A velocity 1/4 m/s is resolved into two components along OA and OB making angles 30degree and 45degree

respectively with the given velocity. Then the component along OB is:

Wrong !

See the axes are not orthogonal . So draw the fig and apply sine rule .

Component along OB would be  : 1/4 * sin 30/sin ( 30 +45 ) = 1/4 * sqrt(2 ) / ( sqrt(3 ) + 1 )

is allowed if the axes r orthogonal  i, e, the angle b/w the axes r 90 degree.

clearly here the angle b/w OA and OB r 75 degree. So this cannot be applied.

Exactly !

See , when u are resolving a vector into two components , all it means that u are finding two vectors whose resultant is the given vector .( U may extend this concept in resolving a vector into more than two components also ! )

In any cases u have to draw the diagram & solve it by purely geometrical methods !

Ok , we know the result for the orthogonal components ; but for all other cases u have to follow the general method !

Hope, this will clear ur doubt .