5:-0 y}=2 xy*
Correct Answer:- Option-D
et C be the positively oriented circle |z| = 4. Then *oint_(CYz~(2}d2)/(z-1)+0int_(CHz™(2)d2)/{((z-1)~(2))="

Correct Answer:- Option-A
Question58:-If f(z) is continuous in a simply connected domain D and if *oint_(C)f(z)dz=0" for every closed path in D, then
f(z} is analytic in D
A:-Liouville's theorem
B:-Morera's theorem
C:-Cauchy's integral theorem
D:-Cauchy’s integral formula
Correct Answer:- Option-B
Question59:-The radius of convergence of the power series 5017) (7=0)^06 ` ((21)1)/((1)^(2))2-2)^()}` 15
ಹಿಂ
68:4”
೧೨3/27
0:00
Correct Answer:- Option-B
Question60:-At z = 0, the function *f(z)=e~((1}/(2))" ೧೩5
A:-a removable singularity
B:-a simple pole
C:-an essential singularity
D:-no singular point
Correct Answer:- Option-C
Question61:-Let *f(z)=(1-cosz}/{(z~(5)} . Then f(z) has
A:-a pole of order 3 and residue *{-1)/(24)" atz=0
B:-a pole 01 ೧೮೮೯ 5 276 7551606 ' )“1(/)24(' ‏٢3‎ 7 0
C:-a pole of order 3 276 7651606 ' (1)/(5) atz=0
D:-a pole of order 5 and residue *(1)/(5) atz=0
Correct Answer:- Option-A

Res 2‘: ‏نے ا‎
Question62:- z=3i 27 +9
‏”(3+10/6)“-ھ‎
‎5 (3006)
ஸு
பம
Correct Answer:- Option-B
Question63:-Which of the following is false 7
A:-Every order topology is Hausdorff
B:-Subspace of a Hausdorff space is Hausdorff
C:-Every Hausdorff space is normal
D:-Product of two Hausdorff space is Hausdorff
Correct Answer:- Option-C
Question64:-Deleted comb space is
A:-connected and path connected
B:-connected but not path connected
C:-not connected but path connected
D:-neither connected nor path connected
Correct Answer:- Option-B
Question65:-Which of the following need not be a normal space 7
A:-product of two normal spaces
B:-a metrizable space
C:-a compact Hausdorff space
D:-a regular space with a countable basis
Correct Answer:- Option-A