complex integration mcq+notes

8/17/2019 Complex Integration MCQ+Notes

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Prepared By Mr R.Manimaran,Assistant Professor,Department Of Mathematics, SRM UNIVERSITY,

Vadapalani Campus -Chennai-26 Page 1

SRM UNIVERSITY

RAMAPURAM PART- VADAPALANI CAMPUS, CHENNAI – 600 026

Department of Mathematics

Sub Title: ADVANCED CALCULUS AND COMPLEX ANALYSIS

Sub Code: 15MA102

UNIT V – COMPLEX INTEGRATION

PART-A

1. A continuous curve which does not have a point of self intersection is called

(a) Simple curve (b)Multiple curve (c)Integral curve (d) None Ans : (a)

2. Simple curve are also called

(a) Multiple curve (b) Jordan curve (c) Integral curve (d) None Ans : (b)

3.

An integral curve along a simple closed curve is called a(a) Multiple Integral (b) Jordan Integral (c) Contour Integral (d) None Ans : (c)

4. A region which is not simply connected is called ... region

(a) Multiple curve (b) Jordan connected (c) Connected curve (d) Multi-connected

Ans : (d)

5. If is analytic and is continuous at all points inside and on a simple closed curve C, then

(a) 0)( C

dz z f (b) 0)( C

dz z f (c) 1)( C

dz z f (d) C

dz z f 1)( Ans : (a)

6. If is analytic and is continuous at all points in the region bounded by the simple closed curve

1C and 2C , then

(a) 21

)()(C C

dz z f dz z f (b) 21

)()(C C

dz z f dz z f (c) 21

)(')('C C

dz z f dz z f

(d) 21

)(')('C C

dz z f dz z f Ans : (a)

7. A point 0 z at which a function )( z f is not analytic is known as a .... of )( z f

(a) Residue (b) Singularity (c) Integrals (d) None Ans : (b)

8. If the principal part contains an infinite number of non zero terms of )( a z then a z is known as

(a) Poles (b) Isolated Singularity (c) Essential Singularity (d) Removable Singularity

Ans : (c)

9. The Singularity of)2)(1(

3)(

z z

z z f are

(a) 3,1 z (b) 0,1 z (c) 2,1 z (d) 3,2 z Ans : (c)

10. A zero of an analytic function )( z f is a value of z for which

(a) 0)( z f (b) 1)( z f (c) 1)( z f (d) 0)( z f Ans : (a)


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11. The poles of

1

1sin

2)(

2 z z

z z f is

(a) 2 (b) 0 (c) 1 (d) None Ans : (a)

12. The poles of2

2

1

1)(

z

z z f

is

(a) 1 (b) -1 (c) 1 (d) 0 Ans : (c)

13.

The poles of 23 )3()2(

1)( z z z f

is 2 z and 3 z is order ... and ... respectively

(a) 2,3 (b) 3,2 (c) 3,3 (d) 2,2 Ans : (b)

14. The pole for the function2)1(

)2/tan()(

i z

z z f

is )1( i of order

(a) 0 (b) 2 (c) undefined (d) 0 Ans : (d)

15. The residue of z z f cot)( at each poles is

(a) 0 (b) 1 (c) 1/2 (d) none Ans : (b)

16. The residue of

z z z

e z f

z

cossin

1)(

at the pole 0 z is

(a) 0 (b) 1 (c) 1 (d) undefined Ans : (b)

17. A singular point 0 z z is said to be an ... singular point of )( z f , if there is no other singular point in the

neighbourhood of 0 z

(a) Poles (b) Isolated (c) Essential (d) Removable Ans: (b)

18. A singular point 0 z z is said to be an ... singular point of )( z f , if )(lim0

z f z z

exists and finite

(a) Poles (b) Isolated (c) Essential (d) Removable Ans: (d)

19. A singular point 0 z z is said to be an ... singular point of )( z f , it is neither an isolated singularity nor a

removable singularity

(a) Poles (b) Isolated (c) Essential (d) Removable Ans: (c)

20. If 0)( a f and 0)(' a f , then a z is called a ....

(a) Simple zero (b) Simple curve (c) Zero of order n (d) none Ans: (a)


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Part – B


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complex integration mcq+notes

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