PUNJAB PUBLIC SERVICE COMMISSION WRITTEN TEST FOR THE POST OF LECTURER IN MATHEMATICS 2011

Time Allowed: Two Hours Marks: 100

Q.01 A ring R is a Boolean Ring if, for all x R

(A) x²= x

(B) x² = -x

(C) x² = 0

(D) x² = 1

**Check Answer**

Q.2 The group of Quaterninons is a non abelian group of order

(A) 6

(B) 8

(C) 10

(D) 4

**Check Answer**

Q.3 Every group of prime order is

(A) an abelian but not cyclic

(B) an abelian group

(C) a non-abelian group

(D) a Cyclic group

**Check Answer**

Q.4 Any two conjugate subgroups of a group G are

(A) Equivalent

(B) Similar

(C) isomorphic

(D) None of these

**Check Answer**

Q.5 If H is a subgroup of index ________ then H is a normal subgroup of G.

(A) 2

(B) 4

(C) Prime number

(D) None of these

**Check Answer**

Q.6 nz is a maximal ideal of a ring Z if and only if n is

(A) Prime number

(B) Composite number

(C) Natural number

(D) None of these

**Check Answer**

Q.7 Let G be a cyclic group of order 24 generated by a then order of is

(A) 2

(B) 12

(C) 10

(D) None of these

**Check Answer**

Q.8 If a vector space V has a basis of n vectors, then every basis must consist of exactly __________ vectors

(A) n+1

(B) n

(C) n-1

(D) None of these

**Check Answer**

Q.9 An indexed set of vectors in is said to be _________ if the vector equation has only the trivial solution.

(A) Linearly independent

(B) Basis

(C) Linearly dependent

(D) None of these

**Check Answer**

Q.10 The set of all, nth roots of unity for a fixed positive integer n is a group under

(A) addition

(B) addition modulo n

(C) multiplication

(D) multiplication modulo n

**Check Answer**

Q.11 Intersection of any collection of normal subgroups of a group G

(A) is normal subgroup

(B) may not be normal subgroup

(C) is cyclic subgroup

(D) is abelian subgroup

**Check Answer**

Q.12 is a quotient group of order

(A) 1

(B) 2

(C) infinite

(D) None of these

**Check Answer**

Q.13 A group G having order______where p is prime is always abelian.

(A) p⁴

(B) p²

(C) 2p

(D) p³

**Check Answer**

Q.14 The number of conjugacy classes of symmetric group of degree 3 is

(A) 6

(B) 2

(C) 3

(D) 4

**Check Answer**

Q.15 ______________ is the set of all those elements of a group G which commutes with all other elements of G.

(A) commutator subgroup

(B) centre of group

(C) automorphisam of G

(D) None of these

**Check Answer**

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