MCQs of Applications of Derivatives

Applications of Derivatives MCQs

MCQs of Applications of Derivatives

Showing 121 to 130 out of 266 Questions

121.

Let f(x) be a polynomial of degree four having extreme values at x = 1 and x = 2. If

\lim_{x \to 0} [1 + \frac{f (x)}{x^{2}}] = 3

, then f(b) is equal to :

(a)	-8
(b)	-4
(c)	0
(d)	4

122.

The distance, from the origin, of the normal to the curve ,

x = 2 \cos t + 2 tsin t, y = 2 \sin t - 2 tcos t

t = \frac{π}{4}

, is :

(a)	4
(b)	$2 \sqrt{2}$
(c)	2
(d)	$\sqrt{2}$

123.

Let the tangents drawn to the circle, x² + y² = 16 from the point P(0, h) meet the x - axis at points A and B. If the area of ΔAPB is minimum , then h is equal to

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

124.

The equation of a normal to the curve,

\sin y = x \sin (\frac{π}{3} + y)

at x = 0, is :

(a)	$2 x + \sqrt{3} y = 0$
(b)	$2 y - \sqrt{3} x = 0$
(c)	$2 y + \sqrt{3} x = 0$
(d)	$2 x - \sqrt{3} y = 0$

125.

Let k and K be the minimum and the maximum values of the function

f (x) = \frac{{(1 + x)}^{૦ . 6}}{1 + x^{0.6}}

in [0, 1] respectively, then the ordered pair (k, K) is equal to :

(a)	$(1, 2^{૦ . 6})$
(b)	$(2^{- 0.4}, 2^{૦ . 6})$
(c)	$(2^{- 0.6}, 1)$
(d)	$(2^{- 0.4}, 1)$

126.

Consider

f (x) = \tan^{- 1} \sqrt{\frac{1 + \sin x}{1 - \sin x}}, x \in (0, \frac{π}{2})

A normal to y = f(x) at

x = \frac{π}{6}

also passes through the point :

(a)	$(\frac{π}{6}, 0)$
(b)	$(\frac{π}{4}, 0)$
(c)	(0, 0)
(d)	$(0, \frac{2 π}{3})$

127.

A wire of length 2 units is cut into two parts which are bent respectively to form a square of side = x units and a circle of radius = r units. If the sum of the areas of the square and the circle so formed is minimum, then :

(a)	x= 2r
(b)	2x = r
(c)	2x = (x + 4)r
(d)	$(4 - π) x = πr$

128.

The minimum distance of a point on the curve

y = x^{2} - 4

from origin is

(a)	$\frac{\sqrt{15}}{2}$
(b)	$\sqrt{\frac{19}{2}}$
(c)	$\sqrt{\frac{15}{2}}$
(d)	$\frac{\sqrt{19}}{2}$

129.

If the tangent at a point P, with parameter t, on the curve

x = 4 t^{2} + 3, y = 8 t^{3} - 1, t \in R

, meets the curve again at a point Q, then the coordinates of Q are :

(a)	$(16 t^{2} + 3, - 64 t^{3} + 1)$
(b)	$(4 t^{2} + 3, - 8 t^{3} - 2)$
(c)	$(t^{3} + 3, t^{3} - 1)$
(d)	$(t^{3} + 3, - t^{3} - 1)$

130.

P and Q are two distinct points on the parabola, y² = 4x , with parameter t and t₁ respectively. If the normal at P passes through Q, then the minimum value of t₁² is :

(a)	8
(b)	4
(c)	6
(d)	2

Showing 121 to 130 out of 266 Questions