Can i use 47uf instead of 10uf in LM317 Adjustable voltage regulated circuit?
You can double-check the design of that power supply using the information in the Texas Instruments LM317 datasheet.

At page 10 you find this:



which is followed by a detailed design procedure.

The important thing to note is that Co is not required for stability, so it simply improves transient response, i.e. it makes the output react faster when the load changes abruptly (the IC is comparatively slow in this respect, if the load change is very quick and you need the output not to change briefly during the transient). So you have substantial freedom in choosing its value. 47uF is OK (it can be also of aluminium electrolytic type, if you don't need particular high frequency rejection), especially if you plan to connect heavy loads at the the output.

Ci is not critical either, but it might be required for stability, if the distance from the 470uF filter cap is substantial (several centimeters, maybe), so it is better to be some ceramic or polymer type (PP or similar), definitely NOT aluminium electrolytic (I often went for some 100-220nF PP type in hobbysts, one-off designs). The 10uF value in your schematic is weird, unless it is of a ceramic type, since it is too high to be a reasonable polymer type, and an aluminium electrolytic doesn't do any good there. 

The diodes D1 and D2 are always a good safety measure, since it is a circuit that is designed to be connected to unknown loads, so who knows how much input capacitance the load has and if you turn off you power supply with a load attached, its internal capacitance could discharge into your LM317 and damage it.

As a side note, the value of R1=240&Omega; might be "wrong" (even in the datasheet!). The datasheet implicitly assumes a "substantial" load is applied to the output. In fact the LM317 needs a minimum of 10mA of load current to work properly, as stated in this table from the datasheet:



R1=240&Omega;, having 1.25V across it, will draw only about 5mA, which is not enough in a worst case scenario with either no or a light load connected (which is not unusual for a lab power supply). It will work for the typical 3.5mA required, but you don't want to rely on that in corner cases. An R1=120&Omega; makes the design more robust and guarantees that the minimum current needed for regulation is drawn even with no load.