which of the following is/are conservative force(s)?

Since, W=∫F→⋅dr→Clearly for forces of option (1) and (2), the integration does not require any information of the path taken. For option (3). W3=∫3(xi^+yj^)x2+y23/2⋅(dxi^+dyj^)=3∫xdx+ydyx2+y23/2Taking x2+y2=t, we get 2xdx+2ydy=dt      xdx=ydy=dt2W3=3∫dt/2t3/2=32∫dtt3/2which will be independent of path after solving. Hence (1), (2), and (3) are conservative forces. But option (4) requires some more information on path to solve it. Hence, it is non-conservative.