Home › Previous year questions › GATE 2015 EE (EE2) › Question 13GATE 2015 EE (EE2) – Question 13 Engineering Mathematics · Calculus: Vector identities, Directional derivatives, Line integral, Surface integral, Volume integral, Stokes's theorem, Gauss's theorem, Divergence theorem, Green's theorem · 1 mark · Multiple choice
Match P: Stokes’ theorem; Q: Gauss’ electric-flux law; R: divergence theorem; S: Cauchy’s integral theorem, to:
1. $\iint_S\mathbf D\cdot d\mathbf S=Q$.
P2,Q1,R4,S3 P4,Q1,R3,S2 P4,Q3,R1,S2 P3,Q4,R2,S1 Practise this question in The GATE Grind →
Show answer and explanation Correct answer: (B) P4,Q1,R3,S2
Explanation Stokes equates surface curl flux to boundary circulation, so P→4. Gauss' electric law equates displacement flux to enclosed charge, Q→1.
The divergence theorem converts volume divergence to closed-surface flux, R→3. Cauchy's theorem gives zero contour integral for a function analytic in the relevant simply connected region, S→2. Thus **B**.
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