Engineering Entrance
Q. How many ways can 3 out of 8 different colored balls be chosen? (2022)
Solution
The number of ways to choose 3 balls from 8 is given by 8C3 = 56.
Correct Answer: A — 56
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Q. How many ways can 3 prizes be awarded to 10 students if no student can win more than one prize?
-
A.
720
-
B.
1000
-
C.
1200
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D.
100
Solution
The number of ways to award 3 prizes is P(10, 3) = 720.
Correct Answer: A — 720
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Q. How many ways can 5 different letters be arranged if 2 letters are always together?
-
A.
48
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B.
120
-
C.
240
-
D.
720
Solution
Treat the 2 letters as one unit. So, we have 4 units to arrange: 4! * 2! = 48.
Correct Answer: C — 240
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Q. How many ways can 5 different letters be arranged if 2 letters must always be together?
-
A.
60
-
B.
120
-
C.
240
-
D.
720
Solution
Treat the 2 letters as one unit. So, we have 4 units to arrange: 4! * 2! = 48.
Correct Answer: C — 240
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Q. How many ways can 6 different letters be arranged if 2 letters are always together?
-
A.
120
-
B.
240
-
C.
720
-
D.
1440
Solution
Treat the 2 letters as one unit. So, we have 5 units to arrange: 5! = 120. The 2 letters can be arranged in 2! = 2 ways. Total = 120 * 2 = 240.
Correct Answer: D — 1440
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Q. How many ways can 7 different books be arranged on a shelf if 3 specific books must be together?
-
A.
720
-
B.
120
-
C.
5040
-
D.
840
Solution
Treat the 3 specific books as one unit. So, we have 5 units to arrange: 5! * 3! = 360.
Correct Answer: C — 5040
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Q. How many ways can 8 different books be arranged on a shelf if 3 specific books must be together?
-
A.
720
-
B.
5040
-
C.
40320
-
D.
2880
Solution
Treat the 3 specific books as one unit. So, we have 6 units to arrange: 6! = 720. The 3 books can be arranged in 3! = 6 ways. Total = 720 * 6 = 4320.
Correct Answer: B — 5040
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Q. How many ways can 8 different colored balls be arranged in a line?
-
A.
40320
-
B.
720
-
C.
1000
-
D.
100
Solution
The number of arrangements is 8! = 40320.
Correct Answer: A — 40320
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Q. How many ways can a committee of 4 be formed from 10 people? (2019)
-
A.
210
-
B.
120
-
C.
100
-
D.
30
Solution
The number of ways to form a committee of 4 from 10 is given by 10C4 = 210.
Correct Answer: A — 210
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Q. How much heat is required to raise the temperature of 250 g of water from 25°C to 75°C? (Specific heat of water = 4.2 J/g°C) (2020)
-
A.
5250 J
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B.
4200 J
-
C.
2500 J
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D.
1000 J
Solution
Heat required = mass × specific heat × change in temperature = 250 g × 4.2 J/g°C × (75°C - 25°C) = 5250 J.
Correct Answer: A — 5250 J
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Q. How much heat is required to raise the temperature of 500 g of water from 25°C to 75°C? (2020)
-
A.
10000 J
-
B.
5000 J
-
C.
20000 J
-
D.
15000 J
Solution
Q = mcΔT = 500 g * 4.2 J/g°C * (75 - 25)°C = 10000 J.
Correct Answer: D — 15000 J
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Q. How much work is done when a force of 10 N moves an object 5 m in the direction of the force?
-
A.
25 J
-
B.
50 J
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C.
75 J
-
D.
100 J
Solution
Work = Force * Distance = 10 N * 5 m = 50 J.
Correct Answer: B — 50 J
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Q. How much work is done when a force of 30 N moves an object 4 m in the direction of the force?
-
A.
120 J
-
B.
90 J
-
C.
60 J
-
D.
30 J
Solution
Work = Force * Distance = 30 N * 4 m = 120 J.
Correct Answer: A — 120 J
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Q. Identify the oxidizing agent in the reaction: 2H2 + O2 → 2H2O. (2023)
-
A.
H2
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B.
O2
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C.
H2O
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D.
None of the above
Solution
O2 is the oxidizing agent as it gains electrons and is reduced to H2O.
Correct Answer: B — O2
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Q. If 0.1 M acetic acid (CH3COOH) is 1% ionized, what is the concentration of H+ ions?
-
A.
0.001 M
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B.
0.01 M
-
C.
0.1 M
-
D.
0.2 M
Solution
Ionization = 1% of 0.1 M = 0.001 M, so [H+] = 0.001 M.
Correct Answer: B — 0.01 M
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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
Solution
[H+] = 10^(-pH) = 10^(-2.87) ≈ 0.001 M.
Correct Answer: B — 0.01 M
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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
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B.
10 g/L
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C.
5 g/L
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D.
15 g/L
Solution
Concentration = (10 g / 0.5 L) = 20 g/L.
Correct Answer: A — 20 g/L
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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
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
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
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B.
0.1 g/mL
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C.
0.15 g/mL
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D.
0.2 g/mL
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 3 moles of glucose are dissolved in 1 liter of solution, what is the molality of the solution? (2023)
-
A.
3 m
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B.
1 m
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C.
2 m
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D.
0.5 m
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)
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
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C.
0.1 M
-
D.
0.5 M
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
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B.
1.5 M
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C.
2 M
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D.
3 M
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
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
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
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B.
4Ω
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C.
5Ω
-
D.
10Ω
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 = 10 m/s²)? (2023)
-
A.
10 m/s
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B.
20 m/s
-
C.
30 m/s
-
D.
40 m/s
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
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
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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