The number of natural numbers lying between 1012 and 23421 that can be formed using the digits 2, 3, 4, 5, 6 (repetition of digits is not allowed) and divisible by 55 is ………… .

4 digit numbers
For divisibility by 55, no. should be div. by 5 and 11 both

Also, for divisibility by 11
$\begin{array}{r}\text{ for }\mathrm{b}=1\mathrm{a}=2,\mathrm{c}=4\\ \mathrm{a}=4,\mathrm{c}=2\\ \text{ for }\mathrm{b}=2\mathrm{a}=3,\mathrm{c}=4\\ \mathrm{a}=4,\mathrm{c}=3\\ \text{ for }\mathrm{b}=3\mathrm{a}=6,\mathrm{c}=2\\ \mathrm{a}=2,\mathrm{c}=6\end{array}$
$\therefore$6 possible four digit no.s are div. by 55 
(II) 5 digit number is not possible 
 

(not possible)