Divergence Theorem MCQ Quiz in मराठी - Objective Question with Answer for Divergence Theorem - मोफत PDF डाउनलोड करा
Last updated on Apr 1, 2025
Latest Divergence Theorem MCQ Objective Questions
Top Divergence Theorem MCQ Objective Questions
Divergence Theorem Question 1:
Evaluate the surface integral
Answer (Detailed Solution Below) 0 - 0.5
Divergence Theorem Question 1 Detailed Solution
Concept:
Gauss-divergence theorem:
The tetrahedron is given as
Equation of xy is
Equation of plane XYZ
x + y + z = 1
Calculation:
= 2y + 0 + 4y = 6y
∴ Integral is 6
Divergence Theorem Question 2:
Find a unit normal to the surface x2y + 2xz = 4 at (2, -2, 3)
Answer (Detailed Solution Below)
Divergence Theorem Question 2 Detailed Solution
ϕ = x2y + 2xz
Grad ϕ is a vector normal to the surface ϕ = constant
∇ϕ = î (2xy + 2z) + ĵ (x2) + k̂ (2x)
Unit normal to the given surface at (2, -2, 3)
Divergence Theorem Question 3:
The direction of vector A is radially outward from the origin, with
Answer (Detailed Solution Below) -2
Divergence Theorem Question 3 Detailed Solution
Divergence of A in spherical coordinates is given as
Given that
Divergence Theorem Question 4:
Find the value of
Answer (Detailed Solution Below) 0
Divergence Theorem Question 4 Detailed Solution
Using divergence theorem
So,
Divergence Theorem Question 5:
Answer (Detailed Solution Below) 0
Divergence Theorem Question 5 Detailed Solution
Using divergence theorem
= 1 + 1 – 2 = 0
So,