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1.
The maximum value of the function 
given by 
, is
given by , is
2.
For a given integer 
, in the interval 
the graph of 
is
, in the interval the graph of is
3.
If 
is the semi vertical angle of a cone of maximum volume and given slant height, then 
is given by
is the semi vertical angle of a cone of maximum volume and given slant height, then is given by
4.
The value of 
for which the function 
is decreasing in the interval 
is given by
for which the function is decreasing in the interval is given by
5.
The function 
decreases in the interval
decreases in the interval
6.
If 
then
then
7.
The maximum value of 
, is
, is
8.
If 
, then maximum value of 
is
, then maximum value of is
9.
A stone is dropped into a quiet lake. If the waves moves in circles at the rate of 30cm/sec when the radius is 50 m, the rate of increase of enclosed area is
10.
The equation of the tangent to the curve 
at the origin is
at the origin is