MCQs of Applications of Derivatives

Applications of Derivatives MCQs

MCQs of Applications of Derivatives

Showing 241 to 250 out of 266 Questions

241.

The side of an equilateral triangle increase at 2 cm/sec. When the length of the side is 10 cm, the rate at which area increases is _____ cm²/sec.

(a)	$\sqrt{3}$
(b)	10
(c)	$10 \sqrt{3}$
(d)	$\frac{10}{\sqrt{3}}$

242.

The point _____ at which normal to the curve

\sqrt{x} + \sqrt{y} = \sqrt{a}

is parallel to X - axis.

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

243.

The point on the curve xy² = 1 that is nearest to the origin is _____.

(a)	$(4, \frac{1}{2})$
(b)	$(\frac{1}{4}, 2)$
(c)	$(2^{\frac{1}{6}}, 2^{- \frac{1}{2}})$
(d)	$(2^{- \frac{1}{3}}, 2^{\frac{1}{6}})$

244.

The equation of the tangent to the curve y = (1 + x)^y + sin^-1(sin²x) at x = 0 is _____ .

(a)	x - y + 1 = 0
(b)	x + y + 1 = 0
(c)	2x - y + 1 = 0
(d)	2x + y - 1 = 0

245.

If f(x) = 3x⁴ + 4x³ - 12x² + 12, then f(x) is _____ function.

(a)	increasing in (-∞,-2) and (0, 1)
(b)	increasing in (-2, 0) and (1,∞)
(c)	decreasing in (-2, 0) and (0, 1)
(d)	decreasing in (-∞,-2) and (1,∞)

246.

A man of height 2 m walks away from electric pole at the speed of 6 km/hour. The rate at which the length of shadow increases is _____ km/hour.

(a)	2
(b)	3
(c)	$\frac{3}{2}$
(d)	6

247.

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)	$\frac{5}{8}$

248.

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)	$\frac{1}{9}$

249.

If y = 4x - 5 is a tangent to the curve y² = px³ + q at (2, 3), then _____ .

(a)	p = 2, q = -7
(b)	p = -2, q = 7
(c)	p = -2, q = -7
(d)	p = 2, q = 7

250.

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

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

Showing 241 to 250 out of 266 Questions