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Q. What is the mode of the following numbers: 4, 4, 5, 6, 6, 7, 8?

A. 4
B. 5
C. 6
D. 7

Solution

The mode is 4, as it appears 2 times, which is more than any other number.

Correct Answer: A — 4

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Q. What is the mode of the following numbers: {2, 3, 4, 4, 5, 5, 5, 6}?

A. 2
B. 4
C. 5
D. 6

Solution

The mode is 5, as it appears 3 times, more than any other number.

Correct Answer: C — 5

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Q. What is the mode of the following numbers: {6, 7, 8, 6, 9, 10, 6, 7}?

A. 6
B. 7
C. 8
D. 9

Solution

The mode is 6, which appears 3 times in the data set.

Correct Answer: A — 6

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Q. What is the mode of the numbers: 1, 1, 2, 3, 3, 3, 4, 4?

A. 1
B. 2
C. 3
D. 4

Solution

The mode is 3, as it appears most frequently (three times) in the data set.

Correct Answer: C — 3

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Q. What is the modular inverse of 3 modulo 11?

A. 4
B. 7
C. 8
D. 9

Solution

The modular inverse of 3 mod 11 is a number x such that 3x ≡ 1 (mod 11). The solution is x = 4, since 3 * 4 = 12 ≡ 1 (mod 11).

Correct Answer: A — 4

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Q. What is the modulus of the complex number 3 + 4i? (2023)

A. 5
B. 7
C. 1
D. 4

Solution

The modulus is calculated as √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

Correct Answer: A — 5

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Q. What is the modulus of the complex number z = -3 + 4i?

A. 5
B. 7
C. 3
D. 4

Solution

The modulus |z| = √((-3)^2 + (4)^2) = √(9 + 16) = √25 = 5.

Correct Answer: A — 5

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Q. What is the molality of a solution containing 3 moles of KCl dissolved in 1 kg of water?

A. 3 m
B. 1.5 m
C. 2 m
D. 4 m

Solution

Molality (m) = moles of solute / kg of solvent = 3 moles / 1 kg = 3 m.

Correct Answer: A — 3 m

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Q. What is the molality of a solution containing 3 moles of solute in 1 kg of solvent? (2022)

A. 3 m
B. 1.5 m
C. 0.5 m
D. 2 m

Solution

Molality (m) = moles of solute / kg of solvent = 3 moles / 1 kg = 3 m.

Correct Answer: A — 3 m

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Q. What is the molality of a solution containing 3 moles of solute in 500 g of solvent? (2021)

A. 6 m
B. 3 m
C. 1.5 m
D. 0.5 m

Solution

Molality (m) = moles of solute / kg of solvent = 3 moles / 0.5 kg = 6 m.

Correct Answer: B — 3 m

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Q. What is the molality of a solution made by dissolving 10 moles of solute in 5 kg of solvent? (2022)

A. 2 m
B. 1 m
C. 0.5 m
D. 3 m

Solution

Molality (m) = moles of solute / kg of solvent = 10 moles / 5 kg = 2 m.

Correct Answer: A — 2 m

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Q. What is the molality of a solution prepared by dissolving 3 moles of KCl in 1 kg of water?

A. 3 m
B. 1.5 m
C. 2 m
D. 4 m

Solution

Molality (m) = moles of solute / kg of solvent = 3 moles / 1 kg = 3 m.

Correct Answer: A — 3 m

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Q. What is the molality of a solution prepared by dissolving 5 moles of NaCl in 2 kg of water?

A. 2.5 mol/kg
B. 5 mol/kg
C. 1.5 mol/kg
D. 3 mol/kg

Solution

Molality (m) = moles of solute / mass of solvent (kg) = 5 moles / 2 kg = 2.5 mol/kg.

Correct Answer: A — 2.5 mol/kg

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Q. What is the molar mass of CaCO3?

A. 100 g/mol
B. 120 g/mol
C. 80 g/mol
D. 60 g/mol

Solution

Molar mass of CaCO3 = 40 + 12 + 16*3 = 100 g/mol.

Correct Answer: A — 100 g/mol

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Q. What is the molar mass of sulfuric acid (H2SO4)?

A. 98 g/mol
B. 96 g/mol
C. 100 g/mol
D. 92 g/mol

Solution

Molar mass = 2*1 + 32 + 4*16 = 98 g/mol.

Correct Answer: A — 98 g/mol

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Q. What is the molar mass of the product formed when 1 mole of Mg reacts with 2 moles of HCl?

A. 24.3 g
B. 36.5 g
C. 58.5 g
D. 74.5 g

Solution

Mg + 2HCl → MgCl2 + H2. Molar mass of MgCl2 = 24.3 + 2*35.5 = 95.3 g.

Correct Answer: D — 74.5 g

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Q. What is the molar mass of the product formed when 1 mole of nitrogen reacts with 3 moles of hydrogen?

A. 28 g
B. 14 g
C. 32 g
D. 18 g

Solution

N2 + 3H2 → 2NH3. Molar mass of NH3 = 14 + 3 = 17 g.

Correct Answer: A — 28 g

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Q. What is the molar mass of water (H2O)?

A. 16 g/mol
B. 18 g/mol
C. 20 g/mol
D. 22 g/mol

Solution

The molar mass of water is calculated as follows: H (1 g/mol) x 2 + O (16 g/mol) = 18 g/mol.

Correct Answer: B — 18 g/mol

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Q. What is the molar mass of water (H2O)? (2023) 2023

A. 16 g/mol
B. 18 g/mol
C. 20 g/mol
D. 22 g/mol

Solution

The molar mass of water is calculated as follows: H (1 g/mol) x 2 + O (16 g/mol) = 2 + 16 = 18 g/mol.

Correct Answer: B — 18 g/mol

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Q. What is the molar volume of an ideal gas at standard temperature and pressure (STP)?

A. 22.4 L
B. 24.5 L
C. 18.0 L
D. 30.0 L

Solution

The molar volume of an ideal gas at STP is 22.4 L.

Correct Answer: A — 22.4 L

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Q. What is the molar volume of an ideal gas at STP (Standard Temperature and Pressure)?

A. 22.4 L
B. 24.5 L
C. 18.0 L
D. 30.0 L

Solution

The molar volume of an ideal gas at STP is 22.4 L.

Correct Answer: A — 22.4 L

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Q. What is the molar volume of an ideal gas at STP?

A. 22.4 L
B. 24.5 L
C. 18.0 L
D. 30.0 L

Solution

The molar volume of an ideal gas at standard temperature and pressure (STP) is 22.4 L.

Correct Answer: A — 22.4 L

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Q. What is the molarity of a solution containing 5 moles of solute in 2 liters of solution?

A. 2.5 M
B. 5 M
C. 10 M
D. 0.5 M

Solution

Molarity (M) = moles of solute / liters of solution = 5 moles / 2 L = 2.5 M.

Correct Answer: A — 2.5 M

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Q. What is the molarity of a solution containing 5 moles of solute in 2 liters of solution? (2021) 2021

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

Solution

Molarity (M) = moles of solute / liters of solution = 5 moles / 2 L = 2.5 M.

Correct Answer: A — 2.5 M

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Q. What is the molarity of a solution containing 58.5 g of NaCl in 1 liter of solution? (2021)

A. 1 M
B. 0.5 M
C. 2 M
D. 0.1 M

Solution

Molarity (M) = moles of solute / liters of solution. Moles of NaCl = 58.5 g / 58.5 g/mol = 1 mol. Therefore, M = 1 mol / 1 L = 1 M.

Correct Answer: A — 1 M

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Q. What is the molarity of a solution if 10 g of glucose (C6H12O6) is dissolved in 250 mL of water? (Molar mass = 180 g/mol)

A. 0.22 M
B. 0.5 M
C. 0.75 M
D. 1 M

Solution

Moles of glucose = 10 g / 180 g/mol = 0.0556 moles. Molarity = 0.0556 moles / 0.25 L = 0.222 M.

Correct Answer: A — 0.22 M

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Q. What is the molarity of a solution if 10 grams of CaCl2 is dissolved in 250 mL of solution? (Molar mass of CaCl2 = 110 g/mol)

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

Solution

Moles of CaCl2 = 10 g / 110 g/mol = 0.0909 moles. Molarity = 0.0909 moles / 0.25 L = 0.3636 M.

Correct Answer: B — 0.5 M

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Q. What is the molarity of a solution if 2 moles of solute are dissolved in 4 liters of solution?

A. 0.5 M
B. 1 M
C. 2 M
D. 4 M

Solution

Molarity (M) = moles of solute / liters of solution = 2 moles / 4 L = 0.5 M.

Correct Answer: B — 1 M

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Q. What is the molarity of a solution if 5 moles of solute are dissolved in 2 liters of solution?

A. 2.5 M
B. 5 M
C. 10 M
D. 0.5 M

Solution

Molarity (M) = moles of solute / liters of solution = 5 / 2 = 2.5 M

Correct Answer: A — 2.5 M

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Q. What is the molarity of a solution prepared by dissolving 5 grams of NaCl in enough water to make 250 mL of solution? (Molar mass of NaCl = 58.5 g/mol) (2023)

A. 0.34 M
B. 0.42 M
C. 0.25 M
D. 0.50 M

Solution

Molarity (M) = moles of solute / liters of solution. Moles of NaCl = 5 g / 58.5 g/mol = 0.0855 moles. Volume of solution = 250 mL = 0.250 L. M = 0.0855 moles / 0.250 L = 0.342 M, approximately 0.34 M.

Correct Answer: A — 0.34 M

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Major Competitive Exams

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