MCQs of Applications of Derivatives

Applications of Derivatives MCQs

MCQs of Applications of Derivatives

Showing 31 to 40 out of 266 Questions

31.

The equation of normal to

3 x^{2} - y^{2} = 8 at (2, - 2)

is_____

(a)	$x + 2 y = - 2$
(b)	$x - 3 y = 8$
(c)	$3 x + y = 4$
(d)	$x + y = 0$

32.

The angle made by the tangent with the +ve direction of X−axis to

x = e^{t} \cos t, y = e^{t} \sin t at t = \frac{π}{4}

is _____

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

33.

The equation of tangent to

y = \cos x at (0, 1)

is _____

(a)	$x = 0$
(b)	$y = 0$
(c)	$x = 1$
(d)	$y = 1$

34.

The equation of normal to

y = \sin x at (\frac{π}{2}, 1)

is _____

(a)	$x = 1$
(b)	$x = 0$
(c)	$y = \frac{π}{2}$
(d)	$x = \frac{π}{2}$

35.

At_____on circle x^{2} + y^{2} - 2 x - 3 = 0, the tangent is horizotal .

(a)	$(0, \pm \sqrt{3})$
(b)	$(2, \pm \sqrt{3})$
(c)	$(1, 2), (1, - 2)$
(d)	$(3, 0)$

36.

The point on

y^{2} = x

where tangent makes angle of measure

\frac{π}{4}

with the positive X-axis is ______

(a)	$(\frac{1}{4}, \frac{1}{2})$
(b)	$(2, 1)$
(c)	$(0, 0)$
(d)	$(- 1, 1)$

37.

A cone with its height equal to the diameter of the base is expanding in volume at the rate of

50 c m^{3} / s e c

. If the base has area

1 m^{2}

, the radius is increasing at the rate _____

(a)	0.0025 cm/sec
(b)	0.25 cm/sec
(c)	1 cm/sec
(d)	4 cm/sec

38.

The rate of increaing of

f (x) = x^{3} - 5 x^{2} + 5 x + 25

is twice the rate of increase of x for x = _____.

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

39.

The radius of a cone increases at the rate of 4 cm/sec and the altitude is decreasing at the rate of 3 cm/sec. When the radius is 3 cm and altitude is 4 cm, the rate of change of lateral surface is _____.

(a)	$30 π c m^{2} / s e c$
(b)	$10 c m^{2} / s e c$
(c)	$20 π c m^{2} / s e c$
(d)	$22 π c m^{2} / s e c$

40.

The rate of change of surface area of a sphere w.r.t. radius is _____

(a)	$8 π (diameter)$
(b)	$3 π (diameter)$
(c)	$4 π (radius)$
(d)	$8 π (radius)$

Showing 31 to 40 out of 266 Questions