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Force acting on a particle moving in the \( x-y \) plane is \( \vec{F}=\left(y^{2} \hat{i}+x \hat{j}\right) \mathrm{N}, x \) and \( y \) are in metre. As shown in figure, the particle moves from the origin \( O \) to point \( A(6 \mathrm{~m}, 6 \mathrm{~m}) \). The figure shows three paths, \( O L A, O M A \), and \( O A \) for the motion of the particle from \( O \) to \( A \).
Which of the following is correct?
(1) There is equal probability for the force being conservative or non-conservative.
(2) Conservative or non-conservative nature of force cannot be predicted on the basis of given information.
(3) The given force is non-conservative.
(4) The given force is conservative.
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