CBSE Test Paper (Calculus: Application of Derivatives (Class - XII Mathematics) Class 12 Notes | EduRev

Class 12 : CBSE Test Paper (Calculus: Application of Derivatives (Class - XII Mathematics) Class 12 Notes | EduRev

 Page 1


CBSE TEST PAPER-03 
CLASS - XII MATHEMATICS (Calculus: Application of Derivatives) 
Topic: - application of derivatives 
1. Sand is pouring from a pipe at the rate of 12cm
3
/s. the falling sand forms a cone on
the ground in much a way that the height of the cone is always one – sixth of the
radius of the here. How fast is the height of the sand cone increasing when the
height in 4cm.
[4] 
2. The total revenue in RS received from the sale of x units of the product is given
by R (x) = 13x
2
 + 26x + 15 find MR when 17 unit are produce.
[4] 
3. 
Prove that 
4sin
2 cos
y
?
?
?
= - +
 is an increasing function = x of ? in ,
2
p
?
? ?
? ?
? ?
[4] 
4. Prove that the function of given by f(x) = log sinx is strictly increasing on
0,
2
p
? ?
? ?
? ?
and strictly decreasing on ,
2
p
p
? ?
? ?
? ?
 
[4] 
5. Find a point on the curve y = (x – 2)
2
 at which the tangent is parallel to the
chord joining the points (2, 0) and (4, 4)
[4] 
6.
Find the equation of tangent to the curve given by 
3 3
sin ,  cos x a t y b t = = at a
point where 
2
t
p
=
[4] 
7. Find the approximate value of f(3.02) where f(x) = 3x
2
 + 5x + 3. [4] 
8. 
Find the approximate value of 
1
5
(32.15)
[4] 
9. A square piece of tin of side 18cm is to be made into a box without top by
cutting a square from each corner and folding of the flaps to form the box.
What should be the side of the square to be cut off so that the volume of the
box is the maximum possible?
[6] 
10. Show that the right circular cylinder of given surface and maximum volume is
much that its height is equal to the diameter of the base.
[6] 
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