Mathematics
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If
, then k is equal to
If
, then k is equal to
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The least integral value
of x such that
, satisfies
The least integral value
of x such that
, satisfies
MathematicsAlgebra
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Let
be the
term of an A.P r=1,2 ., for If for some positive integers m and n, we have
and
the 
Let
be the
term of an A.P r=1,2 ., for If for some positive integers m and n, we have
and
the 
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If
is a factor of the expression
then
If
is a factor of the expression
then
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If
are the roots of
and
are the roots of
then the value of
is
If
are the roots of
and
are the roots of
then the value of
is
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If
be the ratio of the roots of the quadratic equation in
then the least value of m for which
is
If
be the ratio of the roots of the quadratic equation in
then the least value of m for which
is
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Let
be the roots of the quadratic equation 
and
Then,
is equal to
Let
be the roots of the quadratic equation 
and
Then,
is equal to
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Suppose a, b and c are in A.P. and
are in G.P. If
and
, then the value of a is
Suppose a, b and c are in A.P. and
are in G.P. If
and
, then the value of a is
MathematicsAlgebra
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The value of
such that sum of the squares of the roots of the quadratic equation,
has the least value is
The value of
such that sum of the squares of the roots of the quadratic equation,
has the least value is
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If
and
have both the roots common, then
If
and
have both the roots common, then
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The sum of all the real roots of the equation
is
The sum of all the real roots of the equation
is
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Four different integers form an increasing A.P. such that one of them is the square of the remaining numbers. Then the largest number is
Four different integers form an increasing A.P. such that one of them is the square of the remaining numbers. Then the largest number is
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Let
, where
. If f(x) is a factor of both
and
then the least value of f(x) is
Let
, where
. If f(x) is a factor of both
and
then the least value of f(x) is
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The value of expression
when 
The value of expression
when 
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