B737-300 FLT CREW WHILE ON VECTORS TO APCH RECEIVE A GPWS 'TERRAIN WARNING.' FLT CREW EXECUTES AVOIDANCE MANEUVER AND CONTINUES APCH WITHOUT FURTHER INCIDENT.

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WE WERE ON A 110 DEG VECTORED HDG APPROX 10-15 NM NW OF SJC LEVEL AT 4000 FT MSL. WX WAS IMC WITH SCATTERED LIGHT RAIN SHOWERS IN THE VICINITY. WE WERE USING WX MODE ON THE RADAR FOR THE SHOWERS. WE RECEIVED A TERRAIN WARNING; 'TERRAIN; TERRAIN; PULL UP.' I GLANCED DOWN AT THE RADAR BUT IT WAS STILL PAINTING WX. THE EGPWS SOUNDED THE TERRAIN WARNING AGAIN AND I IMMEDIATELY DISENGAGED THE AUTOPLT; APPLIED MAX THRUST; AND ROTATED TO 15 DEGS NOSE UP; MAINTAINING 210 KIAS. THE FO NOTIFIED APCH CTL WE WERE RESPONDING TO A TERRAIN ALERT AND CLBING OUT OF 4000 FT. I STOPPED THE CLB AT 5200 FT MSL. APCH GAVE US A VECTOR TO 030 DEGS AND A DSCNT TO 4000 FT AFTER WHICH WE WERE HANDED OFF TO ANOTHER APCH CTLR. WE WERE ESTABLISHED ON A R DOWNWIND LEG FOR RWY 12R AND CONTINUED THE APCH AND LNDG WITHOUT FURTHER INCIDENT. WE ARE UNSURE WHY WE RECEIVED THE TERRAIN WARNING; LEVEL AT 4000 FT. THERE IS A MOUNTAIN PEAK AT 3231 FT WHICH THE CTLR STATED WAS APPROX 2.5 NM OFF OUR R. A TWR AT 3496 FT AND ONE AT 4081 FT 7-10 NM AHEAD MAY HAVE TRIGGERED THE ALERT.