Vector Calculus NAT Level - 2
10 Questions MCQ Test Topic wise Tests for IIT JAM Physics | Vector Calculus NAT Level - 2
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Evaluate 
where 
and S is the part of the plane 2x + 3y + 6z = 12 which is located in the first octant.
where and S is the part of the plane 2x + 3y + 6z = 12 which is located in the first octant.
= 24
The correct answer is: 24
Find the value of constant (a + b + c) so that the directional derivative of the function f = axy2 + byz + cz2x3 at the point (1, 2, –1) has maximum magnitude 64 in the direction parallel to y axis :
lies along y axis
So, 4a + 3c = 0
2b – 2c = 0
The correct answer is: -20
Evaluate the 
along the portion from path (1, 0, 1) to (3, 4, 5) of the curve C, which is the intersection of the surface z2 = x2 + y2 and z = y + 1.
along the portion from path (1, 0, 1) to (3, 4, 5) of the curve C, which is the intersection of the surface z2 = x2 + y2 and z = y + 1.
can be expressed as gradient of scalar function 
written the common term once
The line integral 
along the portion (1, 0, 1) to (3, 4, 5)
= (375 + 108 – 20) – (1)
= 463 – 1
= 462
The correct answer is: 462
The work done by the force 
in moving a particle over circular path x2 + y2 = 1, z = 0 from (1, 0, 0) to (0, 1, 0) is :
on the curve
The correct answer is: -4.142
where C is the path shown in figure.
Path AO
y = 1
dy = 0
Path OB
x2 + y2 = 1
= –0.416
The correct answer is: -0.416
Let C be any curve x2 + y2 + z2 = 4, z > 0 and the vector field 
find out 
(Ans. upto three decimal places)
Consider a closed surface 
consisting of S and S' i.e
The correct answer is: 25.132
The value of the 
and C is the curve y2 = x joining (0, 0) to (1, 1) is (correct upto three decimal places)
The correct answer is: 0.583
Let 
The correct answer is: 0
along the curve x = sin θ cos θ, y sin2 θ, z = cos θ with θ increasing from 0 to π/2. Find the value of α + β.
= xz dx + y dy + x2 dz
Along the given curve, we have
Putting values
The correct answer is: 43
If f(x, y, z) = x2y + y2z + z2x for all (x, y, x) ∈ R3 and 
then the value of 
at (2, 2, 2) is :
Hence, 
The correct answer is: 12
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