MCQs of Applications of Derivatives

Applications of Derivatives MCQs

MCQs of Applications of Derivatives

Showing 131 to 140 out of 152 Questions

131.

The line which is parallel to X - axis and crosses the curve

y = \sqrt{x}

at an angle of 45° is _____ .

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

132.

Gas is being pumped into a spherical balloon at the rate of 30 feet³/min. Then the rate at which the radius increases when it reaches the value 15 feet is _____ feet/min.

(a)	$\frac{1}{30 π}$
(b)	$\frac{1}{15 π}$
(c)	$\frac{1}{20}$
(d)	$\frac{1}{25}$

133.

The perimeter of a sector is constant. If its area is maximum, the measure of angle between radii is _____ .

(a)	$\frac{π^{c}}{6}$
(b)	$\frac{π^{c}}{4}$
(c)	$4^{c}$
(d)	$2^{c}$ a

134.

If θ is the measure of the angle between the curves xy = 2 and x² + 4y = 0, then tanθ = _____ .

(a)	1
(b)	-1
(c)	2
(d)	3

135.

The condition for which f(x) = x³ + px² + qx + r, x ∈ R has no critical point is _____ .

(a)	p² < 3q
(b)	2p² < q
(c)	$p^{2} < \frac{q}{4}$
(d)	p² > 3q

136.

The measure of the angle between the curves y² = 4x + 4 and y² = 36(9 - x) is _____.

(a)	30°
(b)	45°
(c)	60°
(d)	90°

137.

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)	$\frac{10}{\sqrt{3}}$

138.

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)	$(2^{- \frac{1}{3}}, 2^{\frac{1}{6}})$

139.

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,∞)

140.

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

Showing 131 to 140 out of 152 Questions