47.

48.

49.

50.

51.

52.

53.

If c is the circle je|=1, then fe ‏یں‎ is:
८2 +2iz
ಎಸ್ಸೈ ಗ .
(A) ate (B) 87-671
டு கட a ಸ
O 7 ५ 24
If c is the circle |2|=1, then pede is:
८
۵ ‏ر2‎ ൯) 382i
(© 6 ൯൩) 627i

Let G be an open connected set in € such that G contains an interval X of the real line and
let f, g:G—C be analytic. If f(z) = g(z) forall ze X, then for ze G, g(z) is:

(ಯ) g(z) is real valued (3) g(z) is constant

© ‏)م‎ = (0) ൭57൭

7 : [९ -> [ए is the bounded linear map F'(x,,%2,...%5) =X, + 2%. + 7४3 + 34 + 5. If R’ is
bestowed with the 2-norm | ۳ then |] is:

(A) 8 (8) 14
(൭ 42 (D) 64

Which of the following is a Banach space?

0) = ८०० 28 8 00508८८ ज ए

Gi) c[a, b] asa subspace of L?[a, b], 1< 9 < ००

(111) ൦[൨, 0] with supremum norm

(iv) c’[a, b] with supremum norm
(A) @ and (ii) ൯ ii) only
(C) 61) and (iv) ന) (ii) only

The adjoint of the bounded linear map T: R’—> ந்‌ given by
T (x, y) = (2x -y, 8x-y) is:
(A) T'(x, y)=(2x +8y,-x — y) 0) T’'G, y)=(x-2y, x-y)
(0) 776, 3) 5(-%४+ 29, -&+ 39) ൯൬) 77७, 39) 5 (४-29, 2४-39)

Which of the following is a continuous linear functional on an inner product space X over 0.
For xe X,:
© ‏داع م‎
Gi) f(x) =(x, y) for some ye x
(11) 7) = (y, x) for some ye x
(A) (¢ © Gi)
© ಉ 8೩4 60) (0) Gand Gi)

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