GATE 2024 PI – Question 12
$\mathbf F=(100x+100y)\mathbf i+(-50x+200y)\mathbf j$. Evaluate $\oint_C\mathbf F\cdot d\mathbf l$ along an anticlockwise circle of radius 2, with $d\mathbf l=dx\mathbf i+dy\mathbf j$.
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Correct answer: MTA
Explanation
Green’s theorem gives $\oint(P\,dx+Q\,dy)=\iint(\partial Q/\partial x-\partial P/\partial y)dA$. The integrand is −50−100 = −150 and circle area is 4π. Result: **−600π**, which is absent from the options. The official final key awards **marks to all**, preserved here.