Q.

Consider a set {1,2,3,.....,100}. The number of ways in which a number can be selected from the set so that it is of the form xy, (where x,yN and 2 ), is

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a

11

b

16

c

12

d

5

answer is A.

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Detailed Solution

Perfect square=[100]1=9(excluding one)

Perfect cubes=[1001/3]1=3

Perfect 4th powers=[1001/4]1=2

Perfect 5th powers=[1001/5]1=1

Perfect 6th powers=[1001/6]1=1

Now, perfect 4th powers have already been counted in perfect squares and perfect 6th powers have been counted with perfect squares as well as with perfect cubes Hence the total ways = 9 + 3 + 1 – 1 = 12

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