D:-v(x, y)=2 xy"
Correct Answer:- Option-D

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 ‘sum_(n=0)*oo**((2n)!)/((n!)*(2))(2-2)*(n)° is

A:-0

1/2
0:- 00
Correct Answer:- Option-B

Question60:-At z = 0, the function “f(z)=e%((1)/(z))” has
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 of order 5 and residue ` (-1)/(24) > 2 = 0
C:-a pole of order 3 and residue *(1)/(5)° atz = 0
D:-a pole of order 5 and residue *(1)/(5)° atz =0
Correct Answer:- Option-A

Res a saat
Questioné2:- 273! Z 49
A: (3+)/(6)`
8:-`(3-1/(6)
0-130/9)
0:-`(1-30/(9)`

Correct Answer:- Option-B
Question63:-Which of the following is false ?
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 ?
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