A point z has been plotted in the complex plane, as shown in figure below.<br><img src="/images/question-image/engineering-maths/complex-variable/1689244365-a-point-z-has-been-plotted-in-the-complex-plane.png" title="Complex Variable mcq question image" alt="Complex Variable mcq question image"><br>The plot for point $$\frac{1}{{\text{z}}}$$ is

If the semi-circular contour D of radius 2 is as shown in the figure, then the value of the integral $$\oint\limits_{\text{D}} {\frac{1}{{\left( {{{\text{s}}^2} - 1} \right)}}{\text{ds}}} $$ is

A

jπ

B

-jπ

C

-π

D

π

Consider the line integral $$I = \int_{\text{c}} {\left( {{{\text{x}}^2} + {\text{i}}{{\text{y}}^2}} \right){\text{dz,}}} $$ where z = x + iy. The line c is shown in the figure below

The value of $$I$$ is

A

$$\frac{1}{2}{\text{i}}$$

B

$$\frac{2}{3}{\text{i}}$$

C

$$\frac{3}{4}{\text{i}}$$

D

$$\frac{4}{5}{\text{i}}$$

Contour C in the adjoining figure is described by x² + y² = 16. The value $$\oint\limits_{\text{c}} {\frac{{{{\text{z}}^2} + 8}}{{0.5{\text{z}} - 1.5{\text{j}}}}{\text{dz}}} $$ is (Note: $${\text{j}} = \sqrt { - 1} $$ )

A

-2πj

B

2πj

C

4πj

D

-4πj

An elliptical dislocation loop is gliding on plane ABCD of a single crystal of BCC material as shown in the following figure. It is gliding along the burger vector 'b'. Identify the correct statement.

P. Plane ABCD belongs to the family of (110).
Q. Burger vector 'b' belong to direction.
R. Dislocation has the edge character at point x and the screw character at point z.
S. Dislocation has the screw character at point x

A

P, Q

B

Q, R

C

P, R

D

P, S

The figure shows the plot of y as a function of x

The function shown is the solution of the differential equation (assuming all initial conditions to be zero) is

A

$$\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} = 1$$

B

$$\frac{{{\text{dy}}}}{{{\text{dx}}}} = {\text{x}}$$

C

$$\frac{{{\text{dy}}}}{{{\text{dx}}}} = - {\text{x}}$$

D

$$\frac{{{\text{dy}}}}{{{\text{dx}}}} = \left| {\text{x}} \right|$$

The pictorial view of the frustum of a square pyramid is shown in figure 'X'. Its top view, when viewed in the direction of the arrow, will look like which of the given alternatives 1, 2, 3 and 4?

A

1

B

2

C

3

D

4

The magnitude and phase of the complex Fourier series coefficient a_k of a periodic signal x(t) are shown in the figure. Choose the correct statement from the four choices given. Notation: C is the set of complex number, R is the set of purely real numbers, and P is the set of purely imaginary numbers.

A

$$x\left( t \right) \in R$$

B

$$x\left( t \right) \in P$$

C

$$x\left( t \right) \in \left( {C - R} \right)$$

D

The information given is not sufficient to draw any conclusion about x(t)

Find out the alternative figure which contains figure (X) as its part.

A

1

B

2

C

3

D

4

Find out the alternative figure which contains figure (X) as its part.

A

1

B

2

C

3

D

4

Find out the alternative figure which contains figure (X) as its part.

A

1

B

2

C

3

D

4