Correct Answer:- Option-D
J 2-142

Question64:-Which of the following is the value of [=
‏ا‎
‎8:-2 शा
C:-8
D:-10
Correct Answer:- Option-C
Question65:-The number of roots of *z~*4-6z2+3=0,* with absolute value less than 1 is :
4
B:-1
C:-0
D:-3
Correct Answer:- Option-B
Question66:-If R is the set of real numbers, then which of the following is a metric on R°xx’R.
For *X = (x_1, y_1) and Y = (x_2, # 2)` inR°xx’R.
A:-d (X, Y) = Max *{ |x_1-y_1], |x_2-y_2|}*
B:-d (X, Y) = *|x_1-x 2]
C:-d (X, Y) = “sqrt ((x_L-y_1)*2+(x_2-y_2)*2)°
0:-0 (X, Y) = *(sqrt((x_1-x_2)*2+(y_1-y_2)*2))/(1+sqrt((x_1-x_2)*2+(y_L-y_2)*2))°
Correct Answer:- Option-D
Question67:-If (X, d) is an arbitrary metric space and E is a subset of X, choose the false statement from the following.
A:-Every interior point of E is a limit point of E
B:-The largest open set contained in E can be a closed set
C:-The closure of E can be an open set
D:-Every limit point of E is the limit of a sequence in E
Correct Answer:- Option-A

5-5
Question68:-Let R be the set of real numbers and പ്‌ be the semi open interval topology on R. Then, which of the following
ர
is true for (R, ~ ).
ल्ट
A:-(R, ™ ) is a second countable space.
ലു
B:-(R, ~ ) is a metrizable space.
SS),
C:-(R, ~*) is a separable space.
5
0:8, ೨18 compact space.
Correct Answer:- Option-C

Question69:-Choose the correct statement from the following :

A:-[0, 1) is homeomorphic to the unit circle “S*1,* both have subspace topologies of the usual topologies of R and R
*xxR respectively.

B:-{[a, b] : a ‘epsi’ R, b ‘epsi* R, a < b} is a base for a topology on R.

C:-The projection maps from a product space to the coordinate spaces are always closed.

D:-The torus surface is a quotient space of the unit square.

Correct Answer:- Option-D

5
Question70:-Let X be an uncountable set and 3 be the co-finite topology on X. Then, choose the correct one from the
following :

Ax(X,
B:-(X,
00%

) is a connected, “7 1' - 50906 which is metrizable.

جا ہا

) is a second countable *T_2* - space which is compact

ua

) is a separable compact space which is not metrizable
D:-(X, 3 ) is a second countable ‘T_1* - space which 15 metrizable
Correct Answer:- Option-C
Question71:-From the following given operations on the set of positive integers, choose the one which is a binary operation :
A:-a*b = ` (20)/(2)
B:-a*b=ab’ -*a