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

Case Study III

In drilling world’s deepest hole, the Kola Superdeep Borehole, the deepest man made hole on the earth, it was found that the temperature T in degree Celsius, x km below the earth’s surface was given by, T = 30 + 25(x - 3) and 3 ≤ x ≤ 15. If the temperature lies between 180° C to 330° C, then based on this information, answer the following questions.

1. The linear inequation for the depth of the hole is:

1. 180 < 30 + 25(x − 3) < 330

2. 180 ≤ 30 + 25(x − 3) ≤ 330

3. 330 < 30 + 25(x − 3) ≤ 180

4. 330 < 30 + 25(x − 3) < 180

2. The solution set for the depth is :

1. {x ∈ R : 6 ≤ x ≤ 12}

2. {x ∈ R : 9 ≤ x ≤ 12}

3. {x ∈ R : 3 ≤ x ≤ 15}

4. {x ∈ R : 9 ≤ x ≤ 15}

3. The minimum possible depth of the hole for the given temperature range is:

1. 3 km

2. 6 km

3. 9 km

4. cannot be determined

4. The maximum possible depth of the hole for the given temperature range is:

1. 9 km

2. 12 km

3. 15 km

4. None of these

5. Which of the following is the graphical representation of the solution set for the depth of the hole for the given temperature range?

a.

b.

c.

d.

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) : If 2x - 5 ≤ 5x + 4 < 11, x ∈ I, then greatest value of x is 1.

Reason (R) : Adding or subtracting a negative integer to each side of an inequation does not change the 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