Engineering Entrance
Q. If 0.1 M acetic acid has a pH of 2.87, what is the concentration of H+ ions?
A.
0.001 M
B.
0.01 M
C.
0.1 M
D.
0.5 M
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Solution
[H+] = 10^(-pH) = 10^(-2.87) ≈ 0.001 M.
Correct Answer: B — 0.01 M
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Q. If 0.5 moles of a gas occupy 12.2 liters at STP, what is the molar volume of the gas? (2023)
A.
22.4 L
B.
24 L
C.
12.2 L
D.
6.1 L
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Solution
At STP, 1 mole of gas occupies 22.4 liters. Therefore, the molar volume is 22.4 L.
Correct Answer: A — 22.4 L
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Q. If 1 kg of water is heated from 25°C to 75°C, how much heat is absorbed? (Specific heat of water = 4.2 J/g°C) (2021)
A.
21000 J
B.
42000 J
C.
84000 J
D.
105000 J
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Solution
Q = mcΔT = (1000 g)(4.2 J/g°C)(50°C) = 210000 J.
Correct Answer: B — 42000 J
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Q. If 10 g of sugar (C12H22O11) is dissolved in 200 g of water, what is the mass percent of sugar in the solution? (Molar mass of sugar = 342 g/mol) (2023)
A.
4.76%
B.
5.00%
C.
10.00%
D.
2.50%
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Solution
Mass percent = (mass of solute / total mass of solution) x 100. Total mass = 10 g + 200 g = 210 g. Mass percent = (10 g / 210 g) x 100 = 4.76%.
Correct Answer: A — 4.76%
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Q. If 10 grams of NaCl is dissolved in 500 mL of water, what is the concentration in g/L? (2020)
A.
20 g/L
B.
10 g/L
C.
5 g/L
D.
15 g/L
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Solution
Concentration = (10 g / 0.5 L) = 20 g/L.
Correct Answer: A — 20 g/L
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Q. If 10 grams of NaCl is dissolved in 500 mL of water, what is the mass/volume percent concentration? (2020) 2020
A.
2%
B.
5%
C.
10%
D.
20%
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Solution
Mass/volume % = (mass of solute / volume of solution) * 100 = (10 g / 500 mL) * 100 = 2%.
Correct Answer: B — 5%
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Q. If 1000 J of heat is added to a gas and it expands doing 400 J of work, what is the change in internal energy? (2023)
A.
600 J
B.
400 J
C.
1000 J
D.
200 J
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Solution
Using the first law of thermodynamics: ΔU = Q - W = 1000 J - 400 J = 600 J.
Correct Answer: A — 600 J
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Q. If 1000 J of heat is added to a system and it does 400 J of work, what is the change in internal energy? (2021)
A.
600 J
B.
400 J
C.
1000 J
D.
1400 J
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Solution
Using the first law of thermodynamics, ΔU = Q - W = 1000 J - 400 J = 600 J.
Correct Answer: A — 600 J
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Q. If 15 g of sugar is dissolved in 300 mL of water, what is the concentration in g/mL? (2020)
A.
0.05 g/mL
B.
0.1 g/mL
C.
0.15 g/mL
D.
0.2 g/mL
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Solution
Concentration = mass / volume = 15 g / 300 mL = 0.05 g/mL.
Correct Answer: B — 0.1 g/mL
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Q. If 20 grams of glucose (C6H12O6) is dissolved in 1 liter of water, what is the molarity of the solution? (Molar mass of glucose = 180 g/mol) (2020) 2020
A.
0.11 M
B.
0.5 M
C.
0.2 M
D.
0.33 M
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Solution
Moles of glucose = 20 g / 180 g/mol = 0.111 M. Molarity = 0.111 moles / 1 L = 0.11 M.
Correct Answer: A — 0.11 M
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Q. If 2x = 10, what is the value of x? (2015)
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Solution
Dividing both sides by 2 gives x = 10/2 = 5.
Correct Answer: A — 5
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Q. If 3 moles of glucose are dissolved in 1 liter of solution, what is the molality of the solution? (2023)
A.
3 m
B.
1 m
C.
2 m
D.
0.5 m
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Solution
Molality (m) = moles of solute / kg of solvent; assuming 1 L of water = 1 kg, m = 3 moles / 1 kg = 3 m
Correct Answer: A — 3 m
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Q. If 3x = 12, what is the value of x? (2019)
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Q. If 50 mL of 0.1 M H2SO4 is diluted to 250 mL, what is the new concentration?
A.
0.02 M
B.
0.04 M
C.
0.1 M
D.
0.5 M
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Solution
C1V1 = C2V2; (0.1 M)(50 mL) = C2(250 mL); C2 = 0.02 M.
Correct Answer: B — 0.04 M
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Q. If 50 mL of a 3 M solution is diluted to 200 mL, what is the new molarity? (2020)
A.
0.75 M
B.
1.5 M
C.
2 M
D.
3 M
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Solution
Using M1V1 = M2V2, (3 M)(50 mL) = M2(200 mL) => M2 = (3 M × 50 mL) / 200 mL = 0.75 M.
Correct Answer: A — 0.75 M
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Q. If 500 J of heat is added to a system and it does 200 J of work, what is the change in internal energy? (2022)
A.
300 J
B.
200 J
C.
500 J
D.
700 J
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Solution
According to the first law of thermodynamics, ΔU = Q - W. Here, ΔU = 500 J - 200 J = 300 J.
Correct Answer: A — 300 J
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Q. If a 10 kg object is raised to a height of 5 m, what is the work done against gravity? (g = 9.8 m/s²)
A.
490 J
B.
980 J
C.
150 J
D.
250 J
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Solution
Work = m * g * h = 10 kg * 9.8 m/s² * 5 m = 490 J.
Correct Answer: B — 980 J
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Q. If a 15Ω resistor is connected in parallel with a 5Ω resistor, what is the equivalent resistance? (2023)
A.
3.75Ω
B.
4Ω
C.
5Ω
D.
10Ω
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Solution
1/R_eq = 1/15 + 1/5 = 1/15 + 3/15 = 4/15; R_eq = 15/4 = 3.75Ω.
Correct Answer: A — 3.75Ω
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Q. If a 2 kg object is dropped from a height, what is its velocity just before hitting the ground? (g = 9.8 m/s², h = 20 m) (2023)
A.
14 m/s
B.
19.6 m/s
C.
20 m/s
D.
28 m/s
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Solution
Using v² = u² + 2gh, where u = 0, we find v = √(2 * 9.8 * 20) = 19.6 m/s.
Correct Answer: B — 19.6 m/s
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Q. If a 2 kg object is dropped from a height, what is its velocity just before hitting the ground (g = 10 m/s²)? (2023)
A.
10 m/s
B.
20 m/s
C.
30 m/s
D.
40 m/s
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Solution
Using v = √(2gh), for h = 10 m, v = √(2 * 10 m/s² * 10 m) = √200 = 20 m/s.
Correct Answer: B — 20 m/s
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Q. If a 2 kg object is moving with a velocity of 15 m/s, what is its kinetic energy?
A.
225 J
B.
150 J
C.
300 J
D.
450 J
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Solution
Kinetic Energy = 1/2 * m * v^2 = 1/2 * 2 kg * (15 m/s)^2 = 225 J.
Correct Answer: A — 225 J
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Q. If a 2 kg object is moving with a velocity of 3 m/s, what is its kinetic energy?
A.
9 J
B.
6 J
C.
3 J
D.
12 J
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Solution
Kinetic Energy = 0.5 * m * v² = 0.5 * 2 kg * (3 m/s)² = 9 J.
Correct Answer: A — 9 J
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Q. If a 5 kg object is moving with a velocity of 3 m/s, what is its momentum? (2023)
A.
5 kg·m/s
B.
10 kg·m/s
C.
15 kg·m/s
D.
20 kg·m/s
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Solution
Momentum p = mv = 5 kg * 3 m/s = 15 kg·m/s.
Correct Answer: C — 15 kg·m/s
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Q. If a 5 kg object is subjected to a net force of 20 N, what is its acceleration? (2023)
A.
2 m/s²
B.
4 m/s²
C.
5 m/s²
D.
10 m/s²
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Solution
Using F = ma, we find a = F/m = 20 N / 5 kg = 4 m/s².
Correct Answer: B — 4 m/s²
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Q. If a 5Ω resistor is connected to a 10V source, what is the power dissipated? (2023)
A.
2W
B.
5W
C.
10W
D.
20W
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Solution
Power P = V²/R = (10V)² / 5Ω = 100 / 5 = 20W.
Correct Answer: C — 10W
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Q. If a 6Ω resistor is connected in parallel with a 3Ω resistor, what is the equivalent resistance? (2023)
A.
2Ω
B.
1.5Ω
C.
4Ω
D.
9Ω
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Solution
Using the formula 1/R_eq = 1/R1 + 1/R2, we get 1/R_eq = 1/6 + 1/3 = 1/6 + 2/6 = 3/6, thus R_eq = 2Ω.
Correct Answer: A — 2Ω
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Q. If a 9V battery is connected to a 3Ω resistor, what is the current flowing through it? (2021)
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Solution
Using Ohm's law, I = V/R = 9V / 3Ω = 3A.
Correct Answer: B — 2A
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Q. If A = 2i + 3j and B = 3i + 4j, what is the angle between A and B? (2021)
A.
0 degrees
B.
45 degrees
C.
90 degrees
D.
180 degrees
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Solution
cos(θ) = (A · B) / (|A||B|) = (2*3 + 3*4) / (√(2^2 + 3^2) * √(3^2 + 4^2)) = 0.7071, θ = 45 degrees.
Correct Answer: B — 45 degrees
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Q. If a = 3 and b = 4, what is the value of a^2 + b^2? (2019)
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Solution
a^2 = 9 and b^2 = 16, so 9 + 16 = 25.
Correct Answer: A — 25
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Q. If A = 3i + 4j and B = 2i - j, what is A + B? (2021)
A.
5i + 3j
B.
5i + 5j
C.
1i + 5j
D.
1i + 3j
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Solution
A + B = (3i + 4j) + (2i - j) = (3 + 2)i + (4 - 1)j = 5i + 3j.
Correct Answer: A — 5i + 3j
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