UPDATED ISSUE 2 of 2016_06_13 in view of AG's comments of post #21
Hy NILOTPAL,
As LM317 voltage regulators are normally fairly well behaved, it looks like you have a major fault somewhere, either a batch of faulty LM317 regulators (already stated) or a wiring error: short for example. You could even have a faulty passive component: resistor or capacitor. Also, as has already been stated, the LM317 may be oscillating. Have you definitely got a positive DC voltage on the input of the regulator?
Incidentally, the current through the potentiometer should be 1.25V/R where R is the resistor connected between the LM317 output and adjust. So for a
120 Ohm resistor the current should be:
1.25V/120 Ohms= 10.4 mA which would be no problem for the potentiometer that you show.
(1) Firstly, as Keep says above, you need to add a rectifier diode for protection: for example 1N400x (where x is any number) cathode to the LM317 input pin and anode to the LM317 output pin.
(2) Also as Keep says, there is a minimum current output for the LM317. This minimum current is
10mA, so the resistor between adjust and output should be
120 Ohms maximum not 330 Ohms.
100 Ohms will be fine.
(3) The length of leads and layout are important (the LM317 is a high gain, high current amplifier) to avoid oscillations. Can you post a picture of your physical circuit?
(4) The type of capacitors are also important for good decoupling. In order of preference, they should be, ceramic, polypropylene metalized film, or low-loss aluminum electrolytic.
(5) Use substantial interconnecting wires- not thin. This is to ensure a low impedance which will help prevent oscillations and also improve voltage regulation.
To test your LM317 regulators do the following:
(1) Get a 9V PP3 style battery.
(2) Get a
100 Ohm resistor.
(3) Get a 22 Ohm resistor.
(4) Get a 100nF or higher ceramic capacitor.
(5) Connect the capacitor between the regulator input and adjust (use as short a leads as possible).
(6) Connect the
100 Ohm resistor between output and adjust (use as short leads as possible).
(7) Connect the battery positive to input and and negative to adjust (use as short leads as possible) .
(8) The voltage between the LM317 output and sense should be between 1.2V and 1.3V (1.25V nominal).
(9) Connect a 22 Ohm resistor between the output and adjust.
(10) The voltage between the output pin and adjust should be unchanged from the reading of (8) above.
spec
LM317 Datasheet
https://www.ti.com/lit/ds/symlink/lm317.pdf
IN400x Rectifier Diode Datasheet
https://www.vishay.com/docs/88503/1n4001.pdf