Vector Calculus NAT Level - 2 - Free MCQ Test with solutions for Physics
MCQ Practice Test & Solutions: Vector Calculus NAT Level - 2 (10 Questions)
You can prepare effectively for Physics Topic wise Tests for IIT JAM Physics with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Vector Calculus NAT Level - 2". These 10 questions have been designed by the experts with the latest curriculum of Physics 2026, to help you master the concept.
Test Highlights:
- - Format: Multiple Choice Questions (MCQ)
- - Duration: 45 minutes
- - Number of Questions: 10
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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.Detailed Solution: Question 1
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 :
Detailed Solution: Question 2
lies along y axis
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.Detailed Solution: Question 3
can be expressed as gradient of scalar function 
along the portion (1, 0, 1) to (3, 4, 5)
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 :
in moving a particle over circular path x2 + y2 = 1, z = 0 from (1, 0, 0) to (0, 1, 0) is :Detailed Solution: Question 4
where C is the path shown in figure.
Detailed Solution: Question 5
Let C be any curve x2 + y2 + z2 = 4, z > 0 and the vector field 
find out 
(Ans. upto three decimal places)
Detailed Solution: Question 6
consisting of S and S' i.e 
The value of the 
and C is the curve y2 = x joining (0, 0) to (1, 1) is (correct upto three decimal places)
and C is the curve y2 = x joining (0, 0) to (1, 1) is (correct upto three decimal places)Detailed Solution: Question 7
Detailed Solution: Question 8
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.
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.Detailed Solution: Question 9
If f(x, y, z) = x2y + y2z + z2x for all (x, y, x) ∈ R3 and 
then the value of 
at (2, 2, 2) is :
then the value of at (2, 2, 2) is :Detailed Solution: Question 10
