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Q#1
Calculus
GATE EC 2024
MSQ
+2 marks
-0 marks
Let 
be functions of (x, y, z). Suppose that for every given pair of points A and B in space, the line integral 
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?
For every closed path T, we have 
There exists a differentiable scalar function F(x,y,z) such that
Explanation:
is independent of C
is conservative.
Line Integral of conservative field over a closed curve is 0
is correct
For conservative field the curl is zero 
Hence the conservative field can be expressed as gradient of a scalar field
We can write 
is correct.
Also,
is correct
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