Question49:-The power series ‏شید‎ converges 5

Ae?

1142

ors

رتم

Correct Answer:-Question Cancelled
‘Question50:-Dimensions ‏و‎ ೦೫೮೯ ೩ 15
Aon
Bent
മാ
D:-2n
Correct Answer: Option-D
Question51:-Which of the following is a Banach space
‘A-Space of all polynomial functions on [a,b] with the supremum norm,
B:-Space of all continuous functions on (a,b] with the supremum norm
(C-Space of all polynomial functions on [a,b] with the p-norm
D:-Space of all continuous functions on [a,b] with the p-norm
Correct Answer: Option ®
Question52:-The term Hilbert space stands for a
‘A-Complete inner product space
B:-Compact linear space
C-Complete normed space
D:-Complete metric space
Correct Answer: Option:

‘Question53:-Let H bea Hilbert space and L be a subspace of H. Then which of the following is false.

1" 15 a closed subspace of H

Be" is a subspace of H
८४०५५ =}
5:1612 ‏ہے‎

Correct Answer: Option-D

QuestionS4:-Ifp 221, then which of the following is/are true,

Aol ch,

Correct Answer:- Option ®
Question55:-Consider the following statements about a Hilbert space
P: His separable ifit has a countable dense subset
Q: His separable ifit has a complete orthonormal system
Ac Only Pis true
B:-Only Qis true
CeBoth are true
D-Neither P nor Q are true
Correct Answer:- Option-é
QuestionS6:-f X and Y are normed spaces, and if: + ¥ is a linear operator, then Tis bounded if and only if
கர maps bounded subsets of X into bounded subsets of Y

BT maps open subsets of X into open subsets of Y