Q. If the mode of the data set 1, 2, 2, 3, 4, 4, 4, 5 is removed, what will be the new mode?
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Solution
New mode = 2 (as 4 is removed, 2 is the next most frequent).
Correct Answer: A — 2
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Q. If the mode of the data set 1, 2, 2, 3, 4, 4, 4, 5 is?
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Solution
Mode is the number that appears most frequently. Here, 4 appears 3 times.
Correct Answer: D — 4
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Q. If the mode of the data set 2, 3, 3, 5, 7, 8 is 3, what is the mode of the data set 1, 1, 2, 2, 3, 3, 3, 4?
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Solution
Mode = 3 (most frequent value).
Correct Answer: C — 3
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Q. If the mode of the data set 2, 3, 4, 4, 5, 5, 5, 6 is removed, what is the new mode?
A.
4
B.
5
C.
6
D.
No mode
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Solution
Removing 5 leaves 2, 3, 4, 4, 6. The new mode is 4.
Correct Answer: D — No mode
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Q. If the mode of the data set 2, 3, 4, 4, 5, 5, 5, 6 is?
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Solution
Mode is the value that appears most frequently. Here, 5 appears 3 times.
Correct Answer: C — 5
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Q. If the mode of the data set 3, 4, 4, 5, 6, 6, 6, 7 is removed, what is the new mode?
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Solution
Removing mode 6 leaves 3, 4, 4, 5, 7. New mode = 4.
Correct Answer: A — 4
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Q. If the mode of the data set 3, 7, 7, 2, 5, 7, 8 is x, what is the value of x?
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Solution
Mode is the most frequent value. Here, 7 appears most frequently.
Correct Answer: C — 7
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Q. If the mode of the data set {1, 2, 2, 3, 4, 4, 4, 5} is removed, what is the new mode?
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Solution
Removing mode 4 leaves {1, 2, 2, 3, 5}. New mode = 2.
Correct Answer: B — 2
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Q. If the mode of the data set {3, 5, 7, 3, 9, 3, 5} is x, what is the value of x?
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Solution
Mode is the number that appears most frequently. Here, 3 appears 3 times.
Correct Answer: A — 3
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Q. If the molar mass of a gas is doubled, how does its RMS speed change?
A.
Increases by sqrt(2)
B.
Decreases by sqrt(2)
C.
Remains the same
D.
Increases by 2
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Solution
RMS speed is inversely proportional to the square root of molar mass, so if M is doubled, v_rms decreases by sqrt(2).
Correct Answer: B — Decreases by sqrt(2)
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Q. If the molar mass of a gas is doubled, how does the RMS speed change?
A.
Increases by sqrt(2)
B.
Decreases by sqrt(2)
C.
Remains the same
D.
Increases by 2
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Solution
The RMS speed is inversely proportional to the square root of the molar mass. If M is doubled, v_rms decreases by sqrt(2).
Correct Answer: B — Decreases by sqrt(2)
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Q. If the molar mass of a gas is halved, what happens to its RMS speed?
A.
Increases by a factor of sqrt(2)
B.
Increases by a factor of 2
C.
Decreases by a factor of sqrt(2)
D.
Remains the same
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Solution
If the molar mass is halved, the RMS speed increases by a factor of sqrt(2) because RMS speed is inversely proportional to the square root of molar mass.
Correct Answer: A — Increases by a factor of sqrt(2)
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Q. If the mole fraction of a solute in a solution is 0.2, what is the mole fraction of the solvent?
A.
0.8
B.
0.2
C.
0.5
D.
0.6
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Solution
Mole fraction of solvent = 1 - mole fraction of solute = 1 - 0.2 = 0.8.
Correct Answer: A — 0.8
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Q. If the mole fraction of a solvent in a solution is 0.75, what is the vapor pressure of the solvent if its pure vapor pressure is 100 mmHg?
A.
75 mmHg
B.
100 mmHg
C.
25 mmHg
D.
50 mmHg
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Solution
According to Raoult's Law, the vapor pressure of the solvent in the solution is 0.75 * 100 mmHg = 75 mmHg.
Correct Answer: A — 75 mmHg
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Q. If the mole fraction of a solvent in a solution is 0.8, what is the mole fraction of the solute?
A.
0.2
B.
0.8
C.
0.5
D.
0.1
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Solution
The mole fraction of the solute is 1 - X_solvent = 1 - 0.8 = 0.2.
Correct Answer: A — 0.2
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Q. If the mole fraction of solute in a solution is 0.2, what is the mole fraction of the solvent?
A.
0.8
B.
0.2
C.
0.5
D.
0.6
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Solution
The mole fraction of the solvent is 1 - X_solute = 1 - 0.2 = 0.8.
Correct Answer: A — 0.8
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Q. If the moment of inertia of a body is 10 kg m², what is the angular momentum when it rotates with an angular velocity of 5 rad/s?
A.
50 kg m²/s
B.
10 kg m²/s
C.
5 kg m²/s
D.
2 kg m²/s
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Solution
Angular momentum L = Iω = 10 kg m² * 5 rad/s = 50 kg m²/s.
Correct Answer: A — 50 kg m²/s
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Q. If the moment of inertia of a body is 10 kg m², what is the rotational kinetic energy when it rotates with an angular velocity of 5 rad/s?
A.
125 J
B.
50 J
C.
100 J
D.
75 J
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Solution
Rotational kinetic energy is given by KE = 1/2 I ω² = 1/2 * 10 * 5² = 125 J.
Correct Answer: A — 125 J
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Q. If the moment of inertia of a body is 10 kg·m² and it is subjected to a torque of 20 N·m, what is the angular acceleration?
A.
2 rad/s²
B.
0.5 rad/s²
C.
5 rad/s²
D.
10 rad/s²
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Solution
Using τ = Iα, we have α = τ/I = 20 N·m / 10 kg·m² = 2 rad/s².
Correct Answer: A — 2 rad/s²
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Q. If the moment of inertia of a body is doubled, what happens to its rotational kinetic energy if the angular velocity remains constant?
A.
Doubles
B.
Halves
C.
Remains the same
D.
Quadruples
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Solution
Rotational kinetic energy is given by KE = 1/2 I ω^2. If I is doubled and ω remains constant, KE also doubles.
Correct Answer: A — Doubles
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Q. If the moment of inertia of a body is doubled, what will be the effect on its angular acceleration if the torque applied remains constant?
A.
Doubles
B.
Halves
C.
Remains the same
D.
Increases by a factor of four
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Solution
Angular acceleration α = τ/I. If I is doubled and τ remains constant, α is halved.
Correct Answer: B — Halves
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Q. If the moment of inertia of a body is doubled, what will happen to its angular momentum if the angular velocity remains constant?
A.
Doubles
B.
Halves
C.
Remains the same
D.
Quadruples
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Solution
Angular momentum L = Iω; if I is doubled and ω remains constant, L also doubles.
Correct Answer: A — Doubles
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Q. If the moment of inertia of a body is increased, what happens to its angular acceleration for a constant torque?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
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Solution
According to Newton's second law for rotation, τ = Iα, if I increases and τ is constant, α must decrease.
Correct Answer: B — Decreases
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Q. If the natural frequency of a damped oscillator is 5 rad/s and the damping ratio is 0.2, what is the damped frequency?
A.
4.8 rad/s
B.
5 rad/s
C.
5.2 rad/s
D.
5.5 rad/s
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Solution
Damped frequency (ω_d) = ω_n√(1-ζ^2) = 5√(1-0.2^2) = 5√(0.96) ≈ 4.8 rad/s.
Correct Answer: A — 4.8 rad/s
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Q. If the nth term of a sequence is given by a_n = n^2 + n, what is a_4?
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Solution
a_4 = 4^2 + 4 = 16 + 4 = 20.
Correct Answer: A — 20
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Q. If the object distance is equal to the focal length of a convex lens, what is the nature of the image formed?
A.
Real and inverted
B.
Virtual and upright
C.
At infinity
D.
No image formed
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Solution
When the object distance equals the focal length, the image is formed at infinity.
Correct Answer: C — At infinity
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Q. If the object distance is equal to the focal length of a convex lens, what type of image is formed?
A.
Real and inverted
B.
Virtual and upright
C.
At infinity
D.
No image formed
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Solution
When the object is at the focal length, the image is formed at infinity.
Correct Answer: C — At infinity
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Q. If the odds in favor of an event are 3:2, what is the probability of the event occurring?
A.
0.6
B.
0.4
C.
0.5
D.
0.3
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Solution
Probability = Odds in favor / (Total odds) = 3 / (3 + 2) = 3/5 = 0.6.
Correct Answer: A — 0.6
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Q. If the osmotic pressure of a solution is 3.0 atm at 25 °C, what is the molarity of the solution? (R = 0.0821 L atm/(K mol))
A.
0.12 M
B.
0.15 M
C.
0.18 M
D.
0.20 M
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Solution
Molarity = π / (RT) = 3.0 / (0.0821 * 298) = 0.12 M
Correct Answer: C — 0.18 M
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Q. If the osmotic pressure of a solution is 3.0 atm, what is the molarity of the solution? (R = 0.0821 L atm/(K mol), T = 298 K)
A.
0.12 M
B.
0.15 M
C.
0.10 M
D.
0.20 M
Show solution
Solution
Molarity = π / (RT) = 3.0 / (0.0821 * 298) = 0.12 M
Correct Answer: B — 0.15 M
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