Official PYQ · 2024Set 1 · Q44Vector AnalysisMSQ2 marks

GATE EC 2024 Set 1 Q44 — Vector Analysis

Let $F_{1}, F_{2}$ , and $F_{3}$ be functions of $(x, y, z)$ . Suppose that for every given pair of points $A$ and $B$ in space, the line integral $\int_{C}\left(F_{1} \mathrm{~d} x+F_{2} \mathrm{~d} y+F_{3} \mathrm{~d} z\right)$ evaluates to the same value along any path $C$ that starts at $A$ and ends at $B$ . Then which of the following is/are true?

Select all correct optionsA

For every closed path

\Gamma

, we have

\oint_{\Gamma}\left(F_{1} \mathrm{~d} x+F_{2} \mathrm{~d} y+F_{3} \mathrm{~d} z\right)=0

There exists a differentiable scalar function

f(x, y, z)

such that

F_{1}=\frac{\partial f}{\partial x}, F_{2}=\frac{\partial f}{\partial y}, F_{3}=\frac{\partial f}{\partial z}

\frac{\partial \text{F}_{1}}{\partial x}+\frac{\partial \text{F}_{2}}{\partial y}+\frac{\partial \text{F}_{3}}{\partial z}=0

\frac{\partial \text{F}_{3}}{\partial y}=\frac{\partial \text{F}_{2}}{\partial z}, \frac{\partial \text{F}_{1}}{\partial z}=\frac{\partial \text{F}_{3}}{\partial x}, \frac{\partial \text{F}_{2}}{\partial x}=\frac{\partial \text{F}_{1}}{\partial y}

View answer

Answer: A;B;D

Worked explanation not available yet.

Free practice · Your answers on this page are not saved.

Published 10 Oct 2026

Report a correction

Browse this topic

More Vector Analysis questions

GATE EC 2024 Set 1 Q44 — Vector Analysis

Related questions