Emergency Fund

For emergency needs, I would advise you to keep at-least 2-3 lacs (depending on your location and life style) in liquid assets. If needed, you should be able to withdraw these fund on a very short notice like in a day or two. It may not generate great returns, but amount should be pretty safe and quickly withdraw-able.
For this requirement, I would advise either liquid mutual funds or a savings account with auto sweep facility. These may generate 6-8% returns depending on the period for which amount remains invested. The returns will be added to taxable income and taxed as per your slab rates.

Regarding tax saving aspect, none of the tax saving investment is a fit for emergency fund creation. Minimum period of investment is three years with tax saving mutual funds, which are equity based and pretty risky. Safest and with shortest period tax saving investment as of now are tax saving fixed deposits but lock-in here is five years.

We must understand here that great returns comes with more risks. For emergency funds, we should not be thinking in term of returns but its security.

Ideally we should cut down the need for our own money in emergency situations. This can be done by covering yourself against all unforeseen circumstances. To do this, buy a term insurance (for all earning people), medical insurance (for whole family) with critical illness riders, home construction insurance (to cover cost of reconstruction in case of an earthquake, flood, riot, terrorism, war etc), home items insurance (against fire, burglary, electrical breakdown) and personal accidental insurance (for permanent partial or total disability).