This query finds the backups taken for the database.I found it very useful while troubleshooting the backup issues.
SELECT
bkSet.Backup_Start_Date as BackupStartDate,
bkSet.Backup_Finish_Date as BackupEndDate,
MedFam.Physical_Device_Name AS BackupPath,
MedSet.Software_Name AS SoftwareUsedForBackup,
bkSet.User_Name AS BackupTakenBy,
bkSet.Server_Name AS ServerName,
bkSet.Database_Name As DatabaseName,
CASE bkSet.Type
WHEN 'L' THEN 'TransactionLogBackup'
WHEN 'D' THEN 'FullBackup'
WHEN 'F' THEN 'FileBackup'
WHEN 'I' THEN 'DifferentialBackup'
WHEN 'G' THEN 'DifferentialFileBackup'
WHEN 'P' THEN 'PartialBackup'
WHEN 'Q' THEN 'DifferentialPartialBackup'
ELSE NULL END AS BackupType,
CAST((bkSet.Backup_Size/1048576) AS NUMERIC(10,2)) AS BackupSizeInMB
FROM
msdb..BackupMediaFamily MedFam
INNER JOIN
msdb..BackupMediaSet MedSet
ON
MedFam.Media_Set_ID = MedSet.Media_Set_ID
INNER JOIN
msdb..BackupSet bkSet
ON
bkSet.Media_Set_ID = MedSet.Media_Set_ID
WHERE
--keep your database name in condition
bkSet.Database_Name = 'MENTIS'
ORDER BY
bkSet.Backup_Finish_Date DESC
Source:-http://www.sqlhub.com
