Let me try to answer your question.
The IDLE_TIMEOUT defines the time out time from the 'Pooled' state to 'Does not exist' state for a connection in a pool. For this the state has to be 'Pooled' and not 'In use'. So this time out will not affect the connection which is in, 'In Use' state (by servlet).
Also, the MIN_POOL_SIZE value is 10, which is acceptable and the question does not have any further details on it.
So, let's evaluate eac option,
a) The servlet's connection will be unaffected by the idle timeout.
--> As metnioned earlier, the idle_timeout setting does not affect the connection in use. **Possible right choice.
b) The pool size will be increased by 10 when some other servlet needs a connection.
---> The min_pool_size is 10, but we do not know what is the current pool size, and also, even if the pool size is less than 10, the server never creates the pool with min size or increments the pool size with min size. But it keeps on creating one connection per request until the pool size reaches the min size and this is done only if, there is no connection in the pool that can satisfy the current connection request.
**So in any case this is a wrong choice.
c) After 30 seconds, WebSphere can return the connection to the connection pool.
---> Same explanation as given for choice 'a'. The idle_timeout does not affect the in use connection. This could have true only if, ORPHAN_TIMEOUT would have been set to 15 secs and the connection was not involved in a transaction.
** So this is not a right choice.
d) The servlet's service() method will throw a javax.sql.PooledConnectionException if the servlet attempts to use its connection.
--->There is no exception class by name, javax.sql.PooledConnectionException.
Also, the server will throw only StaleConnectionException in this case, only if the connection was orphaned or the connection was cleaned-up after a transaction (if DISABLE_AUTO_CONN_CLEANUP is false).
** So a wrong choice.
So option 'a' is the right answer.
For Webpshere Connection pooling refer to ,
(can search on google.com)
WebSphere Connection Pooling
Hope it helps.