PPSC Lecturer Mathematics Solved Paper-2011

Q.16  What are Zero divisors in the Ring of integers modulo 6.

(A) 1,2,4

(B) 0,2,3

(C) 0,2,4

(D) 2,3,4

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Q.17 If H is a normal subgroup of G, then Na (H) =

(A) H

(B) G

(C) (e}

(D) None of these 

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Q.18  An n x n matrix with n distinct eigenvalues is

 (A) Diagonalizable

(B) Similar Matrix 

(C) Not diagonalizable

(D) None of these

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Q.19  Let be a linear transformation from an n dimensional vector space U (F) to a vector space V(F) then

(A) dim N(T) + dim R(T) = 0

(B) dim (N(T) + R(T) = 2n

(C) dim N(T) + dim (R(T) = n²

(D) dim (N(T) + dim R(T) = n

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Q.20 The dimension of the row space or column space of a matrix is called the _______________ of the matrix

(A) Basis

(B) Null Space

(C) Rank

(D) None of these

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Q.21   a x (b x c) is a vector lying in the plane containing vectors

(A) a , b and c

(B) a and c

(C) b and c

(D) b and a

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 Q 22   The square matrix A and its transpose have the___________ eigenvalues.

(A)  Same

(B) Diferent

(C) unique

(D) None of these

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Q.23  The set S= of vectors in R² is

(A) Linearly Independent

(B) Linearly dependent

(C) Basis of R²

(D) None of these

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Q.24  Let X and Y be vectors spaces over the field F with dim X = m and dim Y = n then the dim Hom(X, Y) =

(A) mn

(B) n

(C) nm

(D) m²

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Q.25  All subgroups of an abelian group are______subgroups.

(A) cyclic 

(B) normal

(C) characteristic

(D) None of these

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Q.26  The set of all solutions to the homogeneous equation Ax = 0 when A is an m x n matrix is

(A) Null space

(B) Column space

(C) Rank

(D) None of these

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Q.27  If 7 cards are dealt from an- ordinary deck of 52 playing cards, what is the probability that at least 1 of them will be a queen? 

(A) 0.4773

(B) 0.4774

(C) 0.4775

(D) 0.4776

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Q.28  Let G be an abelian group. Then which one of the following is not true.

(A) every commutator of G is identity

(B) if m is divisor of order G then G must have subgroup of order m

(C) center of G is G itself

(D) every subgroup of G is cyclic

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Q.29 Every group of order < 5

(A) cyclice 

(B) abelian

(C) non abelian

(D) none of these

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