A) \[\{12{{n}^{2}}+6n|n\] is a natural number}
B) \[\{24n-12|n\] is a natural number}
C) \[\{60n+30|n\] is a natural number}
D) \[\{12n-6|n\] is a natural number}
Correct Answer: D
Solution :
[d]Let \[A=\{4n+2:n\in N\}\] and \[B=\{3n:n\in N\}\] \[\Rightarrow A=\{6,10,14,18,22,26,30,34,38,42...\}\] And \[B=\{3,6,9,12,15,18,21,24,27,30...\}\] \[\therefore A\cap B=\{6,18,30,42...\}\] \[=6+12n-12=12n-6.\] Hence, \[A\cap B=\{12n-6:n\] is a natural number}.
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