zen engine rpm increases at high rate

firstly

when i start  my zen Lxi (2006) every morning the engine rpm will be very high for few minutes. 

second

after driving my car very fast for 10 to 15 kms my engin rpm will rise and fall wheather i am driving or in stagnent positon.

for both the problems i did not find any solution even though i have given my car for service at authorised maruthi showroom. they have just cleaned the carpet and adjust timing belt.

can any one help me

This behavior is normal.

When the engine is cold, the idling RPM is intentionally kept high to get the engine warmed up, as the engine efficiency is higher at warmer temperatures. Once the engine reaches warm temperature, the idling rate reverts to the normal 700 rpm or so.

The second issue is beyond me except I guess if the AC is on, the RPM gets adjusted for whether the compressor is on or off, in newer cars. In older cars it remains the same (~1k rpm) to keep the engine from stalling because of the compressor load

Hey,

I am facing rpm problem in my zen too. Sometimes the rpm is too high(Now what i mean by too high is even after putting the car in 3rd gear and taking foot off from accelarator she wont stall), sometimes its not that high(she wont stall till 2nd gear without using accelarator, i cann easily pick it up from 2nd gear directly) & sometimes its normal. By the time i take it to mechanic she comes back to normal as if she dont want the mechanic to see it.

Also what is the optimum rpm on starting the car & after a minute or two of starting the car...?? 

Well, it could be that nothing is actually wrong. When you are at speed and put car in 3rd gear and take foot off accelerator, engine will not stall till car speed drops well below that gear's threshold - its because of inertia.

Yes, i know that but she keeps on going as if accelarator is pressed & it becomes quite evident from engine noise too. Even at idle you can tell from engine noise(as if accelarator is pressed) & i guess this is also affecting the FE.

Hmm...so there is RPM surge, correct? I mean even without pressing the accelerator pedal, the RPM increases. I don't know which zen you have but if its the fuel-injected (MPFI) type, then I'd first change the throttle position sensor (TPS). It is a small sensor located exactly opposide the throttle spindle on the engine.

Yup you got it right but the intensity of rpm surge varies from some day to other. Its a '02 make so i guess its a mpfi. Actually a while back there was a problem with wire from alternator that charges the battery. So battery drained out as it wasnt getting charged. As it happened in the middle of my route so couldnt send it to get charged completely. The mechanic came, repaired the wire & jump started the car & to give it initial charge we pushed the accelarator at idle for 10-15 mins & then i headed back home. Now the thing thats bugging me is that, by doing this did i unintentionally remapped the ecu to that higher rpm..??? Could this be the reason..?? 

ECU cannot be remapped this way. The only thing the broken battery cable could have done to the ECU is reset it (i.e., clear any error codes it might have had and bring it back to its "unlearned" state). it will not affect RPM.