Export of jpg in A4 size to drag and drop into existing pdfs (A4-size)

Here's what you need to know first:

• Photoshop is a pixel editor. It doesn't work in sizes. Given the pixel dimensions, physical size is determined by the pixels per inch number, ppi. That's a standard equation, any two variables determine the third.
• Acrobat deals with objects at a certain size. In other words, it treats everything like vector data, even if it is pixel data. There's no resolution in the individual objects, only in the final document.

So you need to translate one into the other and get them to match. Just enter the numbers in the Image Size dialog. An A4 sheet is 210 x 297 millimeters, and the target resolution is 150 pixels per inch. The result of the equation is 1754 x 1240 pixels.

The Image Size dialog will do it all for you, and if you check "resample" it will also scale the file to the required size. The math itself is very simple, image pixels / print size = resolution, but there's no need to take out your calculator when there is one in Photoshop.

Just make sure your original has enough pixels, and you'll be fine. Easy to forget - do the final resizing on a copy so that you don't resize your original!

EDIT: All this assumes that the image already has the correct aspect ratio width:height. If it doesn't, you need to make a decision: crop one side, leave an empty edge, or distort. It's one of three, there's no way around that.