MCQs of Applications of Derivatives

Applications of Derivatives MCQs

MCQs of Applications of Derivatives

Showing 221 to 230 out of 266 Questions

221.

If f (x) = \int e^{x} (x - 1) (x - 2) d x, then f is decreasing function in_____interval .

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

222.

If x + y = k is normal to the parabola y² = x, then k = _____.

(a)	3
(b)	9
(c)	-9
(d)	-3

223.

If f(x) = xe^{x(1 - x)}, then f(x) is _____.

(a)	increasing on $[- \frac{1}{2}, 1]$
(b)	decreasing on R
(c)	increasing on R
(d)	decreasing on $[- \frac{1}{2}, 1]$

224.

Let f(x) = (1 + b²)x² + 2bx + 1 and let m(b) be the minimum value of f(x). As b varies, the range of m(b) is _____.

(a)	[0, 1]
(b)	$(0, \frac{1}{2}]$
(c)	$[\frac{1}{2}, 1]$
(d)	(0, 1]

225.

The equation of motion of a particle is x = at² + bt + c If ac = b², then the particle moves with constant _____ .

(a)	rotation
(b)	velocity
(c)	acceleration
(d)	retardation

226.

The ratio of height of cone of maximum volume inscribed in a sphere to its radius is _____ .

(a)	$\frac{3}{4}$
(b)	$\frac{4}{3}$
(c)	$\frac{1}{2}$
(d)	$\frac{2}{3}$

227.

Tangent from origin to parabola y² + 4 = 4x are inclined at _____ .

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

228.

A particle moves in a straight line so that

S = \frac{y^{2}}{b^{2}}

, then its acceleration is proportional to ______.

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

229.

Line \frac{x}{a} + \frac{y}{b} = 2 touches the curve \frac{x^{n}}{a} + \frac{y^{n}}{b} = 2 point_____.

(a)	(a, -b)
(b)	(a, b)
(c)	(-a, b)
(d)	None of the above

230.

The distance travelled by a motor car in t second after the brakes are applied is s feet, where s = 22t - 12t² the distance travelled by the car before it stops, is _____ feet.

(a)	10.08
(b)	10
(c)	11
(d)	11.5

Showing 221 to 230 out of 266 Questions