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This mock test of Test: Gradient for Electronics and Communication Engineering (ECE) helps you for every Electronics and Communication Engineering (ECE) entrance exam.
This contains 10 Multiple Choice Questions for Electronics and Communication Engineering (ECE) Test: Gradient (mcq) to study with solutions a complete question bank.
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QUESTION: 1

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

Solution:

Answer: b

Explanation: Gradient of any scalar function may be defined as a vector. The vector’s magnitude and direction are those of the maximum space rate of change of φ.

QUESTION: 2

The mathematical perception of the gradient is said to be

Solution:

Answer: c

Explanation: The gradient is the rate of change of space of flux in electromagnetics. This is analogous to the slope in mathematics.

QUESTION: 3

Divergence of gradient of a vector function is equivalent to

Solution:

Answer: a

Explanation: Div (Grad V) = (Del)^{2}V, which is the Laplacian operation. A function is said to be harmonic in nature, when its Laplacian tends to zero.

QUESTION: 4

4. The gradient of xi + yj + zk is

Solution:

Answer: d

Explanation: Grad (xi + yj + zk) = 1 + 1 + 1 = 3. In other words, the gradient of any position vector is 3.

QUESTION: 5

Find the gradient of t = x^{2}y+ e^{z} at the point p(1,5,-2)

Solution:

Answer: b

Explanation: Grad(t) = 2xy i + x^{2} j + e^{z} k. On substituting p(1,5,-2), we get 10i + j + 0.135k

QUESTION: 6

Curl of gradient of a vector is

Solution:

Answer: c

Explanation: Gradient of any function leads to a vector. Similarly curl of that vector gives another vector, which is always zero for all constants of the vector. A zero value in vector is always termed as null vector(not simply a zero).

QUESTION: 7

Find the gradient of the function given by, x^{2} + y^{2} + z^{2} at (1,1,1)

Solution:

Answer: b

Explanation: Grad(x^{2}+y^{2}+z^{2}) = 2xi + 2yj + 2zk. Put x=1, y=1, z=1, the gradient will be 2i + 2j + 2k.

QUESTION: 8

The gradient can be replaced by which of the following?

Solution:

Answer: c

Explanation: Since gradient is the maximum space rate of change of flux, it can be replaced by differential equations.

QUESTION: 9

When gradient of a function is zero, the function lies parallel to the x-axis. State True/False.

Solution:

Answer: a

Explanation: Gradient of a function is zero implies slope is zero. When slope is zero, the function will be parallel to x-axis or y value is constant.

QUESTION: 10

Find the gradient of the function sin x + cos y.

Solution:

Grad (sin x + cos y) gives partial differentiation of sin x+ cos y with respect to x and partial differentiation of sin x + cos y with respect to y and similarly with respect to z. This gives cos x i – sin y j + 0 k = cos x i – sin y j.

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