Engineering Entrance
Q. How many ways can 3 students be selected from a group of 10?
A.
120
B.
90
C.
100
D.
80
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Solution
The number of ways to select 3 students from 10 is given by 10C3 = 120.
Correct Answer: A — 120
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Q. How many ways can 4 different fruits be selected from 8 available fruits? (2021)
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Solution
The number of ways to choose 4 fruits from 8 is given by 8C4 = 70.
Correct Answer: A — 70
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Q. How many ways can 4 different fruits be selected from 8?
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Solution
The number of ways to select 4 fruits from 8 is given by 8C4 = 70.
Correct Answer: B — 56
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Q. How many ways can 4 letters be chosen from the word 'COMBINATION'?
A.
210
B.
120
C.
150
D.
180
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Solution
The number of ways to choose 4 letters from 11 is 11C4 = 330.
Correct Answer: A — 210
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Q. How many ways can 4 prizes be distributed among 10 students if each student can receive at most one prize? (2019)
A.
5040
B.
720
C.
1000
D.
1200
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Solution
The number of ways to distribute 4 prizes among 10 students is 10P4 = 5040.
Correct Answer: A — 5040
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Q. How many ways can 5 different letters be arranged if 2 letters are always together?
A.
48
B.
120
C.
240
D.
720
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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
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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
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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
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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
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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
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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
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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
B.
4200 J
C.
2500 J
D.
1000 J
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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
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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
C.
75 J
D.
100 J
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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
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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
B.
O2
C.
H2O
D.
None of the above
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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
B.
0.01 M
C.
0.1 M
D.
0.2 M
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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
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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 1 mole of a gas occupies 22.4 liters at STP, how many liters will 0.5 moles occupy? (2023)
A.
11.2 L
B.
22.4 L
C.
44.8 L
D.
5.6 L
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Solution
At STP, 1 mole of gas occupies 22.4 L. Therefore, 0.5 moles will occupy 0.5 x 22.4 L = 11.2 L.
Correct Answer: A — 11.2 L
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Q. If 10 g of glucose (C6H12O6) is dissolved in 200 g of water, what is the mass percentage of the solution? (2023)
A.
4.76%
B.
5.00%
C.
10.00%
D.
2.50%
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Solution
Mass percentage = (mass of solute / mass of solution) x 100. Mass of solution = 10 g + 200 g = 210 g. Mass percentage = (10 g / 210 g) x 100 = 4.76%.
Correct Answer: A — 4.76%
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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 g of sugar is dissolved in 100 g of water, what is the mass percentage of sugar in the solution? (2023)
A.
10%
B.
5%
C.
20%
D.
15%
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Solution
Mass percentage = (mass of solute / mass of solution) × 100. Mass of solution = 10 g + 100 g = 110 g. Mass percentage = (10 g / 110 g) × 100 = 9.09%, approximately 10%.
Correct Answer: A — 10%
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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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