MCQs of Applications of Derivatives

Applications of Derivatives MCQs

MCQs of Applications of Derivatives

Showing 61 to 70 out of 152 Questions

61.

A + B = \frac{π}{2}

then maximum value of cosA cosB is _____

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

62.

f (x) = \sin x (1 + \cos x)

is maximum at _____

(a)	$x = \frac{π}{2}$
(b)	$x = \frac{π}{6}$
(c)	$x = \frac{π}{3}$
(d)	$x = π$

63.

Maximum value of is

4 e^{x} + 9 e^{- 2 x}

is _____

(a)	11
(b)	12
(c)	10
(d)	14

64.

Minimum value of is

27^{c o s 2 x} 81^{\sin 2 x}

is _____

(a)	$\frac{1}{243}$
(b)	$\frac{1}{27}$
(c)	-5
(d)	$\frac{1}{5}$

65.

If the surface area of a sphere of radius r is increasing uniformly at the rate 8 cm²/s , then the rate of change of its volume is :

(a)	constant
(b)	proportional to $\sqrt{r}$
(c)	proportional to r²
(d)	proportional to r

66.

The maximum area of a right angled triangle with hypotenuse h is :

(a)	$\frac{h^{3}}{2 \sqrt{2}}$
(b)	$\frac{h^{2}}{2}$
(c)	$\frac{h^{2}}{\sqrt{2}}$
(d)	$\frac{h^{2}}{4}$

67.

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

68.

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)	$10 \sqrt{10}$

69.

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)	$α = - 6, β = - \frac{1}{2}$

70.

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)	$\frac{80}{37}$

Showing 61 to 70 out of 152 Questions