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Let X=x:x=n3+2n+1,nN and

Y=x:x=3n2+7,nN then

 

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By Expert Faculty of Sri Chaitanya
a
X∩Y is a subset of {x:x=3n+5,n∈N}
b
X∩Y⊆x:x=n2+n+1,n∈N
c
34∈X∩Y
d
none of these

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detailed solution

Correct option is C

If n3+2n+1=3n2+7⇒n3−3n2+2n−6=0⇒(n−3)n2+2=0⇒n=3 as n∈NSo, x=3×32+7=34∈X∩Y.In (a) and (b) x≠34, for any n∈N


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