@Matematika
Harbiy
TEST 5. 07. 2019
https://t.me/Matematika
1
Qo’shko’pir 2019
M.
Xudayberganov
https://t.me/Riyoziyot
Matematika
5. 07. 2019
1.
12345...110111 shu sonni hosil qilishda nechta
raqam ishtirok etgan?
A)
153 B) 10 C) 9 D) 225
2.
12345...110111112 shu sonni hosil qilishda
nechta raqam ishtirok etgan?
A)
156 B) 10 C) 9 D) 228
3.
12345...110111 shu sonni hosil qilishda nechta
turli raqam ishtirok etgan?
A)
153 B) 10 C) 9 D) 225
4.
0; 1; 2; 3; 4 raqamlaridan iborat uch xonali
sonlar nechta?
A)
100 B) 125 C) 96 D) 120
5.
1; 2; 3; 4; 5 raqamlaridan iborat uch xonali
sonlar nechta?
A)
100 B) 125 C) 96 D) 120
6.
0; 1; 2; 3; 4; 5; 6 raqamlaridan iborat uch xonali
sonlar nechta?
A)
180 B) 125 C) 96 D) 240
7.
Bilimlar bellashuvida hakamlar hay’ati to’rt
kishidan iborat bo’lib, ular ishtirokchilarni faqat
“1” yoki “0” kabi baholasa, u holda bitta
ishtirokchining necha xil usulda baholanishini
aniqlang.
A)
16 B) 24 C) 32 D) 4
8.
Bilimlar bellashuvida hakamlar hay’ati besh
kishidan iborat bo’lib, ular ishtirokchilarni faqat
“1” yoki “0” kabi baholasa, u holda bitta
ishtirokchining necha xil usulda baholanishini
aniqlang.
A)
16 B) 25 C) 32 D) 120
9.
𝐴 = {𝑎, 𝑏, 𝑐, 𝑑, 𝑒, 𝑓} to’plamda nechta 𝑑
element qatnashgan qism to’plami mavjud?
A)
16 B) 64 C) 32 D) 8
10.
𝐴 = {𝑎, 𝑏, 𝑐, 𝑑, 𝑒, 𝑓} elementli to’plamning
nechta qism to’plamida
𝑏 element bo’lib, 𝑐
element qatnashmaydi?
A)
16 B) 28 C) 32 D) 8
11.
𝐴 = {𝑎, 𝑏, 𝑐, 𝑑, 𝑒, 𝑓} elementli to’plamning
nechta qism to’plamida
𝑐 va 𝑑 elementlar
qatnashmaydi?
A)
16 B) 4 C) 32 D) 8
12.
𝐴 = {𝑎, 𝑏, 𝑐, 𝑑} elementli to’plamning nechta
qism to’plamida
𝑏 va 𝑐 elementlar qatnashadi?
A)
2 B) 8 C) 16 D) 4
13.
𝐴 = {0,1, 2, 5, 6,7, 9} va 𝐵 = {1, 4, 8, 9}
to’plamlar berilgan bo’lsa,
𝐴 ∪ 𝐵 to’plamning
xos qism to’plamlari sonini toping.
A)
128 B) 2 C) 256 D) 254
14.
𝐴 = {𝑥 ∣ 𝑥 = 2𝑛, 𝑛 ∈ 𝑁} va
𝐵 = {𝑥 ∣ 𝑥 = 2𝑛 + 1, 𝑛 ∈ 𝑁} bo’lsa, 𝐴 ∪ 𝐵 ni
toping.
A)
𝑁 B) 𝑍 C) 𝑁\{1} D) ∅
15.
𝐴 = {𝑥 ∣ 𝑥 = 2𝑛, 𝑛 ∈ 𝑁} va
𝐵 = {𝑥 ∣ 𝑥 = 2𝑛 + 1, 𝑛 ∈ 𝑁} bo’lsa, 𝐴 ∩ 𝐵 ni
toping.
A)
𝑁 B) 𝑍 C) 𝑁\{1} D) ∅
16.
1 dan 126 gacha sonlar ichidan nechtasi 2 va 7
ga bo’linmaydi?
A)
36 B) 72 C) 63 D) 54
17.
1 dan 135 gacha sonlar ichidan nechtasi 3 va 5
ga bo’linmaydi?
A)
36 B) 72 C) 63 D) 54
18.
1 dan 200 gacha sonlar ichidan nechtasi 5 va 7
ga bo’linmaydi?
A)
137 B) 53 C) 147 D) 154
19.
324; 255 va 71 sonlarining har birini qanday
natural songa bo’lganda qoldiqlari bir xil
bo’ladi?
A)
31 B) 19 C) 23 D) 43
20.
128
143
sonini
5 ga bo’lgandagi qoldiqni toping.
A)
1 B) 2 C) 3 D) 4
21.
433
333
sonini
5 ga bo’lgandagi qoldiqni toping.
A)
1 B) 2 C) 3 D) 4
22.
233
233
sonini
5 ga bo’lgandagi qoldiqni toping.
A)
1 B) 2 C) 3 D) 4
23.
373
373
sonini
5 ga bo’lgandagi qoldiqni toping.
A)
1 B) 2 C) 3 D) 4
24.
999
2
888999
sonning oxirgi raqamini toping.
A)
1 B) 7 C) 3 D) 9
25.
888
2
999888
sonning oxirgi raqamini toping.
A)
2 B) 4 C) 6 D) 8
26.
Bir nechta natural sonlarning yig’indisi
44 ga
teng. Agar shu sonlarning har biri
2 ga
orttirilib, yig’indi hisoblansa
62 ga teng bo’ladi.
Dastlab yig’indida nechta son qatnashgan?
A)
9 B) 10 C) 7 D) 8
27.
Bir nechta natural sonlarning yig’indisi
52 ga
teng. Agar shu sonlarning har biri
2 ga
orttirilib, yig’indi hisoblansa
72 ga teng bo’ladi.
Dastlab yig’indida nechta son qatnashgan?
A)
9 B) 10 C) 7 D) 8
28.
Ikki sonning yig’indisi ularning ayirmasidan
50% ga ortiq bu sonlar kvadratlarining
yig’indisi ularning ko’paytmasidan necha
foizga ko’p?
A)
420 B) 100 C) 546 D) 740
29.
Natural
𝑎 va 𝑏 sonlar uchun 𝑎
2
− 𝑏
2
= 49
tenglik o’rinli bo’lsa,
3𝑎 − 2𝑏 ning qiymatini
toping.
A)
36 B) 27 C) 18 D) 37
@Matematika
Harbiy
TEST 5. 07. 2019
https://t.me/Matematika
2
Qo’shko’pir 2019
M. Xudayberganov
https://t.me/Riyoziyot
30.
Natural
𝑎 va 𝑏 sonlar uchun 𝑎
2
− 𝑏
2
= 25
tenglik o’rinli bo’lsa,
2𝑎 − 𝑏 ning qiymatini
toping.
A)
10 B) 12 C) 14 D) 17
31.
Natural
𝑎 va 𝑏 sonlar uchun 𝑎
2
− 𝑏
2
= 9
tenglik o’rinli bo’lsa,
2𝑎 − 3𝑏 ning qiymatini
toping.
A)
2 B) −7 C) −2 D) 1
32.
Natural
𝑛 va 𝑚 sonlar uchun
(𝑛 − 𝑚)(𝑛 + 𝑚) = 25 tenglik o’rinli bo’lsa,
𝑛 + 2𝑚 ning qiymatini toping.
A)
36 B) 37 C) 27 D) 38
33.
Hisoblang:
𝑁𝐵𝑆(𝐸𝐾𝑈𝐵(911; 659; 647 + 367))
A)
1 B) 2 C) 3 D) 4
34.
Hisoblang:
𝐸𝐾𝑈𝐾(𝑁𝐵𝑆(144); 51))
A)
510 B) 255 C) 3 D) 85
35.
Ifodani soddalashtiring:
3𝑎 − (5𝑎 − (3𝑎 − (2𝑎 + 𝑏))).
A)
𝑎 + 𝑏 B) −𝑎 − 𝑏 C) −𝑎 + 𝑏 D) 𝑎 − 𝑏
36.
Ifodani soddalashtiring:
5𝑎 − (4𝑎 − (3𝑎 − (2𝑎 − 𝑏))).
A)
2𝑎 + 𝑏 B) 𝑎 + 𝑏
C)
−𝑎 + 𝑏 D) 2𝑎 − 𝑏
37.
Ifodani soddalashtiring:
1
𝑎(𝑎−𝑏)(𝑎−𝑐)
+
1
𝑏(𝑏−𝑎)(𝑏−𝑐)
+
1
𝑐(𝑐−𝑎)(𝑐−𝑏)
.
A)
1 B) −
1
𝑎𝑏𝑐
C)
1
𝑎𝑏𝑐
D)
−1
38.
Ifodani soddalashtiring:
1
𝑎(𝑎−𝑏)(𝑐−𝑎)
+
1
𝑏(𝑎−𝑏)(𝑏−𝑐)
+
1
𝑐(𝑐−𝑎)(𝑏−𝑐)
.
A)
1 B) −
1
𝑎𝑏𝑐
C)
1
𝑎𝑏𝑐
D)
−1
39.
Ifodani soddalashtiring:
𝑎+𝑏
𝑎
2
3
−𝑎
1
3
𝑏
1
3
+𝑏
2
3
−
𝑎−𝑏
𝑎
2
3
+𝑎
1
3
𝑏
1
3
+𝑏
2
3
A)
2√𝑏
3
B)
√𝑎𝑏
3
C)
2√𝑎
3
D)
√𝑎
3
+ √𝑏
3
40.
Ifodani soddalashtiring:
(√𝑎−√𝑏)
3
+2𝑎
2
:√𝑎+𝑏√𝑏
𝑎√𝑎+𝑏√𝑏
+
3√𝑎𝑏−3𝑏
𝑎−𝑏
.
A)
3√𝑎𝑏 B) 1 C) 3 D) −3
41.
Ifodani soddalashtiring:
(√𝑎+√𝑏)
3
+2𝑎
2
:√𝑎−𝑏√𝑏
𝑎√𝑎−𝑏√𝑏
−
3√𝑎𝑏+3𝑏
𝑎−𝑏
.
A)
3√𝑎𝑏 B) 1 C) 3 D) −3
42.
𝑎 = 75, 𝑝 = 4, 𝑞 = 3 bo’lsa, 𝑎 ning 𝑝% 𝑖 va
𝑞‰ ini toping.
A)
3; 0,225 B) 3; 2,25
C)
0,3; 0,225 D) 30;
9
40
43.
Agar
𝑎 > 1 bo’lsa,
quyidagilardan qaysi biri
ma’noga ega emas?
1)
log
𝑎
log
𝑎
lg 5 2) log
𝑎
log
𝑎
(𝑎 + 1)
3)
lg log
𝑎
lg 5
A)
1; 2 B) 2 C) 1; 3 D) 2; 3
44.
Agar
0 < 𝑎 < 1 bo’lsa, quyidagilardan qaysi
biri ma’noga ega?
A)
log
2
log
𝑎
log
2
3 B) log
𝑎
log
𝑎
log
2
3
C)
log
𝑎
log
𝑎+1
𝑎 D) log
𝑎
log
𝑎
log
𝜋
𝜋
3
45.
𝑦 =
2
𝑥
− 3 funksiyaning qiymatlar sohasini
toping.
A) (
−3; ∞) B) (−∞; −3) ∪ (−3; ∞)
C) (
−∞; −3) D) (−∞; 0) ∪ (0; ∞)
46.
𝑦 =
3
𝑥
− 4 funksiyaning qiymatlar sohasini
toping.
A) (
−4; ∞) B) (−∞; −4) ∪ (−4; ∞)
C) (
−∞; −4) D) (−∞; 0) ∪ (0; ∞)
47.
𝑦 =
4
𝑥
− 2 funksiyaning qiymatlar sohasini
toping.
A) (
−2; ∞) B) (−∞; −2) ∪ (−2; ∞)
C) (
−∞; −2) D) (−∞; 0) ∪ (0; ∞)
48.
𝑦 = 𝑎𝑟𝑐𝑐𝑜𝑠2
𝑥
funksiyaning aniqlanish sohasini
toping.
A) [
−1; 1] B) (−∞; 2]
C) (
−∞; 0] D) (−∞; ∞)
49.
𝑦 = 𝑎𝑟𝑐𝑠𝑖𝑛3
𝑥
funksiyaning aniqlanish sohasini
toping.
A) [
−1; 1] B) (−∞; 3]
C) (
−∞; 0] D) (−∞; ∞)
50.
𝑓(𝑥) =
5
𝑥
− √
𝑥−2
𝑥(𝑥+3)
funksiyaning aniqlanish
sohasini toping.
A) (
−3; 0) ∪ (0; ∞) B) (−3; 0) ∪ [2; ∞)
C) (
−∞; −3) ∪ (0; 2] D) (−3; 0) ∪ (2; ∞)
51.
Agar
𝑓(𝑥) funksiya (−∞; ∞) da
aniqlangan
bo’lsa,
𝑦 = 2𝑓(𝑥 − 1) − 7 funksiya qaysi
oraliqda aniqlanadi?
A) (
−∞; ∞) B) 𝑥 ≠ 1
C) (
1; ∞) D) (−∞; 1)
52.
Agar
𝑓(𝑥) funksiya (−∞; ∞) da aniqlangan va
monoton bo’lsa,
𝑦 = 2𝑓(𝑥 − 1) − 7 funksiya
uchun quyidagilardan qaysi biri o’rinli?
A) monoton funksiya
B) kamayuvchi funksiya
C) dastlab kamayadi, so’ng o’zgarmas
D) dastlab o’sadi, so’ng o’zgarmas
53.
Agar
𝑓(𝑥) + 2𝑓 (
1
𝑥
) = 𝑥 bo’lsa, 𝑓(𝑥)
funksiyani toping. (
𝑥 ≠ 0)
A)
𝑓(𝑥) =
𝑥
2
−2
3𝑥
B)
𝑓(𝑥) =
2−𝑥
2
3𝑥
C)
𝑓(𝑥) =
𝑥
2
−3
2𝑥
D)
𝑓(𝑥) =
3−𝑥
2
2𝑥
@Matematika
Harbiy
TEST 5. 07. 2019
https://t.me/Matematika
3
Qo’shko’pir 2019
M. Xudayberganov
https://t.me/Riyoziyot
54.
Agar
𝑓(𝑥) + 𝑥𝑓 (
𝑥
2𝑥−1
) = 2 bo’lsa, 𝑓(𝑥)
funksiyani toping.
(𝑥 ≠ 1, 𝑥 ≠
1
2
)
A)
𝑓(𝑥) =
4𝑥−2
𝑥−1
B)
𝑓(𝑥) =
4−2𝑥
𝑥−1
C)
𝑓(𝑥) =
2−4𝑥
𝑥−1
D)
𝑓(𝑥) =
2𝑥−4
𝑥−1
55.
𝑦 =
𝑥
2
√𝑥
2
+5
funksiyaning hosilasini toping.
A)
𝑥
2
+10𝑥
√(𝑥
2
+5)
3
B)
𝑥
3
+5𝑥
√(𝑥
2
+5)
3
C)
𝑥
2
+5𝑥
√(𝑥
2
+5)
3
D)
𝑥
3
+10𝑥
√(𝑥
2
+5)
3
56.
𝑓(𝑥) = 𝑥
3
− 3𝑥
2
+ 2𝑥 − 1 bo’lsa, 𝑓
′
(2) =?
A)
0 B) 1 C) 2 D) −1
57.
𝑓(𝑥) =
𝑥
3
−8
𝑥
2
+2𝑥+4
bo’lsa,
𝑓(2𝑥 − 1)
funksiyaning
𝑥 = 0 dagi hosilasini toping.
A)
1
2
B)
1 C) −2 D) −1
58.
𝑓(𝑥) =
𝑥
3
−8
𝑥
2
−2𝑥+4
funksiyaning
𝑥 = 0 nuqtadagi
hosilasini toping.
A)
0 B) 1 C) 2 D) −1
59.
𝑓(𝑥) =
𝑥
3
−8
𝑥
2
+2𝑥+4
−2𝑥 + 1 funksiyaning 𝑥 = 2
nuqtadagi hosilasini toping.
A)
0 B) 1 C) 2 D) −1
60.
𝑦 =
𝑥
3
−27
𝑥
2
−3𝑥+9
+3𝑥 funksiyada 𝑦
′
(1) ni toping.
A)
−
5
49
B)
3
44
49
C)
−2
2
49
D)
2
44
49
61.
𝐹
′
(𝑥) = 𝑥 − 4 va 𝐹(2) = 0 bo’lsa, 𝐹(𝑥) ni
toping.
A)
𝑥
2
− 2𝑥 B)
1
2
𝑥
2
− 4𝑥 + 6
C)
1
2
𝑥
2
− 4𝑥 + 4 D)
1
2
𝑥
2
− 4𝑥
62.
𝑓(𝑥) = 2𝑥
2
− 𝑥 funksiyaning 𝑥 = 𝑎 nuqtadagi
orttirmasini toping. Bunda
𝑎 = 4, argument
orttirmasi esa,
∆𝑥 = 0,1 ga teng.
A)
1,5 B) 1 C) 1,52 D) 2
63.
𝑓(𝑥) = 𝑥
2
− 2𝑥 funksiyaning 𝑥 = 3 nuqtadagi
orttirmasini toping. Bunda argument orttirmasi
esa,
∆𝑥 = 0,1 ga teng.
A)
0,82 B) 0,41 C) 1,52 D) 0,19
64.
𝑓(𝑥) = −𝑥
2
+ 2𝑥 funksiyaning 𝑥 = −2
nuqtadagi orttirmasini toping. Bunda argument
orttirmasi esa,
∆𝑥 = 0,1 ga teng.
A)
0,19 B) 0,41 C) 0,49 D) 0,59
65.
Chizmada
𝑦 = 𝑓(𝑥) funksiya grafigi
tasvirlangan.
𝑓(𝑥) ∙ 𝑓
′
(𝑥) ≥ 0 tengsizlikni
[−6; 6] kesmadagi yechimlarini toping.
A) {
−6} ∪ [−4; 0] ∪ {4} ∪ [5; 6]
B) [
−6; −4] ∪ [−3; 0] ∪ [4; 5] ∪ {6}
C) {
−6} ∪ [−4; −3] ∪ [0; 4] ∪ [5; 6]
D) [
−6; −4] ∪ {−3} ∪ [0; 5] ∪ {6}
66.
Chizmada
𝑦 = 𝑓(𝑥) funksiya grafigi
tasvirlangan.
𝑓(𝑥) ∙ 𝑓
′
(𝑥) < 0 tengsizlikni
[−6; 6] kesmadagi yechimlarini toping.
A) (
−4; 0) ∪ (5; 6)
B) (
−6; −4) ∪ (−4; −3) ∪ (4; 5) ∪ (5; 6)
C) (
−4; −3) ∪ (0; 4) ∪ (5; 6)
D) (
−6; −4) ∪ (−3; 0) ∪ (4; 5)
67.
Chizmada
𝑦 = 𝑓(𝑥) funksiya grafigi
tasvirlangan.
𝑓
′
(𝑥)
𝑓(𝑥)
> 0 tengsizlikni [−6; 6]
kesmadagi yechimlarini toping.
A) (
−4; 0) ∪ (5; 6)
B) (
−6; −4) ∪ (−4; −3) ∪ (4; 5) ∪ (5; 6)
C) (
−4; −3) ∪ (0; 4) ∪ (5; 6)
D) (
−6; −4) ∪ (−3; 0) ∪ (4; 5)
68.
0,25𝑦
′
= 𝑦 tenglamani yeching.
A)
𝑦 = 𝐶𝑒
4𝑥
B)
𝑦 = 𝐶𝑒
0,25𝑥
C)
𝑦 = 4𝑒
𝑥
D)
𝑦 = 𝐶𝑒
−4𝑥