Question66:-Which of the following is false ?
A:-the one point compactification of the real line *RR* is homeomorphic to an ellipse
B:-the one point compactification of the open interval (0, 1) is homeomorphic to closed interval [0, 1]
C:-the one point compactification of the open interval (0, 1) is ho meomorphic to the circle *S*(1)°
D:-the one point compactification of *RR*(2)° is homeomorphic to the sphere “S*(2)°
Correct Answer:- Option-B
Question67:-Which of the following is not a topological property ?
A:-length and area
B:-connectedness
C:-continuity
D:-compactness
Correct Answer:- Option-A
Question68:-Let d be a metric defined on *RR* by
மி, rf கத்‌
23 “hi, if a ¢
Then
A:-d is a pseudo metric on *RR*
B:-d is the usual metric on ' 88“
C:-d is the Euclidean metric ‏مه‎ ` रिरि
D:-d is the trivial metric on *RR*
Correct Answer:- Option-D
Question69:-Which of the following is not a basis for 68-൫3)" ?
A: {(1, 1, 1), (1, 1, 0), (1, 0, 0)}*
8:- 10, 1, 1), (0, 1, 1), (1, 0, 0))
(:-६(1, 1, 1), (0, 1, 1), (0, 0, 1))
0:- ६0, 0, 0), (0, 1, 0), (0, 0, 1)}*
Correct Answer:- Option-B
Question70:-Let ‘T : RR*(3)->RR*(3)° be a map defined on *RR*(3)° . Then which of the following is not a linear
transformation ?
A:-T (x, y,Z) = (y, x, 0)
B:-T (x, y,z) = (x+y, y+z,Z+X)
C:-T (x, y, Z) = (xy, yz, x2)
D:-T (x, y, z) = (0, 0, 0)
Correct Answer:- Option-C
Question71:-Let *P_(5)(x)* be the set of all real polynomials of degree ‘<= * 5.Then dimension of the vector space
*P_(5)(x)° ०४८ ` रिरि 15 `
A:-0
8:-1
C:-5
D:-6
Correct Answer:- Option-D
Question72:-Let ‘T:RR*(4)->RR*(5)° be defined by *T(x_(1),x_(2),x_(3),x_(4))=(x_(L),x_(2),x_(3),x_(4),0)° Then the
dimension of the null space is
4: 7()=0 ` `
നട
*n(T)
നട
Correct Answer:- Option-A
Question73:-Characteristic polynomial of *[[1, -1, 0],[0, 1, -1],[-1, 0, LIT is
A:~ lambda*(3)+3lambda*(2)+3Lambda+1=0"
lambda“ (3)-3lambda*(2)+3Lambda-1=0*
C:-‘lambda* (3)-3lambda* (2)+3Lambda-2=0*
D:-‘ lambda *(3)-3lambda*(2)+3Lambda=0°
Correct Answer:- Option-D
Question74:-Let *2x+y-z=4*
*x+3y+2z=1°
“3x+4y+z=5°
The above system of equation is
A:-homogeneous and consistent