MCQs of Applications of Derivatives

Applications of Derivatives MCQs

MCQs of Applications of Derivatives

Showing 31 to 40 out of 152 Questions

31.

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

32.

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

33.

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)	$10 \sqrt{2}$

34.

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

35.

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)	$\frac{1}{2} \sqrt{\frac{S}{π}}$

36.

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)	$\frac{15}{2} π$

37.

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)	$\frac{π}{3}$

38.

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

39.

Function

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

is _____ function.

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

40.

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)	$π$

Showing 31 to 40 out of 152 Questions