What would happen if hydrogen bonds form between any two nitrogenous bases in dna

I believe that identical copies of original DNA wouldn't be formed. 
DNA has a strict pairing rule, adenine can only go with thymine, and cytosine can only go with guanine. 
This is because of thymine and adenine make 2 hydrogen bonds between each other, while cytosine and guanine form 3. Therefore bonding out of this order is impossible (unless it's a mutation in which there are exceptions). 
When DNA replicates, each strand of the original DNA serves as a template for the new strand of DNA. Hence the new strand that goes with the first original DNA strand is the same as the second DNA strand. 
If the bonding between the nitrogen bases is messed up, the new strand of DNA will not be exactly what it should be. To demonstrate, if the nucleotide is thymine for the original strand, the new strand should be adenine. However, if the bonding is arbitrary, then the new strand could be cytosine or guanine as well, therefore there is no definite answer to what the new strand should be. This will make havoc in the genetic codes and will most likely kill the organism. 
I hope this answer has answered your question and good luck with your assignment. I apologise if I am incorrect. Have a good day/night.