Engineering & Architecture Admissions
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 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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Q. In the molecular orbital theory, which of the following orbitals is lower in energy for homonuclear diatomic molecules?
A.
σ2p
B.
π2p
C.
σ2s
D.
π2s
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Solution
The σ2s orbital is lower in energy than the π2p and σ2p orbitals in homonuclear diatomic molecules.
Correct Answer: C — σ2s
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Q. In the molecular orbital theory, which of the following orbitals is the highest occupied molecular orbital (HOMO) in O2?
A.
σ2p
B.
π2p
C.
σ*2p
D.
π*2p
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Solution
In O2, the highest occupied molecular orbital (HOMO) is π2p.
Correct Answer: B — π2p
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Q. In the molecular orbital theory, which of the following orbitals is the highest energy in O2?
A.
σ2p
B.
π2p
C.
σ*2p
D.
π*2p
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Solution
The highest energy orbital in O2 is σ*2p, which is an antibonding orbital.
Correct Answer: C — σ*2p
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Q. In the molecular orbital theory, which of the following pairs of orbitals can combine to form a sigma bond?
A.
s and p
B.
p and p
C.
s and s
D.
d and p
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Solution
s and s orbitals can combine to form a sigma bond.
Correct Answer: C — s and s
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Q. In the molecular orbital theory, which orbitals combine to form sigma bonds?
A.
s and p orbitals
B.
p and d orbitals
C.
s orbitals only
D.
p orbitals only
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Solution
Sigma bonds are formed by the head-on overlap of s and p orbitals.
Correct Answer: A — s and p orbitals
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Q. In the number 0.0004560, how many significant figures are present?
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Solution
The leading zeros are not significant, but the trailing zero is significant. Therefore, it has 4 significant figures.
Correct Answer: B — 4
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Q. In the number 0.007890, how many significant figures are there?
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Solution
The significant figures are 7, 8, 9, and the leading zeros are not counted.
Correct Answer: C — 5
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Q. In the number 2500, how many significant figures are there?
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Solution
Without a decimal point, 2500 has 2 significant figures.
Correct Answer: A — 2
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Q. In the number 5000, how many significant figures are there?
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Solution
5000 has 1 significant figure unless specified with a decimal point (e.g., 5000.).
Correct Answer: A — 1
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Q. In the photoelectric effect, if the frequency of incident light is doubled, what happens to the kinetic energy of the emitted electrons?
A.
It doubles
B.
It quadruples
C.
It remains the same
D.
It becomes zero
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Solution
The kinetic energy of the emitted electrons is given by KE = hf - φ. If the frequency is doubled, the kinetic energy increases by a factor of four, since KE is proportional to the frequency.
Correct Answer: B — It quadruples
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Q. In the photoelectric effect, increasing the intensity of light increases the:
A.
Kinetic energy of emitted electrons
B.
Number of emitted electrons
C.
Wavelength of emitted light
D.
Work function
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Solution
Increasing the intensity of light increases the number of emitted electrons, as intensity is related to the number of photons hitting the surface.
Correct Answer: B — Number of emitted electrons
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Q. In the photoelectric effect, the kinetic energy of the emitted electrons depends on which of the following?
A.
Frequency of the incident light
B.
Intensity of the incident light
C.
Wavelength of the incident light
D.
All of the above
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Solution
The kinetic energy of the emitted electrons in the photoelectric effect depends on the frequency of the incident light, as per Einstein's photoelectric equation.
Correct Answer: A — Frequency of the incident light
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