Applications of Derivatives Test

Result

Applications of Derivatives Test - 45

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Question 1
4 / -1

Two automobiles start from a point A at the same time. One travels towards west at the speed of 60 miles per hour while the other travels towards North at 35 mph. Their distance apart after 3 hours later is increasing at the rate (in mph)

A

B

C

D
None of these

Solution
Question 2
4 / -1

A particle is moving in a straight line. Its displacement at time t is given by s = – 4t² + 2t, then its velocity and acceleration at time t = 1/2 second are

A
–2, –5

B
2, 6

C
–2, 8

D
2, 8

Solution
Question 3
4 / -1

If the distance travelled by a point in time t is s = 180t – 16 t², then the rate of change in velocity is

A
– 16 t unit

B
48 unit

C
– 32 unit

D
None of these

Solution
Question 4
4 / -1

Water is flowing into a vertical cylindrical tank of radius 2ft. at the rate of 8 cubic ft. per minute. The water level is rising at the speed of (ft.per minute)

A

B

C
2

D
None of these

Solution
Question 5
4 / -1

A rectangle of perimeter 24 inches is rotated about one of its sides so as to form a cylinder. To attain the maximum volume of the cylinder what would be the dimensions of the rectangle (in inches)

A
8, 4

B
4, 4

C
8, 8

D
None of these

Solution
Question 6
4 / -1

A ladder is resting with the wall at an angle of 30^o. A man is ascending the ladder at the rate of 3 ft/sec. His rate of approaching the wall is

A
3 ft/sec

B

C

D

Solution
Question 7
4 / -1

If the distance ‘s’ travelled by a particle in time t is s = a sin t + b cos 2t, then the acceleration at t = 0 is

A
a

B
– a

C
4b

D
– 4b

Solution
Question 8
4 / -1

A particle moves so that S = 6 + 48t – t³. The direction of motion reverses after moving a distance of

A
63

B
104

C
134

D
288

Solution
Question 9
4 / -1

If the volume of a spherical balloon is increasing at the rate 900 cm³/sec, then the rate of charge of radius of balloon instant when radius is 15 cm [in cm/sec]

A

B
22

C

D
None of these

Solution
Question 10
4 / -1

If the path of a moving point is the curve x = at, y = b sin at, then its acceleration at any instant

A
Is constant

B
Varies as the distance from the axis of y

C
Varies as the distance from the axis of y

D
Varies as the distance of the point from the origin

Solution