The contour integral $$\oint {\frac{{dz}}{{{z^2} + {a^2}}}} $$   is to be evaluated on a circle of radius 2a centred at the origin. It will have contributions only from the points

The contour integral $$\oint {\frac{{dz}}{{{z^2} + {a^2}}}} $$   is to be evaluated on a circle of radius 2a centred at the origin. It will have contributions only from the points Correct Answer $$ia{\text{ and }} - ia$$

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i. the point z0 = 2 inside the contour c, and
ii. the point z0 = 2 outside the contour c, respectively, are
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A. public class Circle implements Shape { private int radius; }B. public abstract class Circle extends Shape { private int radius; }C. public class Circle extends Shape { private int radius; public void draw(); }D. public abstract class Circle implements Shape { private int radius; public void draw(); }E. public class Circle extends Shape { private int radius; public void draw() { /* code here */ } }F. public abstract class Circle implements Shape { private int radius; public void draw() { /* code here */ } }
The value of the contour integral in the complex plane $$\oint {\frac{{{{\text{z}}^3} - 2{\text{z}} + 3}}{{{\text{z}} - 2}}{\text{dz}}} $$    along the contour |z| = 3, taken counter-clockwise is
A common convention is: • is evaluated first • and are evaluated next • Quantifiers are evaluated next • is evaluated last.
Statement : It has been reported by one of the TV channels that the answer papers of Board examination of one State are evaluated by students studying in the same standard with the help of model answers as instructed by the examiners.

Courses of Action :
I. All such examiners should be immediately suspended from their official positions.
II. All such papers evaluated by the students should be immediately confiscated and got evaluated by qualified teachers.
III. The Board should explore possibilities even though they are remote, of getting the answer papers of this examination evaluated by computerised machines.
A common convention is:
• is evaluated first
• and are evaluated next
• Quantifiers are evaluated next
• is evaluated last.
The integral $$\oint {{\text{f}}\left( {\text{z}} \right){\text{dz}}} $$   evaluated around the unit circle on the complex plane for $${\text{f}}\left( {\text{z}} \right) = \frac{{\cos {\text{z}}}}{{\text{z}}}$$   is
The value of the integral $$\oint\limits_C {\frac{{{e^z}\sin z}}{{{z^2}}}} dz,$$   where the contour C is the unit circle: |z - 2| = 1, is
The contour integral $$\oint\limits_{\text{C}} {{{\text{e}}^{\frac{1}{{\text{z}}}}}{\text{dz}}} $$   with C as the counter-clockwise unit circle in the z-plane is equal to