MCQs of Applications of Derivatives

Applications of Derivatives MCQs

MCQs of Applications of Derivatives

Showing 141 to 150 out of 152 Questions

141.

A spotlight on the ground shines on a wall 12 m away from the light. If a man of height 2 m walks away from the spotlight towards the wall at a speed of

\frac{1}{2}

m/sec, then the rate at which the length of his shadow on the wall is decreasing at the instant when he is 8 m from the wall is _____ m/sec.

(a)	$\frac{3}{4}$
(b)	$\frac{5}{4}$
(c)	$\frac{3}{8}$
(d)	$\frac{5}{8}$

142.

A spherical iron ball of radius 10 cm coated with a layer of ice of uniform thickness melts at a rate of 100π cm³/min. The rate at which the thickness of ice decreases when the thickness of ice is 5 cm is _____ .

(a)	$\frac{1}{54}$
(b)	$\frac{1}{36}$
(c)	$\frac{1}{18}$
(d)	$\frac{1}{9}$

143.

The function f(x) = 2x³ - 15x² + 36x + 4 has local maximum at _____ .

(a)	x = 3
(b)	x = 0
(c)	x = 4
(d)	x = 2

144.

If f : R → R and f(x) = 2x + cosx, then f _____.

(a)	has local minimum at x = π
(b)	has local maximum at x = 0
(c)	is a decreasing function
(d)	is an increasing function

145.

The perimeter of a sector is p. When the radius is _____, its area becomes maximum.

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

146.

The side of a square sheet of metal is increasing at the rate of 3 cm/sec. The rate at which the area increasing when the side is 10 cm is _____ cm²/sec.

(a)	30
(b)	40
(c)	60
(d)	90

147.

If x + y = 60; x, y > 0, then the maximum value of xy³ is _____.

(a)	30
(b)	60
(c)	15(45)³
(d)	45(15)³

148.

If h(x) = f(x) + f(-x), then h(x) has got an extreme at a point where f'(x) is _____ .

(a)	an even function
(b)	an odd function
(c)	zero
(d)	None of the above

149.

f (x) = a \log |x| + b x^{2} + x

has extreme values at x = -1 and x = 2, then _____.

(a)	a = 2, b = -1
(b)	$a = 2, b = - \frac{1}{2}$
(c)	$a = - 2, b = \frac{1}{2}$
(d)	None of the above

150.

The number of values of x where the function

f (x) = \cos x + \cos (\sqrt{2} x)

attains its maximum is _____.

(a)	0
(b)	1
(c)	2
(d)	infinite

Showing 141 to 150 out of 152 Questions