Which of the following intervals contains integers satisfying the following three congruences: Question: Which of the following intervals contains integers satisfying the following three congruences:
$x\equiv 2\pmod 5, x\equiv 3\pmod 7$ and $x\equiv 4\pmod {11}$,
(i) $[401,600]$, (ii) $[601,800]$, (iii) $[801,1000]$, and (iv) $[1001,1200]$  
After solving I have found $x=2292\equiv 367\pmod {385}$. But this does not belong to any of the above option.  How can I find this solution?

The point is that there is no reason to focus on the smallest non negative solution. 
Adding/subtracting an arbitrary amount of times the number $385 $ will yield other solutions. In fact, all of them, by the Chinese Remainder Theorem. 
