Which of the following sets in an finite/infinite set ?
`(i)` Set of divisors of `24`
`(ii)` Set of all real number which lie between `1` and `2`
`(iii)` Set of all humman beings living in India.
`(iv)` Set of all three digit natural numbers
Correct Answer - B
According to the question
`2^m-2^m= 112 `
`rArr 2^n (2^(m-n)-1)= 2^4 xx 7`
Comparing exponets on both sides ,we get
`2^n-2^4 and 2^(m-n)-1= 7 `
Now ,`2^n=...
Correct Answer - B
`(b)` `1000=2^(3)*5^(3)`
Number of divisors `=16` which are
`(2^(0)+2^(1)+2^(2)+2^(3))(5^(0)+5^(1)+5^(2)+5^(3))`
Product of all the `16` divisors is
`=(5^(6))(5^(6))(5^(6))(5^(6))(2^(6))(2^(6))(2^(6))(2^(6))`
`=2^(24)*5^(24)`