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Q. In the context of the Biot-Savart Law, what does the symbol μ₀ represent?
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A.
Electric permittivity
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B.
Magnetic permeability of free space
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C.
Magnetic field strength
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D.
Electric field strength
Solution
The symbol μ₀ represents the magnetic permeability of free space, which is a constant used in the Biot-Savart Law.
Correct Answer: B — Magnetic permeability of free space
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Q. In the context of the Biot-Savart Law, what does the term 'current element' refer to?
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A.
A small segment of wire carrying current
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B.
The total current in the wire
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C.
The direction of current flow
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D.
The magnetic field produced by the current
Solution
A 'current element' refers to a small segment of wire carrying current, which contributes to the overall magnetic field.
Correct Answer: A — A small segment of wire carrying current
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Q. In the equilibrium constant expression Kc, what is the unit for Kc if the reaction is A(g) + B(g) ⇌ C(g)?
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A.
mol/L
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B.
L/mol
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C.
dimensionless
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D.
mol^2/L^2
Solution
The equilibrium constant Kc is dimensionless because it is a ratio of concentrations raised to their stoichiometric coefficients.
Correct Answer: C — dimensionless
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Q. In the equilibrium reaction 2SO2(g) + O2(g) ⇌ 2SO3(g), what happens if SO3 is removed?
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A.
Shift to the right
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B.
Shift to the left
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C.
No change
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D.
Increase in pressure
Solution
Removing SO3 will shift the equilibrium to the right to produce more SO3.
Correct Answer: A — Shift to the right
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Q. In the expansion of (1 + x)^10, what is the coefficient of x^5?
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A.
252
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B.
210
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C.
120
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D.
300
Solution
The coefficient of x^5 is C(10,5) = 10! / (5!5!) = 252.
Correct Answer: A — 252
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Q. In the expansion of (2 + 3x)^4, what is the coefficient of x?
Solution
The coefficient of x is C(4,1) * 2^3 * 3 = 4 * 8 * 3 = 96.
Correct Answer: A — 12
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Q. In the expansion of (2 + 3x)^4, what is the coefficient of x^2?
Solution
The coefficient of x^2 is C(4,2) * (2)^2 * (3)^2 = 6 * 4 * 9 = 216.
Correct Answer: B — 54
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Q. In the expansion of (2x + 3)^4, what is the coefficient of x^1?
Solution
The coefficient of x^1 is C(4,1) * (2)^1 * (3)^3 = 4 * 2 * 27 = 216.
Correct Answer: B — 48
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Q. In the expansion of (2x + 3)^4, what is the coefficient of x^2?
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A.
108
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B.
72
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C.
36
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D.
144
Solution
The coefficient of x^2 is C(4,2) * (2)^2 * (3)^2 = 6 * 4 * 9 = 216.
Correct Answer: B — 72
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Q. In the expansion of (2x + 3)^6, what is the coefficient of x^4?
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A.
540
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B.
720
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C.
810
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D.
900
Solution
The coefficient of x^4 is C(6,4) * (2)^4 * (3)^2 = 15 * 16 * 9 = 2160.
Correct Answer: B — 720
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Q. In the expansion of (2x + 3y)^4, what is the coefficient of x^2y^2?
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A.
108
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B.
72
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C.
36
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D.
144
Solution
The coefficient is C(4,2) * (2)^2 * (3)^2 = 6 * 4 * 9 = 216.
Correct Answer: A — 108
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Q. In the expansion of (2x + 5)^4, what is the coefficient of x^2?
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A.
300
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B.
600
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C.
450
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D.
500
Solution
The coefficient of x^2 is C(4,2) * (2)^2 * (5)^2 = 6 * 4 * 25 = 600.
Correct Answer: A — 300
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Q. In the expansion of (2x - 3)^3, what is the coefficient of x?
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A.
-9
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B.
-18
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C.
-27
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D.
-6
Solution
The coefficient of x is C(3,1) * (2)^1 * (-3)^2 = 3 * 2 * 9 = -54.
Correct Answer: B — -18
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Q. In the expansion of (2x - 3)^5, what is the coefficient of x^1?
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A.
-15
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B.
-30
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C.
30
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D.
15
Solution
The coefficient of x^1 is C(5,1) * (2)^1 * (-3)^4 = 5 * 2 * 81 = 810.
Correct Answer: B — -30
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Q. In the expansion of (2x - 3)^5, what is the coefficient of x^2?
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A.
-90
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B.
-120
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C.
-150
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D.
-180
Solution
The coefficient of x^2 is C(5,2) * (2)^2 * (-3)^3 = 10 * 4 * (-27) = -1080.
Correct Answer: B — -120
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Q. In the expansion of (2x - 3)^5, what is the coefficient of x^3?
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A.
-540
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B.
-720
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C.
-960
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D.
-1080
Solution
The coefficient of x^3 is C(5,3) * (2)^3 * (-3)^2 = 10 * 8 * 9 = -720.
Correct Answer: C — -960
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Q. In the expansion of (2x - 3)^5, what is the coefficient of x^4?
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A.
-90
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B.
-120
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C.
-150
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D.
-180
Solution
The coefficient of x^4 is C(5,4) * (2)^4 * (-3)^1 = 5 * 16 * (-3) = -240.
Correct Answer: B — -120
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Q. In the expansion of (x + 1/x)^6, what is the coefficient of x^0?
Solution
The coefficient of x^0 in (x + 1/x)^6 is given by 6C3 = 20.
Correct Answer: C — 20
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Q. In the expansion of (x + 1/x)^8, what is the coefficient of x^4?
Solution
The coefficient of x^4 is C(8,4) = 70.
Correct Answer: B — 56
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Q. In the expansion of (x + 2)^5, what is the coefficient of x^3?
Solution
The coefficient of x^3 is C(5,3) * (2)^2 = 10 * 4 = 40.
Correct Answer: B — 60
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Q. In the expansion of (x + 2)^6, what is the term containing x^4?
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A.
240
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B.
360
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C.
720
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D.
480
Solution
The term containing x^4 is C(6,4) * (2)^2 * (x)^4 = 15 * 4 * x^4 = 60x^4.
Correct Answer: C — 720
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Q. In the expansion of (x + 2)^7, what is the term containing x^5?
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A.
672
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B.
6720
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C.
67200
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D.
672000
Solution
The term containing x^5 is given by 7C5 * (2)^2 * (x)^5 = 21 * 4 * x^5 = 84x^5. Thus, the term is 84x^5.
Correct Answer: B — 6720
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Q. In the expansion of (x + 5)^6, what is the coefficient of x^3?
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A.
150
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B.
200
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C.
250
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D.
300
Solution
The coefficient of x^3 is C(6, 3) * 5^3 = 20 * 125 = 250.
Correct Answer: B — 200
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Q. In the expansion of (x - 2)^6, what is the coefficient of x^4?
Solution
The coefficient of x^4 is given by C(6,4) * (-2)^2 = 15 * 4 = 60.
Correct Answer: C — 90
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Q. In the expansion of (x - 2)^8, what is the coefficient of x^5?
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A.
-2240
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B.
-1280
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C.
-1120
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D.
-960
Solution
The coefficient of x^5 is C(8,5) * (-2)^3 = 56 * (-8) = -448.
Correct Answer: A — -2240
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Q. In the Freundlich adsorption isotherm, which parameter indicates the extent of adsorption?
Solution
In the Freundlich isotherm, K is the adsorption coefficient that indicates the extent of adsorption.
Correct Answer: A — K
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Q. In the ideal gas equation PV=nRT, what does 'n' represent?
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A.
Pressure
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B.
Volume
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C.
Number of moles
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D.
Temperature
Solution
'n' represents the number of moles of the gas in the ideal gas equation.
Correct Answer: C — Number of moles
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Q. In the kinetic theory of gases, the pressure exerted by a gas is due to:
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A.
Gravitational force
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B.
Molecular collisions with the walls
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C.
Temperature of the gas
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D.
Volume of the gas
Solution
The pressure exerted by a gas is due to the collisions of gas molecules with the walls of the container.
Correct Answer: B — Molecular collisions with the walls
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Q. In the kinetic theory of gases, the term 'ideal gas' refers to:
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A.
A gas that obeys the ideal gas law at all conditions
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B.
A gas with no intermolecular forces
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C.
A gas that has a constant volume
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D.
A gas that can be liquefied easily
Solution
An ideal gas is a theoretical gas that perfectly follows the ideal gas law and has no intermolecular forces, behaving ideally under all conditions.
Correct Answer: B — A gas with no intermolecular forces
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Q. In the kinetic theory of gases, the term 'mean free path' refers to:
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A.
The average distance traveled by a molecule between collisions
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B.
The average speed of gas molecules
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C.
The average time between collisions
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D.
The average distance of the gas from the walls of the container
Solution
The mean free path is defined as the average distance a molecule travels before colliding with another molecule.
Correct Answer: A — The average distance traveled by a molecule between collisions
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