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