Mathematics

Algebraic Expressions and Identities Comparing Quantities Cubes and Cube Roots Data Handling Direct and Inverse Proportions Exponents and Powers Factorisation Introduction to Graphs Linear Equations in One Variable Mensuration Playing with Numbers Practical Geometry Rational Numbers Squares and Square Roots Understanding Quadrilaterals Visualising Solid Shapes

Q. Find x if 5(x - 2) = 3x + 4.

A. x = 6
B. x = 2
C. x = 4
D. x = 8

Solution

Distribute: 5x - 10 = 3x + 4. Subtract 3x from both sides: 2x - 10 = 4. Add 10: 2x = 14. Divide by 2: x = 7.

Correct Answer: C — x = 4

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Q. Find x if 9x - 5 = 4x + 10.

A. x = 3
B. x = 2
C. x = 5
D. x = 4

Solution

Subtract 4x from both sides: 5x - 5 = 10. Add 5: 5x = 15. Divide by 5: x = 3.

Correct Answer: A — x = 3

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Q. How many more units of Product C were sold compared to Product A?

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

Solution

Product C sold 30 more units than Product A based on the data provided.

Correct Answer: C — 30

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Q. If 10 liters of paint can cover 200 square meters, how many liters are needed to cover 500 square meters?

A. 25 liters
B. 20 liters
C. 30 liters
D. 15 liters

Solution

Coverage = 200 m² / 10 L = 20 m²/L. For 500 m², liters needed = 500 m² / 20 m²/L = 25 liters.

Correct Answer: B — 20 liters

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Q. If 12 men can complete a project in 30 days, how many men are needed to complete the project in 15 days?

A. 24 men
B. 18 men
C. 30 men
D. 12 men

Solution

Work done = men * days. 12 men * 30 days = 360 man-days. To finish in 15 days, 360 man-days / 15 days = 24 men.

Correct Answer: A — 24 men

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Q. If 15 kg of sugar costs $45, how much will 10 kg cost?

A. $30
B. $25
C. $35
D. $40

Solution

Cost per kg = $45 / 15 kg = $3. Therefore, 10 kg will cost 10 kg * $3 = $30.

Correct Answer: A — $30

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Q. If 2(x + 3) = 16, what is x?

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

Solution

Divide by 2: x + 3 = 8. Subtract 3: x = 5.

Correct Answer: B — x = 5

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Q. If 2/5 of a number is 12, what is the number?

A. 30
B. 25
C. 20
D. 15

Solution

Let the number be x. Then, (2/5)x = 12. Solving gives x = 12 * (5/2) = 30.

Correct Answer: B — 25

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Q. If 3 machines can produce 150 units in 5 hours, how many units can 5 machines produce in 3 hours?

A. 90 units
B. 100 units
C. 150 units
D. 120 units

Solution

Rate of production = 150 units / (3 machines * 5 hours) = 10 units/machine/hour. In 3 hours, 5 machines produce 5 * 10 * 3 = 150 units.

Correct Answer: D — 120 units

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Q. If 3/4 of a number is 18, what is the number?

A. 24
B. 30
C. 36
D. 20

Solution

Let the number be x. Then, (3/4)x = 18. Solving gives x = 18 * (4/3) = 24.

Correct Answer: A — 24

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Q. If 3x + 5 = 20, what is the value of x?

A. 5
B. 10
C. 15
D. 3

Solution

Subtract 5 from both sides: 3x = 15. Then divide by 3: x = 5.

Correct Answer: A — 5

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Q. If 3x - 4 = 11, what is the value of x?

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

Solution

Add 4 to both sides: 3x = 15. Then divide by 3: x = 5.

Correct Answer: A — x = 5

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Q. If 3^x = 81, what is the value of x?

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

Solution

81 = 3^4, so x = 4.

Correct Answer: C — 4

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Q. If 4^x = 64, what is the value of x?

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

Solution

64 = 4^3, so x = 3.

Correct Answer: B — 3

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Q. If 5 times a number is equal to 45, what is the number?

A. 5
B. 9
C. 7
D. 8

Solution

Let the number be x. Then, 5x = 45. Therefore, x = 45/5 = 9.

Correct Answer: B — 9

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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

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

Correct Answer: A — 5 days

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Q. If 6 people can finish a job in 12 days, how many days will it take for 4 people to finish the same job?

A. 18 days
B. 20 days
C. 24 days
D. 30 days

Solution

Total work = 6 people * 12 days = 72 person-days. For 4 people, days = 72 person-days / 4 people = 18 days.

Correct Answer: C — 24 days

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Q. If 6x + 2 = 20, what is x?

A. x = 3
B. x = 4
C. x = 5
D. x = 2

Solution

Subtract 2 from both sides: 6x = 18. Divide by 6: x = 3.

Correct Answer: B — x = 4

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Q. If a = 2 and b = 3, what is the value of 2a^2 + 3b?

A. 12
B. 15
C. 18
D. 21

Solution

Calculating gives 2(2^2) + 3(3) = 2(4) + 9 = 8 + 9 = 17.

Correct Answer: B — 15

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Q. If a car travels at a speed of 80 km/h, how long will it take to travel 240 km?

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

Solution

Time = Distance / Speed = 240 km / 80 km/h = 3 hours.

Correct Answer: B — 3 hours

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Q. If a cube's volume is 27 cm³, what is the length of one side?

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

Solution

Side length = ∛Volume = ∛27 = 3 cm.

Correct Answer: A — 3 cm

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Q. If a cylinder has a radius of 3 cm and a height of 5 cm, what is its volume?

A. 45π cm³
B. 30π cm³
C. 15π cm³
D. 60π cm³

Solution

Volume of a cylinder = πr²h = π(3)²(5) = 45π cm³.

Correct Answer: A — 45π cm³

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Q. If a graph has 12 edges and 8 vertices, what is the maximum possible degree of any vertex?

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

Solution

The maximum degree can be at most 2 * number of edges / number of vertices. Here, it is 2 * 12 / 8 = 3.

Correct Answer: C — 6

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Q. If a graph has 4 vertices and each vertex is connected to every other vertex, what is the degree of each vertex?

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

Solution

In a complete graph with 4 vertices, each vertex is connected to 3 others, so the degree of each vertex is 3.

Correct Answer: C — 3

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Q. If a graph has 8 vertices and 12 edges, what is the average degree of the vertices?

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

Solution

The average degree of a graph is given by 2 * number of edges / number of vertices. Here, it is 2 * 12 / 8 = 3.

Correct Answer: B — 3

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Q. If a number is divided by 6, the remainder is 4. What is the remainder when the same number is divided by 3?

A. 0
B. 1
C. 2
D. 4

Solution

If a number leaves a remainder of 4 when divided by 6, it can be expressed as 6k + 4. When divided by 3, 6k is divisible by 3 and 4 gives a remainder of 1.

Correct Answer: B — 1

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Q. If a number is tripled and then decreased by 5, the result is 16. What is the number?

A. 7
B. 8
C. 9
D. 10

Solution

Let the number be x. Then, 3x - 5 = 16. Therefore, 3x = 21, and x = 21/3 = 7.

Correct Answer: B — 8

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Q. If a person earns $5000 and spends 60% of it, how much does he save?

A. $2000
B. $1800
C. $1500
D. $1200

Solution

Amount spent = 60% of 5000 = 0.6 * 5000 = $3000. Savings = Total Income - Amount Spent = 5000 - 3000 = $2000.

Correct Answer: B — $1800

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Q. If a person saves 25% of his income and spends the rest, what fraction of his income does he spend?

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

Solution

If he saves 25%, he spends 100% - 25% = 75%. Therefore, fraction spent = 75% = 3/4.

Correct Answer: B — 3/4

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Q. If a person spends 30% of his salary on rent and 20% on groceries, what percentage of his salary is left?

A. 50%
B. 40%
C. 30%
D. 20%

Solution

Total percentage spent = 30% + 20% = 50%. Therefore, percentage left = 100% - 50% = 50%.

Correct Answer: B — 40%

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Mathematics

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