Applications of Derivatives Test- 4 Class 12 Notes | EduRev

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

 Page 1


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
when the radius is 15cm.
[4] 
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
increasing when radius is 3.2cm.
[4] 
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] 
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. 
[4] 
5.
Find the equation of the normal to the curve 
2
4 x y = which passes
through the point (1, 2)
[4] 
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.
[4] 
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.
[4] 
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.
[4] 
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
[6] 
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.
[6] 
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