Case Study I

Shivam's father is a building contractor. One day Shivam got his father’s measuring tape. He used it to find the dimensions of the kitchen garden in his home. He found that the length of the garden is one metre more than twice its breadth. He told his friend Akhil that the perimeter of the garden is more than or equal to 110 m and is less than or equal to 140 m.

Based on this information, answer the following questions:

1. If breadth of the garden is x m, then the algebraic representation of the given information is:

1. 140 ≤ 6x + 2 ≤ 110, x ∈ R

2. 110 ≤ 6x + 2 ≤ 140, x ∈ R

3. 110 ≤ 4x + 2 ≤ 140, x ∈ R

4. 110 ≤ 2x + 1 ≤ 140, x ∈ R

2. The solution set for the breadth of the garden is:

1. {x ∈ R : 18 ≤ x ≤ 23}

2. {x ∈ R : 16 ≤ x ≤ 24}

3. {x ∈ R : 18 ≤ x ≤ 24}

4. {x ∈ R : 20 ≤ x ≤ 28}

3. The greatest possible value of the breadth of the garden is:

1. 18 m

2. 20 m

3. 22 m

4. 23 m

4. What is the least possible length of the garden?

1. 34 m

2. 36 m

3. 37 m

4. none of these

5. What is the greatest possible length of the garden?

1. 47 m

2. 51 m

3. 46 m

4. none of these

Case Study II

A few countries such as the USA officially use Fahrenheit as a unit for measuring temperature. Other countries prefer Celsius over Fahrenheit. The two different scales are related by the linear equation, $\dfrac{F - 32}{9} = \dfrac{C}{5}$. A scientist wants to store an experimental solution between a temperature range of 68°F and 77°F.

Based on the above information, answer the following questions:

1. The algebraic representation of the given information in degree Celsius is :

1. 68 < $\dfrac{5}{9}C$ + 32 ≤ 77, C ∈ R

2. 68 ≤ $\dfrac{5}{9}C$ − 32 ≤ 77, C ∈ R

3. 68 ≤ $\dfrac{9}{5}C$ − 32 < 77, C ∈ R

4. 68 < $\dfrac{9}{5}C$ + 32 < 77, C ∈ R

2. The solution set for the temperature in degree Celsius is:

1. {C ∈ R : 18 < C < 23}

2. {C ∈ R : 20 < C < 25}

3. {C ∈ R : 22 < C < 27}

4. {C ∈ R : 25 < C < 30}

3. What is the range of the temperature in degree Celsius?

1. between 20°C and 25°C

2. between 25°C and 30°C

3. between 18°C and 23°C

4. between 22°C and 27°C

4. Which of the following is the graphical representation of the temperature in degree Celsius?

a.

b.

c.

d.

5. If the minimum temperature that can be maintained in a particular refrigerator is 0°C, what is the possible temperature range of the refrigerator on a Fahrenheit scale?

1. F > $\dfrac{160}{9}$

2. F < $\dfrac{160}{9}$

3. F > 32

4. F < 32

Assertion (A) : If 8 < 5(x + 1) - 2 ≤ 18, x ∈ R, then the smallest integer value of x is 0.

Reason (R) : Multiplying each side of an inequation by the same integer does not change inequality.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

Assertion (A) : For the inequation -12 < 3 - 4x ≤ 11, x ∈ N, the solution set is {1, 2, 3, 4}.

Reason (R) : The set of all those values of x from the replacement set which satisfy the given in equation is called the solution set of inequation.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false