I think they are trying to avoid exposing Ashwin and Kuldeep in this game. Kuldeep has played enough cricket in the country (England) in the past few weeks and Ashwin has recent county experience. The team management is trying to fool the hosts (and probably the fans too) by trying to pass off Jadeja as a possible candidate for a spot in the XI. I have a feeling Ishant Sharma could turn out a revelation on this tour and might even return back to being India's spearhead quick in test cricket. He has had tremendous amount of exposure in county and he has a fantastic hang of the conditions and its showing in this county game too. Him and Yadav should hopefully have a great test series if India have to win it and I am expecting both of them to fire in unison. In that case, Hardik can be the third seamer with Ashwin/Kuldeep as the 2 spinners. And the batting should look good with Hardik and Ashwin in the lower order.
I feel India should push Pujara down the order and have either Rahane or Karthik bat at No. 3. Pujara needs confidence as he is a long term option and a bad series could seal his career up here. Rahane is a good conventional choice for No. 3 considering he is technically solid. Or a more bold and out of the box move will be to play Karthik at No. 3. Karthik has opened the batting for India in a test series in the same country (England) before and has had decent success in that endeavor. Pujara in the form/mindset he is in, desperately needs a good start from the batting order so that he can come in with less pressure and try to resurrect his career around.
Vijay
Rahul
Rahane/Karthik
Kohli
Pujara
Karthik/Rahane
Pandya
Ashwin
Ishant
Yadav
Kuldeep