Mathematics
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:
180 < 30 + 25(x − 3) < 330
180 ≤ 30 + 25(x − 3) ≤ 330
330 < 30 + 25(x − 3) ≤ 180
330 < 30 + 25(x − 3) < 180
2. The solution set for the depth is :
{x ∈ R : 6 ≤ x ≤ 12}
{x ∈ R : 9 ≤ x ≤ 12}
{x ∈ R : 3 ≤ x ≤ 15}
{x ∈ R : 9 ≤ x ≤ 15}
3. The minimum possible depth of the hole for the given temperature range is:
3 km
6 km
9 km
cannot be determined
4. The maximum possible depth of the hole for the given temperature range is:
9 km
12 km
15 km
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.
Related Questions
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:
140 ≤ 6x + 2 ≤ 110, x ∈ R
110 ≤ 6x + 2 ≤ 140, x ∈ R
110 ≤ 4x + 2 ≤ 140, x ∈ R
110 ≤ 2x + 1 ≤ 140, x ∈ R
2. The solution set for the breadth of the garden is:
{x ∈ R : 18 ≤ x ≤ 23}
{x ∈ R : 16 ≤ x ≤ 24}
{x ∈ R : 18 ≤ x ≤ 24}
{x ∈ R : 20 ≤ x ≤ 28}
3. The greatest possible value of the breadth of the garden is:
18 m
20 m
22 m
23 m
4. What is the least possible length of the garden?
34 m
36 m
37 m
none of these
5. What is the greatest possible length of the garden?
47 m
51 m
46 m
none of these
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.
A is true, R is false
A is false, R is true
Both A and R are true
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.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false