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Q. What is the charge of one coulomb equivalent to in terms of electric current and time? (2022)

A. 1 A for 1 s
B. 1 A for 2 s
C. 2 A for 1 s
D. 0.5 A for 1 s

Solution

1 coulomb is the charge that passes through a conductor when a current of 1 ampere flows for 1 second.

Correct Answer: A — 1 A for 1 s

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Q. What is the charge of one coulomb equivalent to in terms of electrons? (2022)

A. 6.25 x 10^18 electrons
B. 1.6 x 10^-19 electrons
C. 3.2 x 10^-19 electrons
D. 1.0 x 10^18 electrons

Solution

One coulomb is equivalent to approximately 6.25 x 10^18 electrons.

Correct Answer: A — 6.25 x 10^18 electrons

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Q. What is the charge of one coulomb in terms of the number of electrons? (2023)

A. 6.25 x 10^18 electrons
B. 1.6 x 10^-19 electrons
C. 3.2 x 10^-19 electrons
D. 1.0 x 10^18 electrons

Solution

One coulomb is equivalent to approximately 6.25 x 10^18 electrons.

Correct Answer: A — 6.25 x 10^18 electrons

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Q. What is the chemical formula for sodium chloride? (2023) 2023

A. NaCl
B. Na2Cl
C. NaCl2
D. Na2Cl2

Solution

The chemical formula for sodium chloride is NaCl.

Correct Answer: A — NaCl

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Q. What is the chemical formula for table salt? (2019)

A. NaCl
B. KCl
C. CaCl2
D. MgCl2

Solution

Table salt is chemically known as sodium chloride, which has the formula NaCl.

Correct Answer: A — NaCl

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Q. What is the chemical formula for the compound formed between strontium and chlorine? (2019)

A. SrCl
B. SrCl2
C. Sr2Cl
D. Sr2Cl3

Solution

Strontium forms a compound with chlorine as SrCl2, where strontium has a +2 charge and chlorine has a -1 charge.

Correct Answer: B — SrCl2

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Q. What is the coefficient of x^0 in the expansion of (2x - 3)^5? (2022)

A. -243
B. 243
C. -81
D. 81

Solution

The constant term is C(5,5)(-3)^5 = -243.

Correct Answer: A — -243

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Q. What is the coefficient of x^0 in the expansion of (3x + 2)^5? (2022)

A. 32
B. 48
C. 64
D. 80

Solution

The coefficient of x^0 is C(5,5) * (3x)^0 * (2)^5 = 1 * 32 = 32.

Correct Answer: C — 64

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Q. What is the coefficient of x^0 in the expansion of (x + 1/x)^8? (2021)

A. 28
B. 56
C. 70
D. 84

Solution

The coefficient of x^0 occurs when k=4, which gives us 8C4 = 70.

Correct Answer: C — 70

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Q. What is the coefficient of x^1 in the expansion of (x + 1)^10? (2021)

A. 10
B. 90
C. 100
D. 1

Solution

The coefficient of x^1 is C(10,1)(1)^9 = 10.

Correct Answer: A — 10

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Q. What is the coefficient of x^1 in the expansion of (x + 5)^6?

A. 30
B. 60
C. 90
D. 120

Solution

The coefficient of x^1 is C(6,1) * 5^5 = 6 * 3125 = 18750.

Correct Answer: C — 90

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Q. What is the coefficient of x^1 in the expansion of (x - 1)^5?

A. -5
B. 5
C. 10
D. 15

Solution

The coefficient of x^1 is given by 5C1 * (-1)^4 = 5 * 1 = 5.

Correct Answer: A — -5

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Q. What is the coefficient of x^2 in the expansion of (2x + 1)^6?

A. 15
B. 30
C. 45
D. 60

Solution

The coefficient of x^2 is C(6,2) * (2)^2 * (1)^4 = 15 * 4 = 60.

Correct Answer: B — 30

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Q. What is the coefficient of x^2 in the expansion of (2x - 1)^5? (2021)

A. 10
B. 20
C. 30
D. 40

Solution

The coefficient of x^2 is C(5,2) * (2)^2 * (-1)^3 = 10 * 4 * (-1) = -40.

Correct Answer: B — 20

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Q. What is the coefficient of x^2 in the expansion of (3x - 4)^6?

A. 540
B. 720
C. 1080
D. 1440

Solution

The coefficient of x^2 is C(6,2) * (3)^2 * (-4)^(6-2) = 15 * 9 * 256 = 34560.

Correct Answer: C — 1080

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Q. What is the coefficient of x^2 in the expansion of (x + 1/2)^8?

A. 28
B. 56
C. 70
D. 84

Solution

The coefficient of x^2 is C(8,2) * (1/2)^2 = 28 * 1/4 = 7.

Correct Answer: C — 70

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Q. What is the coefficient of x^2 in the expansion of (x + 3)^5?

A. 45
B. 60
C. 75
D. 90

Solution

The coefficient of x^2 is given by 5C2 * (3)^3 = 10 * 27 = 270.

Correct Answer: A — 45

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Q. What is the coefficient of x^2 in the expansion of (x + 4)^5?

A. 80
B. 100
C. 120
D. 160

Solution

The coefficient of x^2 is C(5,2) * 4^3 = 10 * 64 = 640.

Correct Answer: A — 80

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Q. What is the coefficient of x^2 in the expansion of (x + 5)^4?

A. 50
B. 100
C. 150
D. 200

Solution

The coefficient of x^2 is C(4,2) * (5)^2 = 6 * 25 = 150.

Correct Answer: B — 100

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Q. What is the coefficient of x^2 in the expansion of (x + 5)^7? (2021)

A. 21
B. 35
C. 105
D. 175

Solution

The coefficient of x^2 is given by 7C2 * 5^5 = 21 * 3125 = 65625.

Correct Answer: B — 35

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Q. What is the coefficient of x^2 in the expansion of (x - 1)^5?

A. -10
B. -5
C. 5
D. 10

Solution

The coefficient of x^2 is C(5,2) * (-1)^3 = 10 * (-1) = -10.

Correct Answer: A — -10

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Q. What is the coefficient of x^2 in the expansion of (x - 2)^5?

A. -40
B. -20
C. 20
D. 40

Solution

The coefficient of x^2 is given by 5C2 * (-2)^3 = 10 * (-8) = -80.

Correct Answer: A — -40

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Q. What is the coefficient of x^3 in the expansion of (5x + 2)^6? (2000) 2000

A. 600
B. 720
C. 800
D. 900

Solution

The coefficient of x^3 is C(6,3) * (5)^3 * (2)^3 = 20 * 125 * 8 = 20000.

Correct Answer: B — 720

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Q. What is the coefficient of x^3 in the expansion of (x + 5)^8?

A. 2800
B. 3360
C. 4000
D. 4200

Solution

The coefficient of x^3 is given by 8C3 * (5)^5 = 56 * 3125 = 175000.

Correct Answer: B — 3360

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Q. What is the coefficient of x^3 in the expansion of (x - 1)^5? (2022)

A. -10
B. 10
C. 5
D. 15

Solution

The coefficient of x^3 is C(5,3)(-1)^2 = 10.

Correct Answer: A — -10

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Q. What is the coefficient of x^3 in the expansion of (x - 2)^5?

A. 10
B. 20
C. 30
D. 40

Solution

The coefficient of x^3 is C(5,3) * (-2)^2 = 10 * 4 = 40.

Correct Answer: A — 10

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Q. What is the coefficient of x^3 in the expansion of (x - 2)^6?

A. -80
B. -120
C. -240
D. -720

Solution

The coefficient of x^3 is C(6,3) * (-2)^3 = 20 * (-8) = -160.

Correct Answer: B — -120

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Q. What is the coefficient of x^4 in the expansion of (2x + 5)^6? (2022)

A. 150
B. 300
C. 600
D. 450

Solution

The coefficient of x^4 is C(6,4) * (2)^4 * (5)^2 = 15 * 16 * 25 = 600.

Correct Answer: D — 450

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Q. What is the coefficient of x^4 in the expansion of (3x + 2)^6?

A. 540
B. 720
C. 810
D. 900

Solution

The coefficient of x^4 is C(6,4) * (3)^4 * (2)^2 = 15 * 81 * 4 = 4860.

Correct Answer: B — 720

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Q. What is the coefficient of x^4 in the expansion of (3x - 2)^5? (2021)

A. 90
B. 120
C. 150
D. 180

Solution

The coefficient of x^4 is given by 5C4 * (3)^4 * (-2)^1 = 5 * 81 * (-2) = -810.

Correct Answer: C — 150

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