Hi Karishma,
I am not familiar with COGNOS so I can't comment on it's capabilities however personally I have handled date ranges via input parameters by using two separate input parameters. ie: one for your start date and a second for your end date. (I'm assuming for some reason you truly need an input parameter and you can't pass the dates in an SQL statement where condition from Cognos?)
Then in my calculation view I'm processing the two dates via a projection like this;
var_out = CE_PROJECTION ( :vartable, ["MENGE" As TOTALQUANTITY, "MJAHR"], '"MJAHR" >= :StartYear and "MJAHR" <= :EndYear');
I hope this helps and maybe somebody else can comment more on cognos capabilities.
-Patrick