Test-2019 1-Variant
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2019 yil 30 ta lik variant
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- GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI
- 11 – Variant
- 12 – Variant.
10 – Variant. 1. 𝑦 = 8
𝑙𝑜𝑔 2 𝑥 − 2 funksiyaning qiymatlar sohasini toping. A) (0; ∞) B) (−2; 0) C) (−2; ∞) D) (0; 2)
2. Hisoblang: 2 sin 19°+2 sin 41° 2 cos 11°+2 sin 79°
A) 0,25 B) 0,5 C) 0,75 D) 1 3.
𝑛 2 −𝑛+1 𝑛+2 kasrning qiymatlar natural son bo’ladigan n ning barcha natural qiymatini toping. A) 1;7 B) 5 C) – 2; 5 D) 7
4. 𝑦 = (𝑥 − 1) 20 ∙ (sin 𝑥 + cos 𝑥)
funksiyaning 𝑥 = 0 nuqtadagi hosilasini toping. A) 21 B) – 19 C) – 21 D) 19
5. Ikki sonning EKUK va EKUB lari ko’paytmasi 280 ga teng bo’lsa, bu ikki sonning ko’paytmasi 31 sonidan qanchaga ko’p? A) 249 B) 239 C) 259 D) 269
6. ∫
𝑥 3 √10+𝑥 4 𝑑𝑥
integralni hisoblang. A)
1 4 √10 + 𝑥 4 + 𝐶
B) 1 2 √10 + 𝑥 4 + 𝐶 C) 2√10 + 𝑥 4 + 𝐶
D) √10 + 𝑥 4 + 𝐶
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 7.
2 𝑥 −𝑝 𝑥−4 = 0
tenglama yechimga ega bo’ladigan barcha p larni toping. A) (0; ∞) B) (0; 4) ∪ (4; ∞) C) 16 D) (0; 16) ∪ (16; ∞)
8.
𝑥 𝑥−1
− 1 𝑥+1 ≤ 0 tengsizlikni yeching. A) (−1; 1] B) [−1; 1) C) [−1; 1] D) (−1; 1)
9. A to’plam 48 ning, B to’plam 72 ning bo’luvchilaridan iborat bo’lsa, 𝑛(𝐴 ∪ 𝐵) ni toping. A) 12 B) 10 C) 8 D) 14
10. ∫ 2𝑥+3 𝑥 2 +3𝑥+2 𝑑𝑥 1 0 aniq integralni hisoblang. A) ln 2 B) ln 3 C) ln 5 D) 0
11. 4 xonali son 8 raqami bilan tugaydi. Oxirgi raqamni boshiga qo’yilsa, oldingi sondan 1890 ga ko’p son hosil bo’ladi.Berilgan sonni toping. A) 6788 B) 6878 C) 6978 D) 6798
12. 𝑓(𝑥) = (𝑥 + 3) 2 − 7
parobola uchi koordinatalari yig’indisini toping. A) – 4 B) 4 C) – 10 D) 10
13. Agar 𝑎 + 𝑏 = 11 bo’lsa, 25 𝑎 + 36 𝑏
ifodaning eng kichik qiymatini toping. A) 6 B) 11 C) 1 11
14. Tenglamani yeching: 12 𝑥−3
= 27 𝑥 ∙ 2 6𝑥
A) 1,5 B) – 1,5 C) 2 3 D) 3 2
15. Hisoblang:
√32+√50−√72 √2
A) 3 B) 15 C) 4 D) 5
16. 3 4 + 31 44 + 331 444
+ 3331
4444 yig’indining qaysi oraliqda ekanligini toping. A) (1; 2) B) (3;4) C) (4;5) D) (2;3)
17. 𝐴 = {𝑥| sin 𝜋𝑥 2 = −1; 𝑥 ∈ 𝑁} bo’lsa, A to’plamga teng to’plamni toping. A) {𝑥|𝑥 = 4𝑛 − 1; 𝑥 ∈ 𝑁} B) {𝑥|𝑥 = 4𝑛 + 1; 𝑥 ∈ 𝑁} C) {𝑥|𝑥 = 4𝑛 − 1; 𝑥 ∈ 𝑍} D) {𝑥|𝑥 = 4𝑛 + 1; 𝑥 ∈ 𝑍}
18. 3 ta matematika va 3 ta fizika kitoblari bor. Vali matematika va fizika kitoblarning yonma-yon bo’lishi sharti bilan bu 6 kitobni javonga jami necha xil usulda joylashtirishi mumkin? A) 9 B) 3 C) 18 D) 36
19. 2𝑐𝑜𝑠 2 𝑥 − 𝑐𝑜𝑠𝑥 − 1 = 0 tenglamaning [0; 2𝜋]
kesmadagi yechimlari sonini toping.
A) 2 B) 3 C) 4 D) 5
20. x,y va z haqiqiy sonlar bo’lib, quyidagi ma’lumotlardan foydalangan holda, x,y va z ning ishoralarini aniqlang. 1) 𝑥
2 ∙ 𝑦 < 0
2) 𝑦 𝑧 > 0 3) 𝑥 ∙ 𝑦 ∙ 𝑧 > 0 A) +,+,+ B) −, −, − C) +, −, − D) +, −, +
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 21. Koordinata sistemasida A(2;3), B(-3;4), C(5;-4), D(6;5) nuqtalar berilgan. Koordinata boshidan qaysi nuqtagacha bo’lgan masofa eng kichik? A) A B) B C) C D) D
22. 𝑎⃗(−1; 3; −5) vektorga yo’nalishdosh birlik vektorni toping. A) 𝑒⃗ (−
1 √35
; 3 √35 ; − 5 √35 )
B) 𝑒⃗ ( 1 √35 ; 3 √35 ; − 5 √35 )
C) 𝑒⃗ (− 1 √35
; 3 √35 ; 5 √35 )
D) 𝑒⃗ ( 1 √35 ; 3 √35 ; 5 √35 )
23. O’lchamlari 𝑎; 𝑏; 𝑐 bo’lgan parallelepipedning to’la sirtining yuzasi 288 ga teng. Agar 1 𝑎 + 1 𝑏 + 1 𝑐 = 4 5 o’rinli bo’lsa, parallelepipedning hajmini toping. A) 864 B) 432 C) 360 D) 180
24. Uchlari A( - 1;1), B(3;1) va C(-1;7) nuqtalarda bo’lgan uchburchak yuzini toping.
A) 10 B) 12 C) 14 D) 18
25. Teng yonli trapetsiyaning diogonali o’tkir burchagining bisektrissasi va katta asosi a ga, perimetri p ga teng bo’lsa, o’rta chizig’ini toping. A)
2𝑎+𝑝 3 B) 2𝑎+𝑝 6
C) 2𝑎+𝑝
4 D) 2𝑎+𝑝 2
26. Ikkita qo’shni burchaklar ayirmasi 12° ga teng bo’lsa, burchaklardan kattasini toping. A) 84
° B) 78° C)
96° D) 102°
27. Tekislikka og’ma va perpendekulyar tushirilgan. Og’ma va perpendekulyar orasidagi burchak 15° ga teng. Perpendekulyar uzunligi 18 + 9√3 ga teng bo’lsa, og’maning tekislikdagi proyeksiyasi uzunligini toping. A) 9 B) 6 C) 18 D) 12
28. Uchtasi bir to’g’ri chiziqda yotmagan A,B,C,D,E,F,H nuqtalar berilgan. Uchi E nuqtada bo’lgan nechta uchburchak yasash mumkin? A) 30 B) 15 C) 45 D) 21
29. To’g’ri burchakli trapetsiyaning kichik asosi 3 ga va ichki chizilgan aylana radiusi 2 ga teng bo’lsa, trapetsiyaning kichik diogonalini toping. A) 4 B) 5 C) 6 D) 8
30. Kesik konusga shar ichki chizilgan bo’lib, konus asoslari radiuslari 3 va 5 ga teng bo’lsa, kesik konus yon sirtini toping. A) 72𝜋 B) 14𝜋 C) 24𝜋 D) 64𝜋
11 – Variant. 1. Qutida M,E,H,N,A,T harflari bor. Tavakkaliga olingan harflardan “MEHNAT”so’zi hosil bo’lish ehtimolini toping. A)
1 120
B) 1 24 C)
1 720
D) 1 6
2. Hisoblang: 4√28 − 10√3 − 1 7+4√3 A) 28 B) 11 C) 13 D) 17
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 3. Tenglamani yeching: 𝑥 2
|𝑥−1| 𝑥−1
− 8 = 0
A) 4;2 B) – 4 ; - 2 C) 4; -4 ;2; -2 D) 4; -4
4. Dastlabki n ta hadining yig’indisi 𝑆 𝑛 = 6𝑛 − 2𝑛 2 formula bilan aniqlanadigan arifmetik progressiyaning ayirmasini toping. A) – 2 B) – 4 C) – 3 D) – 1
5. ∫ sin 𝑥 ∙ 𝑐𝑜𝑠 7 𝑥 𝑑𝑥
integralni hisoblang. A)
𝑠𝑖𝑛 8 𝑥 8 + 𝐶
B) − 𝑐𝑜𝑠
8 𝑥 8 + 𝐶
C) − 𝑠𝑖𝑛 8 𝑥 8 + 𝐶
D) 𝑐𝑜𝑠
8 𝑥 8 + 𝐶
6. | 3 7−𝑥 | ≥ 1 5 9 tengsizlikning butun yechimlari yig’indisini toping. A) 14 B) 11 C) 13 D) 21
7. sin 4𝑥 = 𝑐𝑜𝑠 4 𝑥 − 𝑠𝑖𝑛
4 𝑥 tenglamani yeching. A)
𝜋 4 + 𝜋𝑛 2 ; (−1) 𝑛 ∙ 𝜋 12 + 𝜋𝑛 2 𝑛 ∈ 𝑍
B)
𝜋 4 + 𝜋𝑛 4 ; 𝜋 12 + 𝜋𝑛 2 𝑛 ∈ 𝑍 C)
𝜋 4 + 𝜋𝑛 2 ; 𝜋 12 + 𝜋𝑛 2 𝑛 ∈ 𝑍 D)
𝜋 2 + 𝜋𝑛 2 ; (−1) 𝑛 ∙ 𝜋 6 + 𝜋𝑛 2 𝑛 ∈ 𝑍
𝑏 4 = 10 bo’lsa, 𝑎𝑏 ning eng katta qiymatini toping. A) 40 B) 100 C) 80 D) 120 9. 𝑦 = 𝑘𝑥 + 𝑙 funksiyaning OY o’qiga nisbatan simmetrik funksiyani toping. A) 𝑦 = −𝑘𝑥 + 𝑙 B) 𝑦 = 𝑘𝑥 + 𝑙 C) 𝑦 = −𝑘𝑥 − 𝑙 D) 𝑦 = 𝑘𝑥 − 𝑙
10. ∫ cos 𝑥 ∙ 𝑠𝑖𝑛 3 𝑥 𝑑𝑥
integralni hisoblang. A)
𝑠𝑖𝑛 4 𝑥 4 + 𝐶
B) 𝑠𝑖𝑛
4 𝑥 2 + 𝐶
C) − 𝑠𝑖𝑛 4 𝑥 4 + 𝐶
D) 𝑐𝑜𝑠
4 𝑥 4 + 𝐶
11. Agar 𝑐 > 𝑎 > 𝑏 > 0 bo’lsa, √(𝑐 − 𝑎) 2 ∙ (𝑏 − 𝑎) 2 ∙ (𝑐 − 𝑏) 2 ifodani soddalashtiring. A) (𝑐 − 𝑎)(𝑏 − 𝑎)(𝑐 − 𝑏) B) −(𝑐 − 𝑎)(𝑏 − 𝑎)(𝑐 − 𝑏) C) (𝑐 − 𝑎)(𝑎 − 𝑏)(𝑏 + 𝑐) D) 𝑎 + 𝑏 + 𝑐
12. Agar 𝑥 = 12 bo’lsa, ( 𝑥√𝑥−8
𝑥−4 + 2√𝑥 √𝑥+2 ) : (
4 2−√𝑥
− 1) − 2 ifodaning qiymatini toping. A) −2√3 B) 2√3 C) – 2 D) 10
13. 𝑓(𝑥) = 3 𝑥+1
+3 𝑥+2
+3 𝑥+3
5 𝑥+2
+14∙5 𝑥 bo’lsa, 9𝑓(−1) ning qiymatini toping. A) 9 B) 12 C) 15 D) 18
14. Soddalashtiring: cos( 5𝜋 2 −𝛼)+sin(𝜋+𝛼)+sin(3𝜋+𝛼) sin(
5𝜋 2 +𝛼)+cos(𝛼−2𝜋)+cos(𝛼+𝜋) A) 1 B) – 1 C) 𝑐𝑡𝑔𝛼 D) – 𝑡𝑔𝛼
15. 𝑦 = −𝑥 2 + 6𝑥 − 5
funksiyaning qiymatlar sohasini toping. A) [4; ∞) B) (−∞; −4] C) (−∞; 4] D) [−4; ∞)
16. Mis va ruh qotishmasi 12 kg. Mis qotishmaning 40 %ini tashkil etadi. Ruh qotishmaning 80 %ini tashkil etishi uchun qotishmaga necha kg ruh qo’shish kerak?
A) 12,8 B) 9,4 C) 9,6 D) 12
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 17. Agar A to’plamga 1 ta element qo’shilganda, hosil bo’lgan to’plamning qism to’plamlari soni, A to’plamdan bitta element chiqarilganda hosil bo’lgan to’plamning qism to’plamlari sonidan 12 taga ko’p bo’lsa, A to’plamning qism to’plamlari sonini toping. A) 8 B) 4 C) 16 D) 32
18. 9 𝑙𝑜𝑔 3 (3−𝑥) + (𝑥 − 3) 2 ≥ 18 tengsizlikni yeching. A) (−∞; 0) ∪ (6; ∞) B) (−∞; 0] ∪ [6; ∞) C) (−∞; 3) D) (−∞; 0]
19. Soddalashtiring: sin 8𝑥 − cos 8𝑥 ∙ 𝑐𝑡𝑔 (4𝑥 + 3𝜋 4 ) + 3
A) 1 B) 4 + 2 sin 8𝑥 C) 3 D) 2
20. Hisoblang: 19,126 + 2,7 − 7,117 − 51,2
A) - 36,491 B) -37,441 C) - 38,481 D) -37,471
21. 𝑎⃗(−2; 6; 6) vektorga yo’nalishdosh birlik vektorni toping. A) 𝑒⃗ (−
1 √19
; 3 √19 ; − 3 √19 )
B) 𝑒⃗ ( 1 √19 ; 3 √19 ; − 3 √19 )
C) 𝑒⃗ (− 1 √19
; 3 √19 ; 3 √19 )
D) 𝑒⃗ ( 1 √19 ; 3 √19 ; 3 √19 )
22. Teng yonli trapetsiyaning diogonali o’tkir burchagining bisektrissasi va katta asosi 26 ga, perimetri 56 ga teng bo’lsa, o’rta chizig’ini toping. A) 15 B) 18 C) 20 D) 16 23. Ikkita qo’shni burchaklar ayirmasi 26° ga teng bo’lsa, burchaklardan kichikini toping. A)
77° B) 113° C)
103° D) 87°
24. Uchlari A(1;0). B(0;3) va C(0;0) nuqtalarda bo’lgan uchburchakning CM medianasi o’tkazilgan bo’lsa, M nuqtaning koordinatasini toping. A) ( 3√2
4 ; 3√2 4 ) B) ( 4 3√2
; 4 3√2 )
C) ( 3 4 ; 3 4 ) D) ( 4 3 ; 4 3 )
25. Uchtasi bir to’g’ri chiziqda yotmagan a,b,c,d,e,f nuqtalar berilgan. Uchi a nuqtada bo’lgan nechta uchburchak yasash mumkin? A) 5 B) 15 C) 10 D) 12
26. Soatning minut mili 31 minutda necha gradusga buriladi? A) 186 B) 62 C) 15,5 D) 93
27. To’g’ri burchakli uchburchak katetlari 12 va 16 ga teng. Uchburchakka ichki va tashqi chizilgan aylanalar orasidagi yuzani toping. A) 42𝜋 B) 64𝜋 C) 84𝜋 D) 81𝜋
12 va 16 ga teng. Uchburchakka ichki va tashqi chizilgan aylanalar markazlari orasidagi masofani toping. A) 4√5 B) 2√5 C) 6 D) 5
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 29. Tekisilikda Ikki parallel to’g’ri chiziqlar berilgan. Ularning birida 6 ta va ikkinchisida 5 ta nuqta olingan. Uchi shu nuqtalarda bo’lgan jami nechta to’rtburchak mavjud? A) 60 B) 75 C) 30 D) 135
30. Markazi (0;0) nuqtada bo’lgan aylanadagi 𝐴 ( √3 2 ; 1 2 ) nuqtani soat strelkasi harakati yo’nalishida aylana bo’ylab 60° ga burish natijasida hosil bo’lgan nuqtaning koordinatalarini toping.
A) (− √3 2 ; 1 2 ) B) ( √3 2
1 2 ) C) ( -1;0) D) (0;-1)
12 – Variant. 1. Agar 44𝑛 ko’paytma biror sonning kvadrati bo’lsa, 𝑛 + 13 ning eng kichik qiymatini toping. A) 17 B) 24 C) 57 D) 101
2. 4 2𝑥−2 𝑥 = √2 𝑥+2 tenglamani yeching. A) 2 B) 4 C) 2; 4 D) 0;2
3. |2 4𝑥 2 −1 − 5| = 3 tenglama nechta ildizga ega? A) 1 B) 4 C) 3 D) 2
4. Soddalashtiring: sin 𝑥 + cos(𝑥 − 6𝜋) ∙ 𝑐𝑡𝑔 ( 𝑥 2 − 13𝜋
4 )
A) 1 B) 0 C) – 1 D) 1 + 2 sin 𝑥
5. Mis va ruh qotishmasi 18 kg. Mis qotishmaning 70 %ini tashkil etadi. Ruh qotishmaning 40 %ini tashkil etishi uchun qotishmaga necha kg ruh qo’shish kerak?
A) 2 B) 3 C) 4 D) 5
6. sin 2𝑥 = cos 𝑥 tenglamaning eng kichik musbat ildizini toping. A)
𝜋 8 B) 𝜋 6 C) 𝜋 12 D) 𝜋 2
7. Hisoblang: (2 + √4 − 2√3) 2 − 4 A) 0 B) √3 C) 2√3 D) – 2
8. Agar 95𝑛 biror sonning kvadrati bo’lsa, 𝑛 + 18 ning eng kichik qiymatini toping.
A) 23 B) 37 C) 103 D) 113
9. Agar A to’plamga 1 ta element qo’shilganda, hosil bo’lgan to’plamning qism to’plamlari soni, A to’plamdan bitta element chiqarilganda hosil bo’lgan to’plamning qism to’plamlari sonidan 96 taga ko’p bo’lsa, A to’plamning qism to’plamlari sonini toping. A) 16 B) 32 C) 64 D) 128
10. 𝑦 = 3 − √16 − |2𝑥 − √3| funksiyaning qiymatlar sohasini toping. A) [
√3 2 ; 3] B) [ - 1;3] C) [-4;-1] D) [-3;1]
11. = −4𝑥 + 15 funksiyaning OY o’qiga nisbatan simmetrik funksiyani toping. A) 𝑦 = −4𝑥 + 15 B) 𝑦 = 4𝑥 + 15 C) 𝑦 = −4𝑥 − 15 D) 𝑦 = 4𝑥 − 15
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 12. Agar 𝑎 + 𝑏 3
bo’lsa, 𝑎𝑏 ning eng katta qiymatini toping. A) 36 B) 24 C) 48 D) 60
13. ∫ sin 𝑥 ∙ 𝑐𝑜𝑠 3 𝑥 𝑑𝑥
integralni hisoblang. A)
𝑠𝑖𝑛 4 𝑥 4 + 𝐶
B) − 𝑐𝑜𝑠
4 𝑥 4 + 𝐶
C) − 𝑠𝑖𝑛 4 𝑥 4 + 𝐶
D) 𝑐𝑜𝑠
4 𝑥 4 + 𝐶
14. Merganning bitta otgan o’qining nishonga tegishi ehtimoli 0,8 ga teng bo’lsa, otilgan ikkita o’qning ikkitasi ham nishonga tegishi ehtimolini toping. A) 0,8 B) 0,16 C) 0,32 D) 0,64
15. [1;200] oraliqda 9 ga bo’lining 12 ga bo’linmaydigan natural sonlar nechta? A) 5 B) 17 C) 22 D) 11
16. A(-2;9) nuqta 𝑦 = 𝑘𝑥 2 − 3
funksiyaga tegishli bo’lsa, k ni toping. A) 1 B) 2 C) 3 D) 4
17. Agar 𝑎 2 + 𝑏
2 + 𝑐
2 + (𝑎 + 𝑏 + 𝑐) 2 = 8
bo’lsa, (𝑎 + 𝑏)(𝑏 + 𝑐)(𝑎 + 𝑐) ning eng katta qiymatini toping. A) 16 9 √6 B) 8 9 √6 C)
16 3 √6 D) 16 9
18. Aniqmas integralni hisoblang: ∫ 𝑥𝑠𝑖𝑛4𝑥𝑑𝑥
A) −
𝑥𝑐𝑜𝑠4𝑥 4 + 1 16 𝑠𝑖𝑛4𝑥 + 𝐶 B) −
𝑥𝑐𝑜𝑠4𝑥 4 + 1 16 𝑠𝑖𝑛8𝑥 + 𝐶 C) −
𝑐𝑜𝑠4𝑥 4 + 1 16 𝑠𝑖𝑛4𝑥 + 𝐶 D)
𝑥𝑐𝑜𝑠4𝑥 4 − 1 16 𝑠𝑖𝑛4𝑥 + 𝐶 19. Hisoblang: 4(𝑡𝑔435° − 𝑡𝑔555°)(𝑠𝑖𝑛70° ∙ 𝑠𝑖𝑛50° ∙ 𝑠𝑖𝑛10°) 2 : 𝑠𝑖𝑛60° A) 0,5 B) 0,25 C) 0,75 D) 1
20. 𝑦 = 𝑥 2 − 5𝑥 + 9
funksiyani (0;0) nuqtaga nisbatan simmetrik ko’chirishdan hosil bo’lgan funksiyani toping.
A) 𝑦 = 𝑥 2 + 5𝑥 + 9 B) 𝑦 = −𝑥 2 + 5𝑥 − 9
C) 𝑦 = −𝑥 2 − 5𝑥 − 9
D) 𝑦 = −𝑥 2 + 5𝑥 + 9
21. Teng yonli trapetsiyaning diogonali o’tkir burchagining bisektrissasi va katta asosi 25 ga, perimetri 55 ga teng bo’lsa, o’rta chizig’ini toping. A) 16 B) 16,5 C) 17 D) 17,5
22. Ikkita qo’shni burchaklar ayirmasi 36° ga teng bo’lsa, burchaklardan kichikini toping.
A) 84 ° B) 72° C) 96° D) 108°
23. Uchtasi bir to’g’ri chiziqda yotmagan A,B,C,D,E nuqtalar berilgan. Uchi B nuqtada bo’lmagan nechta uchburchak yasash mumkin? A) 4 B) 5 C) 6 D) 12 GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 24. Uchlari A(2;0). B(0;1) va C(0;0) nuqtalarda bo’lgan uchburchakning CM bisektrissasi o’tkazilgan bo’lsa, M nuqtaning koordinatasini toping. A) (
2√2 3 ; 2√2 3 ) B) ( 3 2√2 ; 3 2√2 )
C) ( 2 3 ; 2 3 ) D) ( 3 2 ; 3 2 )
25. ABCDEF muntazam oltiburchak berilgan. 𝐸𝐵 ⃗⃗⃗⃗⃗⃗ vector quyidagilardan qaysi biriga teng. A) −2(𝐵𝐶 ⃗⃗⃗⃗⃗⃗ − 𝐵𝐴 ⃗⃗⃗⃗⃗⃗) B) −2(𝐵𝐶 ⃗⃗⃗⃗⃗⃗ + 𝐵𝐴 ⃗⃗⃗⃗⃗⃗) C) 2(𝐵𝐶
⃗⃗⃗⃗⃗⃗ − 𝐵𝐴 ⃗⃗⃗⃗⃗⃗) D) 2(𝐵𝐶 ⃗⃗⃗⃗⃗⃗ + 𝐵𝐴 ⃗⃗⃗⃗⃗⃗)
26. Uchburchakning ikki tomoni uzunligi 4√5 va 10 ga teng. Agar ularga tushirilgan medianalar o’zaro perpendekulyar bo’lsa, uchburchakning uchinchi tomonini toping. A) 6 B) 8 C) 12 D) 16
27. Uchburchakning burchaklari 1:2:3 kabi nisbatda. Agar uchburchakning eng kichik tomoni 6 cm ga teng bo’lsa, uning eng katta tomonini toping. A) 8 B) 10 C) 3√3 D) 12
28. Uchburchakli piramida asosining ikki tomoni uzunligi 6 dm va 7 dm ga teng. Ular orasidagi burchak 45°. Yon qirrasi uzunligi 8 dm ga teng. Agar yon qirrasi va asos tekisligi orasidagi burchak 30° ni tashkil etsa, piramidaning hajmini toping. A) 28√3
3 B) 56√3 3
C) 14√2
3 D) 56√2 4
29. ABC uchburchakning AB va BC tomonlari 6 av 8 ga teng va B burchak bisektrissasi AC yomonni D nuqtada kesib o’tadi. 𝐴𝐷 𝐷𝐶 ni toping. A)
4 3 B) 3 4
C) 7 3 D) 7 4
30. Markazi (0;0) nuqtada bo’lgan aylanadagi A(0;2) nuqtani soatyo’nalishida 60° ga burganda hosil bo’lgan nuqtaning koordinatalari yig’indisini toping. A) −1 − √3 B) −1 + √3 C) 1 + √3 D) 1 − √3
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