MCQs of Applications of Derivatives

Applications of Derivatives MCQs

MCQs of Applications of Derivatives

Showing 231 to 240 out of 266 Questions

231.

The maximum value of the curve, y = -x³ + 3x² + 9x - 27 is _____ .

(a)	0
(b)	12
(c)	16
(d)	32

232.

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

233.

The curves x = y² and xy = a³ are orthogonal , then a² =______ .

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

234.

In a ΔABC if sides a and b remain constant such that α is the error in C, then relative error in its area is _____ .

(a)	α cot C
(b)	α sin C
(c)	α tan C
(d)	α cos C

235.

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)	$\frac{1}{25}$

236.

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

237.

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

238.

The circumference of a circle is measured as 56 cm with an error 0.02 cm. The percentage error in its area is _____ %.

(a)	$\frac{1}{7}$
(b)	$\frac{1}{28}$
(c)	$\frac{1}{14}$
(d)	$\frac{1}{56}$

239.

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

240.

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°

Showing 231 to 240 out of 266 Questions