Applications of Derivatives Test

Result

Applications of Derivatives Test - 28

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Question 1
4 / -1

A spherical balloon is filled with 4500π cu m of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72 π cu m/min, then the rate (in m/min) at which the radius of the balloon decreases 49 min after the leakage began is

A
9/7

B
7/9

C
2/9

D
9/2

Solution
Question 2
4 / -1

If y = 2x³ - 2x² + 3x -5, then for x = 2 and ∆x = 0.1, value of ∆y is

A
2.002

B
1.9

C
0

D
0.9

Solution
Question 3
4 / -1

The distance (in metres) travelled by a vehicle in time t (in seconds) is given by the equation s = 3t³ + 2t² + t +1. The difference in the acceleration between t = 2 and t = 4 is

A
36 m/s²

B
38 m/s²

C
45 m/s²

D
46 m/s²

Solution
Question 4
4 / -1

The equation of motion of a particle moving along a straight line is s = 2t³ - 9t² + 12 t, where the units of s and t are cm and s. The acceleration of the particle will be zero after

A
3/2 s

B
2/3 s

C
1/2 s

D
1 s

Solution
Question 5
4 / -1

A particle is moving in a straight line. At time t, the distance between the particle from its starting point is given by x = t - 6t² + t³. Its acceleration will be zero at

A
t = 1 unit time

B
t = 2 units time

C
t = 3 units time

D
t = 4 units time

Solution
Question 6
4 / -1

The distance covered by a particle in t sec is given by x = 3 + 8t - 4t²

A
0 unit

B
3 units

C
4 units

D
7 units

Solution
Question 7
4 / -1

If a particle moves such that the displacement is proportional to the square of the velocity acquired, then its acceleration is

A
proportional to s²

B
proportional to 1/s²

C
proportional to 1/s

D
a constant

Solution
Question 8
4 / -1

Let f : [0,1] → R(the set of all real numbers) be a function. Suppose the function f is twice differentiable,
f(0) = f(1) = 0 and satisfies f \'\'(x) - 2f \'(x) + f(x) ≥ e^x, x ϵ [0,1].
Which of the following is correct for 0 < x < 1?

A

B

C

D

Solution
Question 9
4 / -1

The function f(x) = tan^-1 (sin x + cos x) is an increasing function in

A

B

C

D

Solution
Question 10
4 / -1

A
p = q = r = 0

B
p = 0, q = 0, r is any real number

C
q = 0, r = 0, p is any real number

D
r = 0, p = 0, q is any real number

Solution