Question66:-Which of the following is false 7
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 homeomorphic 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 7
A:-length and area
B:-connectedness
C:-continuity
D:-compactness
Correct Answer:- Option-A
Question68:-Let d be a metric defined on *RR* by

൭, प 258
व (वि 2) न ಗ್ಯ 1; ९ +¢

Then
A:-d is a pseudo metric on “RR*
B:-d is the usual metric on *RR*
C:d is the Euclidean metric ೦೧ ` दिरिः
D:-d is the trivial metric on ` रिरि
Correct Answer:- Option-D

Question69:-Which of the following is not a basis for 8-൫) 7
&:-` {(1, 1, 1), (1, 1, 0), (1, 0, 0}}"
8:-(1, 1,1), (0, 1, 1), (1, 0, 0)]`
6148 ௩1), 6 1, 1), (0 0, 11“
೧:-:((1, 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 7

ಮಿ 0८ ೫,2)

8;-7 0 ೫, 2) ಎ 04 3, 33 2, 23-20)

6: (% v, 2} = (xy, yz, x2}

D:-T {x, ೫, 2) ಎ (0, 0, 0)

Correct Answer:- Option-C
Question71:-Let 7 (5)00” be the set of all real polynomials of degree * <= " 5.Then dimension of the vector space
“P_(5)}x)" over'RR’ is""

ಹಿಂ

B:-1

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_{1}x_(2),x_(3).x_{4),0)" Then the
dimension of the null space ‏کا‎

௨0)

0:-` ` ` 7()=5`
Correct Answer:- Option-A
Question73:-Characteristic polynomial of *[[1, -1, 01,0, 1, -11,11, 0, 111 ‏ا‎

A:-'lambda”(3)}+3lambda”(2}+3Lambda+
B:-"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