Curl MCQ Quiz - Objective Question with Answer for Curl - Download Free PDF
Last updated on May 16, 2025
Latest Curl MCQ Objective Questions
Curl Question 1:
If f1 and f2 are differentiable scalar functions and v is differentiable vector function such that f1v = ∇f2, then v . curl v is
Answer (Detailed Solution Below)
Curl Question 1 Detailed Solution
Explanation:
v . curl v = v . ∇ × v = [v ∇ v] = 0
Option (4) is true.
Curl Question 2:
If f1 and f2 are differentiable scalar functions and v is differentiable vector function such that f1v = ∇f2, then v . curl v is
Answer (Detailed Solution Below)
Curl Question 2 Detailed Solution
Explanation:
v . curl v = v . ∇ × v = [v ∇ v] = 0
Option (4) is true.
Curl Question 3:
If
Answer (Detailed Solution Below)
Curl Question 3 Detailed Solution
Explanation:
Then
= curl ×
=
Option (1) is true.
Curl Question 4:
If
Answer (Detailed Solution Below)
Curl Question 4 Detailed Solution
Explanation:
⇒ Since
The curl of
⇒
⇒ where P = x + 2y + az, Q = bx - 3y - z, R = 4x + cy + 2z.
⇒
⇒ Expanding the determinant
⇒
⇒
Since
c + 1 = 0, 4 - a = 0, b - 2 = 0
⇒
⇒
Hence option 4 is correct
Curl Question 5:
If
Answer (Detailed Solution Below)
Curl Question 5 Detailed Solution
If
Explanation:
Then
=
Now,
⇒
⇒
⇒
As given
⇒ m= -2
Top Curl MCQ Objective Questions
If v = yz î + 3zx ĵ + z k̂, then curl v is
Answer (Detailed Solution Below)
Curl Question 6 Detailed Solution
Download Solution PDFConcept:
The curl of a vector is given by the expansion of the following matrix
If
Then
Calculation:
Given vector is
Than
The vector function expressed by
Represents a conservative field, where ax, ay, az are unit vectors along x, y and z directions, respectively. The values of constant k1, k2, k3 are given by:
Answer (Detailed Solution Below)
Curl Question 7 Detailed Solution
Download Solution PDFConcept:
For a vector F = F1i + F2j + F3k
For irrotational (or) conservative field
Calculation:
Given that,
k3 – 3 = 0 ⇒ k3 = 3
-4 + k1 = 0 ⇒ k1 = 4
k2 – 5 = 0 ⇒ k2 = 5
The required values are: k1 = 4, k2 = 5, k3 = 3The vector function
Answer (Detailed Solution Below)
Curl Question 8 Detailed Solution
Download Solution PDFGiven that,
We know that, for any scalar function ‘f’
What is the curl of the vector field 2x2yi + 5z2j - 4yzk?
Answer (Detailed Solution Below)
Curl Question 9 Detailed Solution
Download Solution PDFConcept:
Consider the vector field
In a vector field; Divergence of the gradient is
Answer (Detailed Solution Below)
Curl Question 10 Detailed Solution
Download Solution PDFDiv (grad ϕ) =
Let ϕ be a function of (x, y, z)
Then grad
Divergence (grad ϕ)
Which is Laplacian
= yz î + 3xz ĵ + z k̂, then Curl
Answer (Detailed Solution Below)
Curl Question 11 Detailed Solution
Download Solution PDFConcept:
Curl of a Vector:
Let
Then the curl of the vector function v is given by:
Where ∇ =
Calculation:
Given:
Given the vector A = (cos x)(sin y)âx + (sin x)(cos y) ây, ây denote unit vectors along x,y directions, respectively. The magnitude of the curl of 𝑨 is ______.
Answer (Detailed Solution Below) 0
Curl Question 12 Detailed Solution
Download Solution PDFConcept:
Let
The curl of A is evaluated as:
Analysis:
Given
Ax = cos x sin y
Ay = sin x cos y
Az = 0
If φ is a scalar point function, the value of curl Grad φ is
Answer (Detailed Solution Below)
Curl Question 13 Detailed Solution
Download Solution PDFConcept:
Let ϕ be a function of (x, y, z)
Then grad
curl (grad (ϕ))
curl (grad (ϕ))
curl (grad (ϕ)) = 0
The true statement is:
Answer (Detailed Solution Below)
Curl Question 14 Detailed Solution
Download Solution PDFConcept:
Gradient: Let a function F(x, y, z) then the gradient of F or ∇F is denoted as:
∇F =
Curl: In 3 dimensional cartesian coordinate the curl of a vector field
curl
Divergence: In 3 dimensional cartesian coordinate the divergence of a continuously differentiable vector field F = Fxi + Fyj + Fzk is defined as the scalar valued function.
It is denoted by divF = ∇.F
∇.F =
∇.F =
Formula Used:
Calculation:
We have,
⇒
⇒
⇒
⇒
⇒
⇒
⇒
⇒
⇒
⇒
⇒
⇒
⇒
⇒
∴ The true statement is
The value of the curl of the vector
Answer (Detailed Solution Below)
Curl Question 15 Detailed Solution
Download Solution PDFConcept:
If a vector function is given by
Then
Calculation:
Given:
⇒