MCQs of Applications of Derivatives

Applications of Derivatives MCQs

MCQs of Applications of Derivatives

Showing 251 to 260 out of 266 Questions

251.

The x-co-ordinate of the point where tangent is parallel to X - axis to the curve y = x³ - 3x² + 9x + 5 is _____ .

(a)	-1, 3
(b)	-3, 1
(c)	1, -1
(d)	0

252.

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

253.

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)	$\frac{p}{4}$

254.

The equation of the tangent to the curve (1 + x²)y = 2 - x where it intersects X - axis is _____.

(a)	x + 5y = 2
(b)	x - 5y = 2
(c)	5x - y = 2
(d)	5x + y - 2 = 0

255.

If the curve y = 2x³ + ax² + bx + c passes through origin and tangent at x = -1 and x = 2 are parallel to X - axis, then the values of a, b and c are _____respectively.

(a)	12, -3, 0
(b)	-3, -12, 0
(c)	-3, 12, 0
(d)	3, -12, 0

256.

At the point _____ of the curve y² = x tangent makes an angle of measure 45° with the positive direction of X - axis.

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

257.

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

258.

If the curves y² = 4x and xy = k are mutually orthogonal, then k² = _____.

(a)	16
(b)	36
(c)	32
(d)	8

259.

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

260.

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

Showing 251 to 260 out of 266 Questions