Page 71 - Mathematics Class - XII

Case-Study Based Questions
Case-Study Based Questions

The fuel cost per hour for running a truck is proportional to the square of the speed it generates in km per hour.
If the fuel cost ` 48 per hour at speed 16 km/h and the fixed charges to run the truck amount to ` 1200 per hour.
Assume the speed of truck is υ km/h.
Based upon the above information, give the answer of the following questions.
1. Given that the fuel cost per hour in m times the square of the speed of truck generates in km/h, the value
of m is

(a) 16 (b) 1 (c) 3 (d) 3
3 3 16
2. If the truck has travelled a distance of 500 km then the total cost of running the truck is given by

(a) 15 600000 (b) 375 600000 (c) 5 150000 (d) 3 6000
2
16 4 16 16
3. The most economical speed to run the truck is

(a) 18 km/h (b) 5 km/h (c) 80 km/h (d) 40 km/h
4. The fuel cost for the truck to travel 500 km at the most economical speed is
(a) ` 3750 (b) ` 75000 (c) ` 7500 (d) ` 15000

Assertion-Reason Based Questions
Assertion-Reason Based Questions
Directions for Questions 1 to 3: In each of the questions given below, there are two statements marked as
Assertion (A) and Reason (R). Mark your answer as per the codes provided below:

(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false. (d) A is false but R is true.
Q. 1. Assertion (A) : If x is real, then the minimum value of x – 8 x + 17 is 1.
2
Reason (R) : If f (x) > 0 at critical point, then the value of the function at critical point will be
''
the minimum value of the function.
Q. 2. Assertion (A) : The absolute maximum value of the function 2x – 24 x in the interval [1, 3] is 89.
3
Reason (R) : The absolute maximum value of the function can be obtained from the value of the
function at critical points and at boundary points.

Q. 3. Assertion (A) : The function, f (x) = sin x decreases on the interval 0,

2

Reason (R) : The function, f (x) = cos x decreases on the interval 0,

2
Answers

Case-Study Based Questions: 1. (d) 2. (b) 3. (c) 4. (c)
Assertion-Reason Based Questions: 1. (a) 2. (d) 3. (d)

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