Download GIMP and open your pdf file. It will ask for resolution. There you can enter number pixels or select pixel/in etc.
Now just went to Image >> Mode >> Grayscale. That is your complete pdf file is converted to grayscale.
Now Go to File >> Export As >> yourfilename.pdf and press export.
If you have problem getting large size file. You can opt for following options(In toto you have to achieve minimum number of colors to reduce your file size. If you understand that you get the solution.)
Image >> Mode >> Grayscale
Image >> Mode >> Indexed >> Generate optimum palette(Here you will find 256 numbers of colors) >> change the Maximum number of colors to 10 or any other value that suits your file size.
If you want to reduce the file size further. Than you can opt for this step.
Image >> Mode >> Indexed >> Generate optimum palette >> Here this time select for Use web-optimized palette.
Note even if you want small size color pdf you can skip the step 1.
The reason for large size of pdf is number of colors.