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Q. If A = 1 and B = 1, what is the output of the XOR gate?

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

Solution

An XOR gate outputs 1 only when the inputs are different. Since both inputs are 1, the output is 0.

Correct Answer: A — 0

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Q. If a = 1 and b = 2, what is the value of a³ + b³?

A. 3
B. 5
C. 9
D. 11

Solution

a³ + b³ = 1³ + 2³ = 1 + 8 = 9.

Correct Answer: C — 9

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Q. If a = 1 and b = 4, what is the value of a³ + b³?

A. 65
B. 65
C. 125
D. 125

Solution

a³ + b³ = 1³ + 4³ = 1 + 64 = 65.

Correct Answer: A — 65

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Q. If A = 1, B = 1, and C = 0, what is the output of A OR (B AND C)?

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

Solution

B AND C = 1 AND 0 = 0. Then, A OR 0 = 1 OR 0 = 1.

Correct Answer: B — 1

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Q. If A = 1, B = 1, and C = 0, what is the output of the expression (A OR B) AND C?

A. 0
B. 1
C. 2
D. 3

Solution

First, evaluate A OR B, which is 1 OR 1 = 1. Then, 1 AND 0 = 0.

Correct Answer: A — 0

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Q. If A = 1, B = 2, C = 3, ..., Z = 26, what is the code for the word 'CAT'?

A. 24
B. 20
C. 23
D. 21

Solution

'C' = 3, 'A' = 1, 'T' = 20. So, 3 + 1 + 20 = 24.

Correct Answer: A — 24

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Q. If A = 1, B = 2, C = 3, then what is the code for 'CAB'? (2021)

A. 123
B. 321
C. 213
D. 132

Solution

CAB = 3, 1, 2 = 321

Correct Answer: B — 321

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Q. If A = 1i + 1j + 1k and B = 1i + 1j + 1k, what is A · B?

A. 1
B. 2
C. 3
D. 4

Solution

A · B = (1)(1) + (1)(1) + (1)(1) = 1 + 1 + 1 = 3.

Correct Answer: C — 3

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Q. If A = 1i + 1j + 1k and B = 1i + 2j + 3k, find A · B.

A. 6
B. 5
C. 4
D. 3

Solution

A · B = (1)(1) + (1)(2) + (1)(3) = 1 + 2 + 3 = 6.

Correct Answer: A — 6

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Q. If A = 1i + 1j + 1k and B = 1i + 2j + 3k, what is A · B?

A. 6
B. 5
C. 4
D. 3

Solution

A · B = (1)(1) + (1)(2) + (1)(3) = 1 + 2 + 3 = 6.

Correct Answer: B — 5

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Q. If A = 1i + 1j + 1k and B = 2i + 2j + 2k, find A · B.

A. 6
B. 4
C. 2
D. 8

Solution

A · B = (1)(2) + (1)(2) + (1)(2) = 2 + 2 + 2 = 6.

Correct Answer: A — 6

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Q. If A = 1i + 1j + 1k and B = 2i + 2j + 2k, what is A · B?

A. 6
B. 4
C. 2
D. 0

Solution

A · B = (1)(2) + (1)(2) + (1)(2) = 2 + 2 + 2 = 6.

Correct Answer: A — 6

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Q. If A = 1i + 1j and B = 1i - 1j, what is the scalar product A · B?

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

Solution

A · B = (1)(1) + (1)(-1) = 1 - 1 = 0.

Correct Answer: A — 0

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Q. If A = 1i + 2j + 3k and B = 4i + 5j + 6k, what is A · B?

A. 32
B. 26
C. 20
D. 18

Solution

A · B = (1)(4) + (2)(5) + (3)(6) = 4 + 10 + 18 = 32.

Correct Answer: B — 26

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Q. If a = 2 and b = 3, what is the value of (a + b)² - (a² + b²)?

A. 0
B. 2
C. 4
D. 6

Solution

(a + b)² = (2 + 3)² = 25; a² + b² = 2² + 3² = 4 + 9 = 13; thus, 25 - 13 = 12.

Correct Answer: C — 4

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Q. If a = 2 and b = 3, what is the value of (a + b)²?

A. 25
B. 30
C. 20
D. 15

Solution

(a + b)² = (2 + 3)² = 5² = 25.

Correct Answer: A — 25

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Q. If a = 2 and b = 3, what is the value of 2a + 3b?

A. 12
B. 11
C. 10
D. 9

Solution

Substituting the values gives 2(2) + 3(3) = 4 + 9 = 13.

Correct Answer: A — 12

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Q. If a = 2 and b = 3, what is the value of a^2 + b^2?

A. 5
B. 7
C. 13
D. 12

Solution

a^2 = 4 and b^2 = 9, so 4 + 9 = 13.

Correct Answer: C — 13

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Q. If a = 2 and b = 3, what is the value of a^3 + b^3? (2021)

A. 35
B. 27
C. 10
D. 8

Solution

a^3 = 2^3 = 8 and b^3 = 3^3 = 27, so 8 + 27 = 35.

Correct Answer: A — 35

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Q. If a = 2 and b = 3, what is the value of a^b + b^a?

A. 11
B. 17
C. 19
D. 25

Solution

Calculating, a^b = 2^3 = 8 and b^a = 3^2 = 9, thus a^b + b^a = 8 + 9 = 17.

Correct Answer: B — 17

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Q. If a = 2 and b = 3, what is the value of the expression 2a^2 + 3b?

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

Solution

Substituting gives 2(2^2) + 3(3) = 8 + 9 = 17.

Correct Answer: B — 15

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Q. If a = 2 and b = 5, what is the value of (a + b)²?

A. 49
B. 25
C. 36
D. 64

Solution

(a + b)² = (2 + 5)² = 7² = 49.

Correct Answer: A — 49

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Q. If a = 2 and b = 5, what is the value of a² + 2ab + b²?

A. 49
B. 25
C. 36
D. 64

Solution

a² + 2ab + b² = 2² + 2*2*5 + 5² = 4 + 20 + 25 = 49.

Correct Answer: A — 49

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Q. If A = 2i + 2j and B = 2i + 3j, find A · B.

A. 10
B. 12
C. 8
D. 6

Solution

A · B = (2)(2) + (2)(3) = 4 + 6 = 10.

Correct Answer: A — 10

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Q. If A = 2i + 2j and B = 2i - 2j, find A · B. (2021)

A. 0
B. 4
C. 8
D. 16

Solution

A · B = (2)(2) + (2)(-2) = 4 - 4 = 0.

Correct Answer: B — 4

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Q. If A = 2i + 2j and B = 2i - 2j, what is the scalar product A · B?

A. 0
B. 8
C. 4
D. 2

Solution

A · B = (2)(2) + (2)(-2) = 4 - 4 = 0.

Correct Answer: C — 4

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Q. If A = 2i + 2j and B = 3i + 3j, what is the angle between A and B?

A. 0°
B. 45°
C. 90°
D. 60°

Solution

A · B = 2*3 + 2*3 = 12. |A| = √(2^2 + 2^2) = 2√2, |B| = √(3^2 + 3^2) = 3√2. cos(θ) = 12 / (2√2 * 3√2) = 1, θ = 0°.

Correct Answer: A — 0°

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Q. If A = 2i + 2j and B = 3i + 3j, what is the scalar product A · B?

A. 12
B. 10
C. 8
D. 6

Solution

A · B = (2)(3) + (2)(3) = 6 + 6 = 12.

Correct Answer: A — 12

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Q. If A = 2i + 2j and B = 3i + 4j, what is the angle between A and B?

A. 45 degrees
B. 60 degrees
C. 30 degrees
D. 90 degrees

Solution

cos(θ) = (A · B) / (|A||B|) = (2*3 + 2*4) / (√(2^2 + 2^2) * √(3^2 + 4^2)) = 0.5, θ = 60 degrees.

Correct Answer: B — 60 degrees

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Q. If A = 2i + 3j + k and B = i - 2j + 4k, find the scalar product A · B.

A. 10
B. 12
C. 14
D. 8

Solution

A · B = (2)(1) + (3)(-2) + (1)(4) = 2 - 6 + 4 = 0.

Correct Answer: B — 12

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Major Competitive Exams

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