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-02 
CLASS - XII MATHEMATICS (Calculus: Application of Derivatives) 
Topic: - application of derivatives 
1. A ladder 5m long is leaning against a wall. The bottom of the ladder is
pulled along the ground away from the wall, at the rate 2cm/s. how fast is
its height on the wall decreasing when the foot of the ladder is 4m away
from the wall.
[4] 
2. A particle moves along the curve 6y = x
3
 + 2. Find the points on the curve at
which the y-coordinate is changing 8 times as fast as the x – coordinate.
[4] 
3. 
Find the interval in which increase/decrease. ( ) sin 3 , 0,
2
f x x x
p
? ?
= ?
? ?
? ?
[4] 
4. Find the intervals in which the function f given by 
( ) sin cos , 0 2 f x x x x p = + = = is strictly increasing or decreasing.
[4] 
5. Find the equation, of the tangent line to the curve y = x
2
 – 2x + 7 which is
(a) Parallels to the line 2x – y + 9 = 0 
(b) Perpendicular to the line 5y – 15x = 13 
[4] 
6. 
Find the equation of the tangent to the hyperbola 
2 2
2 2
1
x y
a b
- = at the point
(x o, y o). 
[4] 
7. 
Find the approximate value of ( )
1
2
0.0037
[4] 
8. 
Using differentiates find the approximate value of ( )
3
2
3.968
[4] 
9. Show that the right circular cone of least curved surface area and given
volume has an altitude equal to 2 time the radius of the base.
[6] 
10. Show that semi – vertical angle of right circular cone of given surface area
and maximum volume is 
1
1
sin
3
- ? ?
? ?
? ?
 
[6] 
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