Binomial Theorem Part 1

11n>10n+9n
⇒11n−9n>10n
⇒(10+1)n−(10−1)n>10n
⇒{‌nC1.10n−1+‌nC310n−0+‌nC510n−5 +......}>10n
⇒2n.10n−1+2{‌nC310n−3+‌nC510n−5 +.......}>10n ........(1)
For n=5
105+2{‌5C3102+‌5C5}>105 (True)
For n=6,7,8,.......100
2n10n−1>10n
⇒2n10n−1+2{‌nC310n−3+‌nC510n−5 +........}>10°
⇒11n−9n>10n For n=5,6,7,.......100
For n=4, Inequality (1) is not satisfied
⇒ Inequality does not hold good for
N=1,2,3,4
So, required number of elements =96