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Question

For every positive integer n,n77+n55+2n33−n105 is

A
an integer
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B
a rational number
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C
a negative real number
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D
an odd integer
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Solution

The correct option is A an integer
n77+n55+2n33n105
where n is a positive integer.
When n=1, we get,
n77+n55+2n33n105
=15n7+21n5+70n3n105
=15+21+701105=105105=1 which is an integer.
When n=2,
we get;
n77+n55+2n33n105
=15n7+21n5+70n3n105
=(15×128)+(21×32)+(70×28)2105
=1920+672+5602105
=3105105=30 which is an even positive integer.


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