MCQs of Applications of Derivatives

Applications of Derivatives MCQs

MCQs of Applications of Derivatives

Showing 61 to 70 out of 266 Questions

61.

The variable diameter of a balloon in shape of sphere is

\frac{3}{2} (2 x + 1)

. When x = 2, then increase in its volume w.r.t. x is _____

(a)	$\frac{675 π}{8}$
(b)	$\frac{675 π}{4}$
(c)	$- \frac{675 π}{8}$
(d)	$\frac{15}{2} π$

62.

For which angle of measure θ, the rate of its increase is two times the rate of increase of sinθ ?

(a)	$\frac{π}{4}$
(b)	$\frac{π}{6}$
(c)	$\frac{3 π}{4}$
(d)	$\frac{π}{3}$

63.

Two cycle riders move on different road which is mutually perpendicular to each other from junction with the velocity of 3 m/sec and 4 m/sec. The rate at which both the cycle-riders move away from each other is _____ m/sec.

(a)	5
(b)	7
(c)	6
(d)	3

64.

Function

f (x) = \frac{e^{2 x} - 1}{e^{2 x} + 1}

is _____ function.

(a)	increasing
(b)	decreasing
(c)	even
(d)	none of these

65.

The length of the longest interval in which the function 3sinx - 4sin³x, is increasing, is _____

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

66.

f (x) = 1 - x^{2} - x^{5}

is decreasing function for _____

(a)	$1 \leq x \leq 5$
(b)	$x \leq 1$
(c)	$x \geq 1$
(d)	$\forall x \in R$

67.

f (x) = \frac{1}{x + 1} - \log (x + 1), x > 0

(a)	increasing function
(b)	decreasing function
(c)	both increasing and decreasing function
(d)	none of these

68.

f (x) = {(x (x - 2))}^{2}

is increasing function in

(a)	$(- \infty, 0) \cup (2, \infty)$
(b)	$(- \infty, 1)$
(c)	$(0, 1) \cup (2, \infty)$
(d)	$(1, 2)$

69.

f (x) = \cos x - 2 p x

is strictly increasing for

(a)	$p < \frac{1}{2}$
(b)	$p > \frac{1}{2}$
(c)	$p < 2$
(d)	$p > 2$

70.

f (x) = \cos |x| - 2 a x + b

is increasing for all x∈R then

(a)	$a \leq b$
(b)	2a = b
(c)	$2 a \leq - 1$
(d)	$2 a \geq - 3$

Showing 61 to 70 out of 266 Questions