝐷 dioganalni mos ravishda 𝑃 va 𝑄 nuqtalarda kesib o’tadi. Agar 𝐷𝑁𝑄 uchburchak yuzi 12 ga teng bo’lsa, 𝐴𝐵𝐶𝐷 parallelogrammning yuzini toping. A) 36 B) 48 C) 108 D) 72 287. Agar 𝑥𝑦 = 𝑎 2 bo’lsa, 𝑥(𝑦−𝑎) 2 −𝑦(𝑥−𝑎) 2 𝑥(𝑦−𝑎)−𝑦(𝑥−𝑎) ning qiymatini toping. A) 0 B) 𝑎 2 B) 𝑎 C) −𝑎 288. Agar 𝑃 = 3𝑎 2 − 5𝑎𝑏 va 𝑄 = 𝑎 2 + 2𝑎𝑏
bo’lsa, 𝑃 + 𝑄 − 2𝑎 2 ni toping. A) 6𝑎 2 − 3𝑎𝑏 B) 2𝑎 2 − 7𝑎𝑏 C) 2𝑎 2
2 − 7𝑎𝑏
289. 3𝑛 + 1 sonining 60%i 51 ga teng bo’lsa, 𝑛 ning qiymatini toping. A) 28 B) 29 C) 30 D) 31 290. 𝑚, 𝑛𝜖𝑁 sonlar uchun 2𝑛 + 3𝑚 = 66 tenglik o’rinli bo’lsa, 𝑛 ning eng katta qiymatini toping. A) 31 B) 30 C) 32 D) 29 291.
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