select * from Test
where Type = @type and
(coalesce(@inst, 1) = 1 or Institute = @inst)
coalesce returns first of its argument which is not null, so when @inst is null your condition will be like Type = @type and (1=1 or Institute = null).
The case when @inst has value will be Type = @type and ('abc' = 1 or Institute = 'abc').
I hope this helps.