Correct Answer:- Option-D
| ‏ا-<|‎
‏إكا‎ -1

Question64:-Which of the following is the value of
Al

نت
0-0
‎Correct Answer:- Option-C‏
‎Question65:-The number of roots of *z~4-6z+3=0," with absolute value less than 1 is :‏
‎A4‏
‏1-:8
‎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™C'R.‏
‎For X ={x_1,y 1}and Y = (x_2, y 2} inR"%CR.‏
‎A (X, Y) = Max ( [141,022‏
یں ‎(X,‏ -:8
‎യ കി 2(72(“‏
‎१) = “(02215 2)*2)/(5 (02-21 22)”‏ .9( 4-:0
‎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.‏
ع آه ‎A:-Every interior point of E is a limit point‏
‎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

ابچ

Question68:-Let R be the set of real numbers and ~ be the semi open interval topology on R. Then, which of the following
प्र

is true for (R, ~ )

الچ
‎AR, ചി }is a second countable space.‏
‎o‏
‎B:-(R. - } is a metrizable space.‏
‎o‏
‎is a separable space.‏ } ٹہ ‎नारे,‏

5
0:-)۸ -3 1158 compact space.
Correct Answer:- Option-C
Question69:-Choose the correct statement from the following :
A:-[0, 1) is homeomorphic to 076 ‏٢۲ہ‎ (೧೮6 7577,” 0007 ೧೩೪೬ 50502೧6 topologies of the usual topologies of R and R
இது respectively.
B:-{[a, b]: 2 “epsi’ R, 0 ` €` 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 न be the co-finite topology on X. Then, choose the comrect one from the
following :

کا ھ
‎B:-(X,‏
‏کات

}is a connected, *T_1" - space which is metrizable.

ट ९

}is a second countable *T 2" - space which is compact

L3

115 8 separable compact space which is not metrizable

D:-(X, 3 }is a second countable *T_1" - space which is 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 = “(0/2
B:-a*b=ab’ - व
C:-a*b=ab+b
D:-a*b=a’-'b