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## Application of Derivatives Class 12 Multiple Choice Test

/10

Thank you for answering the multiple choice test

Application of Derivatives Class 12 (120601)

General Instruction:

1. There are 10 MCQ’s in the Test.

2. Passing %age is 50.

3. After time gets over, test will be submitted itself.

1 / 10

What is the value of ‘a’ in the function $$x^4 – 62x^2 + ax + 9$$, if the function attains its maximum value at $$x = 1$$ on the interval [0, 2]?
A) 33
B) 45
C) 28
D) 51

2 / 10

Find the maximum and minimum values of the function $$x + sin 2x$$ on the interval $$[0, 2\pi]$$.
A) Maximum value: 3, Minimum value: -1
B) Maximum value: 2, Minimum value: -2
C) Maximum value: 4, Minimum value: 0
D) Maximum value: 1, Minimum value: -3

3 / 10

Find two positive numbers x and y such that their sum is 35 and the product $$x^2 y^5$$ is a maximum.
A) x = 5, y = 30
B) x = 10, y = 25
C) x = 15, y = 20
D) x = 20, y = 15

4 / 10

A square piece of tin of side 18 cm is to be made into a box without a top. What should be the side of the square to be cut off so that the volume of the box is the maximum possible?
A) 3 cm
B) 4 cm
C) 5 cm
D) 6 cm

5 / 10

A ball, thrown into the air from a building 60 meters high, travels along a path given by $$h(x) = 60 – x^2$$. What is the maximum height the ball will reach?
A) 60 meters
B) 30 meters
C) 45 meters
D) 15 meters

6 / 10

An Apache helicopter of the enemy is flying along the path given by the curve $$f(x) = x^2 + 7$$. A soldier, placed at the point (1, 2), wants to shoot the helicopter when it is nearest to him. What is the nearest distance?
A) $$\sqrt{10}$$ units
B) $$\sqrt{5}$$ units
C) 5 units
D) 10 units

7 / 10

Find two positive numbers whose sum is 16 and the sum of whose cubes is minimum.
A) 4 and 4
B) 3 and 5
C) 2 and 6
D) 5 and 3

8 / 10

For what values of a, the function f given by $$f(x) = x^2 + ax + 1$$ is increasing on [1, 2]?
A) All values of a
B) No values of a
C) Some values of a
D) None of these

9 / 10

A rectangular sheet of tin 45 cm by 24 cm is to be made into a box without a top. What should be the side of the square to be cut off so that the volume of the box is maximum?
A) 6 cm
B) 8 cm
C) 10 cm
D) 12 cm

10 / 10

Find two positive numbers x and y such that $$x + y = 60$$ and $$xy^3$$ is maximum.
A) x = 15, y = 45
B) x = 20, y = 40
C) x = 25, y = 35
D) x = 30, y = 30