34.

35.

36.

87.

38.

39.

The degree of the splitting field x° -3x° +x" -3 over Q is:
(A) 2 (8) 8
© 4 0) 8

Let G be the Galois group of the splitting field of x° -2 over Q. Then:

@ ~~ Gis cyclic,

Gi) Gis non-abelian

(11) Ghas order 20

(iv) Ghas an element of order 4
(^ All @, (ii), Gii) and (iv) are true (B) (i), Gi) and (11) are true
(C) ൮), ii) and (iv) are true 0) (0), Gii) and (iv) are true

Let 7 be the topology on N (natural numbers) consists of g and all subsets of IN of the form
A, ={n,n+1, n+2,...}, ne N. The set of all accumulation points of the set A ={8, 21, 33, 55}
is:
(^) {1, 2, 3, ...7} (B)
) ١ 4 (D)

Let X be a non-empty set, under which of the following topologies 2, and 7, on X the identity
function, I =(X, t,) > (X, t,) is continuous?

@ 7, and മു are only two topologies on X
(ii) മ - indiscrete topology and 7, - discrete topology
(11) 7, - any topology, 7, - indiscrete topology
(iv) 1, - discrete topology, 7, - any topology
(A) _ all of the above (i), (ii), (iii) and (iv) ൯ only (iv)
(0) only (ii) and (iii) (D) _ only (iii) and (iv)

‎त 1‏ درد
‎In the set R with infinite topology, the sequence இ , ne N converges to:‏
‎n‏

‎(^) Oonly (B) all real numbers

‎(C) the numbers 1, + only (D) Oand 1 only

‎॥

‎ble
‎cole

‎Which of the following set is dense in R under the topology on R consisting of R, g and all
open intervals of the form (x, -), xe 7

‎(A) £10, -5, 0, 5, 10,...} (B) (10, -9, -8,...,9, 10}
(©) {.-6,-3, 0, 3} ௫) {10, 12, 20}

‎9 083/2023
[P.T.0.]