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1.
The value of the determinant 
is equal to
is equal to
2.
If 
(where 
is a real valued function of 
then the value of 
(where is a real valued function of then the value of
3.
The value of 
is equal
is equal
4.
The roots of the equation
5.
If 
is a square matrix of order 
such that its elements are polynomial in 
and its 
-rows become identical for 
then
is a square matrix of order such that its elements are polynomial in and its -rows become identical for then
6.
If
The value of
is
The value of
is
7.
If 
are elements of a 
with usual meaning. Then, the value of 
is
are elements of a with usual meaning. Then, the value of is
8.
The value of the determinant 
where 
are the 
and 
terms of a H.P., is
where are the and terms of a H.P., is
9.
If 
are in AP, then the value of 
is
are in AP, then the value of is
10.
For the values of 
the value of
the value of