MCQs of Applications of Derivatives

Applications of Derivatives MCQs

MCQs of Applications of Derivatives

Showing 111 to 120 out of 266 Questions

111.

The cost of running a bus from A to B, is Rs.

(a v + \frac{b}{v})

where v km/h is the average speed of the bus. When the bus travels at 30 km/h the cost comes out to be Rs. 75 while at 40 km/h, it is Rs.65, Then the most economical speed(in km/h) of the bus is :

(a)	45
(b)	50
(c)	60
(d)	40

112.

A spherical balloon is being inflated at the rate of 35 cc/min. The rate of increase in the surface area (in cm²/min) of the balloon when its diameter is 14 cm is :

(a)	10
(b)	$\sqrt{10}$
(c)	100
(d)	$10 \sqrt{10}$

113.

If an equation of a tangent to the curve ,

y = \cos (x + y), - 1 \leq x \leq 1 + π

is x + 2y = k then k is equal to :

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

114.

If x = -1 and x = 2 are extreme points of

f (x) = α \log |x| + β x^{2} + x

than :

(a)	$α = 2, β = - \frac{1}{2}$
(b)	$α = 2, β = \frac{1}{2}$
(c)	$α = - 6, β = \frac{1}{2}$
(d)	$α = - 6, β = - \frac{1}{2}$

115.

f (x) = {(\frac{3}{5})}^{x} + {(\frac{4}{5})}^{x} - 1, x \in R

then the equation f(x) = 0 has :

(a)	no solution
(b)	one solution
(c)	two solution
(d)	more than two solution

116.

Two ships A and B are sailing straight away from a fixed point O along routes such that ∠AOB is always 120°. At a certain instance, OA = 8, OB = 6 km and the ship A is sailing at the rate of 20 km/hr. while the ship B sailing at the rate of 30 km/hr. Then the distance between A and B is changing at the rate (km/hr)

(a)	$\frac{260}{\sqrt{37}}$
(b)	$\frac{260}{37}$
(c)	$\frac{80}{\sqrt{37}}$
(d)	$\frac{80}{37}$

117.

The volume of the largest possible right circular cylinder that can be inscribed that can be in a sphere of radius =

\sqrt{3}

is _____

(a)	$\frac{4}{3} \sqrt{3} π$
(b)	$\frac{8}{3} \sqrt{3} π$
(c)	$4 π$
(d)	$2 π$

118.

Let f and g be two differentiable functions on R such that f'(x) > 0 and g'(x) < 0 for all

\forall x \in R

Then for all x :

(a)	$f (g (x)) > f (g (x - 1))$
(b)	$f (g (x)) > f (g (x + 1))$
(c)	$g (f (x)) > g (f (x - 1))$
(d)	$g (f (x)) < g (f (x + 1))$

119.

If the volume of a spherical ball is increasing at the rate of 4π cm/sec, then the rate of increase of its radius (in cm/sec ) when the volume is 288π cc is :

(a)	$\frac{1}{6}$
(b)	$\frac{1}{9}$
(c)	$\frac{1}{36}$
(d)	$\frac{1}{24}$

120.

The normal to the curve, x² + 2xy - 3y² = 0, at (1, 1) :

(a)	does not meet the curve again.
(b)	meets the curve again in the second quadrant.
(c)	meets the curve again in the third quadrant.
(d)	meets the curve again in the fourth quadrant.

Showing 111 to 120 out of 266 Questions