MCQs of Applications of Derivatives

Applications of Derivatives MCQs

MCQs of Applications of Derivatives

Showing 71 to 80 out of 152 Questions

71.

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)	$2 π$

72.

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)	$g (f (x)) < g (f (x + 1))$

73.

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)	$\frac{1}{24}$

74.

Let f(x) be a polynomial of degree four having extreme values at x = 1 and x = 2. If

\lim_{x \to 0} [1 + \frac{f (x)}{x^{2}}] = 3

, then f(b) is equal to :

(a)	-8
(b)	-4
(c)	0
(d)	4

75.

Let k and K be the minimum and the maximum values of the function

f (x) = \frac{{(1 + x)}^{૦ . 6}}{1 + x^{0.6}}

in [0, 1] respectively, then the ordered pair (k, K) is equal to :

(a)	$(1, 2^{૦ . 6})$
(b)	$(2^{- 0.4}, 2^{૦ . 6})$
(c)	$(2^{- 0.6}, 1)$
(d)	$(2^{- 0.4}, 1)$

76.

A wire of length 2 units is cut into two parts which are bent respectively to form a square of side = x units and a circle of radius = r units. If the sum of the areas of the square and the circle so formed is minimum, then :

(a)	x= 2r
(b)	2x = r
(c)	2x = (x + 4)r
(d)	$(4 - π) x = πr$

77.

The minimum distance of a point on the curve

y = x^{2} - 4

from origin is

(a)	$\frac{\sqrt{15}}{2}$
(b)	$\sqrt{\frac{19}{2}}$
(c)	$\sqrt{\frac{15}{2}}$
(d)	$\frac{\sqrt{19}}{2}$

78.

Let

f (x) = \sin^{4} x + \cos^{4} x

, Then f is increasing function in the interval :

(a)	$[\frac{5 π}{8}, \frac{3 π}{4}]$
(b)	$[\frac{π}{2}, \frac{5 π}{8}]$
(c)	$[\frac{π}{4}, \frac{π}{2}]$
(d)	$[0, \frac{π}{4}]$

79.

log

|\sin x|

is _____ function on

(0, \frac{π}{3})

(a)	increasing
(b)	decreasing
(c)	constant
(d)	impossible

80.

Rate of increase of the area of a square w.r.t its perimeter is _____ (l = length of a side of the square).

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

Showing 71 to 80 out of 152 Questions