Consider a group u(15)= {1, 2, 4, 7, 8, 11, 13, 14} under muluplication modulo 15. then order of the element 7 is: (b) 4 (a) 3 (d) none of these (c) 5 letg be a

Consider a group U(15)= {1, 2, 4, 7, 8, 11, 13, 14} under muluplication modulo 15. Then order of the element 7 is: (B) 4 (A) 3 (D) None of these (C) 5 LetG be a group and G' be the commutator subgroup of G, Then cho05 he correct statement (A) G is a normal subgroup of G. (B) G/G is Abelian. t M is a normal subgroup of G such that G/M is Abelian, then G' C M (D) All of these 2Let P, (1) be a vector space of all polynomials of degree n. Then (A) dim P, (?) = n-1 (B) dim P, (1) = n (C) dim P, (t) = n +1 (D) None of these 15. Let G= S,, n 25; then GE) for k=1, 2, 3, ... contains every.ssons O1 Sy (A) 3-cycle (B) 4-cycle (C) 5-cycle (D) None of these 74. Which of the statements is correct (A) G is solvable G)= (e) for some integer k. (B) G) =(e) for some integer k > G is solvable. C) Both (A) and (B) (D) None of these XE(H-3)-MAT(6) (16)

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