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1.
If 
, for every real number 
, then the minimum value of 
, for every real number , then the minimum value of
2.
The function 
, where 
assume its minimum value only at one point if
, where assume its minimum value only at one point if
3.
If the function 
is increasing for all values of 
then
is increasing for all values of then
4.
A man of 2m height walks at a uniform speed of 6 km/h away from a lamp post of 6 m height. The rate at which the length of his shadow increase is
5.
is not right angled and is inscribed in a fixed circle. If 
be slightly varied keeping 
fixed, then
is not right angled and is inscribed in a fixed circle. If be slightly varied keeping fixed, then
6.
A value of 
for which the conclusion of Mean value theorem holds for the function 
on the interval [1, 3] is
for which the conclusion of Mean value theorem holds for the function on the interval [1, 3] is
7.
If 
for all positive values of and 
are positive constants, then
for all positive values of and are positive constants, then
8.
Let 
. Then, at 
has
. Then, at has
9.
The line 
touches the curve 
at the point 
for
touches the curve at the point for
10.
The pressure 
and volume 
of a gas are connected by the relation 
The percentage increase in the pressure corresponding to a deminition of 
in the volume is
and volume of a gas are connected by the relation The percentage increase in the pressure corresponding to a deminition of in the volume is