Major Competitive Exams

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Q. If 5 g of CaCO3 decomposes completely, how many grams of CaO are produced?

A. 2 g
B. 3 g
C. 4 g
D. 5 g

Solution

CaCO3 → CaO + CO2. Molar mass of CaCO3 = 100 g, CaO = 56 g. 5 g of CaCO3 produces (5 g * 56 g) / 100 g = 2.8 g of CaO.

Correct Answer: C — 4 g

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Q. If 5 liters of a 20% solution is mixed with 15 liters of a 30% solution, what is the percentage concentration of the resulting mixture?

A. 24%
B. 26%
C. 28%
D. 30%

Solution

Total salt = (0.2*5) + (0.3*15) = 1 + 4.5 = 5.5 liters. Total volume = 5 + 15 = 20 liters. Concentration = (5.5/20)*100 = 27.5%.

Correct Answer: A — 24%

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Q. If 5 moles of KCl are dissolved in 1 kg of water, what is the molality of the solution?

A. 5 m
B. 2.5 m
C. 10 m
D. 1 m

Solution

Molality (m) = moles of solute / kg of solvent = 5 moles / 1 kg = 5 m.

Correct Answer: A — 5 m

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Q. If 5 moles of KCl are dissolved in 3 kg of water, what is the molality of the solution?

A. 1.67 m
B. 2.5 m
C. 1.25 m
D. 0.5 m

Solution

Molality (m) = moles of solute / kg of solvent = 5 moles / 3 kg = 1.67 m.

Correct Answer: A — 1.67 m

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Q. If 5 moles of NaCl are dissolved in water, how many moles of Na+ ions are present?

A. 5 moles
B. 10 moles
C. 2.5 moles
D. 0 moles

Solution

Each mole of NaCl dissociates into 1 mole of Na+ ions. Therefore, 5 moles of NaCl will produce 5 moles of Na+ ions.

Correct Answer: A — 5 moles

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Q. If 5 times a number is decreased by 3, the result is 12. What is the number?

A. 3
B. 4
C. 5
D. 6

Solution

Let the number be x. The equation is 5x - 3 = 12. Adding 3 to both sides gives 5x = 15. Dividing by 5 gives x = 3.

Correct Answer: B — 4

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Q. If 5 workers can complete a task in 10 days, how many days will 10 workers take to complete the same task? (2023)

A. 5 days
B. 10 days
C. 15 days
D. 20 days

Solution

If 5 workers take 10 days, 10 workers will take 10/2 = 5 days.

Correct Answer: A — 5 days

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Q. If 5 workers can complete a task in 10 days, how many days will it take for 10 workers to complete the same task?

A. 5 days
B. 10 days
C. 15 days
D. 20 days

Solution

Work done = Workers * Days. Total work = 5 * 10 = 50 worker-days. For 10 workers, Days = Total work / Workers = 50 / 10 = 5 days.

Correct Answer: A — 5 days

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Q. If 50 g of KCl is dissolved in 250 mL of solution, what is the molarity? (Molar mass of KCl = 74.5 g/mol)

A. 2.68 M
B. 1.34 M
C. 0.67 M
D. 0.25 M

Solution

Moles of KCl = 50 g / 74.5 g/mol = 0.672 moles. Molarity = 0.672 moles / 0.25 L = 2.688 M.

Correct Answer: B — 1.34 M

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Q. If 50 grams of a solute is dissolved in 200 mL of solution, what is the mass/volume percent concentration?

A. 25%
B. 20%
C. 15%
D. 10%

Solution

Mass/volume percent = (mass of solute / volume of solution) * 100 = (50 g / 200 mL) * 100 = 25%.

Correct Answer: A — 25%

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Q. If 50 grams of NaCl is dissolved in 1 liter of solution, what is the molarity? (Molar mass of NaCl = 58.5 g/mol)

A. 0.85 M
B. 1.0 M
C. 1.5 M
D. 2.0 M

Solution

Moles of NaCl = 50 g / 58.5 g/mol = 0.854 moles. Molarity = 0.854 moles / 1 L = 0.854 M.

Correct Answer: B — 1.0 M

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Q. If 50 grams of NaOH is dissolved in 1 liter of solution, what is the molarity? (Molar mass of NaOH = 40 g/mol)

A. 1.25 M
B. 2.5 M
C. 0.5 M
D. 1 M

Solution

Moles of NaOH = 50 g / 40 g/mol = 1.25 moles. Molarity = 1.25 moles / 1 L = 1.25 M.

Correct Answer: B — 2.5 M

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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

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 0.1 M HCl is mixed with 50 mL of 0.1 M NaOH, what is the resulting pH?

A. 7
B. 1
C. 14
D. 0

Solution

HCl and NaOH neutralize each other, resulting in a neutral solution with pH = 7.

Correct Answer: A — 7

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Q. If 50 mL of a 2 M HCl solution is diluted to 200 mL, what is the new molarity?

A. 0.25 M
B. 0.5 M
C. 1 M
D. 2 M

Solution

Using the dilution formula M1V1 = M2V2, (2 M)(50 mL) = M2(200 mL) => M2 = 0.5 M.

Correct Answer: B — 0.5 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

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 50% of a group like reading, 30% like writing, and 10% like both, what percentage like only reading?

A. 40%
B. 30%
C. 20%
D. 10%

Solution

The percentage of people who like only reading is 50% - 10% = 40%.

Correct Answer: A — 40%

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Q. If 50% of a group of 200 people like apples, 30% like bananas, and 10% like both, what percentage like only apples?

A. 40%
B. 30%
C. 20%
D. 10%

Solution

The percentage of people who like only apples is 50% - 10% = 40%.

Correct Answer: A — 40%

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Q. If 50% of a group prefers tea, 30% prefers coffee, and 10% prefers both, what is the percentage that prefers either tea or coffee?

A. 70%
B. 80%
C. 60%
D. 50%

Solution

The percentage that prefers either tea or coffee is 50% + 30% - 10% = 70%.

Correct Answer: A — 70%

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Q. If 50% of students like soccer, 30% like basketball, and 10% like both, what percentage of students like only soccer?

A. 40%
B. 30%
C. 20%
D. 10%

Solution

The percentage of students who like only soccer is 50% - 10% = 40%.

Correct Answer: A — 40%

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Q. If 500 J of heat is added to a system and 200 J of work is done by the system, what is the change in internal energy?

A. 300 J
B. 500 J
C. 700 J
D. 200 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 500 J of heat is added to a system and 200 J of work is done by the system, what is the change in internal energy of the system?

A. 300 J
B. 500 J
C. 700 J
D. 200 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 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 5m + 15 = 45, what is the value of m? (2023)

A. 5
B. 6
C. 7
D. 8

Solution

5m + 15 = 45 => 5m = 30 => m = 6.

Correct Answer: A — 5

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Q. If 5x - 7 < 3, what is the range of x?

A. x < 2
B. x > 2
C. x < 1
D. x > 1

Solution

5x - 7 < 3 => 5x < 10 => x < 2

Correct Answer: A — x < 2

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Q. If 5x - 7 < 3, what is the value of x?

A. x < 2
B. x > 2
C. x < 1
D. x > 1

Solution

5x - 7 < 3 => 5x < 10 => x < 2

Correct Answer: A — x < 2

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Q. If 5x - 7 < 3x + 1, what is the range of x?

A. x < 4
B. x > 4
C. x < 2
D. x > 2

Solution

5x - 7 < 3x + 1 => 2x < 8 => x < 4.

Correct Answer: A — x < 4

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Q. If 5x = 25, what is the value of x? (2019)

A. 5
B. 10
C. 15
D. 20

Solution

5x = 25, so x = 25/5 = 5.

Correct Answer: A — 5

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Q. If 5x = 45, what is the value of x?

A. 5
B. 6
C. 7
D. 8

Solution

5x = 45; x = 45 ÷ 5 = 9.

Correct Answer: B — 6

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Q. If 5x ≡ 10 (mod 15), what is the value of x?

A. 0
B. 1
C. 2
D. 3

Solution

Dividing both sides by 5 gives x ≡ 2 (mod 3), which means x can be 2.

Correct Answer: C — 2

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Major Competitive Exams

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