MCQs of Applications of Derivatives

Applications of Derivatives MCQs

MCQs of Applications of Derivatives

Showing 51 to 60 out of 266 Questions

51.

The minimum value of

s e c x, x \in [\frac{2 π}{3}, π]

is _____.

(a)	1
(b)	-2
(c)	2
(d)	$π$

52.

The maximum value of

cosecx, x \in [\frac{π}{6}, \frac{π}{3}]

is_____.

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

53.

f

is decreasing in

[a, b]

, its minimum and maximum values are respectively _____ and _____.

(a)	$f (a) a n d f (b)$
(b)	$f (b) a n d f (a)$
(c)	$f (\frac{a + b}{2}) a n d f (a)$
(d)	$f (b) a n d f (\frac{a + b}{2})$

54.

The side of an equilateral triangle expands at the rate of

\sqrt{3} c m / s e c .

When the side is

12 c m,

the rate of increase of its area is_____.

(a)	$12 c m^{2} / s e c$
(b)	$18 c m^{2} / s e c$
(c)	$3 \sqrt{3} c m^{2} / s e c$
(d)	$10 c m^{2} / s e c$

55.

At_____on circle x^{2} + y^{2} - 2 x - 3 = 0, the tangent is horizontal .

(a)	$(0, \pm \sqrt{3})$
(b)	$(2, \pm \sqrt{3})$
(c)	$(1, 2), (1, - 2)$
(d)	(3, 0)

56.

A particle moving in a straight line. has velocity v at any point, where v² = 2 - 3x.If x represents its distance from a fixed point at time t then, acceleration of particle is _____

(a)	constant
(b)	zero
(c)	variable
(d)	undefined

57.

When x= 3 then rate of change of w.r.t. is _____

(a)	$- \frac{12}{5}$
(b)	$\frac{6}{5}$
(c)	$- \frac{6}{5}$
(d)	3

58.

The rate of increase of the diagonal of a square is 0.5 cm/sec. When area of square is 400 cm² then the rate of change of its area is _____ cm²/sec.

(a)	$5 \sqrt{2}$
(b)	$\frac{1}{10 \sqrt{2}}$
(c)	$\frac{10}{\sqrt{2}}$
(d)	$10 \sqrt{2}$

59.

If displacement x of particle at a time t is x = At² + Bt + c(where A, B and C are constant) and velocity is v then, 4Ax - v² =

(a)	4AC + B²
(b)	4AC - B²
(c)	2AC - B²
(d)	2AC + B²

60.

The rate of increase of volume of sphere w.r.t. its surface area S is _____

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

Showing 51 to 60 out of 266 Questions