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# 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

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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.

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.

3.
Find the interval in which increase/decrease. ( ) sin 3 , 0,
2
f x x x
p
? ?
= ?
? ?
? ?

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.

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

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).

7.
Find the approximate value of ( )
1
2
0.0037

8.
Using differentiates find the approximate value of ( )
3
2
3.968

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.

10. Show that semi – vertical angle of right circular cone of given surface area
and maximum volume is
1
1
sin
3
- ? ?
? ?
? ?


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