CMOS is there in Mobile??

>How the mobile phones retain Correct Date and Time while they may be switched off for days?
>they still remains all data if we removed the battery?

There is in nearly every phone an additional battery or a goldcap(a kind of big capacitor)

>is mobile has CMOS Battery like our desktop had?

That's the point

But not every phone has it (i know about a few cheap Nokias (no Symbian devices)) that will lose their settings, if you
remove the batterie for a couple of minutes.

regards;
CG

>goldcap(a kind of big capacitor) for how long it provides backup for mobile?
I think they use very small goldcaps (small for goldcaps not for real capacitors). I think max 1/2 Farad

Q = I * t = C * U (Q = charge, I = current, t = time, C = capacity, U = voltage)

so you get t = (C * U) / I

You must know the voltage inside the goldcap and need the current that the 'rest'-electronic needs. I think for an oszillator at low frequency (usually 32.768 kHz) which
will drive only a few CMOS-arrays you need only a few uA (I mean micro).
I think half a year is no problem (only my estimation)...

>coz capacitors (as  i know ) leak the power after very short time.
goldcaps are no real capacitors. They are something between capacitors and accumulators/batteries. They have very small leak-current.

regards;
CG