Title  

Gradient of a function is a constant. State True/False 

The mathematical perception of the gradient is said to beThe mathematical perception of the gradient is said to be
The answer is:
C. slope


Divergence of gradient of a vector function is equivalent toDivergence of gradient of a vector function is equivalent to
The answer is:
A. laplacian operation


Curl of gradient of a vector isCurl of gradient of a vector is
The answer is:
C. null vector


Find the gradient of the function given by, x2 + y2 + z2 at (1,1,1)Find the gradient of the function given by, x2 + y2 + z2 at (1,1,1)
The answer is:
B. 2i + 2j + 2k


Find the gradient of the function sin x + cos yFind the gradient of the function sin x + cos y.
The answer is:
A. cos x i – sin y j


The gradient can be replaced by which of the following?The gradient can be replaced by which of the following?
The answer is:
C. differential equation


The divergence of a vector is a scalar. State True/False 

The divergence concept can be illustrated using Pascal’s law. State True/FalseThe divergence concept can be illustrated using Pascal’s law. State True/False
The answer is:
A. true


Compute the divergence of the vector xi + yj + zk 

Find the divergence of the vector yi + zj + xk 

Find the divergence of the vector F= xex i + y j – xz kFind the divergence of the vector F= xex i + y j – xz k
The answer is:
A. (1 – x)(1 + ex)


Find whether the vector is solenoidal, E = yz i + xz j + xy kFind whether the vector is solenoidal, E = yz i + xz j + xy k
The answer is:
A. yes, solenoidal


Find the divergence of the field, P = x2yz i + xz kFind the divergence of the field, P = x2yz i + xz k
The answer is:
B. 2xyz + x


Identify the nature of the field, if the divergence is zero and curl is also zeroIdentify the nature of the field, if the divergence is zero and curl is also zero.
The answer is:
C. solenoidal, irrotational


Curl is defined as the angular velocity at every point of the vector field. State True/FalseCurl is defined as the angular velocity at every point of the vector field. State True/False.
The answer is:
A. true


The curl of curl of a vector is given by,The curl of curl of a vector is given by,
The answer is:
B. grad(div v) – (del)2v


Which of the following theorem use the curl operation?Which of the following theorem use the curl operation?
The answer is:
C. stoke’s theorem


Is the vector is irrotational. E = yz i + xz j + xy k 

The curl of a curl of a vector gives aThe curl of a curl of a vector gives a
The answer is:
B. vector

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