Downsapled and blurred image I have an image with size $256*256$ then i get the Fourier transform of the image, If i only take the central region of the Fourier transform whose size is $64*64$ and get the inverse FT ,What is the effect on the output image$(64*64)$?

Down-sampling, Blurring, or both.
Have you fftshifted your results or not? The answers will be different: 

If you fftshift your $256$ x $256$ 2-dimensional Fourier transform result, retain only the $64$ x $64 $ central co-efficients, inverse fftshift, and then inverse fourier transform the result, the effect will be a blurring of your original image. 

This is because you have culled our your images' high frequency components, hence, the effect will be a blurring. 

If however you have not fftshifted, then you are doing the opposite, and will actually be doing a high pass filtering. (Your image will certainly not be blurred).

By the way, hard thresholding fourier co-efficients like this is certainly used, but will give you ringing effects. However, those effects might be negligible and/or removable based on your application.