LP2951: Some design queries related to LP2951 adjustable regulator

HI Jagdish,

See the answers to your questions below in blue:

1. I shall use LP2951 to regulate 10V from input 15V as shown below. Input 15V will be from SMPS output having approx switching freq. of 100KHz & below. Now output capacitor has ESR ( as per simulation) of 0.008E at 100K, so is 1E sufficient or still lower value is recommended? 

The output capacitor you have listed on your schematic has ESR of 4 mOhm when I look it up using Murata's Sim Surfing tool. I'm unfamiliar with the 1E notation but I assume it indicates 1 Ohm, if that is correct then from a stability standpoint it should be stable. Since the cap has 4 mOhm of ESR and this LDO requires 30 mOhm to 5 Ohms of ESR any resistor between 36 mOhm and 4.996mOhm will suffice for stability. 

Can this series resistor affect transient response of LP2951? If yes, then what best value of series resistance is recommended like 0.5E or so? I don't have pulsating load & current is constant 25mA.

Yes the series resistor will change the output voltage transient response since the larger it is the more it will reduce the current the output capacitor can provide during load transients. However if you have a constant load this shouldn't effect your application. 

2. Is there is any harm in keeping sense, VTAP & Error pins open in noisy environment or do we shunt them with 0.01uF/25V due to noise concern? Please advice.

Most likely it would be fine to leave VTAP SENSE, and ERROR open however, if you are worried about noise it would be better to simply short them to GND.

3. As per datasheet output capacitor should have resonant freq. greater than 500K, now min. ESR of below mentioned capacitor happens to be near 1M, so can we say selected capacitor is OK for this application or needs any other consideration? Please advice.

The output capacitor you have listed on your schematic has a resonant frequency of ~1MHz when I look at Murata's Sim Surfing tool so that's good for the resonant frequency requirement. Since you are using a ceramic capacitor you are almost guaranteed to require a series resistor (which you have, R1) to meet the minimum ESR requirement. So it looks like everything is accounted for.