\[(a)\;2 \quad (b)\;4 \quad (c)\;6 \quad (d)\;8 \]

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Answer: 2

Work done is zero if force is perpendicular to the displacement .

Force is represented by the vector $=(2 i+3j)N$, where the slope of the line joining (2,3) to origin ($y=\large\frac{3}{2}$$x+c$) is 3/2

Equation of the line, the particle is moved on is $3y+kx =5$

$\Rightarrow y=\large\frac{-k}{3}$$x+\large\frac{5}{3}$

Work done by force is zero, hence force is perpendicular to displacement $\rightarrow m_1m_2=-1$

$\Rightarrow \bigg(\large\frac{3}{2}\bigg)\bigg(\large\frac{-k}{3}\bigg)$$=-1 \rightarrow$ $k=2$

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