Q. Which of the following functions is even?
A.
f(x) = x^3
B.
f(x) = x^2
C.
f(x) = x + 1
D.
f(x) = sin(x)
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Solution
A function is even if f(-x) = f(x). Here, f(x) = x^2 is even.
Correct Answer: B — f(x) = x^2
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Q. Which of the following functions is not a polynomial function?
A.
f(x) = x^2 + 3x + 1
B.
g(x) = 2x^3 - 4
C.
h(x) = sqrt(x)
D.
k(x) = 5
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Solution
h(x) = sqrt(x) is not a polynomial function.
Correct Answer: C — h(x) = sqrt(x)
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Q. Which of the following functions is not a polynomial?
A.
f(x) = x^3 + 2x^2 - 5
B.
g(x) = 1/x
C.
h(x) = 4x - 7
D.
k(x) = 2
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Solution
g(x) = 1/x is not a polynomial because it has a negative exponent.
Correct Answer: B — g(x) = 1/x
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Q. Which of the following functions is not continuous at x = 0?
A.
f(x) = x^3
B.
f(x) = e^x
C.
f(x) = 1/x
D.
f(x) = ln(x)
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Solution
The function f(x) = 1/x is not defined at x = 0, hence it is not continuous there.
Correct Answer: C — f(x) = 1/x
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Q. Which of the following functions is not continuous at x = 1?
A.
f(x) = x^2
B.
f(x) = 1/x
C.
f(x) = sin(x)
D.
f(x) = { x, x < 1; 2, x >= 1 }
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Solution
The function has a jump discontinuity at x = 1, hence it is not continuous.
Correct Answer: D — f(x) = { x, x < 1; 2, x >= 1 }
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Q. Which of the following functions is not continuous?
A.
f(x) = x^2
B.
f(x) = 1/x
C.
f(x) = sin(x)
D.
f(x) = e^x
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Solution
f(x) = 1/x is not continuous at x = 0.
Correct Answer: B — f(x) = 1/x
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Q. Which of the following functions is not differentiable at x = 0? f(x) = x^2 sin(1/x) for x ≠ 0 and f(0) = 0.
A.
f(x)
B.
g(x) =
C.
x
D.
.
h(x) = x^3
.
k(x) = x^2
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Solution
The function f(x) is not differentiable at x = 0 due to the oscillatory nature of sin(1/x) as x approaches 0.
Correct Answer: A — f(x)
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Q. Which of the following functions is periodic?
A.
f(x) = x
B.
f(x) = cos(x)
C.
f(x) = e^x
D.
f(x) = ln(x)
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Solution
The cosine function is periodic with a period of 2π.
Correct Answer: B — f(x) = cos(x)
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Q. Which of the following gases behaves most ideally under standard conditions?
A.
NH3
B.
CO2
C.
He
D.
H2O
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Solution
Helium (He) behaves most ideally under standard conditions due to its low intermolecular forces.
Correct Answer: C — He
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Q. Which of the following gases behaves most like an ideal gas? (2023)
A.
Helium
B.
Carbon dioxide
C.
Water vapor
D.
Ammonia
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Solution
Helium behaves most like an ideal gas due to its low intermolecular forces and small size, making it closer to the ideal gas behavior.
Correct Answer: A — Helium
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Q. Which of the following gases has the highest density at STP?
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Solution
CO2 has the highest density at STP among the given gases.
Correct Answer: D — CO2
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Q. Which of the following gases has the highest rate of diffusion at the same temperature?
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Solution
According to Graham's law, lighter gases diffuse faster; H2 has the lowest molar mass.
Correct Answer: D — H2
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Q. Which of the following gases has the highest RMS speed at the same temperature?
A.
Oxygen (O2)
B.
Nitrogen (N2)
C.
Hydrogen (H2)
D.
Carbon Dioxide (CO2)
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Solution
RMS speed is inversely proportional to the square root of molar mass. Hydrogen (H2) has the lowest molar mass among the options, thus it has the highest RMS speed.
Correct Answer: C — Hydrogen (H2)
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Q. Which of the following gases is most likely to behave ideally?
A.
NH3
B.
H2O
C.
He
D.
CO2
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Solution
Helium (He) behaves most ideally due to its small size and weak intermolecular forces.
Correct Answer: C — He
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Q. Which of the following gases is most soluble in water?
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Solution
CO2 is more soluble in water compared to O2, N2, and H2 due to its ability to form carbonic acid.
Correct Answer: C — CO2
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Q. Which of the following gases is primarily responsible for the greenhouse effect?
A.
Ozone
B.
Carbon Dioxide
C.
Nitrogen
D.
Methane
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Solution
Carbon Dioxide is a major greenhouse gas that traps heat in the atmosphere, contributing to global warming.
Correct Answer: B — Carbon Dioxide
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Q. Which of the following gases is produced when aluminum reacts with hydrochloric acid?
A.
Hydrogen
B.
Oxygen
C.
Chlorine
D.
Nitrogen
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Solution
Hydrogen gas is produced when aluminum reacts with hydrochloric acid.
Correct Answer: A — Hydrogen
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Q. Which of the following gases will diffuse the fastest under identical conditions?
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Solution
According to Graham's law of effusion, lighter gases diffuse faster; hence, He will diffuse the fastest.
Correct Answer: A — He
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Q. Which of the following gases will have the highest average speed at the same temperature?
A.
Oxygen (O2)
B.
Nitrogen (N2)
C.
Hydrogen (H2)
D.
Carbon Dioxide (CO2)
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Solution
Hydrogen (H2) has the lowest molar mass, thus it will have the highest average speed according to the kinetic theory.
Correct Answer: C — Hydrogen (H2)
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Q. Which of the following gases will have the highest rate of diffusion at a given temperature?
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Solution
According to Graham's law of effusion, lighter gases diffuse faster; H2 has the lowest molar mass and will diffuse the fastest.
Correct Answer: D — H2
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Q. Which of the following gases will have the highest rate of diffusion at the same temperature?
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Solution
According to Graham's law, lighter gases diffuse faster. H2 has the lowest molar mass.
Correct Answer: D — H2
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Q. Which of the following gases will have the highest RMS speed at the same temperature?
A.
Oxygen (M = 32 g/mol)
B.
Nitrogen (M = 28 g/mol)
C.
Hydrogen (M = 2 g/mol)
D.
Carbon Dioxide (M = 44 g/mol)
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Solution
RMS speed is inversely proportional to the square root of molar mass. Hydrogen has the lowest molar mass, hence it will have the highest RMS speed.
Correct Answer: C — Hydrogen (M = 2 g/mol)
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Q. Which of the following gases will have the highest root mean square speed at the same temperature?
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Solution
The root mean square speed is inversely proportional to the square root of the molar mass. H2 has the lowest molar mass, hence it has the highest root mean square speed.
Correct Answer: C — H2
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Q. Which of the following gases would have the highest average speed at a given temperature?
A.
Oxygen (O2)
B.
Nitrogen (N2)
C.
Hydrogen (H2)
D.
Carbon Dioxide (CO2)
Show solution
Solution
At a given temperature, lighter gases like hydrogen (H2) have higher average speeds compared to heavier gases like oxygen (O2) or carbon dioxide (CO2).
Correct Answer: C — Hydrogen (H2)
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Q. Which of the following gases would have the highest average speed at the same temperature? (2020)
A.
Oxygen (O2)
B.
Nitrogen (N2)
C.
Hydrogen (H2)
D.
Carbon Dioxide (CO2)
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Solution
At the same temperature, lighter gases have higher average speeds. Hydrogen (H2) has the lowest molar mass and thus the highest average speed.
Correct Answer: C — Hydrogen (H2)
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Q. Which of the following gases would have the highest rate of diffusion at a given temperature?
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Solution
Hydrogen (H2) has the lowest molar mass and thus the highest rate of diffusion according to Graham's law.
Correct Answer: D — H2
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Q. Which of the following gases would have the highest root mean square speed at the same temperature?
A.
Oxygen (O2)
B.
Nitrogen (N2)
C.
Hydrogen (H2)
D.
Carbon Dioxide (CO2)
Show solution
Solution
Hydrogen (H2) has the lowest molar mass among the given gases, thus it will have the highest root mean square speed at the same temperature, as v_rms is inversely proportional to the square root of molar mass.
Correct Answer: C — Hydrogen (H2)
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Q. Which of the following gates is a universal gate?
A.
AND
B.
OR
C.
NAND
D.
XOR
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Solution
The NAND gate is a universal gate because it can be used to create any other gate.
Correct Answer: C — NAND
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Q. Which of the following gates is considered a universal gate?
A.
AND Gate
B.
OR Gate
C.
NAND Gate
D.
XOR Gate
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Solution
The NAND gate is considered a universal gate because it can be used to create any other gate.
Correct Answer: C — NAND Gate
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Q. Which of the following gates is equivalent to an AND gate followed by a NOT gate?
A.
OR
B.
NAND
C.
NOR
D.
XOR
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Solution
The output of an AND gate followed by a NOT gate is a NAND gate.
Correct Answer: B — NAND
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