BY FLIGHT : There are 2 flights come to Srinagar by Trivandrum like Jet Airways ,Air India but they are multiple flights they all operates daily and take 34 to 35 hours to reach Srinagar with one or two night stay in Delhi.
BY TRAIN : There is also option to come by train. There is only one direct train from Trivandrum to Jammu i.e. Himsagar express they operate only Friday. The total distance is 3628 kms & take approx 70 hours to reach. but train drops you at Jammu Tawi Railway and than you choose taxi for further journey.
BY ROAD : There is no bus service or operator from Trivandrum to Jammu Kashmir. You take bus from Trivandrum to Delhi ISBT i.e. 2900 kms 43 hours to reach delhi & than take another Bus from ISBT Kashmiri Gate Delhi to Jammu Bus stand the approx distance is 600 kms & it will take 11 hours approx to reach Jammu by road. In Jammu there are various option to reach Kashmir you take local sharing Cabs local bus service and individual cabs . Bus service operates in the night only you take Volvo buses as well as local buses from Jammu Bus stand & rest services like individual taxi & sharing cabs you take from exit point of Railway station , Jammu Bus stand & Gumat chowk they operates whole day. The distance between Jammu to Kashmir is approx 300 Kms & it will take 8 to 10 hours to reach Kashmir.