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-01 
CLASS - XII MATHEMATICS (Calculus: Application of Derivatives) 
Topic: - Application of Derivatives 
1. The length x of a rectangle is decreasing at the rate of 3 cm/ mint and the width y
is increasing at the rate of 2cm/min. when x = 10cm and y = 6cm, find the ratio of
change of (a) the perimeter (b) the area of the rectangle.
[4] 
2. Find the interval in which the function of given by f(x) = 4x
3
 – 6x
2 
– 72x + 30
is (a) strictly increasing (b) strictly decreasing.
[4] 
3. 
Find point on the curve
2 2
1
4 25
x y
+ = at which the tangents are (i) parallel to x –
axis  (ii) parallel to y – axis 
[4] 
4. 
Use differentiate to approximate ( )
1
3
25
[4] 
5. Prove that the volume of the largest cone that can be inscribed in a sphere of
radius R is 
8
27
 of the volume of the sphere.
[6] 
6. The volume of a cube is increasing at a rate of 9cm
3
/s. How fast is the surface
area increasing when the length of on edge is 10cm?
[4] 
7. Find the interval in which the function is strictly increasing and decreasing.
(x+1)
3
 (x-3)
3
[4] 
8.
Find the equations of the tangent and normal to curve 
2 3 2 3
2 x y + = at (1, 1)
[4] 
9. IF the radius of a sphere is measured as 9cm with an error of 0.03cm, then
find the approximate error in calculating its volume.
[4] 
10. A wire of length 28m is to be cut into two pieces. One of the pieces is to be
made into a square and the other into a circle. What should be the length of
the two pieces to that the combined areas of the square and the circle is
minimum.
[6] 
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