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Q. What is the value of (2 + 3)^3?

A. 25
B. 30
C. 35
D. 40

Solution

Using the binomial theorem, (2 + 3)^3 = C(3,0)(2)^3 + C(3,1)(2)^2(3) + C(3,2)(2)(3)^2 + C(3,3)(3)^3 = 8 + 36 + 54 + 27 = 125.

Correct Answer: B — 30

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Q. What is the value of (2 + 3i) - (1 + 2i)? (2014)

A. 1 + i
B. 1 + i^2
C. 2 + i
D. 3 + i

Solution

(2 + 3i) - (1 + 2i) = (2 - 1) + (3i - 2i) = 1 + i.

Correct Answer: A — 1 + i

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Q. What is the value of (2 + 3i) / (1 + i)? (2015)

A. 1 + 2i
B. 2 - i
C. 3 + 2i
D. 1 - 2i

Solution

Multiply numerator and denominator by the conjugate of the denominator: (2 + 3i)(1 - i) / (1 + i)(1 - i) = (2 - 2i + 3i + 3) / (1 + 1) = (5 + i) / 2 = 2.5 + 0.5i.

Correct Answer: B — 2 - i

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Q. What is the value of (2 + 3i)(2 - 3i)? (2019)

A. 13
B. 1
C. 12
D. 7

Solution

Using the difference of squares: (a + b)(a - b) = a² - b². Here, (2)² - (3i)² = 4 - (-9) = 4 + 9 = 13.

Correct Answer: A — 13

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Q. What is the value of (2 - 3)^5?

A. -1
B. -32
C. -243
D. -125

Solution

Using the binomial theorem, (2 - 3)^5 = (-1)^5 = -1.

Correct Answer: D — -125

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Q. What is the value of (3 + 4i) / (1 + i)? (2021)

A. 2 + i
B. 1 + 2i
C. 3 - 4i
D. 1 - i

Solution

Multiplying numerator and denominator by the conjugate of the denominator: (3 + 4i)(1 - i) / (1 + i)(1 - i) = (3 - 3i + 4i + 4) / 2 = (7 + i) / 2 = 2 + i.

Correct Answer: A — 2 + i

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Q. What is the value of (3 + 5) × (2 + 4)? (2020)

A. 48
B. 56
C. 42
D. 36

Solution

(3 + 5) = 8 and (2 + 4) = 6, so 8 × 6 = 48.

Correct Answer: B — 56

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Q. What is the value of (3 + 5) × (2 - 1)? (2020)

A. 8
B. 16
C. 10
D. 6

Solution

(3 + 5) = 8 and (2 - 1) = 1, so 8 × 1 = 8.

Correct Answer: A — 8

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Q. What is the value of (3 + 5) × (6 - 2)? (2020)

A. 32
B. 24
C. 40
D. 28

Solution

(3 + 5) = 8 and (6 - 2) = 4, so 8 × 4 = 32.

Correct Answer: B — 24

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Q. What is the value of (3 + 5) × 2? (2023)

A. 16
B. 14
C. 12
D. 10

Solution

(3 + 5) × 2 = 8 × 2 = 16.

Correct Answer: B — 14

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Q. What is the value of (3 - 2)^5 using the binomial theorem?

A. 1
B. 0
C. -1
D. -2

Solution

Using the binomial theorem, (3 - 2)^5 = 1^5 = 1.

Correct Answer: A — 1

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Q. What is the value of (3^3) - (2^3)? (2016)

A. 19
B. 27
C. 21
D. 18

Solution

3^3 = 27 and 2^3 = 8, so 27 - 8 = 19.

Correct Answer: A — 19

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Q. What is the value of (x + 1)^5 when x = 2?

A. 32
B. 64
C. 128
D. 256

Solution

Using the binomial theorem, (x + 1)^5 = C(5,0)(2)^5 + C(5,1)(2)^4 + C(5,2)(2)^3 + C(5,3)(2)^2 + C(5,4)(2)^1 + C(5,5)(2)^0 = 32 + 80 + 80 + 40 + 10 + 1 = 243.

Correct Answer: C — 128

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Q. What is the value of 100 - 37? (2014)

A. 63
B. 67
C. 73
D. 60

Solution

100 - 37 = 63.

Correct Answer: A — 63

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Q. What is the value of 100 ÷ 4 + 6? (2023) 2023

A. 25
B. 30
C. 28
D. 26

Solution

100 ÷ 4 = 25, so 25 + 6 = 31.

Correct Answer: C — 28

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Q. What is the value of 12 × 12? (2020)

A. 144
B. 124
C. 156
D. 132

Solution

12 × 12 = 144.

Correct Answer: A — 144

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Q. What is the value of 12 × 8? (2020)

A. 96
B. 88
C. 104
D. 80

Solution

12 × 8 = 96.

Correct Answer: A — 96

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Q. What is the value of 12 ÷ (2 + 4)? (2018)

A. 2
B. 3
C. 4
D. 6

Solution

12 ÷ (2 + 4) = 12 ÷ 6 = 2.

Correct Answer: B — 3

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Q. What is the value of 12 ÷ 4 × 3? (2023)

A. 9
B. 6
C. 3
D. 12

Solution

12 ÷ 4 = 3, then 3 × 3 = 9.

Correct Answer: B — 6

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Q. What is the value of 12% of 250? (2020)

A. 30
B. 25
C. 35
D. 20

Solution

12% of 250 = (12/100) * 250 = 30.

Correct Answer: A — 30

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Q. What is the value of 15% of 200? (2014)

A. 30
B. 25
C. 35
D. 20

Solution

15% of 200 = (15/100) * 200 = 30.

Correct Answer: A — 30

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Q. What is the value of 5 × (6 + 4)? (2016)

A. 50
B. 40
C. 30
D. 20

Solution

6 + 4 = 10, then 5 × 10 = 50.

Correct Answer: A — 50

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Q. What is the value of 5! (5 factorial)? (2016) 2016

A. 120
B. 60
C. 100
D. 150

Solution

5! = 5 × 4 × 3 × 2 × 1 = 120.

Correct Answer: A — 120

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Q. What is the value of 5! (5 factorial)? (2023) 2023

A. 120
B. 100
C. 150
D. 110

Solution

5! = 5 × 4 × 3 × 2 × 1 = 120.

Correct Answer: A — 120

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Q. What is the value of 7^2 + 3^2? (2023) 2023

A. 58
B. 49
C. 73
D. 70

Solution

7^2 = 49 and 3^2 = 9, so 49 + 9 = 58.

Correct Answer: A — 58

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Q. What is the value of 8 × (2 + 3)? (2023) 2023

A. 40
B. 50
C. 30
D. 20

Solution

2 + 3 = 5, so 8 × 5 = 40.

Correct Answer: A — 40

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Q. What is the value of 9 + 6 × 2? (2022)

A. 21
B. 18
C. 15
D. 12

Solution

According to BODMAS, 6 × 2 = 12, then 9 + 12 = 21.

Correct Answer: B — 18

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Q. What is the value of 9 - 3 × 2? (2015)

A. 3
B. 6
C. 0
D. 9

Solution

Using BODMAS, 3 × 2 = 6, so 9 - 6 = 3.

Correct Answer: B — 6

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Q. What is the value of 9 × 9? (2014)

A. 81
B. 72
C. 90
D. 99

Solution

9 × 9 = 81.

Correct Answer: A — 81

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Q. What is the value of 9^2 - 4^2? (2016)

A. 65
B. 77
C. 81
D. 45

Solution

9^2 = 81 and 4^2 = 16, so 81 - 16 = 65.

Correct Answer: A — 65

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