The docs note:

ORA-01102: cannot mount database in exclusive mode

Cause: An instance tried to mount the database in exclusive mode, but some other instance has already mounted the database in exclusive or parallel mode.

Action: Either mount the database in parallel mode or shut down all other instances before mounting the database in exclusive mode.

The ORA-01102 is a "false" error in this regard (assuming that you are not using data guard), and this note may be helpful:

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http://www.orafaq.com/forum/t/40030/0/

database is started in EXCLUSIVE mode by default. Therefore, the
ORA-01102 error is misleading and may have occurred due to one of the
following reasons:

- there is still an "sgadef<sid>.dbf" file in the "ORACLE_HOME/dbs"
directory
- the processes for Oracle (pmon, smon, lgwr and dbwr) still exist
- shared memory segments and semaphores still exist even though the
database has been shutdown
- there is a "ORACLE_HOME/dbs/lk<sid>" file

The "lk<sid>" and "sgadef<sid>.dbf" files are used for locking shared memory.
It seems that even though no memory is allocated, Oracle thinks memory is
still locked. By removing the "sgadef" and "lk" files you remove any knowledge
oracle has of shared memory that is in use. Now the database can start.

POSSIBLE SOLUTION:
Verify that the database was shutdown cleanly by doing the following:

1. Verify that there is not a "sgadef<sid>.dbf" file in the directory
"ORACLE_HOME/dbs".

% ls $ORACLE_HOME/dbs/sgadef<sid>.dbf

If this file does exist, remove it.

% rm $ORACLE_HOME/dbs/sgadef<sid>.dbf

2. Verify that there are no background processes owned by "oracle"

% ps -ef | grep ora_ | grep $ORACLE_SID

If background processes exist, remove them by using the Unix
command "kill". For example:

% kill -9 <Process_ID_Number>

3. Verify that no shared memory segments and semaphores that are owned
by "oracle" still exist

% ipcs -b

If there are shared memory segments and semaphores owned by "oracle",
remove the shared memory segments

% ipcrm -m <Shared_Memory_ID_Number>

and remove the semaphores

% ipcrm -s <Semaphore_ID_Number>

NOTE: The example shown above assumes that you only have one
database on this machine. If you have more than one
database, you will need to shutdown all other databases
before proceeding with Step 4.

4. Verify that the "$ORACLE_HOME/dbs/lk<sid>" file does not exist

5. Startup the instance