Q. In a binary solution of A and B, if the vapor pressure of pure A is 80 mmHg and that of pure B is 40 mmHg, what is the vapor pressure of the solution if the mole fraction of A is 0.6?
A.
64 mmHg
B.
72 mmHg
C.
80 mmHg
D.
56 mmHg
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Solution
Using Raoult's Law, the vapor pressure of the solution = (0.6 * 80 mmHg) + (0.4 * 40 mmHg) = 64 mmHg.
Correct Answer: B — 72 mmHg
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Q. In a binary solution of A and B, if the vapor pressure of pure A is 80 mmHg and pure B is 40 mmHg, what is the vapor pressure of the solution if the mole fraction of A is 0.6?
A.
64 mmHg
B.
72 mmHg
C.
80 mmHg
D.
56 mmHg
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Solution
Using Raoult's Law, the vapor pressure of the solution = (0.6 * 80 mmHg) + (0.4 * 40 mmHg) = 64 mmHg.
Correct Answer: B — 72 mmHg
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Q. In a binary solution of A and B, if the vapor pressure of pure A is 80 mmHg and pure B is 40 mmHg, what is the vapor pressure of component A if the mole fraction of A is 0.6?
A.
48 mmHg
B.
64 mmHg
C.
80 mmHg
D.
32 mmHg
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Solution
Using Raoult's Law, the vapor pressure of A in the solution is 0.6 * 80 mmHg = 48 mmHg.
Correct Answer: B — 64 mmHg
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Q. In a binary solution of A and B, if the vapor pressure of pure A is 80 mmHg and pure B is 40 mmHg, what is the total vapor pressure when the mole fraction of A is 0.5?
A.
60 mmHg
B.
70 mmHg
C.
80 mmHg
D.
50 mmHg
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Solution
Total vapor pressure = P_A + P_B = (0.5 * 80) + (0.5 * 40) = 40 + 20 = 60 mmHg.
Correct Answer: B — 70 mmHg
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Q. In a binary solution of A and B, if the vapor pressure of pure A is 80 mmHg and that of pure B is 40 mmHg, what is the total vapor pressure when the mole fraction of A is 0.6?
A.
64 mmHg
B.
72 mmHg
C.
80 mmHg
D.
88 mmHg
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Solution
Using Raoult's Law, the total vapor pressure = (0.6 * 80 mmHg) + (0.4 * 40 mmHg) = 48 mmHg + 16 mmHg = 64 mmHg.
Correct Answer: B — 72 mmHg
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Q. In a body-centered cubic (BCC) structure, how many atoms are there in one unit cell? (2022)
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Solution
In a body-centered cubic (BCC) structure, there are 2 atoms per unit cell (1 from the center and 1 from the corners).
Correct Answer: B — 2
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Q. In a box of 10 balls, 4 are red and 6 are blue. What is the probability of picking a red ball?
A.
0.4
B.
0.5
C.
0.6
D.
0.7
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Solution
Probability = Number of red balls / Total balls = 4/10 = 0.4.
Correct Answer: A — 0.4
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Q. In a box of 100 balls, 30 are red, 50 are blue, and 20 are green. What is the probability of picking a red ball?
A.
0.3
B.
0.5
C.
0.2
D.
0.1
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Solution
Probability = Number of red balls / Total balls = 30/100 = 0.3.
Correct Answer: A — 0.3
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Q. In a box, there are 5 white and 3 black balls. If a ball is drawn and it is black, what is the probability that the next ball drawn is white?
A.
0.625
B.
0.5
C.
0.375
D.
0.25
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Solution
After drawing a black ball, there are 5 white and 2 black balls left. The probability of drawing a white ball next is 5/(5+2) = 5/7 ≈ 0.625.
Correct Answer: A — 0.625
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Q. In a buffer solution, which component resists changes in pH? (2020)
A.
Strong acid
B.
Weak acid and its salt
C.
Strong base
D.
Water
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Solution
A buffer solution typically consists of a weak acid and its conjugate base (salt), which helps to resist changes in pH when small amounts of acid or base are added.
Correct Answer: B — Weak acid and its salt
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Q. In a buffer solution, which of the following components is essential? (2023)
A.
Strong acid
B.
Weak acid and its salt
C.
Strong base
D.
Water
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Solution
A buffer solution is made from a weak acid and its conjugate base (salt), which helps maintain pH.
Correct Answer: B — Weak acid and its salt
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Q. In a capacitor, if the charge is doubled while the voltage remains constant, what happens to the capacitance? (2019)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
Capacitance (C) is defined as C = Q/V. If the charge (Q) is doubled while the voltage (V) remains constant, the capacitance also doubles.
Correct Answer: A — It doubles
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Q. In a capacitor, if the plate area is increased while keeping the distance constant, what happens to the capacitance? (2023)
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
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Solution
Increasing the plate area while keeping the distance constant increases the capacitance, as capacitance is directly proportional to the area of the plates.
Correct Answer: A — Increases
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Q. In a capacitor, if the plate area is increased while keeping the separation constant, what happens to the capacitance?
A.
It increases
B.
It decreases
C.
It remains the same
D.
It becomes zero
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Solution
Capacitance is directly proportional to the plate area A. Increasing A increases capacitance.
Correct Answer: A — It increases
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Q. In a capacitor, what does the dielectric constant represent?
A.
The ability to store charge
B.
The ability to resist electric field
C.
The ability to increase capacitance
D.
The ability to conduct electricity
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Solution
The dielectric constant represents the ability of a material to increase the capacitance of a capacitor compared to a vacuum.
Correct Answer: C — The ability to increase capacitance
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Q. In a capacitor, what is the relationship between charge (Q), capacitance (C), and voltage (V)?
A.
Q = C + V
B.
Q = C * V
C.
Q = V / C
D.
Q = C - V
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Solution
The relationship is given by Q = C * V, where Q is the charge, C is the capacitance, and V is the voltage.
Correct Answer: B — Q = C * V
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Q. In a capillary tube, how does the viscosity of a fluid affect the height to which it rises?
A.
Higher viscosity leads to higher rise
B.
Higher viscosity leads to lower rise
C.
Viscosity has no effect
D.
It depends on the tube diameter
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Solution
Higher viscosity results in a lower height of rise in a capillary tube due to greater resistance to flow.
Correct Answer: B — Higher viscosity leads to lower rise
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Q. In a Carnot engine operating between 500 K and 300 K, what is the maximum efficiency of the engine? (2021)
A.
40%
B.
60%
C.
50%
D.
20%
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Solution
Efficiency (η) = 1 - (T_cold / T_hot) = 1 - (300 K / 500 K) = 0.4 or 40%.
Correct Answer: B — 60%
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Q. In a Carnot engine operating between temperatures of 500 K and 300 K, what is the maximum efficiency? (2023)
A.
40%
B.
60%
C.
50%
D.
70%
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Solution
Efficiency (η) = 1 - (T_cold / T_hot) = 1 - (300 K / 500 K) = 0.4 or 40%.
Correct Answer: B — 60%
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Q. In a Carnot engine operating between temperatures of 500 K and 300 K, what is the efficiency of the engine? (2023)
A.
40%
B.
50%
C.
60%
D.
70%
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Solution
Efficiency (η) = 1 - (T_cold / T_hot) = 1 - (300 K / 500 K) = 0.4 or 40%.
Correct Answer: C — 60%
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Q. In a Carnot engine operating between temperatures T1 and T2, what is the efficiency (η) of the engine? (2023)
A.
1 - T2/T1
B.
T1/T2
C.
T2/T1
D.
T1 - T2
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Solution
The efficiency of a Carnot engine is given by η = 1 - T2/T1.
Correct Answer: A — 1 - T2/T1
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Q. In a Carnot engine operating between two heat reservoirs at temperatures 500 K and 300 K, what is the maximum efficiency of the engine? (2023)
A.
40%
B.
60%
C.
80%
D.
20%
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Solution
Efficiency (η) = 1 - (T_cold / T_hot) = 1 - (300 K / 500 K) = 0.4 or 40%.
Correct Answer: B — 60%
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Q. In a Carnot engine, the efficiency depends on which of the following? (2023)
A.
Temperature of the hot reservoir
B.
Temperature of the cold reservoir
C.
Both temperatures
D.
Type of working substance
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Solution
The efficiency of a Carnot engine is determined by the temperatures of the hot and cold reservoirs, given by the formula η = 1 - (T_c/T_h).
Correct Answer: C — Both temperatures
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Q. In a Carnot engine, what does the efficiency depend on?
A.
The temperature of the hot reservoir
B.
The temperature of the cold reservoir
C.
Both temperatures
D.
None of the above
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Solution
The efficiency of a Carnot engine depends on both the temperature of the hot reservoir and the cold reservoir.
Correct Answer: C — Both temperatures
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Q. In a Carnot engine, what is the efficiency dependent on?
A.
The work done
B.
The temperatures of the hot and cold reservoirs
C.
The type of working substance
D.
The volume of the gas
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Solution
The efficiency of a Carnot engine is dependent on the temperatures of the hot and cold reservoirs, given by η = 1 - (Tc/Th).
Correct Answer: B — The temperatures of the hot and cold reservoirs
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Q. In a Carnot engine, which of the following is true?
A.
It operates between two temperatures
B.
It is 100% efficient
C.
It can operate with any working substance
D.
It is a perpetual motion machine
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Solution
A Carnot engine operates between two temperatures, absorbing heat from a hot reservoir and rejecting heat to a cold reservoir.
Correct Answer: A — It operates between two temperatures
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Q. In a certain arrangement, A is to the left of B, and C is to the right of A. If D is to the left of C, which of the following statements is true?
A.
A is to the right of D
B.
B is to the left of C
C.
D is to the right of A
D.
C is to the left of B
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Solution
Since A is to the left of B and C is to the right of A, D being to the left of C means A is indeed to the right of D.
Correct Answer: A — A is to the right of D
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Q. In a certain arrangement, if A is taller than B, and B is shorter than C, which of the following is true?
A.
A is shorter than C
B.
C is taller than A
C.
B is taller than A
D.
C is taller than B
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Solution
Since A is taller than B and B is shorter than C, it follows that C is taller than B.
Correct Answer: D — C is taller than B
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Q. In a certain city, the probability of a person being a smoker is 0.3. If two people are selected at random, what is the probability that both are smokers?
A.
0.09
B.
0.21
C.
0.3
D.
0.6
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Solution
The probability that both are smokers is 0.3 * 0.3 = 0.09.
Correct Answer: A — 0.09
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Q. In a certain city, the probability of rain on any given day is 0.1. What is the probability that it does not rain on a particular day?
A.
0.9
B.
0.1
C.
0.5
D.
0.75
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Solution
The probability that it does not rain = 1 - P(rain) = 1 - 0.1 = 0.9.
Correct Answer: A — 0.9
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