Questind9:-The power 5616572 "2९५३ converges 5

॥

[2

Ors

عم

Correct Answer: Option-D
‘Question50:-Dimensions of ©“ over 2 15
Aon
[
മാ
D:-2n
Correct Answer: Option-D
QuestionS1:-Which of the following is ३ Banach space
‘A:-Space of all polynomial functions on [a,b] with the supremum norm
B:-Space of all continuous functions on [க] with the supremum norm
50208 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: 8
QuestionS2:-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:

‘QuestionS3:-Let H be a Hilbert space and L be a subspace of H. Then which of the following is false,

1५15 a closed subspace of H

Be" 15 a subspace of ಗ.
ഡ്‌)
51612 ‏ہے‎

Correct Answer: Option-D

QuestionS4:-Ifp 2921, 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
6: His separable ifit has a complete orthonormal system
‘AcOnly Pis true
B:-Only Qis true
೦-8007 are true
D-Neither ೧೦೯೦ are true
Correct Answer: Option-C
QuestionS6:-f X and ४ are normed spaces, and ‏)أ‎ 7:۰۷ ¥ is a linear operator, then Tis bounded if and only it
‏كنم‎ maps bounded subsets of X into bounded subsets of ¥

छत maps open subsets of X into open subsets of Y