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1.  What is the value of the limit ̅ ?a.

 

1

b.  -1

c. 

0

d. 

Does not exist

2. 

Function   is continuousa.

 

Only at z=0

b.  Not continuous at z=0

c. 

Continuous everywhere in the finite plane

d.  Not continuous anywhere

3.  Evaluate the limit  a.  1

b. 

Doesn’t exist 

c.  2

d. 

0

4.  Function   isa.  Purely real

b. 

Purely imaginary

c.  Complex having both real and imaginary

parts (Non-zero)

d. 

Not a valid function

5.  If   is an analytic function where  then  isa.   b.   

c.   d.   

6.  If  is analytic function, then  isa.  Necessarily analytic

b. 

Necessarily harmonic

c.  Not harmonic

d. 

May or may not be harmonic

7.  ∫  is equal to, where C is the left half of the unit circle in the clockwise direction,a.  0

b. 

2

c.   

d. 

18.  ∫  is equal to, where C is the line  from (0,0) to (4,2)

a.  b. 

c.  d. 

9.  ∫  is where C is  and (i) , (ii) , then value of in both cases (i) and (ii)will be

a. 

Different

b.  Same

c. 

Not sufficient information available

d.  Will be same for some values of  anddifferent for some other values of

 

10. 

Argument of , where  is(a)    (b)   (c) ⁄   (d) none of these

11.  The value of  is(a)

 

0 (b)1  (c) -1 (d) 2

12.  The value of  for which  is real

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(a)    (b) ,    (c) ,    (d) ,   13. Cauchy-Riemann equation is a

(a)necessary condition for analyticity (b) sufficient condition for analyticity

(c) necessary and sufficient condition for analyticity (d) none of these

14. Which of the following is an Entire function

(a)  (b)  +2 (c)   (d) all the above

15. Which of the following is a correct statement?

(a)sinz is analytic in finite z-plane (b)cosz is analytic in finite z-plane

(c) is analytic in finite z-plane (d) all the above

16. A curve is said to be simple

(a)If it intersects itself (b)if it doesn’t intersect itself   (c) if it is a straight line (d) none of these

17. Evaluate ∫  (a)  (b)   (c)    (d)   

18. Evaluate

∫

 

(a)   (b)    (c)   (d)   19. For the following function .   

A. 

18 +  B.  18+2

  

C.  18 -  

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D. 

None of these

20. Which The following statements are true?

1. If F is continuous at z then f must have derivative at this point.

2.     implies the continuity at z =  A. Both 1 and 2 are true.

B. Only 1 is true

C. Only 2 is true

A. 

Neither of 1 and 2 is true

21.      {  ̅

 A.  Doesn’t exist 

B.  Equals zero

C.  Equals one

D.  None of these

22. The following function is analytic at

A. 

At origin only

B.  At Every Integer

C. 

Everywhere In the complex plane

D. 

Nowhere at the complex plane.

23. The points where the function ̅  is analyticA.  At origin only

B. 

At Every Integer

C.  In all the complex plane

D.  Nowhere at the complex plane.

24. The derivative of   { ̅

  at z=0A.

 

Doesn’t exist 

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B. 

Equals zero

C. 

Equals one

D. 

None of these

24. Find

.

A. 

 +

 

 

B. 

 +  C.

 

 +  

D.  None of these

26. Find

A. 

 +  

B. 

 +  C. 

 +   

D. 

None of these

27. If n

, a lies inside the closed curve c is

A.2 B.  C.0

D.None of these

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28.  a.    b.   c.   d.  

29. General value of  a.    b.   c.   d. 0 

30. Find the limit of  a.    b.   c.   d.  

31. According to   – equation for analytic function which of the following is truea.  b.   c.   d.  32. If  is analytic function and  is constant then

a.   is constant b.   is constant c. both a and b d. v is not constant

33. If  then  isa.    b.   c.   d.  

34. The value of ∫   on  isa.    b. 0 c.   d. 2

35. The length of the curve  a.

    b.   c. 2 d. 436. If  is analytic then integration of  from  to  is

a.  Independent of the path

b. 

Dependent of the path

c.  May or may not depend upon path

d.  None of them

37. The value of ∮   on | |  isa.  0 b.   c.   d. 2

38. ∮  a.    b.   c.   d.  

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39. The region  is(a) Bounded (b) Closed (c) Not connected (d) open

40. The region ()  is(a)

 

Open (b) Not Closed (c) not connected (d) unbounded

41. The function

 is not defined at

(a) 

0 (b) i (c) –1 (d) 1

43. The image of the function ̅  at 2+7i is(a)  2 (b) 7i (c) 11+23i (d) 18+16i

44.

  i z 

iz 

i z 

1lim  3

 

(a) 

-4i (b) -3i (c) 0 (d) does not exist

45.

 z 

 z 

 z  x y paththe Along 

0

lim,

 

(a)  i (b) -i (c) 0 (d) does not exist

46. Which of the following is not a entire function?

A)      B)     C)     D)  

 

47. Let   be an analytic function. Choose the most appropriate optionA)

 

First order partial derivatives of  exist.B)  Cauchy Riemann equation is satisfied by  C)

 

 both are continuous function.D)

 

All of above

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