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 \in R

(A) x²= x

(B) x² = -x

(C) x² = 0

(D) x² = 1

Check Answer
a

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

(A) 6

(B) 8

(C) 10

(D) 4

Check Answer
b

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
d

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

(A) Equivalent

 (B) Similar

(C) isomorphic 

(D) None of these

Check Answer
c

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
a

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
a

Q.7  Let G be a cyclic group of order 24 generated by a then order of   a^{10}   is

(A) 2

(B) 12

(C) 10

(D) None of these

Check Answer
b

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
b

Q.9  An indexed set of vectors  (v_1,v_2,...,v_n)    in  R^n   is said to be _________ if the vector equation x_1v_1+x_2v_2+...+x_pv_p=0 has only the trivial solution.

(A) Linearly independent

(B) Basis

(C) Linearly dependent

(D) None of these

Check Answer
a

Q.10  The set C_n 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
c

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
a

Q.12  \frac{Z}{2Z} is a quotient group of order

(A) 1

(B) 2 

(C) infinite

(D) None of these

Check Answer
c

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

(A) p⁴

(B) p²

(C) 2p

(D) p³

Check Answer
b

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

(A) 6 

(B) 2 

(C)  3 

(D) 4 

Check Answer
c

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
b

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

This Post Has One Comment

  1. Iqra Tariq

    very very informative & help full for me

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