KVPY SX SB Exam 2013 Question Paper

Question : 2 of 120

Marks: +1, -0

Let

n

be a positive integer such that

\log _2 \log _2\log _2\log _2\log _2(n)

< 0 <

\log _2\log _2\log _2\log _2(n)

Let

l

be the number of digits in the binary expansion of

n

. Then the minimum and the maximum possible values of

l

are

Solution:

\log _2 \log _2\log _2\log _2\log _2(n)

< 0 <

\log _2\log _2\log _2\log _2(n)

16 < n <2^16

no. of digits in the binary expansion of 16 is 5
no. of digits in the binary expansion of

2 ^16

is 17
so no. of digits in the binary expansion of n lies in 5 to 16

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