CAT 2018 Question Paper Shift 2 Solved Paper

Question : 100 of 100

Marks: +1, -0

If N and x are positive integers such that

N^N

= 2160 and

N^2

2^N

is anintegral multiple of

2^x

, then the largest possible x is

Solution:

Given

{N}^{ {N}}=2^{160}=2^{5 × 32}

=(2^{5})^{32} ⇒ {N}^{ {N}}=32^{32}

⇒ {N}=32

{N}^{2}+2^{ {N}}=32^{2}+2^{32}

⇒(2^{5})^{2}+2^{32}

⇒ 2^{10}+2^{32}

=2^{10}(1+2^{22})

x

is 10

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