Major Competitive Exams
Q. In the expansion of (2x - 3)^5, what is the coefficient of x^1?
A.
-15
B.
-30
C.
30
D.
15
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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?
A.
-90
B.
-120
C.
-150
D.
-180
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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?
A.
-540
B.
-720
C.
-960
D.
-1080
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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?
A.
-90
B.
-120
C.
-150
D.
-180
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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?
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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?
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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?
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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?
A.
240
B.
360
C.
720
D.
480
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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?
A.
672
B.
6720
C.
67200
D.
672000
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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?
A.
150
B.
200
C.
250
D.
300
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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?
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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?
A.
-2240
B.
-1280
C.
-1120
D.
-960
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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 expression 0.00450 + 0.0034, how many significant figures should the result have?
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Solution
The result should have 3 significant figures, as 0.0034 has the least precision.
Correct Answer: B — 4
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Q. In the Freundlich adsorption isotherm, which parameter indicates the extent of adsorption?
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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?
A.
Pressure
B.
Volume
C.
Number of moles
D.
Temperature
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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:
A.
Gravitational force
B.
Molecular collisions with the walls
C.
Temperature of the gas
D.
Volume of the gas
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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:
A.
A gas that obeys the ideal gas law at all conditions
B.
A gas with no intermolecular forces
C.
A gas that has a constant volume
D.
A gas that can be liquefied easily
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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:
A.
The average distance traveled by a molecule between collisions
B.
The average speed of gas molecules
C.
The average time between collisions
D.
The average distance of the gas from the walls of the container
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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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Q. In the kinetic theory of gases, what does the term 'ideal gas' refer to?
A.
A gas that obeys the ideal gas law at all conditions.
B.
A gas with no intermolecular forces.
C.
A gas that has a fixed volume.
D.
A gas that can be liquefied easily.
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Solution
An ideal gas is defined as a gas that has no intermolecular forces and occupies no volume, allowing it to perfectly obey the ideal gas law under all conditions.
Correct Answer: B — A gas with no intermolecular forces.
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Q. In the kinetic theory of gases, which of the following quantities is directly proportional to the square of the speed of gas molecules?
A.
Pressure
B.
Volume
C.
Temperature
D.
Density
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Solution
According to the kinetic theory, pressure is directly proportional to the average kinetic energy of the gas molecules, which is proportional to the square of their speed.
Correct Answer: A — Pressure
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Q. In the Langmuir adsorption isotherm, what assumption is made about the adsorption sites?
A.
They are identical and have the same energy
B.
They are different and have varying energy
C.
They can accommodate multiple layers
D.
They are not limited in number
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Solution
The Langmuir isotherm assumes that all adsorption sites are identical and have the same energy.
Correct Answer: A — They are identical and have the same energy
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Q. In the Langmuir adsorption isotherm, what does the term 'b' represent?
A.
Adsorption energy
B.
Surface area
C.
Equilibrium constant
D.
Adsorption capacity
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Solution
'b' in the Langmuir isotherm represents the equilibrium constant related to the adsorption process.
Correct Answer: C — Equilibrium constant
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Q. In the measurement 0.007890, how many significant figures are present?
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Solution
The significant figures are 7, 8, 9, and 0, totaling 4 significant figures.
Correct Answer: C — 5
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Q. In the measurement 0.03040, how many significant figures are present?
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Solution
In 0.03040, the leading zeros do not count, but the trailing zero after the decimal does. Therefore, there are 4 significant figures.
Correct Answer: B — 4
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Q. In the measurement 123.45, how many significant figures are present?
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Solution
All digits in 123.45 are significant, giving a total of 5 significant figures.
Correct Answer: C — 5
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Q. In the measurement 150.0, how many significant figures are present?
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Solution
The significant figures are 1, 5, and the trailing zero after the decimal point.
Correct Answer: C — 4
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Q. In the measurement 2500 kg, how many significant figures are there?
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Solution
The number 2500 kg has two significant figures unless specified otherwise (e.g., with a decimal point).
Correct Answer: A — 2
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Q. In the molecular orbital diagram of diatomic nitrogen (N2), which orbitals are filled first?
A.
σ2s, σ*2s
B.
σ2p, π2p
C.
π2p, σ2p
D.
σ*2p, π*2p
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Solution
In N2, the 2s orbitals (σ2s and σ*2s) are filled before the 2p orbitals.
Correct Answer: A — σ2s, σ*2s
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Q. In the molecular orbital theory, which of the following is true for the π molecular orbitals?
A.
They are formed by end-to-end overlap.
B.
They are lower in energy than σ orbitals.
C.
They can accommodate a maximum of 2 electrons.
D.
They are always bonding.
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Solution
π molecular orbitals can accommodate a maximum of 2 electrons, similar to all molecular orbitals.
Correct Answer: C — They can accommodate a maximum of 2 electrons.
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Q. In the molecular orbital theory, which of the following orbitals is lower in energy than the 2p orbitals?
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Solution
The 2s molecular orbitals are lower in energy than the 2p molecular orbitals.
Correct Answer: A — 2s
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