Applications of Derivatives Test

Result

Applications of Derivatives Test - 44

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Weekly Quiz Competition

Question 1
4 / -1

A stone is thrown vertically upwards from the top of a tower 64 metres high according to the law s = 48t – 16t². The greatest height attained by the stone above the ground is

A
100 metre

B
64 metre

C
36 metre

D
32 metre

Solution
Question 2
4 / -1

A

B

C

D

Solution
Question 3
4 / -1

A particle is moving in a straight line according to the formula s = t² + 8t + 12. If s be measured in metre and t be measured in second, then the average velocity of the particle in third second is

A
14 m/sec

B
13 m/sec

C
15 m/sec

D
None of these
Question 4
4 / -1

A 10 cm long rod AB moves with its ends on two mutually perpendicular straight lines OX and OY. If the end A be moving at the race of 2 cm/sec, then when the distance of A from O is 8 cm, the rate at which the end B is moving, is

A

B

C

D
None of these

Solution
Question 5
4 / -1

A triangular park is enclosed on two side on two sides by a fence and on the third side by straight river bank. The two sides having fence are of same length x. The maximum are enclosed by the park is

A

B

C

D

Solution
Question 6
4 / -1

If y = x³ + 5 and x changes from 3 to 2.99, then the approximate change in y is

A
2.7

B
–0.27

C
27

D
None of these

Solution
Question 7
4 / -1

A particle is moving on a straight line, where its position’s (in metre) is a function of time t (in seconds) given by = at² + bt + 6 ≥ 0. If it is known that the particle comes to rest after 4 seconds at a distance of 16 metre from the starting position (t = 0), then the retardation in its motion is

A
–1 m/s²

B

C

D

Solution
Question 8
4 / -1

The equation of particle is x = t³ – 9t² + 3t + 1 and v = –24, then a =

A
3

B
2

C
1

D
0

Solution
Question 9
4 / -1

A ball thrown vertically upwards falls back on the ground after 6 second, Assuming that the equation of motion is of the form s = ut – 4.9t², where is in metre and t is in second, find the velocity at t = 0

A
0 m/s

B
1 m/s

C
29.4 m/s

D
None of these

Solution
Question 10
4 / -1

Radius of a circle is increasing uniformly at the rate of 3 cm/sec. The rate of increasing of area when radius is 10 cm, will be

A
π cm²/s

B
2π cm²/s

C
10π cm²/s

D
None of these

Solution