MCQs of Applications of Derivatives

Applications of Derivatives MCQs

MCQs of Applications of Derivatives

Showing 181 to 190 out of 266 Questions

181.

The rate of change of surface area of a sphere w.r.t. time is 16π cm²/sec. Find the rate of the change in its volume with to time at the moment when the radius is 2 cm.

(a)	32
(b)	8
(c)	16
(d)	4

182.

The rate of change of volume of sphere with respect to its surface area S is _____ .

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

183.

The total revenue received from the sale of x units is given by R(x) = 10x² + 20x + 1500. The marginal revenue, when x = 2015, is _____.

(a)	40300
(b)	4032
(c)	40320
(d)	403

184.

Approximate value of

\cos^{- 1} (- 0.49)

is ______ .

(a)	$\frac{π}{3} + \frac{1}{50 \sqrt{3}}$
(b)	$\frac{2 π}{3} + \frac{1}{50 \sqrt{3}}$
(c)	$\frac{2 π}{3} - \frac{1}{50 \sqrt{3}}$
(d)	$\frac{π}{3} - \frac{1}{50 \sqrt{3}}$

185.

If y = f(x) = sinx, then differential dy = ______, where

x = \frac{π}{6}

,dx = 0.01.

(a)	$\sqrt{3}$
(b)	$\sqrt{3} (0.005)$
(c)	$\sqrt{3} (0.05)$
(d)	$\sqrt{3} (0.5)$

186.

The critical point for

f (x) = x^{\frac{3}{5}} (4 - x), x \in R^{+} \cup \{0\}

is _____.

(a)	$0, \frac{- 2}{3}$
(b)	$0, \frac{- 3}{2}$
(c)	$0, \frac{3}{2}$
(d)	$0, \frac{2}{3}$

187.

The position of a particle is given by s = t³ - 6t² - 15t, where s is in meters, t is in seconds. If the particles is at rest, then time t = ______ .

(a)	0
(b)	5
(c)	1
(d)	5, 1

188.

For a curve y² =ax³ + b if the slope of the tangent at point (2, 3) is 4, then a = _____ .

(a)	-7
(b)	-2
(c)	2
(d)	7

189.

If the radius of a sphere is 2, the rate of change of volume of a sphere with respect to its surface area is _____.

(a)	1
(b)	2
(c)	3
(d)	None of the above

190.

If the error in measuring the area of a circle is 4%, then the error in measuring radius is _____ %.

(a)	2
(b)	4
(c)	6
(d)	8

Showing 181 to 190 out of 266 Questions