DTM Test Matematika — Questions and Answers

Question 1: Agar x² - 5x + 6 = 0 bo'lsa, x ning qiymatlarini toping.

x = 2 va x = 3 (Correct answer)
x = -2 va x = -3
x = 1 va x = 6
x = -1 va x = -6

Correct answer: x = 2 va x = 3

x² - 5x + 6 = 0 tenglamasini yechish uchun uni ko'paytuvchilarga ajratamiz: (x-2)(x-3) = 0. Bu yerdan x - 2 = 0 yoki x - 3 = 0, ya'ni x = 2 yoki x = 3.

Question 2: log₂(32) ning qiymatini toping.

4
5 (Correct answer)
6
3

Correct answer: 5

log₂(32) = log₂(2⁵) = 5. Chunki 2⁵ = 32.

Question 3: sin(30°) + cos(60°) ning qiymatini toping.

1/2
√3/2
1 (Correct answer)
√2/2

Correct answer: 1

sin(30°) = 1/2 va cos(60°) = 1/2. Shuning uchun sin(30°) + cos(60°) = 1/2 + 1/2 = 1.

Question 4: To'g'ri burchakli uchburchakda gipotenuz 10 sm, bir kateti 6 sm bo'lsa, ikkinchi kateti necha sm?

6 sm
4 sm
8 sm (Correct answer)
7 sm

Correct answer: 8 sm

Pifagor teoremasi: a² + b² = c². 6² + b² = 10². 36 + b² = 100. b² = 64. b = 8 sm.

Question 5: Agar f(x) = 3x² - 2x + 1 bo'lsa, f(2) ning qiymatini toping.

12
9 (Correct answer)
10
8

Correct answer: 9

f(2) = 3(2)² - 2(2) + 1 = 12 - 4 + 1 = 9.

Question 6: Arifmetik progressiyaning birinchi hadi 3, umumiy farqi 4 bo'lsa, 10-hadini toping.

35
39 (Correct answer)
43
31

Correct answer: 39

a₁₀ = 3 + 9·4 = 39.

Question 7: tan(45°) ning qiymatini toping.

√3
1/√2
1 (Correct answer)
√3/2

Correct answer: 1

tan(45°) = 1.

Question 8: Doira yuzasi 36π sm² bo'lsa, uning radiusi necha sm?

9 sm
3 sm
6 sm (Correct answer)
4 sm

Correct answer: 6 sm

πr² = 36π → r² = 36 → r = 6 sm.

Question 9: 3^(x+1) = 81 tenglamasini yeching.

x = 4
x = 2
x = 5
x = 3 (Correct answer)

Correct answer: x = 3

3^(x+1) = 3⁴ → x+1 = 4 → x = 3.

Question 10: 5 ta son: 2, 4, 6, 8, 10. Ularning o'rta arifmetigi qancha?

6 (Correct answer)
5
7
8

Correct answer: 6

(2+4+6+8+10)/5 = 30/5 = 6.

Question 11: cos(0°) ning qiymatini toping.

0
1/2
√2/2
1 (Correct answer)

Correct answer: 1

cos(0°) = 1.

Question 12: Uchburchak tomonlari 3, 4, 5 sm. Yuzasini toping.

7,5 sm²
6 sm² (Correct answer)
8 sm²
10 sm²

Correct answer: 6 sm²

Yuz = (3·4)/2 = 6 sm².

Question 13: log₃(81) - log₃(9) ni hisoblang.

3
1
2 (Correct answer)
4

Correct answer: 2

4 - 2 = 2.

Question 14: Geometrik progressiyaning birinchi hadi 2, ko'rsatkich 3. 4-hadini toping.

18
54 (Correct answer)
162
27

Correct answer: 54

b₄ = 2·3³ = 54.

Question 15: sin²(α) + cos²(α) = ?

2
0
1 (Correct answer)
sin(2α)

Correct answer: 1

sin²(α) + cos²(α) = 1.

Question 16: To'g'ri to'rtburchak AB=8, BC=6. Diagonal AC=?

10 sm (Correct answer)
7 sm
14 sm
12 sm

Correct answer: 10 sm

AC² = 64+36 = 100 → AC = 10 sm.

Question 17: |2x - 3| = 7 tenglamasini yeching.

x=5 yoki x=2
x=5 yoki x=-2 (Correct answer)
x=-5 yoki x=-2
x=5 yoki x=-5

Correct answer: x=5 yoki x=-2

x=5 yoki x=-2.

Question 18: cos(60°) = ?

√3/2
1/2 (Correct answer)
1
√2/2

Correct answer: 1/2

cos(60°) = 1/2.

Question 19: 9 kitobdan 3 tasini tanlash necha usulda? (tartib muhim emas)

252
504
84 (Correct answer)
168

Correct answer: 84

C(9,3) = 84 usul.

Question 20: Doira diametri 14 sm. Perimetri? (π≈22/7)

44 sm (Correct answer)
88 sm
22 sm
154 sm

Correct answer: 44 sm

P = (22/7)·14 = 44 sm.

Question 21: 2x-3y=12 va x+y=1 tizimini yeching.

x=3, y=-2 (Correct answer)
x=-3, y=4
x=2, y=-1
x=4, y=-3

Correct answer: x=3, y=-2

y=-2, x=3.

Question 22: sin(90° - α) = ?

sin(α)
tan(α)
cos(α) (Correct answer)
-cos(α)

Correct answer: cos(α)

sin(90°-α) = cos(α).

Question 23: Parallelogramm asosi 12, balandligi 7. Yuzi = ?

38 sm²
84 sm² (Correct answer)
42 sm²
96 sm²

Correct answer: 84 sm²

S = 12·7 = 84 sm².

Question 24: Ikki zar tashlanganda yig'indi 7 bo'lish ehtimoli?

1/9
1/8
1/6 (Correct answer)
5/36

Correct answer: 1/6

6/36 = 1/6.

Question 25: log₅(125) = ?

4
2
5
3 (Correct answer)

Correct answer: 3

log₅(125) = 3.

Question 26: Trapetsiya: a=6, b=10, h=4. Yuzi=?

32 sm² (Correct answer)
40 sm²
24 sm²
28 sm²

Correct answer: 32 sm²

S = (16/2)·4 = 32 sm².

Question 27: eˣ = e³ tenglamasini yeching.

x=1/3
x=9
x=3 (Correct answer)
x=e³

Correct answer: x=3

x = 3.

Question 28: 10 o'quvchidan 2 navbatchi (tartib muhim). Necha usulda?

20
90 (Correct answer)
45
100

Correct answer: 90

10·9 = 90 usul.

Question 29: sin(150°) = ?

1/2 (Correct answer)
-1/2
√3/2
-√3/2

Correct answer: 1/2

sin(150°) = 1/2.

Question 30: x² - 4 > 0 tengsizligini yeching.

-2<x<2
x>4 yoki x<-4
x<-2 yoki x>2 (Correct answer)
x>2

Correct answer: x<-2 yoki x>2

x>2 yoki x<-2.

Question 31: Muntazam olti burchak tomoni 4. Yuzi=?

24√3 sm² (Correct answer)
48 sm²
24 sm²
16√3 sm²

Correct answer: 24√3 sm²

S = (3√3/2)·16 = 24√3 sm².

Question 32: 2log₃(x) = 4. x=?

6
27
81
9 (Correct answer)

Correct answer: 9

x = 3² = 9.

Question 33: 5 sanoq: 7,3,9,5,6. Medianani toping.

5
7
6 (Correct answer)
9

Correct answer: 6

Mediana = 6.

Question 34: tan(α)=3/4, o'tkir burchak. sin(α)=?

3/4
4/5
3/5 (Correct answer)
4/3

Correct answer: 3/5

sin(α) = 3/5.

Question 35: Shar yuzasida tasodifiy nuqta. Gumbaz (hemisfera) yuzasida bo'lish ehtimoli?

1/4
3/4
1/3
1/2 (Correct answer)

Correct answer: 1/2

Ehtimollik = 1/2.

Question 36: Kub tomoni 3 sm. Hajmi=?

9 sm³
18 sm³
27 sm³ (Correct answer)
81 sm³

Correct answer: 27 sm³

V = 27 sm³.

DTM Test Matematika

Agar x² - 5x + 6 = 0 bo'lsa, x ning qiymatlarini toping.