NIMCET 2016 Question Paper with solutions

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Question : 58 of 120

Marks: +1, -0

If X = {

4^n

- 3n - 1 , n ∊ N} and Y = {9n - 9 , n ∊ N} , then X ∪ Y is equal to;

Y
X
N
None of these

Solution:

Given,

X=\{4^n-3n-1,n∊N\}

and

Y=\{9n-9,n∊N\}

∵4^n-3n-1=(1+3)^n-3n-1

=(^nC_{0}+^nC_{1}×3+^nC_{2}×3^{2}+. . .+^nC_{n}3^n)-(3n+1)

[∵(1+x)^{n}=3^{2}(^nC_{0}+^nC_{3}+.... ^nC_{n}3^{n-2})]

∴ X contains same multiples of 9
∴ X ∪ Y equal to Y.

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