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# Applications of Derivatives Test- 4 Class 12 Notes | EduRev

## Class 12 : Applications of Derivatives Test- 4 Class 12 Notes | EduRev

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CBSE TEST PAPER-04
CLASS - XII MATHEMATICS (Calculus: Application of Derivatives)
Topic: - application of derivatives
1. A balloon, which always remains spherical on inflation, is being inflated by
pumping in 900cm
3
/s. find the rate at which the radius of the balloon increase

2. A circular disc of radius 3cm is being heated. Due to expansion, their
radius increase at the rate of 0.05 cm/s. find the rate at which its area is

3. Find the intervals in which the function f given by
4sin 2 cos
( )
2 cos
x x x x
f x
x
- - =
+
is (i) increasing (ii) decreasing

4.
Find the interval in which the function f given by
3
3
1
( ) , 0 f x x x
x
= + ? is
(i) increasing (ii) decreasing.

5.
Find the equation of the normal to the curve
2
4 x y = which passes
through the point (1, 2)

6. Show that the normal at any point ? to the curve cos .sin , x a a ? ? ? = +
sin .cos y a a ? ? ? = - is at a constant distance from origin.

7. Show that the altitude of the right circular cone of maximum volume that
can be inscribed in a sphere of radius r is 4r/3.

8. Show that the height of the cylinder of maximum volume that can be
inscribed in a sphere of radius R is
2
3
R
Also find the maximum volume.

9. Show that the height of the cylinder of greatest volume which can be
inscribed in a right circular cone of height h and having semi-vertical
angle a is one third that of the cone and the greatest volume of cylinder is
3
4
tan .
27
h p a

10. Show that the right circular cone of least curved surface and given volume
has an altitude equal to 2 times the radius of the base.

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