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\hline Q.31 & A vector field \\
$\qquad \begin{array}{l}\text { is defined over a conical region having height } h=2, \text { base radius } r=3 \text { and axis } \\
\text { along } z \text {, as shown in the figure. The base of the cone lies in the } x-y \text { plane and is } \\
\text { centered at the origin. } \\
\text { If } n \text { denotes the unit outward normal to the curved surface } S \text { of the cone, the } \\
\text { value of the integral }\end{array}$ \\
equals $x, y)=x \hat{\imath}-2 z \hat{\mathrm{k}}$
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