MCQs of Applications of Derivatives

Applications of Derivatives MCQs

MCQs of Applications of Derivatives

Showing 121 to 130 out of 152 Questions

121.

A spherical balloon is filled with 4500π cubic meter of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72π cubic metre/minute, the rate (in metres per minute) at which the radius of the balloon decreases 49 minutes after the leakage begins is _____ metre/minute.

(a)	$\frac{9}{7}$
(b)	$\frac{7}{9}$
(c)	$\frac{2}{9}$
(d)	$\frac{9}{2}$

122.

On the interval [0, 1] the function x²⁵(1 - x)⁷⁵ takes its maximum value at the point x = _____.

(a)	0
(b)	$\frac{1}{4}$
(c)	$\frac{1}{2}$
(d)	$\frac{1}{3}$

123.

If f (x) = \int e^{x} (x - 1) (x - 2) d x, then f is decreasing function in_____interval .

(a)	$(- \infty, - 2)$
(b)	$(- 2, - 1)$
(c)	$(1, 2)$
(d)	$(2, \infty)$

124.

If f(x) = xe^{x(1 - x)}, then f(x) is _____.

(a)	increasing on $[- \frac{1}{2}, 1]$
(b)	decreasing on R
(c)	increasing on R
(d)	decreasing on $[- \frac{1}{2}, 1]$

125.

Let f(x) = (1 + b²)x² + 2bx + 1 and let m(b) be the minimum value of f(x). As b varies, the range of m(b) is _____.

(a)	[0, 1]
(b)	$(0, \frac{1}{2}]$
(c)	$[\frac{1}{2}, 1]$
(d)	(0, 1]

126.

The equation of motion of a particle is x = at² + bt + c If ac = b², then the particle moves with constant _____ .

(a)	rotation
(b)	velocity
(c)	acceleration
(d)	retardation

127.

The ratio of height of cone of maximum volume inscribed in a sphere to its radius is _____ .

(a)	$\frac{3}{4}$
(b)	$\frac{4}{3}$
(c)	$\frac{1}{2}$
(d)	$\frac{2}{3}$

128.

A particle moves in a straight line so that

S = \frac{y^{2}}{b^{2}}

, then its acceleration is proportional to ______.

(a)	${(velocity)}^{3}$
(b)	velocity
(c)	${(velocity)}^{2}$
(d)	${(velocity)}^{\frac{3}{2}}$

129.

The distance travelled by a motor car in t second after the brakes are applied is s feet, where s = 22t - 12t² the distance travelled by the car before it stops, is _____ feet.

(a)	10.08
(b)	10
(c)	11
(d)	11.5

130.

The maximum value of the curve, y = -x³ + 3x² + 9x - 27 is _____ .

(a)	0
(b)	12
(c)	16
(d)	32

Showing 121 to 130 out of 152 Questions