Giving reasons identify the compound which will go sn1 reaction faster? CH3-CCl2-CH3 OR CH3-CH3-CHCl-CH3. how can we sort out whether a secondary halo derivative will undergo SN1 OR SN2?

It depends upon the stability of carbocation. A general SN1 reaction is: 

In the given compounds, the formed carbocation will be  CH3-(+)CCl-CH3 and

CH3-CH3-(+)CH-CH3. AMong these two the second carbocation which is a tertiary carbocation, is far more stable. SO, 2, 2- dichloropropane will react faster in SN1.